FIN143 · Complete MCQ Answer Guide

Founder position

Easy (1/8)

W1-S006 · Source slide 6

A founder has deep experience in her target industry and enough investable capital for the business she plans. She wants flexibility and fulfilling work, with no current ambition to scale or sell. How is she positioned?

1. Constrained, novice, growth
2. Capitalized, novice, lifestyle
3. Constrained, expert, growth
4. Capitalized, expert, growth
5. Capitalized, expert, lifestyle

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A control tradeoff

Easy (1/8)

W1-S014 · Source slide 14

A founder is offered capital that could accelerate growth. The deal requires shared board control and joint approval of major decisions. She declines because retaining authority matters more to her than the potential financial gain. Which framework most directly explains her choice?

1. Effectuation: reasoning from available means
2. The E-Myth: technical skill versus business management
3. Bootstrapping: financing from limited internal or personal resources
4. Rich vs. King: control versus potential financial value
5. Product-market fit: evidence that customers want the offering

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Rich versus King

Medium (4/8)

W1-S016 · Source slide 16

A founder is choosing between two equity investment offers. Each provides $1.8 million and leaves her with 65% economic ownership of the company.

Angel offer: The founder appoints two of the company's three directors.

Venture-fund offer: The fund appoints two of the three directors and can replace the CEO by a majority board vote. The fund also offers distribution relationships that could increase the company's eventual value.

The founder chooses the angel offer. She explains that keeping decision authority matters more to her than the additional financial upside the fund might provide.

Which framework best explains her decision?

1. The E-Myth: she prefers making decisions herself over accepting outside help. That preference shows she considers her technical skills sufficient to manage company growth.
2. Affordable loss: she uses retained authority to limit her financial downside. The angel offer therefore meets her loss limit despite raising the same capital.
3. Effectuation: she chooses the angel to preserve her existing resources. Accepting venture funding would replace her current starting point with goals chosen by investors.
4. Wealth maximization: she keeps the same ownership under either offer and therefore retains equivalent control. The distribution relationships do not create a meaningful tradeoff.
5. Rich versus King: she gives up potential financial upside to preserve decision authority. Equal ownership percentages do not make the offers equivalent in control.

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Reasoning from means

Easy (1/8)

W1-S020 · Source slide 20

A founder begins by listing her capabilities, relevant knowledge, and contacts. She explores what those resources make possible and limits the next experiment to a loss she can absorb. Which concept best fits?

1. Effectuation, reasoning from available means
2. Causation, selecting means for a defined goal
3. Rich vs. King, choosing between wealth and control
4. An entrepreneurial seizure, assuming technical skill is sufficient
5. Structural-hole brokerage, connecting otherwise disconnected groups

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Effectuation and causation

Medium (4/8)

W1-S022 · Source slide 22

Two founders are developing software for independent clinics. They take different approaches to deciding what to build:

Mira: She starts with her scheduling expertise, relationships with three clinic owners, and $4,000 she can afford to lose. Commitments from pilot customers help her decide which product to build and which clinics to serve first.

Jon: He starts with a goal of serving 50 clinics within one year. He estimates the resources needed, then develops a hiring and financing plan to reach that goal.

Both founders interview customers, prepare budgets, and revise their assumptions. An industry report forecasts 12% annual market growth.

Which explanation best distinguishes the decision-making approach each founder is using?

1. Mira uses causation: she starts with resources she already knows. Jon uses effectuation: he adjusts his resources to pursue a newly identified market opportunity.
2. Mira uses effectuation: she limits the personal money at risk. Jon uses causation: he considers outside financing, making their funding sources the key distinction.
3. Mira uses effectuation: available resources and customer commitments shape her plans. Jon uses causation: a specific goal determines which resources he needs to acquire.
4. Both use effectuation: customer interviews and revised assumptions make their plans experimental. The resources or goals they start with do not change that classification.
5. Both use causation: budgets and market forecasts make their plans predictive. How they choose the initial product and customer segment does not change that.

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Affordable loss

Hard (6/8)

W1-S024 · Source slide 24

A founder sets aside money to test a tutoring platform. Before beginning, she has $42,000 of personal savings and reserves $30,000 for household needs. She limits her total loss on the experiment to $12,000, including money already spent.

Her commitments are as follows:

She has already spent $2,400, which she cannot recover.

The next pilot requires a nonrefundable $6,800 vendor payment.

If the pilot fails, she may also owe a $1,200 termination payment.

A customer has provided a refundable $2,000 deposit, but it must be held separately and cannot fund the experiment. The founder forecasts $60,000 of annual profit if the product succeeds.

What is the largest additional nonrefundable marketing commitment she can make without exceeding her loss limit if the pilot fails and the termination payment becomes due?

1. $1,600.
2. $2,800.
3. $4,000.
4. $5,200.
5. $9,600.

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Introversion and the evidence

Medium (4/8)

W1-S028 · Source slide 28

An introverted founder asks whether her personality could make entrepreneurship harder. Which interpretation best combines the personality studies?

1. The 2006 comparison shows that entrepreneurs must be more extraverted than managers.
2. No status difference in 2006 means extraversion cannot matter for performance.
3. The later performance association is small. Assess her actual capabilities and role demands.
4. Introversion establishes that she has high neuroticism and poor stress tolerance.
5. The performance association proves that introversion causes venture failure.

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Personality and observed behavior

Medium (4/8)

W1-S030 · Source slide 30

An investor evaluates a founder with high conscientiousness and low agreeableness. References describe her as disciplined, receptive to feedback, and effective at resolving disagreements. How should the investor use the assessment?

1. Give standardized scores priority because they eliminate subjective bias.
2. Ignore the assessment because favorable references settle the issue.
3. Compare trait scores with observed behavior, references, and context.
4. Predict team conflict from low agreeableness despite the behavioral evidence.
5. Average scores and reference comments into a single founder-quality rating.

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Confidence and evidence

Medium (4/8)

W1-S033 · Source slide 33

A founder treats enthusiastic interviews with four friends as evidence of broad demand. She also believes that her effort can overcome any competitor response. Which response best addresses the two reasoning risks?

1. Raise the sales target and use additional interviews with friends to validate it.
2. Lower the sales target and treat competitor behavior as entirely unpredictable.
3. Test demand beyond the small sample and distinguish influence from control.
4. Increase the cash reserve and use the founder’s confidence as demand evidence.
5. Hire an experienced seller and retain the same demand and control assumptions.

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Different starting resources

Medium (4/8)

W1-S036 · Source slide 36

Two founders are evaluating the same opportunity. Founder A has ten years of directly relevant experience and 18 months of personal runway. Founder B has no relevant experience and three months of personal runway. Why should their advice differ?

1. Capital mainly determines market attractiveness, while expertise determines the founder’s goals.
2. Capital affects runway and loss capacity, while expertise informs customer understanding and execution.
3. Capital determines the revenue model, while expertise determines the amount of equity to raise.
4. Capital and expertise reduce risk in the same way, so either can replace market validation.
5. Expertise makes short runway a secondary concern when the opportunity is attractive.

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Capital without domain expertise

Easy (1/8)

W1-S038 · Source slide 38

A founder sold her previous company and has ample investable capital. She now enters an industry where she has never worked. Which resource profile and coaching priority fit best?

1. Bootstrap Expert: focus primarily on a shortage of cash.
2. Career Changer: develop domain knowledge before major commitments.
3. Primed Founder: rely on expertise established by the previous exit.
4. Aspiring Founder: address a shortage of both capital and experience.
5. Career Changer: assume a lifestyle goal and plan a small business.

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Funding ahead of expertise

Medium (4/8)

W1-S043 · Source slide 43

A founder has raised substantial capital, has never worked in the target industry, and wants to scale aggressively. She has not yet tested the key customer assumptions. What should an advisor prioritize?

1. Deploy capital quickly to establish market presence.
2. Avoid all spending until customer revenue fully funds the business.
3. Replace the growth goal with a lifestyle goal.
4. Add domain expertise and require validation milestones before major expansion.
5. Raise another round before assessing the nonfinancial gaps.

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One opportunity, different strategies

Medium (4/8)

W1-S045 · Source slide 45

Alex and Priya are evaluating the same attractive software opportunity. Alex has limited personal capital, deep industry expertise, and wants to retain control. Priya has substantial resources, accepts shared ownership, and wants to build quickly. Which approach best fits these differences?

1. Alex explores capital-efficient growth. Priya evaluates investing or raising capital to accelerate progress.
2. Both use the same financing and growth plan because the opportunity is identical.
3. Alex prioritizes a large equity raise because expertise makes control preferences less relevant.
4. Priya limits growth because having personal capital reduces the need to expand.

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Connecting industry networks

Easy (1/8)

W1-S049 · Source slide 49

A career changer has strong contacts in her old industry. An advisor introduces her to a group in her new industry that rarely interacts with the first. She begins connecting people and sharing relevant ideas across the groups. Which concept explains the potential value of that position?

1. Weak ties guarantee access to the resources she needs.
2. Brokerage across a structural hole provides access to different information.
3. Affordable loss determines which contacts she should trust.
4. The E-Myth establishes that her technical skills are inadequate.
5. Rich vs. King explains the information flowing between the groups.

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Different reasons to grow

Easy (0/8)

W1-S052 · Source slide 52

Two founders have similar capital and expertise, and both want to scale. One emphasizes wealth and competitive success. The other emphasizes advancing a societal cause. Which framework most directly distinguishes those motivations?

1. The Big Five personality framework
2. Smith’s Craftsman vs. Opportunistic Entrepreneur typology
3. Wasserman’s Rich vs. King tradeoff
4. Sarasvathy’s effectuation and causation
5. Fauchart and Gruber’s founder identities

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The founder as a bottleneck

Easy (1/8)

W1-S056 · Source slide 56

A founder built the business through personal selling, customization, and direct problem-solving. Demand is now recurring and the team has reached 25 people, but routine decisions stall while waiting for her approval. Which action most directly addresses the stated bottleneck?

1. Improve financial forecasts and cash planning.
2. Standardize sales and customer onboarding.
3. Delegate decision authority and establish management routines.
4. Narrow the product range to reduce complexity.
5. Hire experienced executives to add capabilities.

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Darius’s next commitment

Medium (4/8)

W1-S060 · Source slide 60

Darius knows the product but is new to retail distribution and lacks grocery-buyer contacts. His savings are limited relative to his national ambition. Which next step best addresses these gaps while limiting financial exposure?

1. Raise venture capital immediately, before evaluating the retail channel.
2. Replace his national ambition with a lifestyle business.
3. Commit his savings to national inventory to secure shelf space.
4. Run a limited retail test and build relevant buyer relationships.
5. Focus first on becoming more extraverted.

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Elena’s investment decision

Easy (1/8)

W1-S063 · Source slide 63

Elena has deep expertise and adequate capital, but explicitly wants a small business with sustainable income and manageable hours. Compared with Darius, which coaching emphasis best fits her goals?

1. Validate locally and then scale nationally, just as Darius hopes to do.
2. Raise outside capital because her resources and experience may attract it.
3. Match business size and spending to her income and lifestyle goals.
4. Prioritize hiring domain experts because capitalized founders lack expertise.
5. Set an exit in five to seven years to match Darius’s timetable.

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Founder and financing judgment

Hard (6/8)

W1-S065 · Source slide 65

A founder has deep industry experience and wants to build a national business. Her company has five months of runway under its current plan. Paying customers in its initial region show promising retention, but demand in other regions has not been tested.

She is considering two alternatives:

Funded expansion: A venture fund offers enough capital for a 16-month expansion plan in exchange for shared board authority.

Narrower operating plan: The company postpones hiring, preserves founder control, and extends runway to nine months. It expects to complete a regional customer-validation milestone in month five.

The founder values both financial upside and decision authority but has not decided which matters more to her.

Which analysis would provide the strongest basis for choosing between the two plans?

1. Compare customer retention and hiring capacity, then favor expansion if staffing supports it. Treat current regional loyalty as sufficient evidence that national demand is established.
2. Compare investor commitments and the regional test, then favor expansion. Treat the fund's willingness to invest as stronger evidence of national demand than customer testing.
3. Compare expected company values, then favor whichever plan offers greater upside. Treat her national ambition as evidence that financial gains outweigh sharing the board's authority.
4. Compare runway and planned spending, then favor the narrower plan. Treat preserving control and reducing spending as sufficient evidence that this choice best serves her.
5. Compare each plan's cash coverage, demand evidence, and governance terms. Clarify her priorities for wealth and control before she commits to expansion into new regions.

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The CEO role

Easy (1/8)

W1-S070 · Source slide 70

An investor offers funding and experienced executives who could help build a more valuable company. The agreement would let the board replace the founder as CEO. She rejects it because remaining CEO is her overriding priority. Which explanation fits best?

1. Effectuation, because she starts from existing means
2. The E-Myth, because she is acting only as a technician
3. Rich vs. King, because she prioritizes authority over potential financial value
4. Bootstrapping, because external funding necessarily increases financial risk
5. The Big Five, because her decision establishes low agreeableness

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Two decision logics

Easy (0/8)

W1-S072 · Source slide 72

Which statement best distinguishes effectuation from causation?

1. Effectuation begins with available means and develops possible goals. Causation begins with a defined goal and selects the means.
2. Effectuation begins with forecasts and expected return. Causation begins with means and affordable loss.
3. Effectuation prioritizes founder control. Causation prioritizes company value.
4. Effectuation explains technical-skill gaps. Causation explains domain expertise.
5. Effectuation requires outside equity. Causation requires bootstrapping.

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An unexpected customer pilot

Medium (4/8)

W1-S074 · Source slide 74

A founder starts without a fixed business idea. She inventories what she knows, whom she knows, and what she can afford to lose. After several conversations, a potential customer offers to pilot a use case she had not originally considered. Which response best reflects effectual reasoning?

1. Accept the pilot if the downside is affordable, and let the customer’s commitment help shape the venture.
2. Reject the pilot until she has fixed the target market and long-term strategy.
3. Forecast every market, choose the highest expected return, and pursue only that opportunity.
4. Raise enough money to enter several markets at once before choosing a direction.
5. Wait until demand can be forecast reliably before making a commitment.

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The affordable-loss limit

Easy (1/8)

W1-S076 · Source slide 76

A founder is testing a tutoring platform. She has $20,000 in savings, but losing more than $5,000 would compromise her emergency reserve. Customer demand remains uncertain. Which initial decision best follows affordable loss?

1. Commit all $20,000 because the opportunity looks attractive.
2. Choose the highest forecast NPV even if the potential loss exceeds $5,000.
3. Limit potential loss to $5,000 or less while testing demand.
4. Spend nothing until demand can be forecast with confidence.
5. Raise outside equity immediately to pursue the largest possible launch.

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Profitable firms, different goals

Medium (4/8)

W1-S078 · Source slide 78

Maya and Jordan run equally profitable consulting firms with similar opportunities. Maya wants to serve about 15 clients, preserve Fridays off, and retain full control. Jordan wants a national firm, significant hiring, and an eventual sale. Which financing approach best fits?

1. Maya raises expansion capital because her existing business is profitable.
2. Both choose the same financing strategy because their business economics are similar.
3. Maya may decline expansion capital, while Jordan may consider it to accelerate growth.
4. Jordan avoids outside capital because rapid growth necessarily reduces founder value.

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Scaling and founder transition

Easy (1/8)

W1-S080 · Source slide 80

A founder succeeds early by personally selling, customizing the product, and solving problems directly.

Demand is now recurring, the team has grown to 25 employees, and most decisions still flow through the founder.

What should an advisor emphasize at this stage?

1. Transition from direct execution to building scalable systems and delegating authority.
2. Maintain personal oversight of all key operations to preserve early product quality.
3. Immediately raise growth capital to expand the sales team before changing internal processes.
4. Focus exclusively on product customization to win larger enterprise contracts.

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Runway, growth, and control

Medium (4/8)

W1-S082 · Source slide 82

A domain expert wants to build a national company. Her business has four months of runway. An investment offer would extend runway and support hiring, but requires shared governance. She also values control. Which analysis best integrates the course concepts?

1. Compare liquidity needs, growth milestones, and the offer’s governance tradeoffs.
2. Continue self-funding because expertise and effectuation make more capital unnecessary.
3. Accept the offer because national ambitions determine the financing choice.
4. Treat the offer as necessary because short runway outweighs control preferences.
5. Defer the funding decision because expertise makes runway less important.

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Evidence of product–market fit

Easy (1/8)

W2-S010 · Source slide 10

Which observation provides the strongest evidence that a recurring-revenue startup has moved beyond early interest toward product–market fit?

1. A large waitlist follows a widely shared social-media post, but few prospects have been asked to pay.
2. Interviews consistently describe a painful problem, but the company has not launched a paid offering.
3. A discounted launch generates many signups, but usage falls sharply after the promotion ends.
4. A competitor raises a large financing round, suggesting investor interest in the category.
5. Paid cohorts renew, usage remains strong, customers expand, and referrals bring additional paying customers.

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Product-market fit

Hard (6/8)

W2-S012 · Source slide 12

Two teams sell the same type of monthly workflow software to comparable small businesses. Both have operated for nine months.

An investor wants to assess whether customers find enough value in the product to continue paying for it.

Which conclusion is best supported by the evidence?

1. South shows stronger evidence that customers will keep paying, while North shows broader reach. Neither result establishes profitable growth across new customer groups or channels.
2. North shows stronger evidence that customers will keep paying because its larger initial customer group offsets weaker retention. South mainly demonstrates interest among early enthusiasts.
3. Both teams show similar evidence that customers will keep paying because similar numbers remain. Different starting customer counts and initial discounts do not affect comparability.
4. South shows stronger demand and more efficient customer acquisition because customers renew at the intended price. North's broader reach provides weaker evidence of acquisition efficiency.
5. North shows stronger evidence of scalable demand because its waitlist contains more prospective customers. South's renewals mainly confirm service delivery rather than willingness to pay.

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Identifying the revenue model

Easy (0/8)

W2-S016 · Source slide 16

A platform acts as an agent connecting buyers and providers. It earns a percentage of completed booking value, and major transaction costs include payment processing and insurance. Which revenue-model archetype best fits?

1. Product sales.
2. Intellectual-property licensing.
3. Advertising.
4. Services delivered directly by the company.
5. Marketplace / commission.

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Revenue growth and cost structure

Easy (1/8)

W2-S021 · Source slide 21

A software company and a consulting firm each grow revenue 50%. Software supports much of the extra volume without proportional hiring; consulting adds professionals roughly with new client work. With comparable remaining cost behavior, which concept best explains the difference?

1. Software has greater operating leverage because its fixed-cost base supports additional revenue before headcount must rise proportionally.
2. Consulting has greater operating leverage because adding labor with client work keeps costs closely aligned with revenue.
3. Software has stronger product–market fit because lower staffing requirements imply better customer retention.
4. Consulting necessarily has stronger overall economics because variable labor reduces unused-capacity risk.
5. Software has a network effect because revenue grows faster than headcount, even when other users do not change customer value.

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Operating leverage

Hard (6/8)

W2-S023 · Source slide 23

Atlas Software and Beacon Consulting each report quarterly revenue of $1.50 million, operating profit of $150,000, and cash of $800,000. Their cost structures differ:

Next quarter, revenue falls by 10% at both companies. Prices, sales mix, variable-cost percentages, and total fixed costs remain unchanged.

What operating profit will each company report, and which company's operating profit is more sensitive to the revenue decline?

1. Atlas: $90,000; Beacon: $30,000; greater profit sensitivity: Beacon.
2. Atlas: $120,000; Beacon: $60,000; greater profit sensitivity: Beacon.
3. Atlas: $135,000; Beacon: $135,000; greater profit sensitivity: neither.
4. Atlas: −$120,000; Beacon: −$60,000; greater profit sensitivity: Atlas.
5. Atlas: $30,000; Beacon: $90,000; greater profit sensitivity: Atlas.

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A founder’s pricing method

Medium (4/8)

W2-S026 · Source slide 26

A founder prices a differentiated product using fully loaded cost plus a 25% markup. The product solves an expensive customer problem, and customers may pay substantially more. Which pricing approach is being used, and what is its main limitation?

1. Competition-based pricing; competitors’ price reductions may trigger a price war.
2. Value-based pricing; uncertain customer benefits may lead to overstated willingness to pay.
3. Penetration pricing; a low introductory reference price may be difficult to increase.
4. Cost-plus pricing; ignoring willingness to pay may leave substantial value uncaptured.
5. Freemium pricing; free users may never convert to a profitable paid tier.

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Pricing and contribution

Hard (6/8)

W2-S031 · Source slide 31

A company currently sells 1,000 units per month at $75 each. It set that price using a 25% markup on a fully loaded unit cost of $60, consisting of $42 in variable cost and $18 in allocated fixed overhead.

Management is comparing three pricing plans:

All three sales volumes are within existing capacity. Total fixed costs remain unchanged, and variable cost stays at $42 per unit. Customers report saving about $900 annually by using the product.

Using these sales estimates, which price produces the highest monthly contribution, and how much does contribution change from the current plan?

1. Price: $68; change in monthly contribution: +$10,000.
2. Price: $75; change in monthly contribution: $0.
3. Price: $90; change in monthly contribution: −$3,000.
4. Price: $90; change in monthly contribution: +$5,400.
5. Price: $90; change in monthly contribution: +$9,000.

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Gross margin and the customer relationship

Medium (4/8)

W2-S037 · Source slide 37

A startup has positive gross margin after delivery costs. Over the expected customer relationship, however, contribution becomes negative after all additional variable sales, marketing, onboarding, and customer-success costs. What does this indicate?

1. The economics are attractive because acquisition and onboarding costs sit outside the relevant contribution analysis.
2. Delivery economics are necessarily broken because variable sales and service costs should all be classified as product COGS.
3. Fixed overhead must be causing the loss, rather than acquisition or customer-service costs.
4. The problem is mainly cash timing because acquisition spending occurs before recurring customer payments.
5. Delivery leaves gross profit, but variable acquisition and additional service costs make the full customer relationship unattractive.

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Gross margin and contribution

Hard (6/8)

W2-S039 · Source slide 39

An equipment-accessory startup completes 500 one-time customer orders during a month and charges $160 per order. Its records show the following costs:

The acquisition spending and the payment, onboarding, and service costs are additional to the $100 cost of revenue. All orders are collected in cash, and no repeat purchases are assumed.

What are the month's gross margin percentage and total contribution before fixed overhead?

1. Gross margin: 37.5%; total contribution: −$2,500.
2. Gross margin: 37.5%; total contribution: $20,000.
3. Gross margin: 37.5%; total contribution: $30,000.
4. Gross margin: 60.0%; total contribution: −$2,500.
5. Gross margin: 37.5%; total contribution: −$20,500.

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Payback from revenue and gross margin

Medium (4/8)

W2-S042 · Source slide 42

An early-stage SaaS company spends $25,000 in complete acquisition costs to acquire 50 customers. Each generates $100 monthly revenue at 40% gross margin. Revenue and margin stay constant, and customers do not churn during recovery. What is gross-profit CAC payback?

1. 5.0 months, because CAC is recovered using monthly revenue.
2. 8.0 months, because gross margin reduces the acquisition cost to recover.
3. 12.5 months, because CAC is $500 and monthly gross profit is $40 per customer.
4. 20.0 months, because every customer must recover the entire acquisition campaign.
5. 25.0 months, because acquisition cost is deducted from monthly revenue first.

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CAC payback

Medium (4/8)

W2-S044 · Source slide 44

A SaaS company spends $78,000 on sales and marketing during a quarter. Its records separate that spending into two activities:

Acquiring new customers: $60,000 to acquire 100 new paying customers.

Renewing existing customers: $18,000 to renew the 400 paying customers it had at the start of the quarter. All 400 remain customers.

Each new customer generates $125 of monthly recurring revenue at a 64% gross margin. There are no other acquisition costs.

Assume no churn, expansion, discounting, or collection delays. Use only the acquisition costs attributable to the new customers.

How many months of gross profit from a new customer are needed to recover that customer's acquisition cost?

1. 1.50 months.
2. 4.80 months.
3. 5.25 months.
4. 7.50 months.
5. 9.75 months.

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Customer churn with new signups

Medium (3/8)

W2-S047 · Source slide 47

A subscription business begins the month with 200 customers. Ten of those starting customers cancel. Thirty new customers join and remain active. What is monthly customer churn?

1. 5%.
2. 10%.
3. 15%.
4. 20%.
5. 90%.

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Revenue from the starting cohort

Medium (3/8)

W2-S050 · Source slide 50

A company begins the month with $100,000 monthly recurring revenue (MRR). Existing customers add $15,000 through expansion, lose $5,000 through downgrades, and lose $20,000 through cancellations. New customers add $30,000 MRR. With no other changes, what is net revenue retention (NRR)?

1. 75%.
2. 90%.
3. 95%.
4. 110%.
5. 120%.

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Estimating gross-profit LTV

Easy (2/8)

W2-S053 · Source slide 53

A SaaS customer pays $120 monthly. Gross margin is 75%, and monthly customer churn is a constant 3%. Assume stable revenue and margin, no expansion, and no discounting. Using the simple gross-profit LTV approximation, what is estimated LTV?

1. $1,200.
2. $3,000.
3. $3,600.
4. $4,000.
5. $4,800.

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LTV and churn

Medium (4/8)

W2-S056 · Source slide 56

A subscription business is testing how higher churn would affect the value of a customer. The following inputs remain the same in both scenarios:

Monthly revenue per customer: $180.

Gross margin: 70%.

Customer acquisition cost (CAC): $900.

The base case assumes constant monthly customer churn of 3.5%. The downside case increases that rate to 5.25%. Management still expects strong growth in new customers, but that growth does not change the retention or spending of the customer being valued.

Use the gross-profit lifetime value (LTV) approximation. Assume no expansion, reactivation, discounting, or other customer cash flows.

What are LTV and LTV/CAC in the downside case? Round LTV to the nearest dollar and the ratio to two decimal places.

1. LTV of $1,500 and LTV/CAC of 1.67×.
2. LTV of $1,800 and LTV/CAC of 2.00×.
3. LTV of $2,400 and LTV/CAC of 2.67×.
4. LTV of $3,429 and LTV/CAC of 3.81×.
5. LTV of $3,600 and LTV/CAC of 4.00×.

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Sizing a construction-software opportunity

Medium (4/8)

W2-S060 · Source slide 60

A founder presents $12 trillion of global construction activity as the market for specialized software sold only to large U.S. commercial contractors. What is the main analytical correction?

1. Keep global construction spending as software TAM because the product could influence activity throughout the industry.
2. Use only the current prospect pipeline as total market size because unidentified buyers should not count.
3. Multiply eligible contractors by software spending and treat the entire amount as obtainable revenue without testing reach or sales capacity.
4. Define eligible buyers, relevant geography, and annual software spending, then distinguish total, serviceable, and obtainable opportunity.
5. Replace market sizing with unit economics because positive contribution makes market scale unimportant.

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TAM, SAM, and SOM

Hard (7/8)

W2-S062 · Source slide 62

A software company is estimating its market opportunity and the revenue scale it could reach over the next 12 months. It has the following information:

The company has no existing customers, expects no churn, and faces no other constraints. Its pitch also cites $600 billion of annual construction activity.

For this question, measure SOM as year-end annual recurring revenue (ARR) from customers actually onboarded, not revenue recognized during the year.

Which combination of TAM, SAM, and SOM follows from these assumptions?

1. TAM: $108.0 million; SAM: $32.4 million; SOM: $0.36 million of year-end ARR.
2. TAM: $108.0 million; SAM: $32.4 million; SOM: $0.72 million of year-end ARR.
3. TAM: $108.0 million; SAM: $32.4 million; SOM: $1.08 million of year-end ARR.
4. TAM: $108.0 million; SAM: $32.4 million; SOM: $3.24 million of year-end ARR.
5. TAM: $108.0 million; SAM: $108.0 million; SOM: $0.72 million of year-end ARR.

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From strategy to a forecast

Hard (6/8)

W2-S069 · Source slide 69

A software startup claims a durable advantage because it uses the same commercial AI model as its rivals. One data supplier can raise prices at renewal, and customer interviews suggest demand for a simpler workflow. Which next step best connects the strategy frameworks to financial assumptions?

1. Model supplier pricing power, test whether capabilities are hard to copy, and validate willingness to pay.
2. Model supplier costs as fixed, treat the shared model as rare, and project an immediate price premium.
3. Model market growth as demand, use the shared model as a moat, and hold acquisition costs constant.
4. Model a permanent premium, treat workflow interest as payment, and exclude rival responses from risk.
5. Model only cloud cost savings, treat scale as exclusivity, and use interview counts as contracted sales.

Related Week 2 deck

Providers and customer value

Easy (1/8)

W2-S073 · Source slide 73

A digital platform connects customers with independent service providers. More providers bring greater selection, shorter wait times, and better availability. Customer value rises even though the number of customers stays unchanged. Which mechanism explains this?

1. Direct network effect: customers benefit primarily from more customers joining.
2. Economies of scale: average operating cost falls as transaction volume increases.
3. Cross-side network effect: growth on the provider side improves value for customers.
4. Switching costs: customers become more reluctant to move to another platform.
5. Economies of scope: several services share production resources.

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Network effects

Hard (6/8)

W2-S075 · Source slide 75

A marketplace runs three tests while keeping prices, promotions, and advertising intensity unchanged:

In comparable neighborhoods, adding qualified sellers raises buyers' order-completion rate from 62% to 80%.

In a separate test, adding active buyers increases sellers' utilization and willingness to stay on the platform.

In another test, moving to a different cloud system reduces processing cost per transaction. The numbers of buyers, sellers, and completed orders do not change.

The marketplace continues to subsidize delivery.

Which conclusion correctly identifies what these results show about network effects, cost efficiency, and contribution?

1. More participants improve value across the marketplace's two sides; the cloud change improves processing efficiency. Together, these improvements establish positive contribution after subsidized delivery costs.
2. More participants improve value within the marketplace's individual sides; the cloud change improves processing efficiency. Contribution still depends on delivery subsidies and other variable costs.
3. More participants improve value across the marketplace's two sides; the cloud change improves processing efficiency. Lower processing costs establish that marginal delivery costs also decline.
4. More participants improve processing efficiency; the cloud change improves value across the marketplace's two sides. Contribution still depends on delivery subsidies and other variable costs.
5. More participants improve value across the marketplace's two sides; the cloud change improves processing efficiency. Contribution still depends on delivery subsidies and other variable costs.

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Current cash runway

Easy (2/8)

W2-S079 · Source slide 79

A startup has $900,000 usable cash, $180,000 monthly operating cash outflows, and $105,000 monthly operating cash inflows. Both flows remain constant, with no financing or other cash flows. What is current runway?

1. 12 months.
2. 8.6 months.
3. 7.5 months.
4. 5 months.
5. 15 months.

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Growth, commitments, and runway

Easy (1/8)

W2-S083 · Source slide 83

A startup raises capital, hires aggressively, and signs a long office lease. Six months later, growth is below plan, cash will run out before profitability, and committed costs cannot fall quickly. Which course concept best describes the situation?

1. Default alive, because a previous capital raise establishes access to future financing.
2. Product–market fit, because management was confident enough to hire ahead of profitability.
3. Operating leverage, because committed fixed costs automatically improve margins as time passes.
4. The fatal pinch: slow growth and short runway leave little time to respond, while locked-in costs limit flexibility.
5. Affordable loss, because using investor money establishes that the expansion’s downside was tolerable.

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Default dead and the fatal pinch

Medium (4/8)

W2-S085 · Source slide 85

A startup raised capital eight months ago. Its current plan shows the following:

Existing cash will cover five more months of operations.

With expenses held constant and recent revenue growth continuing, the company will reach profitability 14 months from now.

Growth has slowed, and most payroll and lease commitments cannot be reduced quickly.

An investor has requested a presentation but has not committed any money. The founder argues that the previous financing round and the investor's interest make the company default alive.

Which assessment best describes the company's position and the implication for its financing plan?

1. Default dead: cash runs out before projected profitability. Slower growth and fixed commitments increase fatal-pinch risk, so planning must allow for the raise to fail.
2. Default alive: the prior financing shows that external capital supports the operating plan. Current investor interest justifies including another round when calculating the remaining runway.
3. Default dead: current costs exhaust cash too soon. The forecast should recognize lower spending when management announces reductions, even if payroll and lease commitments remain.
4. Default dead: the forecast shows a temporary cash gap. Management should retain current commitments and include the prospective round because the investor has requested information.
5. Default alive: projected revenue eventually covers expenses. The gap before profitability is a financing issue that should be assessed separately from the company's default-alive classification.

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Burn multiple and cash needs

Medium (3/8)

W2-S088 · Source slide 88

During one quarter, a SaaS venture consumes $900,000 of net cash under a consistently defined burn measure. ARR rises from $2.4 million to $3.0 million. Recognized revenue is $720,000, and a financing round adds $2 million of cash. What is the quarter’s burn multiple and the strongest interpretation?

1. 0.30×; each dollar of ending ARR required thirty cents of quarterly net burn.
2. 1.25×; each dollar of recognized revenue required $1.25 of quarterly net burn.
3. 3.33×; each dollar of added ARR required $3.33 of financing proceeds.
4. 1.50×; each dollar of net new ARR required $1.50 of quarterly net burn.
5. 6.00×; each dollar of quarterly revenue growth required six dollars of net burn.

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Founder capability and opportunity economics

Easy (0/8)

W2-S092 · Source slide 92

Why does the Venture Economics Framework assess the opportunity separately from the founder?

1. Founder quality stops mattering when the market is large.
2. Even a strong founder needs evidence that demand, unit economics, and cash can support the opportunity.
3. Investors evaluate businesses and never consider founders.
4. The Founder Archetype Matrix already establishes that the opportunity is sound.
5. Opportunity assessment removes the need for financial modeling.

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Problem–solution fit and product–market fit

Easy (0/8)

W2-S096 · Source slide 96

What distinguishes problem–solution fit from product–market fit?

1. Problem–solution fit supports a meaningful problem and a workable solution; product–market fit adds sustained demand for the specific product.
2. The terms describe the same stage and are interchangeable.
3. Product–market fit must be established before understanding the customer’s problem.
4. Problem–solution fit requires net revenue retention above 120%.
5. A landing-page signup establishes product–market fit.

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Evidence from interviews and a waitlist

Easy (1/8)

W2-S098 · Source slide 98

A founder has completed 30 discovery interviews and built a 400-person waitlist, but no one has paid. What is the highest demonstrated level on the course evidence ladder?

1. Level 5: Repeat purchase is demonstrated.
2. Level 1: The founder has assumptions only.
3. Level 4: A paid pilot has demonstrated willingness to pay.
4. Level 3: Customers have expressed interest, but payment is unproven.
5. Level 7: Positive unit economics have been demonstrated.

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Customer traction versus market interest

Easy (1/8)

W2-S100 · Source slide 100

An early-stage software company is trying to determine whether it has customer traction rather than simply market interest. Which evidence provides the strongest support?

1. Eight large companies sign nonbinding letters of intent, but none purchases the product.
2. Three customers complete paid pilots, but none chooses to continue afterward.
3. Twelve customers pay for the product, nine have renewed, and four have expanded their purchases.
4. Website traffic increases 50% after favorable media coverage, but few visitors become paying customers.
5. Thirty prospects say in interviews that they would probably purchase at the proposed price.

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What unpaid demand establishes

Medium (4/8)

W2-S102 · Source slide 102

A startup completes 40 customer interviews and collects 600 waitlist signups. Target customers consistently describe the problem as important, but none has paid. Which conclusion is best supported?

1. The large number of interested prospects establishes product–market fit for an early-stage company.
2. Problem relevance and customer interest have support, while willingness to pay and repeat demand remain unproven.
3. Joining the waitlist establishes willingness to pay because it is a meaningful commitment.
4. The waitlist establishes repeatable demand if it exceeds the first-year paying-customer forecast.
5. Unpaid demand establishes viable unit economics because it should reduce future acquisition costs.

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Scaling software and consulting

Easy (1/8)

W2-S104 · Source slide 104

In this case, a SaaS firm can double revenue using existing capacity with modest incremental staffing. A consulting firm adds delivery professionals roughly in proportion to client work. What explains the difference?

1. SaaS necessarily operates at a lower gross margin.
2. Consulting firms have no fixed costs.
3. The software firm can spread its fixed-cost base across additional revenue.
4. Consulting revenue is recurring, while software revenue cannot be recurring.
5. SaaS businesses never require capital investment.

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The cost-based pricing rule

Easy (0/8)

W2-S106 · Source slide 106

A founder starts with fully loaded cost and adds an amount to achieve a target margin. Which pricing approach is this, and what is its main risk?

1. Value-based pricing; communicating the customer benefit may be difficult.
2. Cost-plus pricing; customer willingness to pay may be ignored.
3. Competition-based pricing; matching rivals may trigger a price war.
4. Freemium pricing; a generous free tier may weaken paid conversion.
5. Penetration pricing; premium customer segments may be overlooked.

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Monthly operating cash break-even

Easy (2/8)

W2-S108 · Source slide 108

A venture sells for $65 per unit, incurs $25 variable cash cost per unit, and pays $24,000 fixed monthly cash operating costs. Sales are collected and costs paid that month. With no other cash flows, how many units cover the monthly operating cash costs?

1. 369 units.
2. 480 units.
3. 600 units.
4. 800 units.
5. 960 units.

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A price increase with fewer customers

Medium (4/8)

W2-S110 · Source slide 110

Customers pay $50 per month for a product serving 5,000 customers. Variable cost is $30 per customer, and fixed monthly costs are $100,000. Price rises 20% to $60 and customer count falls 10%. With unit variable cost and fixed costs unchanged, what is monthly operating profit?

1. Profit falls because losing customers always reduces profit.
2. Profit stays at zero, the original break-even level.
3. The business records an $8,000 operating loss.
4. Operating profit rises to $35,000 per month.
5. Profit cannot be estimated without a separate churn rate.

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A $900 annual contract

Medium (4/8)

W2-S112 · Source slide 112

A product has a $900 annual contract value, with no unusual expansion opportunity. Which go-to-market motion is the strongest initial candidate to test on economic grounds?

1. Self-serve adoption, product-led growth, and efficient paid acquisition.
2. Field enterprise sales with lengthy procurement cycles for each account.
3. Outbound representatives who spend substantial time personally closing each deal.
4. Six-month pilots with custom implementation for each customer.
5. A dedicated customer-success manager assigned to every account.

Related Week 2 deck

Gross-profit CAC payback

Easy (2/8)

W2-S114 · Source slide 114

A startup spends $48,000 in complete sales and marketing acquisition costs to acquire 80 new customers. Each customer produces $60 monthly gross profit. Ignoring churn, expansion, discounting, and other cash flows, what is gross-profit CAC payback?

1. 6 months.
2. 8 months.
3. 10 months.
4. 12 months.
5. 15 months.

Related Week 2 deck

The effect of higher churn

Medium (4/8)

W2-S116 · Source slide 116

Two SaaS firms have $200 monthly revenue per customer, 80% gross margin, and $2,000 CAC. Their only difference is constant monthly churn: 2.8% versus 6%. Under the simple LTV model, what is the main effect of higher churn?

1. Simple CAC payback automatically lengthens to 24 months.
2. Gross margin falls to 40%.
3. Expected lifetime roughly halves, and LTV:CAC falls from about 2.9:1 to 1.3:1.
4. Nothing material changes because price and CAC stay unchanged.
5. The higher-churn firm becomes default alive.

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Positive CM1 and negative CM2

Easy (1/8)

W2-S118 · Source slide 118

For a one-time purchase, CM1 subtracts variable delivery and service costs from revenue. CM2 also subtracts variable selling and acquisition costs. A business has positive CM1 but negative CM2. What does this mean?

1. Delivery loses money, but customer acquisition is economically sound.
2. The company is already profitable.
3. Accounting gross margin must be negative.
4. Churn is necessarily the only problem.
5. Delivery contributes positively, but variable selling and acquisition costs consume more than that contribution.

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A broad industry figure in a software pitch

Easy (1/8)

W2-S120 · Source slide 120

A founder cites $12 trillion of global construction activity as the opportunity for construction software, without identifying buyers or software budgets. What is the main credibility problem?

1. The pitch substitutes broad industry activity for spending on the defined software product.
2. Software SOM must always exceed TAM.
3. The number must understate the software opportunity.
4. Investors should always receive the largest available market figure.
5. Market size becomes irrelevant once unit economics are positive.

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Evidence for a marketplace network effect

Easy (1/8)

W2-S122 · Source slide 122

A two-sided marketplace argues that it has a cross-side network effect. Which evidence most directly supports that claim?

1. Higher transaction volume lowers infrastructure cost per transaction as fixed technology costs are spread more widely.
2. Brand awareness lowers paid acquisition costs for both buyers and sellers.
3. More transaction history improves internal processing algorithms, reducing processing time and operating expense.
4. More users increase total activity, while individual participant value remains roughly unchanged.
5. More qualified sellers attract buyers, while more buyers attract sellers and improve the value of participation on both sides.

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TablePilot expansion and cash

Medium (4/8)

W2-S133 · Source slide 133

TablePilot has $300,000 usable cash. Expansion costs $75,000 immediately. Current monthly receipts are $24,000 and total outflows are $49,000; expansion adds $15,000 monthly outflows. With no incremental receipts, financing, or other cash flows, and constant monthly flows, what runway remains after the upfront payment?

1. 12.0 months.
2. 7.5 months.
3. 5.6 months.
4. 4.6 months.
5. 20.0 months.

Related Week 2 deck

Gross-profit CAC payback

Medium (4/8)

P001 · New quantitative practice

A subscription firm spends $93,600 on sales and marketing and acquires 120 new customers. Each pays $125 per month. Gross margin is 65%; the firm also reports fixed corporate overhead of $18,000 per month. Assume all acquisition spending is attributable to these customers, monthly billings equal revenue, and there is no churn. What is gross-profit CAC payback, expressed in months and rounded to one decimal place?

1. 1152.0 months
2. 115.2 months
3. 6.2 months
4. 17.8 months
5. 9.6 months

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Operating cash break-even volume

Medium (3/8)

P002 · New quantitative practice

A company sells one monthly service plan for $240 per customer. Variable cash delivery and support costs are $90 per customer per month. Fixed monthly operating cash costs are $54,000. The founder has already paid $45,000 for equipment, and monthly depreciation is $2,000. Ignore taxes, financing, further equipment purchases, and working-capital changes. How many active customers are needed for monthly operating cash break-even?

1. 373
2. 360
3. 225
4. 660
5. 600

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Retention of the starting customer cohort

Medium (3/8)

P003 · New quantitative practice

A SaaS company starts with 1,800 customers. It loses 2.5% of the remaining starting cohort at each month-end for 9 months. It also adds 100 new customers each month, whose retention is tracked separately. No customer in the starting cohort returns after leaving. How many customers from the original cohort remain after month 9, rounded to the nearest customer?

1. 367
2. 1,433
3. 2,333
4. 1,395
5. 1,470

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Net revenue retention with new customer growth

Medium (3/8)

P004 · New quantitative practice

Beginning annual recurring revenue from existing customers is $480,000. During the year, those customers add $96,000 of expansion ARR, reduce subscriptions by $24,000, and cancel $72,000 of ARR. New customers contribute another $180,000 of ARR. All figures are measured on the same annualized basis. What is net revenue retention for the beginning customer cohort, expressed as a percentage and rounded to one decimal place?

1. 100.0%
2. 0.0%
3. 105.0%
4. 80.0%
5. 137.5%

Related Week 2 deck

Gross-profit LTV relative to CAC

Medium (4/8)

P005 · New quantitative practice

A subscription business has monthly revenue per customer of $160, gross margin of 75%, and constant monthly customer churn of 4.0%. CAC is $1,200. Use the simplified expected-lifetime model with no discounting, no expansion, and no reactivation; expected lifetime in months is the reciprocal of monthly churn. What is gross-profit LTV divided by CAC, rounded to two decimals?

1. 0.21×
2. 3.33×
3. 0.40×
4. 0.83×
5. 2.50×

Related Week 2 deck

Gross-profit CAC payback

Medium (4/8)

P013 · New quantitative practice

A subscription firm spends $126,000 on sales and marketing and acquires 140 new customers. Each pays $150 per month. Gross margin is 60%; the firm also reports fixed corporate overhead of $18,000 per month. Assume all acquisition spending is attributable to these customers, monthly billings equal revenue, and there is no churn. What is gross-profit CAC payback, expressed in months and rounded to one decimal place?

1. 1400.0 months
2. 10.0 months
3. 15.0 months
4. 6.0 months
5. 120.0 months

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Operating cash break-even volume

Medium (3/8)

P014 · New quantitative practice

A company sells one monthly service plan for $320 per customer. Variable cash delivery and support costs are $120 per customer per month. Fixed monthly operating cash costs are $76,000. The founder has already paid $45,000 for equipment, and monthly depreciation is $2,000. Ignore taxes, financing, further equipment purchases, and working-capital changes. How many active customers are needed for monthly operating cash break-even?

1. 380
2. 390
3. 605
4. 633
5. 238

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Retention of the starting customer cohort

Medium (3/8)

P015 · New quantitative practice

A SaaS company starts with 2,400 customers. It loses 3.5% of the remaining starting cohort at each month-end for 8 months. It also adds 100 new customers each month, whose retention is tracked separately. No customer in the starting cohort returns after leaving. How many customers from the original cohort remain after month 8, rounded to the nearest customer?

1. 1,870
2. 595
3. 1,728
4. 1,805
5. 2,605

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Net revenue retention with new customer growth

Medium (3/8)

P016 · New quantitative practice

Beginning annual recurring revenue from existing customers is $650,000. During the year, those customers add $117,000 of expansion ARR, reduce subscriptions by $39,000, and cancel $52,000 of ARR. New customers contribute another $210,000 of ARR. All figures are measured on the same annualized basis. What is net revenue retention for the beginning customer cohort, expressed as a percentage and rounded to one decimal place?

1. 4.0%
2. 86.0%
3. 110.0%
4. 136.3%
5. 104.0%

Related Week 2 deck

Gross-profit LTV relative to CAC

Medium (4/8)

P017 · New quantitative practice

A subscription business has monthly revenue per customer of $210, gross margin of 70%, and constant monthly customer churn of 3.5%. CAC is $1,400. Use the simplified expected-lifetime model with no discounting, no expansion, and no reactivation; expected lifetime in months is the reciprocal of monthly churn. What is gross-profit LTV divided by CAC, rounded to two decimals?

1. 4.29×
2. 1.29×
3. 0.25×
4. 0.33×
5. 3.00×

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Connecting profit and cash

Hard (6/8)

W3-S006 · Source slide 6

A startup collects $180,000 on January 1 for twelve months of service delivered evenly. It purchases $36,000 of equipment the same day, depreciated straight-line over three years with no residual value. Ignore taxes and all other activity.

At January 31, which combination is correct?

1. Profit $15,000; net cash increase $144,000; deferred revenue $165,000.
2. Profit $14,000; net cash increase $144,000; deferred revenue $165,000.
3. Profit $14,000; net cash increase $179,000; deferred revenue $165,000.
4. Profit $14,000; net cash increase $144,000; deferred revenue $180,000.
5. Profit $179,000; net cash increase $144,000; deferred revenue $0.

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Vertical analysis

Easy (0/8)

W3-S010 · Source slide 10

An analyst wants to see what share of each revenue dollar goes to cost of goods sold and operating expenses. Which tool answers this directly?

1. Horizontal analysis
2. Peer benchmarking
3. Vertical analysis
4. Cohort analysis
5. Terminal value analysis

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Ratios and payment capacity

Hard (6/8)

W3-S013 · Source slide 13

A startup reports $300,000 cash, $600,000 net receivables, $400,000 inventory, and $200,000 prepaid costs. Current liabilities are $1 million. There are no marketable securities. Most receivables arrive in 90 days, while a large supplier payment is due in 30 days. Under the stated course definitions, which assessment is correct?

1. Current ratio 0.90×; quick ratio 1.50×; the receivable balance proves timely payment capacity.
2. Current ratio 1.50×; quick ratio 0.90×; the collection and payment schedule still needs testing.
3. Current ratio 1.50×; quick ratio 1.30×; inventory should be included in the quick-ratio numerator.
4. Current ratio 1.30×; quick ratio 0.90×; prepaid costs should be excluded from current assets.
5. Current ratio 1.50×; quick ratio 1.10×; prepaid costs can fund the upcoming supplier payment.

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Analyst posture

Easy (1/8)

W3-S017 · Source slide 17

A founder presents financials that recognize revenue at signing and emphasize cash inflows over outflows.. What posture should the analyst take?

1. Accept the statements, since founders know the business best
2. Reject the company as uninvestable on accounting grounds
3. Verify data quality and reconcile to cash
4. Require audited GAAP statements before any analysis
5. Rely on the income statement and set the cash flows aside

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Agent revenue

Medium (3/8)

W3-S022 · Source slide 22

A platform facilitates $10 million of customer transactions during the year and retains a 15% commission on each transaction. The platform has 250,000 active users, an average transaction value of $40, and incurred $600,000 of marketing costs and $400,000 of platform-development costs during the year. The third-party sellers are responsible for fulfilling the orders, and the platform does not control the underlying goods or services before they are transferred to customers.

Under ASC 606, how much revenue should the platform report?

1. $10 million, the full amount it processed
2. $8.5 million, net of the fee it pays out
3. $11.5 million gross, with the payout as expense
4. $1.5 million, the fee it retains as agent
5. Either amount, since net income is the same

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Cash collections

Easy (0/8)

W3-S026 · Source slide 26

A founder says the company 'did $5 million last quarter.' Which figure most directly shows cash actually received from customers during that quarter?

1. Bookings
2. Cash collections
3. Billings
4. Recognized revenue
5. Annual recurring revenue

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Deferred revenue

Easy (1/8)

W3-S029 · Source slide 29

A startup's operating cash flow is positive because customers increasingly pay before the company delivers, creating deferred revenue. This indicates that:

1. Delivered revenue is growing strongly this period
2. The company carries no future delivery obligations
3. Net income is being understated this period
4. The cash can be recognized as revenue now
5. Cash arrived ahead of an obligation to deliver

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Deferred revenue and refunds

Hard (6/8)

W3-S031 · Source slide 31

A SaaS company begins the year with $84,000 of deferred revenue. Customers pay before the related service revenue is recognized, and the company has no accounts receivable.

The company reports the following activity for the first three quarters:

Every refund returns an unearned customer advance already included in deferred revenue. None reverses revenue that was previously recognized, and there are no other changes to the deferred-revenue balance.

Management highlights the strong third-quarter cash collections in its investor update.

At September 30, what is the deferred-revenue balance, and how do year-to-date customer cash collections after refunds compare with year-to-date recognized revenue?

1. Deferred revenue: $60,000; net collections are $24,000 below recognized revenue.
2. Deferred revenue: $75,000; net collections are $9,000 below recognized revenue.
3. Deferred revenue: $99,000; net collections are $15,000 above recognized revenue.
4. Deferred revenue: $105,000; net collections are $21,000 above recognized revenue.
5. Deferred revenue: $123,000; net collections are $39,000 above recognized revenue.

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Operating cash flow

Hard (7/8)

W3-S036 · Source slide 36

A SaaS company begins the year with $250,000 of cash and reports a $450,000 net loss for the year. The net loss includes $120,000 of depreciation and amortization and $90,000 of noncash stock-based compensation.

The following operating balances change during the year:

These changes arise only from ordinary operating transactions. The increase in deferred revenue comes from customers paying in advance for future services.

The company also pays $210,000 for capital expenditures, receives $300,000 from new borrowing, and repays $60,000 of loan principal.

Assume no other noncash adjustments, working-capital changes, tax or interest timing adjustments, or cash flows. Use the indirect method under U.S. GAAP.

What are cash flow from operations and the total change in cash for the year?

1. Operating cash flow: −$330,000; total cash change: −$300,000.
2. Operating cash flow: $60,000; total cash change: $90,000.
3. Operating cash flow: $150,000; total cash change: $180,000.
4. Operating cash flow: $390,000; total cash change: $180,000.
5. Operating cash flow: $470,000; total cash change: $500,000.

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Compounding over one and two years

W3-S041 · Source slide 41

One year

You invest $1,000 today at 5% per year, compounded annually, with no additional deposits or withdrawals. How much will you have at the end of one year?

Two years

Leave the same $1,000 invested for two years at 5%, with no deposits or withdrawals. Is the ending balance $1,100, or does compounding produce a different result? Explain before calculating.

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Present value of a future target

W3-S043 · Source slide 43

PV = FV / (1 + r)ⁿ.

Discounting expresses a future amount in today’s dollars at the stated rate.

You want $2,000 at the end of five years and can earn 5% per year, compounded annually. There will be no additional contributions or withdrawals.

How much must you invest today?

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Discounted prepayments

Easy (1/8)

W3-S048 · Source slide 48

A company lifted this quarter's cash by offering customers 50% discounts to prepay annually. On a cash-basis view, the inflow is best read as:

1. Cash arrives earlier, while future delivery obligations remain
2. A durable improvement in operating performance
3. Evidence of strong underlying unit economics
4. Irrelevant, since cash is always the best signal
5. A reduction in the company's deferred revenue

Related Week 3 deck

Discounted prepayments

Hard (7/8)

W3-S050 · Source slide 50

A company offers a three-year service contract under two payment options:

Annual billing: The customer pays $140,000 at the end of each year for three years.

Prepayment: The customer pays the full three-year contract price today and receives an 18% discount from the total undiscounted price.

If the customer prepays, the company also incurs an $8,400 processing and contract-administration cost today. This cost is not incurred under annual billing.

The company can immediately reinvest any cash it receives in another business line that is expected to earn a 22% annual return over the next three years. The company incurs $28,000 of service-delivery costs at the end of each year under either payment option.

Assume the service obligations are identical, all amounts are collected as scheduled, and there are no taxes or other incremental cash flows. Treat 22% as the appropriate annual opportunity cost of capital for this comparison.

What is the incremental NPV today to the company of accepting prepayment rather than annual billing, rounded to the nearest $100?

1. −$84,000
2. −$12,800
3. −$7,100
4. +$50,100
5. +$58,500

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Growth and collection timing

Easy (1/8)

W3-S053 · Source slide 53

A startup earns a positive contribution margin on every new customer. Customer acquisition spending is paid immediately, but customers pay invoices 60 days later. Sales are accelerating rapidly. Which conclusion is most accurate?

1. Positive contribution margin should reduce financing needs as sales grow because customer-level profit eventually offsets acquisition spending.
2. The 60-day collection lag matters mainly for working-capital presentation, while funding needs depend primarily on customer contribution margin.
3. Faster growth can increase short-term financing needs because acquisition cash is paid before the related customer cash is collected.
4. Faster growth should improve liquidity if the company maintains the same acquisition cost and contribution margin per customer.
5. The company is likely default alive if contribution margin remains positive, even when customer collections continue to lag acquisition spending.

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Profit and delayed collections

Hard (7/8)

W3-S056 · Source slide 56

A startup is preparing its first-quarter forecast. It begins January with $180,000 of cash and no accounts receivable or accounts payable.

Each one-time order has the following terms:

The company recognizes $1,200 of revenue when it delivers the order.

Acquisition and delivery costs total $900, paid and expensed in the delivery month.

The customer pays in full at the end of the second month after delivery. For example, January orders are collected at the end of March.

Fixed operating costs are $15,000 per month, paid and expensed monthly. An investor has mentioned a possible $500,000 investment in a nonbinding letter, but the forecast includes no financing.

Assume all scheduled orders are delivered, with no taxes, noncash items, payment deferrals, or other cash flows. A negative projected cash balance represents an unfunded shortfall.

What are projected first-quarter operating profit and the March 31 cash balance before financing?

1. Operating profit: −$129,000; cash before financing: $75,000.
2. Operating profit: $75,000; cash before financing: −$225,000.
3. Operating profit: $75,000; cash before financing: −$129,000.
4. Operating profit: $75,000; cash before financing: $255,000.
5. Operating profit: $120,000; cash before financing: −$84,000.

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Collection timing and cash required

Medium (4/8)

W3-S061 · Source slide 61

Annual credit sales are $3.65 million and average receivables are $500,000. Sales occur evenly, bad debts are negligible, and inventory and supplier terms remain unchanged. Management can reduce DSO to 35 days without affecting sales or margins.

Using 365 days, what are current DSO and the one-time cash released when receivables reach the target?

1. Current DSO: 35 days; cash released: $150,000.
2. Current DSO: 50 days; cash released: $350,000.
3. Current DSO: 50 days; cash released: $500,000.
4. Current DSO: 50 days; cash released: $150,000.
5. Current DSO: 73 days; cash released: $150,000.

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Working capital and FCFF

Easy (0/8)

W3-S066 · Source slide 66

In the FCFF formula, how does an increase in net operating working capital, excluding cash and financing debt, affect free cash flow?

1. It increases FCFF, as a source of cash
2. It has no effect on FCFF either way
3. It increases FCFF only when debt rises
4. It decreases FCFF, as a use of cash
5. It reduces net income but not FCFF

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Free cash flow to the firm

Hard (7/8)

W3-S068 · Source slide 68

A profitable equipment-software company reports the following annual results:

EBIT: $6.40 million, after $0.90 million of depreciation and amortization.

Capital expenditures: $1.70 million.

Tax rate: 25%.

Its only operating working-capital accounts are shown below. All balances are in millions of dollars.

During the year, the company also pays $0.40 million of interest, issues $0.90 million of new debt, and repays $0.25 million of debt principal.

Assume no loss carryforwards, tax timing differences, or other noncash adjustments.

What is the company's annual free cash flow to the firm (FCFF)?

1. $3.00 million.
2. $3.35 million.
3. $3.70 million.
4. $4.00 million.
5. $4.65 million.

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Runway

Easy (2/8)

W3-S071 · Source slide 71

A pre-revenue startup holds $1.8 million in cash and burns $150,000 net per month. What is its runway?

1. 9 months
2. 18 months
3. 6 months
4. 15 months
5. 12 months

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Runway and the cash floor

Hard (7/8)

W3-S073 · Source slide 73

A startup has $1.08 million in its bank accounts. Of that amount, $180,000 is restricted and cannot be used for operations. On day one, the company pays $120,000 for equipment from its usable cash.

Its operating cash forecast is:

The equipment payment is additional to these outflows. Net operating cash use occurs evenly within each month. The company wants to maintain at least $180,000 of usable cash and has no additional financing or other cash flows.

How many months after day one will usable cash first fall to the $180,000 minimum?

1. 5.00 months.
2. 6.50 months.
3. 7.50 months.
4. 8.00 months.
5. 8.75 months.

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Net revenue retention

Easy (1/8)

W3-S078 · Source slide 78

Two SaaS companies each report $10 million ARR. One has 120% net revenue retention; the other has 85%. The difference tells you that:

1. The existing customer revenue base expands at 120% NRR and contracts at 85% NRR
2. The two firms are equivalent, since ARR is identical
3. The 85% firm has higher gross margins by definition
4. The 120% firm must be spending more to acquire users
5. Net revenue retention is a vanity metric here

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Cohort decay

Easy (1/8)

W3-S081 · Source slide 81

A startup grows revenue 30% year over year, but each customer cohort loses 40% of its revenue within 12 months. The most accurate read is:

1. Retention is strong and the growth is durable
2. The business has clearly reached product-market fit
3. Aggregate growth understates true performance
4. New customer revenue must offset substantial losses from earlier cohorts
5. Cohort decay does not matter while ARR rises

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PEG Ratio Calculation

Medium (4/8)

W3-S087 · Source slide 87

A company’s stock trades at $84 per share. Current EPS is $4.00, and analysts expect EPS to reach $6.91 in three years. Assume earnings grow at a constant annual rate.

What is the company’s approximate PEG ratio?

1. 0.29
2. 0.61
3. 1.05
4. 1.52
5. 5.25

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Valuation Metrics Multiple Choice

Hard (7/8)

W3-S089 · Source slide 89

A company has:

Market capitalization: $3.9 billion

Diluted shares outstanding: 50 million

Current net income: $160 million

Expected net income in three years: $280 million

Expected diluted shares in three years: 52 million

Peer median P/E: 25.0x

Peer median PEG: 1.25x

Assume EPS grows at a constant annual rate. An investor considers the stock attractive only if both its P/E and PEG are below the peer medians. Which analysis is correct?

1. P/E = 24.4x; PEG = 1.29x; does not meet the criteria
2. P/E = 24.4x; PEG = 1.19x; meets the criteria
3. P/E = 24.4x; PEG = 0.98x; meets the criteria
4. P/E = 14.5x; PEG = 0.77x; meets the criteria
5. P/E = 25.0x; PEG = 1.29x; does not meet the criteria

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P/E versus PEG

Hard (6/8)

W3-S091 · Source slide 91

An analyst is comparing two profitable technology companies:

For both companies, trailing earnings per share (EPS) covers the same most recent 12 months, and forecast EPS covers the following 12 months. Assume no stock splits or changes in the share basis.

Use trailing P/E and the conventional PEG ratio based on expected EPS growth from the trailing year to the forecast year.

Which answer gives the correct P/E and PEG for each company, rounded to two decimal places?

1. Orion: P/E 23.33×, PEG 1.17; Vega: P/E 16.07×, PEG 1.34.
2. Orion: P/E 28.00×, PEG 0.80; Vega: P/E 18.00×, PEG 0.75.
3. Orion: P/E 28.00×, PEG 1.17; Vega: P/E 18.00×, PEG 1.20.
4. Orion: P/E 28.00×, PEG 1.40; Vega: P/E 18.00×, PEG 1.50.
5. Orion: P/E 28.00×, PEG 1.68; Vega: P/E 18.00×, PEG 1.68.

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Customer concentration

Easy (1/8)

W3-S098 · Source slide 98

In diligence, a startup's top three customers are 60% of revenue with no long-term contracts. In a quality-of-earnings review this most represents:

1. Customer concentration and durability risk
2. A working capital timing distortion to normalize
3. An unrecorded liability that should be accrued
4. A gross-versus-net revenue misstatement
5. A terminal value assumption that is too high

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Participating preferred

Easy (1/8)

W3-S103 · Source slide 103

A startup exit leaves $8 million available to equity after debt and transaction costs. An investor holds an uncapped 1x participating preferred on a $4 million investment. Versus a 1x non-participating investor, the participating investor generally receives:

1. Only the $4 million preference and nothing more
2. The $4 million back, then a share of the rest
3. Exactly the same amount under either structure
4. Nothing until common shareholders are paid
5. Three times the original amount invested

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Value Lease A’s level cash flows

Easy (2/8)

W3-S109 · Source slide 109

Optional NPV practice

Lease A costs the landlord $20,000 today and produces net cash flow of $90,000 at each of the next three year-ends. At an 8% annual discount rate, the three-year ordinary-annuity present-value factor is 2.57709699.

Assume these are all relevant lease cash flows, with no terminal value. What is NPV, rounded to the nearest dollar?

1. $191,939
2. $211,939
3. $231,939
4. $250,000
5. $270,000

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Value Lease B’s unequal cash flows

Medium (5/8)

W3-S111 · Source slide 111

Optional NPV practice

Lease B costs the landlord $45,000 today and produces net cash flow of $100,000, $102,000, and $104,000 at the ends of Years 1, 2, and 3, respectively. The annual discount rate is 8%. There is no terminal value or other relevant cash flow.

What is NPV, rounded to the nearest $100?

1. $217,600
2. $212,700
3. $238,600
4. $261,000
5. $262,600

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PEG ratio

Medium (4/8)

W3-S113 · Source slide 113

A profitable technology company trades at $120 per share and reports current EPS of $3.00. Analysts expect EPS of $4.50 next year. The company’s industry average P/E is 28×, its dividend yield is 1.5%, and revenue grew 35% this year.

Using expected EPS growth, what is the company’s PEG ratio?

Convention: Use current EPS to calculate P/E.

1. 0.80
2. 0.9
3. 1.14
4. 1.33
5. 1.43

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Analyst posture

Medium (4/8)

W3-S115 · Source slide 115

A founder presents investor materials showing $6.0 million of “revenue” based largely on contracts signed during the year. Cash collections were $3.8 million, customer-related cash outflows were $2.9 million, and several contracts require services to be delivered over the next 12 months. The company does not yet prepare audited financial statements.

What is the most appropriate analytical approach?

1. Use the $6.0 million figure because signed contracts provide the clearest measure of current operating performance.
2. Use the $3.8 million of collections as revenue because cash receipts are more reliable than management estimates.
3. Reconstruct revenue and cash flow using contract terms, delivery obligations, collections, and other verifiable information.
4. Exclude the company from analysis until audited GAAP financial statements become available.
5. Focus primarily on net cash generation because accounting revenue is less relevant for an early-stage company.

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Deferred revenue

Medium (4/8)

W3-S117 · Source slide 117

A SaaS startup reports a $1.2 million net loss for the year. Its cash flow statement includes $400,000 of depreciation and amortization, $300,000 of stock-based compensation, a $500,000 increase in accounts receivable, and a $2.2 million increase in deferred revenue. The company also spent $1.5 million on capital expenditures during the year.

Most of the increase in deferred revenue resulted from customers paying annually in advance for subscription services that will be provided over the next 12 months.

The company reports positive operating cash flow of $1.2 million. Which interpretation is most accurate?

1. Advance collections increased revenue and operating cash flow because customers had already paid the company.
2. Deferred revenue increased operating cash flow because cash was collected before the related revenue was earned.
3. Deferred revenue did not affect operating cash flow because it represents a noncash accounting liability.
4. Positive operating cash flow shows the underlying business generated cash independently of customer prepayments.
5. Capital expenditures should reduce operating cash flow because they support delivery of future subscription services.

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Deferred revenue

Medium (5/8)

W3-S119 · Source slide 119

A SaaS company begins the year with $40,000 of deferred revenue. All customer consideration is collected before the related revenue is recognized. Assume there are no refunds or other contract liability adjustments.

At September 30, which statement is correct?

1. Deferred revenue is $25,000 because cash collections exceeded revenue by $25,000 year to date
2. Deferred revenue remains $40,000 because cash collections do not affect revenue recognition
3. Deferred revenue is $65,000, and year-to-date cash collections exceed GAAP revenue by $25,000
4. Deferred revenue is $65,000, and year-to-date GAAP revenue exceeds cash collections by $25,000
5. Deferred revenue is $90,000 because only Q3 activity determines the September 30 balance

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Discounted prepayments

Hard (6/8)

W3-S121 · Source slide 121

A company normally charges $100,000 per year for three years, payable at the end of each year. It offers a customer a 20% discount to prepay the entire three-year contract at signing, resulting in an immediate cash payment of $240,000.

The company can reinvest available cash in a business unit expected to earn 25% annually. Assume 25% represents the appropriate opportunity cost of capital. Ignore taxes and operating costs.

What is the approximate incremental NPV of accepting the prepaid contract rather than collecting $100,000 annually?

1. $(60,000)
2. $0
3. $15,000
4. $44,800
5. $87,500

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Free cash flow to the firm

Medium (4/8)

W3-S123 · Source slide 123

A company reports EBIT of $5.0 million, a 25% tax rate, $700,000 of depreciation and amortization, and $1.4 million of capital expenditures. During the year, accounts receivable increased by $900,000, inventory increased by $400,000, and accounts payable increased by $500,000.

Assume these are the only changes in operating working capital. What is the company’s FCFF?

1. $3.85 million
2. $3.05 million
3. $2.25 million
4. $1.75 million
5. $1.25 million

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Revenue to cash collections

Medium (3/8)

P006 · New quantitative practice

A startup recognizes $1,650,000 of credit revenue during the year. Accounts receivable rises from $310,000 to $455,000. Customers make no advance payments, and there are no write-offs, refunds, cash sales, or foreign-exchange effects. The company also raises $600,000 of equity during the year. How much cash was collected from customers?

1. $2,105,000
2. $1,505,000
3. $1,795,000
4. $1,195,000
5. $1,650,000

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Deferred revenue after a customer refund

Medium (3/8)

P007 · New quantitative practice

Opening deferred revenue is $75,000. Customers pay $460,000 in advance during the year, and the company recognizes $395,000 of revenue from those contracts and the opening deferred-revenue balance. It also refunds $18,000 for services never delivered; this refund reduces deferred revenue and does not reverse recognized revenue. There are no receivables or other adjustments. What is closing deferred revenue?

1. −$8,000
2. $158,000
3. $47,000
4. $140,000
5. $122,000

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Operating cash flow from the indirect method

Medium (4/8)

P008 · New quantitative practice

All amounts are in millions. A startup reports net income of -1.40, depreciation of 0.45, and noncash stock compensation of 0.30. Accounts receivable increases by 0.55, accounts payable by 0.20, and deferred revenue by 1.65. These are the only noncash adjustments and operating working-capital changes. The company also pays 0.90 for equipment. What is operating cash flow, expressed in millions and rounded to two decimal places?

1. −$1.00 million
2. $0.35 million
3. $1.75 million
4. −$0.25 million
5. $0.65 million

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Revenue to cash collections

Medium (3/8)

P018 · New quantitative practice

A startup recognizes $2,140,000 of credit revenue during the year. Accounts receivable rises from $420,000 to $565,000. Customers make no advance payments, and there are no write-offs, refunds, cash sales, or foreign-exchange effects. The company also raises $600,000 of equity during the year. How much cash was collected from customers?

1. $2,140,000
2. $2,595,000
3. $2,285,000
4. $1,995,000
5. $1,575,000

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Deferred revenue after a customer refund

Medium (3/8)

P019 · New quantitative practice

Opening deferred revenue is $92,000. Customers pay $580,000 in advance during the year, and the company recognizes $510,000 of revenue from those contracts and the opening deferred-revenue balance. It also refunds $22,000 for services never delivered; this refund reduces deferred revenue and does not reverse recognized revenue. There are no receivables or other adjustments. What is closing deferred revenue?

1. $184,000
2. $48,000
3. $162,000
4. $0
5. $140,000

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Operating cash flow from the indirect method

Medium (4/8)

P020 · New quantitative practice

All amounts are in millions. A startup reports net income of -1.70, depreciation of 0.60, and noncash stock compensation of 0.40. Accounts receivable increases by 0.65, accounts payable by 0.25, and deferred revenue by 2.00. These are the only noncash adjustments and operating working-capital changes. The company also pays 0.90 for equipment. What is operating cash flow, expressed in millions and rounded to two decimal places?

1. $0.50 million
2. −$1.10 million
3. −$0.00 million
4. $2.20 million
5. $0.90 million

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Present value of beginning-of-year payments

Medium (4/8)

P027 · New quantitative practice

A startup signs a 4-year equipment lease requiring $72,000 at the beginning of each year. The first payment is due today and the final payment is due at time 3. Use a 10% effective annual discount rate. Ignore tax effects, residual values, deposits, and all other costs. What is the present value of the lease payments, rounded to the nearest dollar?

1. $228,230
2. $171,473
3. $276,159
4. $251,053
5. $288,000

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Monthly reserve deposits for a future obligation

Medium (4/8)

P028 · New quantitative practice

A startup needs $240,000 exactly 24 months from today to meet a planned equipment payment. It currently has no money set aside for this obligation. It will make equal deposits at each month-end into an account earning a nominal annual rate of 6.0%, compounded monthly. The last deposit is made on the payment date. What monthly deposit is required, rounded to the nearest dollar?

1. $10,637
2. $10,000
3. $4,723
4. $9,437
5. $9,390

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Present value of beginning-of-year payments

Medium (4/8)

P033 · New quantitative practice

A startup signs a 5-year equipment lease requiring $84,000 at the beginning of each year. The first payment is due today and the final payment is due at time 4. Use a 12% effective annual discount rate. Ignore tax effects, residual values, deposits, and all other costs. What is the present value of the lease payments, rounded to the nearest dollar?

1. $420,000
2. $302,801
3. $339,137
4. $379,834
5. $192,436

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Monthly reserve deposits for a future obligation

Medium (4/8)

P034 · New quantitative practice

A startup needs $360,000 exactly 30 months from today to meet a planned equipment payment. It currently has no money set aside for this obligation. It will make equal deposits at each month-end into an account earning a nominal annual rate of 7.2%, compounded monthly. The last deposit is made on the payment date. What monthly deposit is required, rounded to the nearest dollar?

1. $12,000
2. $3,676
3. $10,988
4. $10,923
5. $13,148

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Compound growth

Easy (2/8)

W4-S006 · Source slide 6

An employee earning $40,000 wants to reach $200,000 in 10 years. What annual rate must they sustain?

1. About 40%, since income must multiply five times
2. About 16%, the simple average of the raises
3. About 50%, front-loaded in the early years
4. About 17.5%, the compound annual growth rate
5. About 10%, one-tenth of the total increase

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TTM revenue

Easy (2/8)

W4-S010 · Source slide 10

Last fiscal-year revenue was $4.2 million. Current year-to-date revenue is $1.6 million, and revenue for the comparable prior-year year-to-date period was $1.1 million. What is trailing-twelve-month revenue?

1. $4.7 million.
2. $5.3 million.
3. $5.8 million.
4. $6.9 million.
5. $7.0 million.

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TTM and recurring run rate

Hard (6/8)

W4-S013 · Source slide 13

At September 30, a startup is preparing an investor update using these revenue figures:

September's recognized revenue is $780,000. That amount includes $180,000 from a one-time implementation project and $600,000 of recurring subscription revenue. Management forecasts $9.40 million of revenue for the next 12 months.

For this comparison, include one-time items in historical trailing-twelve-month (TTM) total revenue. Base the recurring annualized run rate only on September's recurring revenue.

What are TTM total revenue through September 30 and the recurring annualized run rate at that date?

1. TTM total revenue: $6.72 million; recurring annualized run rate: $7.20 million.
2. TTM total revenue: $6.90 million; recurring annualized run rate: $7.20 million.
3. TTM total revenue: $6.90 million; recurring annualized run rate: $9.36 million.
4. TTM total revenue: $6.90 million; recurring annualized run rate: $9.40 million.
5. TTM total revenue: $10.80 million; recurring annualized run rate: $7.20 million.

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Operating drivers

Easy (1/8)

W4-S018 · Source slide 18

Which approach provides the strongest operating foundation for a driver-based revenue forecast?

1. Revenue grows 250% because management believes that growth rate is necessary to support the next financing valuation.
2. Bookings are built from productive sales capacity, qualified opportunities, conversion rates, deal size, and timing assumptions.
3. Revenue equals 2% of TAM because capturing a small share of a large market is a conservative assumption.
4. Revenue is set equal to the amount required for the company to reach breakeven by the end of the forecast period.
5. Revenue grows at the industry growth rate because individual company execution is too uncertain to model directly.

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Customer additions and churn

Easy (1/8)

W4-S021 · Source slide 21

Scenario: A subscription business is preparing next year’s revenue forecast. Management expects to begin the year with 8,000 customers, add 500 customers per month, lose 2% of customers each month, and earn an average of $40 per customer per month. Which approach best reflects driver-based forecasting?

1. Increase last year’s revenue by management’s expected overall growth rate.
2. Use the average revenue growth rate from the prior three years.
3. Forecast revenue from customer additions, churn, and revenue per customer.
4. Use the most recent month’s revenue and annualize it for twelve months.
5. Forecast revenue equal to the midpoint of management’s historical guidance range.

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Profit and cash

Easy (0/8)

W4-S028 · Source slide 28

Among the eleven guidelines, why does the module insist on always building a cash flow model?

1. Because the income statement is not allowed in a model
2. Because cash flow replaces the need for revenue forecasts
3. Because a profitable company can still run out of cash
4. Because investors never read the income statement
5. Because cash flow is easier to forecast than expenses

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Model structure

Medium (4/8)

W4-S030 · Source slide 30

A founder builds a five-year model using annual revenue growth assumptions, hard-coded formulas, and a single base case. The model shows accounting profit, but does not separately forecast cash balances or operating drivers. Which change would most improve the model?

1. Add more expense line items so the model appears more detailed.
2. Extend the forecast to ten years to show a longer strategic horizon.
3. Build monthly cash flow from operating drivers and centralized assumptions.
4. Increase the revenue growth rate to better reflect management’s ambition.
5. Replace the base case with an upside case to show investor potential.

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Sales ramp

Easy (1/8)

W4-S037 · Source slide 37

A rep is hired in January with a 90-day time to productivity. When does the model credit that rep with sales?

1. Immediately in January, on the start date
2. Never, until the rep is formally promoted
3. In February, after one full month on the job
4. Around April, once the ramp period has passed
5. Only at the very end of the fiscal year

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Sales ramp and revenue

Hard (7/8)

W4-S039 · Source slide 39

A SaaS company is forecasting first-quarter bookings and revenue. Its sales team has two groups:

Experienced representatives: Three representatives each close two annual contracts per month in January, February, and March.

New representatives: Two representatives join on February 1. They close no contracts in February. In March, each closes contracts at 50% of the experienced representatives' monthly rate.

Every contract has a $24,000 annual value. Contracts close at month-end, and customers pay the full amount immediately. Service begins on the first day of the following month, with revenue earned evenly over the next 12 months.

Assume no existing contracts, discounts, or cancellations.

What are total first-quarter bookings and recognized revenue?

1. Bookings of $480,000 and recognized revenue of $36,000.
2. Bookings of $480,000 and recognized revenue of $76,000.
3. Bookings of $480,000 and recognized revenue of $480,000.
4. Bookings of $528,000 and recognized revenue of $36,000.
5. Bookings of $624,000 and recognized revenue of $44,000.

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Annual churn

Easy (2/8)

W4-S043 · Source slide 43

A subscription business has 2% monthly churn. Roughly how much of its base does it lose in a year?

1. About 2%
2. About 22%
3. About 6%
4. About 50%
5. About 24%

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Forecast revenue, receivables, and cash

Hard (6/8)

W4-S050 · Source slide 50

A monthly forecast starts with $80,000 cash and $30,000 receivables. Credit sales are $120,000, collections are $95,000, and cash operating expenses are $70,000. Equipment costs $40,000 cash; monthly depreciation is $4,000. There are no other accruals, taxes, or financing flows.

Which forecast is internally consistent?

1. Profit $46,000; ending receivables $55,000; ending cash $65,000.
2. Profit $46,000; ending receivables $55,000; ending cash $61,000.
3. Profit $46,000; ending receivables $25,000; ending cash $65,000.
4. Profit $6,000; ending receivables $55,000; ending cash $65,000.
5. Profit $46,000; ending receivables $55,000; ending cash $90,000.

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Runway

Easy (2/8)

W4-S055 · Source slide 55

A startup holds $900,000 in cash and burns $150,000 net per month. What is its runway?

1. 3 months
2. 9 months
3. 12 months
4. 15 months
5. 6 months

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A delayed collection

Medium (4/8)

W4-S058 · Source slide 58

A startup begins March with $160,000 of cash and requires a $50,000 minimum cash balance. A $140,000 customer collection expected in March moves to April, while March payroll and vendor payments of $210,000 remain unchanged. Management also wants to spend $25,000 on a discretionary growth experiment in March. What minimum additional financing or cost deferral is required to maintain the cash floor and complete the experiment?

1. $75,000.
2. $100,000.
3. $125,000.
4. $140,000.
5. $235,000.

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The lowest cash point

Hard (7/8)

W4-S061 · Source slide 61

A startup begins May with $220,000 of usable cash. Management wants to maintain at least $60,000 at the end of every month.

A $150,000 customer payment expected in May has been delayed until July. The updated forecast separates that payment from other receipts:

Management also plans to complete a $30,000 experiment in May. Its cost is additional to the required payments in the table. Monthly depreciation of $12,000 is a noncash expense and is not included in these cash payments.

Any new financing arrives before May's payments and is available throughout the forecast. Assume no financing fees, repayments, or other cash flows.

What is the smallest financing amount that allows the company to complete the experiment and maintain the $60,000 minimum at every month-end?

1. $60,000.
2. $80,000.
3. $110,000.
4. $140,000.
5. $200,000.

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The gross funding request

Hard (6/8)

W4-S064 · Source slide 64

A startup is deciding how much capital to raise before its next milestone. Its forecast shows:

Usable opening cash of $430,000.

Cumulative net cash use of $1.48 million before reaching the milestone.

A required cash balance of at least $270,000 at the milestone.

The milestone is the lowest cash point in the forecast. There are no other financing sources, and the forecast excludes fundraising transaction costs.

At the financing closing, the company must pay a $40,000 legal bill and a placement fee equal to 4% of the gross amount raised. Both costs are paid from the proceeds.

What is the minimum gross amount the company needs to raise, rounded to the nearest $1,000?

1. $1,320,000.
2. $1,360,000.
3. $1,375,000.
4. $1,414,000.
5. $1,417,000.

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Growth versus retention

Hard (6/8)

W4-S071 · Source slide 71

A SaaS company begins the quarter with $120,000 of monthly recurring revenue (MRR). During the quarter, it records the following changes:

The cancellation and downgrade amounts do not overlap. Assume no reactivations, foreign-exchange effects, or other changes.

Management argues that the increase in total MRR shows the existing customer base is becoming more valuable.

What are total MRR growth and net revenue retention (NRR), and what do they indicate about the customers present at the start of the quarter? Round both percentages to one decimal place.

1. Total MRR growth: −10.0%; NRR: 90.0%; the starting cohort contracts.
2. Total MRR growth: 33.3%; NRR: 75.0%; the starting cohort contracts.
3. Total MRR growth: 33.3%; NRR: 90.0%; the starting cohort contracts.
4. Total MRR growth: 33.3%; NRR: 133.3%; the starting cohort expands.
5. Total MRR growth: 43.3%; NRR: 90.0%; the starting cohort contracts.

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Revenue-basis LTV

Easy (2/8)

W4-S073 · Source slide 73

A SaaS product earns $200 ARPU per month at 2% monthly churn. What is the revenue-basis LTV?

1. $400
2. $2,400
3. $10,000
4. $100
5. $4,000

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Stress-testing collection delays

Medium (4/8)

W4-S079 · Source slide 79

Before new financing, the forecast cash low point is $260,000 at June 30. The required cash floor is $100,000. A customer payment of $200,000 expected that day could slip to July 31. All other cash flows remain unchanged; without this delay, no other date is lower.

What is the June 30 effect, and the minimum additional cash needed to preserve the floor?

1. Cash is $60,000; the company needs $100,000 of additional cash.
2. Cash is $160,000; the company needs $0 of additional cash.
3. Cash is $60,000; the company needs $160,000 of additional cash.
4. Cash is $260,000; the company needs $0 of additional cash.
5. Cash is $60,000; the company needs $40,000 of additional cash.

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Sensitivity and scenarios

Easy (0/8)

W4-S081 · Source slide 81

How does the one-variable sensitivity method used here differ from business scenario analysis?

1. One-variable sensitivity isolates an input; a scenario tests a coherent set of assumptions
2. Sensitivity is optional while scenario is legally required
3. Sensitivity uses actuals; scenario uses only forecasts
4. Sensitivity is for revenue; scenario is for expenses
5. Sensitivity applies to startups; scenario to public firms

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Timing variance

Easy (1/8)

W4-S084 · Source slide 84

A customer payment expected in March arrived in April. How should variance analysis classify this?

1. A permanent variance requiring immediate strategic change
2. A timing variance, right in direction but off in period
3. An error that should be ignored as ordinary noise
4. A signal that the customer has churned permanently
5. A reason to abandon the current forecast entirely

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Annualized run rate

Easy (1/8)

W4-S095 · Source slide 95

A SaaS company generated $1.5 million of revenue in its most recent month after launching a major new product. Management refers to a $18 million annual revenue run rate. Which statement best describes this figure?

1. It represents the company’s actual revenue earned over the last twelve months.
2. It assumes the latest monthly revenue continues for the next twelve months.
3. It is more reliable than TTM revenue because it uses the most recent operating data.
4. It adjusts recent revenue for seasonality before estimating annual performance.
5. It represents the revenue management expects to recognize under signed contracts.

Related Week 4 deck

TTM, run rate, and NTM

Medium (4/8)

W4-S098 · Source slide 98

A startup reports TTM revenue of $3 million, a current annualized run-rate of $6 million based on its strongest recent month, and management NTM revenue of $9 million. What should an investor conclude from the spread before relying on the $9 million forecast?

1. Use NTM as the primary basis because it incorporates management’s latest information, provided the assumptions are internally consistent.
2. Use TTM as the primary basis because it is historical, treating run-rate and NTM only as secondary sensitivity cases.
3. Average the three measures to reduce dependence on any single period and smooth the effect of recent volatility.
4. Use run-rate as the primary basis because it reflects current momentum, then reconcile management’s NTM forecast to that annualized level.
5. Treat the gap as an unproven inflection and test whether the recent spike and forward assumptions are repeatable.

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Productive sales capacity

Medium (3/8)

W4-S101 · Source slide 101

Four fully productive sales representatives each close three contracts per quarter at $20,000 per contract. Two additional representatives start on January 1 but require a 90-day ramp before they can close business. What bookings should the model attribute to the team during the first quarter?

1. $120,000.
2. $240,000.
3. $280,000.
4. $320,000.
5. $360,000.

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The cash buffer

Medium (3/8)

W4-S104 · Source slide 104

A startup projects $1.25 million of cumulative net burn before its next major milestone. It starts with $550,000 of cash and wants at least $300,000 remaining at the milestone. Management proposes raising $700,000 because current cash plus the raise equals projected burn. Which assessment is correct?

1. The $700,000 raise is sufficient because current cash plus new capital covers projected burn, and the cash buffer can be rebuilt after the milestone.
2. The company should raise $850,000 because the $300,000 buffer should be added to current cash before comparing available funds with projected burn.
3. The company should raise $950,000 because only part of current cash should be considered available when planning for operating uncertainty.
4. The company should raise $1.0 million because burn plus the desired ending buffer, less current cash, leaves a $1.0 million funding requirement.
5. The company should raise $1.55 million because projected burn and the desired ending buffer should both be financed entirely with new capital.

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Growth and cohort retention

Medium (4/8)

W4-S107 · Source slide 107

A subscription startup reports 40% year-over-year revenue growth, but each new customer cohort loses roughly half of its recurring revenue within 12 months. Management argues that aggregate growth proves durable product-market fit. What should an analyst examine next?

1. The total market size, because a sufficiently large TAM can offset weak retention for an extended period.
2. The latest month’s revenue, because run-rate growth is more important than historical cohort behavior.
3. The number of website visitors, because stronger top-of-funnel activity is the clearest test of customer value.
4. The company’s gross margin, because positive gross margin is sufficient to demonstrate that retention is economically sustainable.
5. Cohort retention and the acquisition cost required to replace lost recurring revenue, because new sales may be masking customer decay.

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TTM EBITDA

Medium (3/8)

W4-S111 · Source slide 111

A company’s fiscal year ended December 31, 2025. Through June 30, 2026, it reports year-to-date EBITDA of $7.0 million. EBITDA for the first six months of 2025 was $5.5 million, and full-year 2025 EBITDA was $12.0 million. What is TTM EBITDA as of June 30, 2026?

1. $7.0 million
2. $12.0 million
3. $13.5 million
4. $14.0 million
5. $19.0 million

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Customers lost to churn

Easy (2/8)

W4-S114 · Source slide 114

A subscription business starts the year with 1,000 customers and has 2% monthly churn. Assuming no new customers are added, approximately how many of the original customers will be lost after 12 months?

1. About 20
2. About 215
3. About 60
4. About 500
5. About 240

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Financing need

Easy (2/8)

W4-S116 · Source slide 116

Cumulative net burn to the milestone is $1.8M, minimum cash is $0.45M, and cash on hand is $0.8M. What is the financing need?

1. $1.45 million
2. $2.60 million
3. $1.00 million
4. $1.15 million
5. $0.55 million

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Gross raise required at the cash trough

Hard (7/8)

P010 · New quantitative practice

All amounts are in millions. A startup has unrestricted cash of 0.42 today. Its four quarterly net cash flows before financing are -0.28, -0.38, +0.14, -0.32, respectively. The company must maintain at least 0.20 at every quarter-end and today. A financing closes today with an issuance fee of 4% of gross proceeds deducted immediately. No other cash flows occur. What gross raise is required, expressed in millions and rounded to two decimal places?

1. $0.65 million
2. $0.79 million
3. $0.06 million
4. $0.62 million
5. $0.60 million

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Sales ramp and recognized subscription revenue

Hard (6/8)

P011 · New quantitative practice

A company hires 3 sales representatives on January 1. They spend January through March training and close no contracts during those months. Starting April 1, each representative signs 5 new customers on the first day of every month through December. Each customer pays $1,200 per month and service begins immediately. Recognize revenue monthly; assume no churn, discounts, bad debts, or prior customers. How much revenue is recognized in the calendar year?

1. $1,404,000
2. $810,000
3. $648,000
4. $162,000
5. $1,944,000

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Growth required to reach the revenue target

Medium (3/8)

P012 · New quantitative practice

A startup’s current annual revenue is $1.8 million. The operating plan targets $5.4 million in annual revenue exactly 4 years from now. Assume the same percentage growth rate each year and no acquisitions. Management also forecasts a 65% gross margin at the target scale. What annual compound revenue growth rate is required, expressed as a percentage and rounded to one decimal place?

1. 50.0%
2. 31.6%
3. 44.2%
4. 18.2%
5. 200.0%

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Gross raise required at the cash trough

Hard (7/8)

P022 · New quantitative practice

All amounts are in millions. A startup has unrestricted cash of 0.50 today. Its four quarterly net cash flows before financing are -0.35, -0.42, +0.18, -0.30, respectively. The company must maintain at least 0.25 at every quarter-end and today. A financing closes today with an issuance fee of 5% of gross proceeds deducted immediately. No other cash flows occur. What gross raise is required, expressed in millions and rounded to two decimal places?

1. $0.86 million
2. $0.67 million
3. $0.64 million
4. $0.11 million
5. $0.61 million

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Sales ramp and recognized subscription revenue

Hard (6/8)

P023 · New quantitative practice

A company hires 4 sales representatives on January 1. They spend January through March training and close no contracts during those months. Starting April 1, each representative signs 4 new customers on the first day of every month through December. Each customer pays $1,500 per month and service begins immediately. Recognize revenue monthly; assume no churn, discounts, bad debts, or prior customers. How much revenue is recognized in the calendar year?

1. $864,000
2. $216,000
3. $1,080,000
4. $1,872,000
5. $2,592,000

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Growth required to reach the revenue target

Medium (3/8)

P024 · New quantitative practice

A startup’s current annual revenue is $2.5 million. The operating plan targets $7.5 million in annual revenue exactly 5 years from now. Assume the same percentage growth rate each year and no acquisitions. Management also forecasts a 65% gross margin at the target scale. What annual compound revenue growth rate is required, expressed as a percentage and rounded to one decimal place?

1. 200.0%
2. 14.3%
3. 31.6%
4. 24.6%
5. 40.0%

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Method selection

Hard (6/8)

W5-S005 · Source slide 5

A startup has a working product, a few paying customers, negative free cash flow, and little resalable equipment. Its public peers are much larger and more profitable. Which valuation approach is most defensible?

1. Capitalize next year’s forecast profit as a stable perpetuity because the product is already working.
2. Build cash-flow scenarios from operating drivers, use suitable discount rates, and challenge the range with adjusted market evidence.
3. Apply the public peers’ median revenue multiple unchanged because all companies sell similar products.
4. Use the equipment’s resale value as the going-concern value because the startup has negative cash flow.

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Equity value

Easy (0/8)

W5-S008 · Source slide 8

Which calculation estimates equity value when enterprise value, excess cash, and debt are known and no other claims exist?

1. Enterprise value plus debt and excess cash.
2. Enterprise value divided by debt.
3. Enterprise value plus excess cash minus debt.
4. Enterprise value minus excess cash plus debt.

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Matching cash flow and value

Medium (4/8)

W5-S011 · Source slide 11

An analyst forecasts FCFF before interest and debt repayments. WACC is 10% and the cost of equity is 14%. The company has $6M of excess cash, $18M of debt, and no other claims. Which procedure correctly estimates equity value?

1. Discount FCFF at 14%, then add $6M and subtract $18M.
2. Discount FCFF at 10% and report the result directly as equity value.
3. Subtract interest from FCFF, discount the result at 10%, then subtract $18M of debt.
4. Discount FCFF at 10%, then add $6M and subtract $18M.

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FCFF

Medium (4/8)

W5-S014 · Source slide 14

Assumptions: Net working capital means operating NWC, excluding excess cash and debt. Apply the 25% tax rate to EBIT.

EBIT is $5M, tax rate 25%, D&A $0.8M, CapEx $1.2M, and net working capital rose $0.3M. What is FCFF?

1. $5.00M
2. $3.75M
3. $2.55M
4. $4.30M
5. $3.05M

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Present value

Easy (2/8)

W5-S017 · Source slide 17

A year-end FCFF of $1.1 million is discounted one year at 10%. What is its present value?

1. $1.1 million.
2. $0.9 million.
3. $1.21 million.
4. $1 million.

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Discounted prepayments

Hard (7/8)

W5-S020 · Source slide 20

A software company offers a four-year service contract under two payment options:

Annual billing: The customer pays $180,000 at the end of each year for four years.

Prepayment: The customer pays today and receives a 15% discount from the total undiscounted contract price.

Accepting prepayment creates a one-time $12,000 processing cost today. That cost does not apply to annual billing. Service-delivery costs are $40,000 at the end of each year under either option.

The appropriate opportunity cost of capital for comparing these cash flows is 18% annually. Service obligations are identical, all payments occur as scheduled, and there are no taxes or other incremental cash flows.

What is the incremental NPV today of accepting prepayment rather than annual billing, rounded to the nearest $100?

1. −$120,000
2. +$28,600
3. +$115,800
4. +$127,800
5. +$8,200

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CAPM

Easy (2/8)

W5-S023 · Source slide 23

The risk-free rate is 4%, beta is 1.2, and the equity risk premium is 5%. What is the CAPM cost of equity?

1. 5.0%
2. 10.0%
3. 9.0%
4. 11.2%
5. 6.0%

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WACC calculation

Medium (4/8)

W5-S025 · Source slide 25

A company’s target financing mix is 70% equity and 30% debt, measured at market value. Its cost of equity is 14%, current pre-tax borrowing cost is 8%, and tax rate is 25%. The interest deduction is fully usable. What is WACC?

1. 12.20%
2. 9.15%
3. 11.60%
4. 9.80%

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Terminal-value calculation

Medium (4/8)

W5-S032 · Source slide 32

Assumptions: FCF means FCFF. Stable growth starts after Year n. All rates are annual.

Final-year FCF is $10M, WACC is 10%, and perpetuity growth is 3%. What is the terminal value at Year n?

1. $100.0M
2. $333.3M
3. $147.1M
4. $103.0M
5. $127.5M

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DCF and exit multiples

Hard (7/8)

W5-S034 · Source slide 34

An analyst prepares a DCF for a growing company. All FCFF occurs at year-end and already reflects operating taxes and required reinvestment.

The analyst applies a 7.5× multiple to Year 3 EBITDA to estimate terminal enterprise value at the end of Year 3. That terminal value represents operating value from Year 4 onward. WACC is 12% annually.

At today's valuation date, excess cash is $1.6 million and debt is $5.2 million. There are no other claims or nonoperating assets.

What is equity value today, rounded to $0.01 million?

1. Equity value today: $25.42 million.
2. Equity value today: $29.02 million.
3. Equity value today: $23.85 million.
4. Equity value today: $35.80 million.
5. Equity value today: $11.54 million.

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DCF and equity value

Hard (7/8)

W5-S036 · Source slide 36

An analyst values a startup immediately before any new financing. Forecast FCFF is negative $1.2 million in Year 1, positive $0.6 million in Year 2, and positive $2.4 million in Year 3. All forecast cash flows occur at year-end.

Year 3 FCFF excludes one-time items and is the starting amount for the long-term forecast. From Year 4 onward, FCFF grows 3% per year forever. All FCFF amounts are after operating taxes and the reinvestment needed to support the stated growth. A 14% annual WACC is appropriate throughout the forecast.

The company has $2.1 million of cash, of which $0.8 million is required for operations and already reflected in operating value. Debt is $3.8 million. There are no other claims or nonoperating assets.

What are enterprise value and equity value today, rounded to the nearest $0.01 million?

1. Enterprise value: $17.25 million; equity value: $14.75 million.
2. Enterprise value: $23.50 million; equity value: $21.00 million.
3. Enterprise value: $15.76 million; equity value: $13.26 million.
4. Enterprise value: $16.20 million; equity value: $14.50 million.
5. Enterprise value: $16.20 million; equity value: $13.70 million.

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Growth, reinvestment, and terminal value

Hard (6/8)

W5-S041 · Source slide 41

A DCF's explicit forecast ends at Year 4. After-tax operating profit in Year 5, the first stable year, is $6m. Thereafter it grows 3% annually. Sustainable ROIC is 15%, WACC is 9%, and the stable reinvestment relationship applies. All cash flows are at year-end.

What are Year 5 FCFF and terminal value at the end of Year 4?

1. Year 5 FCFF: $6.00m; terminal value: $100.00m.
2. Year 5 FCFF: $4.80m; terminal value: $82.40m.
3. Year 5 FCFF: $4.80m; terminal value: $80.00m.
4. Year 5 FCFF: $5.10m; terminal value: $85.00m.
5. Year 5 FCFF: $4.80m; terminal value: $56.67m.

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Terminal-value risk

Medium (4/8)

W5-S043 · Source slide 43

A model’s terminal value is most of its enterprise value. Which follow-up is appropriate?

1. Report the result as certain.
2. Stress-test perpetual growth or exit-multiple assumptions and compare valuation methods.
3. Ignore terminal assumptions because they concern later years.
4. Use the highest available multiple without adjustment.

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Terminal-value sensitivity

Hard (7/8)

W5-S045 · Source slide 45

An analyst has already discounted a company's Year 1–3 FCFF to today at a 12% annual WACC. The combined present value is $4.8 million; this amount covers only those three years.

FCFF at the end of Year 3 is $2.4 million. It excludes one-time items and is after operating taxes and required reinvestment. Use this amount as the starting point for growth from Year 4 onward.

The analyst compares two perpetual-growth assumptions, both beginning in Year 4:

All future FCFF occurs at year-end. Terminal value is measured at the end of Year 3 and covers Year 4 onward. Keep the Year 1–3 forecast unchanged. For this exercise, assume each scenario's future FCFF already reflects enough reinvestment to sustain its stated growth rate forever.

How much does enterprise value today increase in the sensitivity case, and what percentage of base-case enterprise value comes from the present value of terminal value? Report the increase in millions of dollars and the terminal-value share as a percentage, each to two decimal places.

1. EV increase: $6.72 million; base-case terminal-value share: 83.61%.
2. EV increase: $4.78 million; base-case terminal-value share: 78.40%.
3. EV increase: $4.27 million; base-case terminal-value share: 78.06%.
4. EV increase: $5.36 million; base-case terminal-value share: 80.26%.
5. EV increase: $0.35 million; base-case terminal-value share: 78.40%.

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Interpreting IRR

Easy (1/8)

W5-S049 · Source slide 49

Why can a high IRR be hard to interpret as a realized compound return when interim distributions are material?

1. It applies a discount rate that is set far too low
2. It ignores the initial cash outflow entirely
3. It always produces a negative return
4. It double-counts the terminal cash flow at exit
5. Interim distributions may not be reinvestable at the IRR

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Return percentage versus value created

Hard (6/8)

W5-S052 · Source slide 52

Two projects are mutually exclusive, have comparable risk, and require only an initial investment followed by one year-end receipt. Capital is available for either. Project A costs $100 and returns $140. Project B costs $1,000 and returns $1,300. The appropriate required return is 10%. Which choice maximizes value?

1. Choose A because its 40% IRR exceeds B’s 30% IRR.
2. Choose A because its smaller initial outlay proves it has lower risk.
3. Choose both because each has positive NPV.
4. Choose B because its NPV is about $181.82, versus $27.27 for A.

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Failure risk counted once

Hard (6/8)

W5-S055 · Source slide 55

In a one-year illustration, a venture pays $100M with 60% probability and $0 otherwise. Assume 20% is the appropriate discount rate for the probability-weighted payoff. Discounting the success-only $100M at 100% would produce the same value. An analyst instead discounts the expected $60M at 100%. Which assessment is correct?

1. $30M is correct because all VC investments require a 100% discount rate.
2. Value is $50M under the stated expected-payoff method; $30M counts the same failure adjustment twice.
3. Value is $83.33M because the 60% success probability should not affect the forecast.
4. Value is $60M because probability weighting removes the need to discount.

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P/E versus PEG

Hard (6/8)

W5-S061 · Source slide 61

An analyst compares two profitable growth companies using the following information:

The EPS figures already exclude one-time gains and losses and use consistent accounting policies. No further earnings adjustments are needed. Use trailing EPS for P/E and expected EPS growth over the next 12 months for PEG.

Which answer gives the correct P/E and PEG for each company, rounded to two decimal places, and identifies the company with the lower PEG?

1. Atlas: P/E 24.00×, PEG 0.96; Beacon: P/E 19.13×, PEG 1.28. Lower PEG: Atlas.
2. Atlas: P/E 30.00×, PEG 1.20; Beacon: P/E 22.00×, PEG 1.47. Lower PEG: Atlas.
3. Atlas: P/E 30.00×, PEG 0.75; Beacon: P/E 22.00×, PEG 1.83. Lower PEG: Atlas.
4. Atlas: P/E 30.00×, PEG 1.50; Beacon: P/E 22.00×, PEG 1.69. Lower PEG: Atlas.
5. Atlas: P/E 30.00×, PEG 0.40; Beacon: P/E 22.00×, PEG 0.37. Lower PEG: Beacon.

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Comparable companies

Medium (4/8)

W5-S063 · Source slide 63

Public comparables have very different growth and retention from the subject startup. What should the analyst do?

1. Treat equal revenue as proof of equal value.
2. Discard every market comparison without analysis.
3. Explain comparability limits and adjust the selected range using relevant evidence.
4. Apply the highest multiple unchanged.

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Comparable-company valuation

Hard (7/8)

W5-S066 · Source slide 66

An analyst selects three public peers with similar forward growth, margins, and revenue definitions. Use the median of their enterprise-value-to-next-twelve-months-revenue multiples for this exercise.

The startup has $10 million of next-twelve-months revenue, $8 million of revenue for the previous twelve months, $8 million of debt, and $4 million of cash. Of that cash, $1 million is required for operations and already reflected in enterprise value. No other claims or adjustments apply.

What enterprise value and equity value result, rounded to the nearest $0.01 million?

1. Enterprise value: $56.00 million; equity value: $51.00 million.
2. Enterprise value: $61.67 million; equity value: $56.67 million.
3. Enterprise value: $70.00 million; equity value: $66.00 million.
4. Enterprise value: $70.00 million; equity value: $65.00 million.
5. Enterprise value: $70.00 million; equity value: $75.00 million.

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Control transactions

Easy (1/8)

W5-S069 · Source slide 69

Assumptions: Relevant, reasonably comparable transactions involving acquisitions of control are available.

You are valuing a company for an acquisition of control. Which comparable set is most appropriate, and why?

1. Trading comps, because they exclude any premium
2. Neither, since only DCF applies to acquisitions
3. Precedent transactions, because they reflect prices actually paid for control
4. Trading comps, because control carries no value
5. The cost approach, since assets set the price

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Ownership sold

Easy (2/8)

W5-S072 · Source slide 72

A venture raises $2 million at $6 million pre-money, with no other capitalization changes. What ownership is sold?

1. 20%.
2. 75%.
3. 25%.
4. 33.33%.

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VC hurdle versus WACC

Easy (1/8)

W5-S076 · Source slide 76

Why does the VC method discount at a target return rather than WACC?

1. The target return reflects stage risk, illiquidity, dilution, and skewed portfolio outcomes
2. WACC is always higher than any VC target return
3. The VC method ignores the time value of money
4. Pre-revenue firms have a precise, observable beta
5. WACC cannot be computed for public companies

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VC pricing with an exit-value bridge

Medium (4/8)

W5-S078 · Source slide 78

A VC invests $5M and requires a 5× total investment multiple over five years. Projected exit enterprise value is $120M, exit excess cash is $10M, and exit debt is $30M. Assume no other claims, future dilution, interim distributions, or preferences. What ownership today and implied post-money equity value meet the target?

1. 20.8% ownership and $24M post-money.
2. 25% ownership and $25M post-money.
3. 25% ownership and $20M post-money.
4. 5% ownership and $100M post-money.

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Ownership before dilution

Easy (2/8)

W5-S081 · Source slide 81

Assumptions: 30% dilution means a 30% proportional reduction in the existing stake. The investor makes no follow-on investment.

A VC needs 10% ownership at exit and expects 30% dilution before then. What ownership must they take today?

1. 10.0%
2. 7.0%
3. 13.0%
4. 40.0%
5. 14.3%

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VC pricing and dilution

Hard (7/8)

W5-S083 · Source slide 83

A VC considers investing $4 million today. The investor requires a 40% annual compound return over five years and receives no cash distributions before exit.

At the end of Year 5, the assumed sale enterprise value is $150 million. Debt is expected to be $15 million and excess cash $5 million. No other claims or sale costs apply. The investment converts into common equity at exit with no preferential payout.

Two later financings will reduce the investor's ownership percentage by 20% and then by another 10%, each relative to the percentage immediately before that financing. The investor will not participate in either round. Use the stated exit scenario and return requirement consistently, without an additional probability adjustment.

What initial ownership and corresponding pre-money valuation meet the investor's return requirement?

1. Initial ownership: 21.34%; pre-money valuation: $14.74 million.
2. Initial ownership: 19.92%; pre-money valuation: $16.08 million.
3. Initial ownership: 21.95%; pre-money valuation: $14.22 million.
4. Initial ownership: 15.37%; pre-money valuation: $22.03 million.
5. Initial ownership: 5.56%; pre-money valuation: $68.00 million.

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Founder proceeds

Medium (4/8)

W5-S087 · Source slide 87

Assumptions: Exit means net equity proceeds. The preference is uncapped; founders own the other 80%. No other claims, dividends, fees, or dilution apply.

On a $30M exit, a $5M investor at $20M pre (20%) holds a 2x participating preference. What do founders receive?

1. $24M, the same as a 1x non-participating
2. $16M, after the investor takes $14M
3. $25M, since the preference is capped
4. $0, because preferred takes everything
5. $20M, split evenly with the investor

Related Week 5 deck

Reconciling valuation ranges

Medium (4/8)

W5-S091 · Source slide 91

For the same company, date, currency, and enterprise-value basis, a DCF indicates $30M–$45M while trading comparables indicate $60M–$80M. What is the strongest next step?

1. Average the two midpoints to $53.75M and call it the most defensible value.
2. Investigate forecast and peer differences, assess evidence quality, and explain the range supported by that analysis.
3. Use $60M–$80M automatically because market prices always override cash-flow analysis.
4. Raise perpetual growth until the DCF overlaps the comparable range.

Related Week 5 deck

Reconciling DCF and comps

Hard (6/8)

W5-S094 · Source slide 94

A startup's DCF indicates enterprise value of $28–34 million. Applying public-peer revenue multiples produces $40–52 million. Both analyses use the same valuation date, currency, and forward-revenue period.

The startup's net revenue retention is 95% and gross margin is 60%, compared with 125% and 80% for the peers. The DCF also assumes rapid revenue growth with almost no increase in annual capital spending or investment in operating working capital. Neither the retention gap nor the margin gap is expected to disappear during the forecast.

The founder proposes using the midpoint of the combined enterprise-value range as the starting point for financing negotiations. Before recommending a valuation range, which approach best addresses the evidence?

1. Weight the two methods equally after matching dates, then justify a midpoint because combining independent estimates reduces each method’s individual errors.
2. Use the DCF range as the pricing anchor, then treat peer differences as confirmation that the lower estimate is more reliable.
3. Use the peer range as the pricing anchor, then treat reinvestment uncertainty as a reason to discount the DCF evidence substantially.
4. Increase forecast growth until the DCF reaches comparable values, then justify the aligned range using the agreement between both valuation methods.
5. Test forecast reinvestment and retention, assess material peer differences, and justify a valuation range using the available evidence supporting each method.

Related Week 5 deck

Valuation-method judgment

Hard (6/8)

W5-S096 · Source slide 96

An investment committee reviews two companies:

Each comparison uses the same valuation date, currency, and definition of enterprise or equity value. The committee wants a defensible price recommendation, not simply the highest model output.

Which recommendation best accounts for the strengths and limitations of the evidence?

1. For Launchly, treat matching DCF and comps as independent confirmation of enterprise value; for Harbor, evaluate operating risk and reinvestment before concluding that its lower PEG indicates undervaluation.
2. For Launchly, compare revenue multiples with scenario cash flows while examining shared assumptions; for Harbor, prefer its lower PEG because growth adjustment resolves the differences in operating risk.
3. For Launchly, use revenue comps and scenario DCF while recognizing shared terminal assumptions; for Harbor, investigate risk and reinvestment before interpreting its lower PEG as evidence of undervaluation.
4. For Launchly, prioritize DCF because discounting terminal proceeds removes dependence on current peer pricing; for Harbor, compare PEG after aligning the earnings base and the forecast growth horizon.
5. For Launchly, equally weight DCF and revenue comps because neither method dominates the available evidence; for Harbor, transfer the peer PEG after matching industry and forecast earnings growth.

Related Week 5 deck

Full DCF and equity bridge

Hard (7/8)

W5-S100 · Source slide 100

Year-end FCFF is $2M in Year 1 and $3M in Year 2. An 8.0× exit EV/EBITDA multiple applies to Year 2 EBITDA of $5M. It estimates terminal EV at the end of Year 2, covering cash flows from Year 3 onward. WACC is 10%. Excess cash today is $4M and debt is $10M, with no other claims. What is equity value today, rounded to two decimals?

1. $31.36M
2. $37.36M
3. $38.30M
4. $28.88M

Related Week 5 deck

Comparable multiple and equity bridge

Medium (4/8)

W5-S102 · Source slide 102

After analyzing comparable companies, you select 4.0× next-twelve-month revenue. The startup’s next-twelve-month revenue is $12M, trailing revenue is $8M, excess cash is $3M, and debt is $7M. The multiple is an enterprise-value multiple and no other claims exist. What is the indicated equity value?

1. $44M
2. $48M
3. $28M
4. $52M

Related Week 5 deck

Expected value

Easy (2/8)

W5-S104 · Source slide 104

Assumptions: All values are today’s equity values for the same claim. Scenarios are mutually exclusive and exhaustive.

Scenarios: failure 20% at $0, downside 25% at $15M, base 35% at $50M, upside 20% at $120M. What is the expected value?

1. $46.25M
2. $50.00M
3. $36.25M
4. $45.25M
5. $61.75M

Related Week 5 deck

The three approaches

Easy (1/8)

W5-S107 · Source slide 107

For an early-stage venture, how do the three master approaches fit together?

1. The cost approach is primary because assets are certain
2. Only the market approach matters, since price is observable
3. Use the method that fits the facts, then triangulate across methods
4. The three always produce the same single number
5. The income approach is irrelevant for growth companies

Related Week 5 deck

Terminal value as a share of EV

Medium (3/8)

W5-S109 · Source slide 109

A DCF has $10M of present value from explicit forecast FCFF and $30M of present value from terminal value. Which interpretation is correct?

1. Terminal value represents 75% of EV, so the long-run assumptions deserve careful sensitivity analysis.
2. Terminal value must fall between 60% and 80% of EV for any valid DCF.
3. Terminal value should be removed because cash flows beyond the explicit forecast cannot contribute value.
4. Equity value must equal $40M regardless of cash, debt, or other claims.

Related Week 5 deck

Historical stage-risk interpretation

Easy (1/8)

W5-S111 · Source slide 111

In Bhagat’s (2014) model, what can happen to the return applied to success-case proceeds as the probability of success increases, holding other assumptions constant?

1. Rise steadily from seed to late stage
2. Stay fixed at the market cost of equity
3. Match CAPM closely at every stage
4. Fall as the company de-risks
5. Turn negative near an IPO

Related Week 5 deck

FCFF with a working-capital bridge

Medium (5/8)

P009 · New quantitative practice

All amounts are in millions. EBIT is 6.80, depreciation and amortization is 1.10, and capital expenditures are 1.90. Accounts receivable increases by 0.70, inventory by 0.35, and operating accounts payable by 0.45. Use a 25% tax rate on EBIT. There are no other operating working-capital changes or tax adjustments. Interest expense is 0.60 and new borrowing is 1.00. What is FCFF, expressed in millions and rounded to two decimal places?

1. $4.70 million
2. $3.25 million
3. $3.70 million
4. $2.60 million
5. $4.90 million

Related Week 5 deck

FCFF with a working-capital bridge

Medium (5/8)

P021 · New quantitative practice

All amounts are in millions. EBIT is 8.40, depreciation and amortization is 1.30, and capital expenditures are 2.40. Accounts receivable increases by 0.90, inventory by 0.40, and operating accounts payable by 0.55. Use a 25% tax rate on EBIT. There are no other operating working-capital changes or tax adjustments. Interest expense is 0.60 and new borrowing is 1.00. What is FCFF, expressed in millions and rounded to two decimal places?

1. $4.00 million
2. $5.95 million
3. $3.15 million
4. $4.45 million
5. $5.45 million

Related Week 5 deck

Incremental NPV of an advance payment

Hard (7/8)

P025 · New quantitative practice

A service company can collect $165,000 at each year-end for 3 years, or collect the entire undiscounted contract price today less a 17% prepayment discount. Prepayment alone creates a $9,600 administration cost today. Service delivery costs $34,000 at each year-end under either option. Use 21% as the appropriate annual opportunity cost of capital. Service obligations are identical, all cash is collected as scheduled, and there are no taxes or other cash flows. What is incremental NPV of prepayment over annual billing, rounded to the nearest dollar?

1. −$93,750
2. $59,051
3. −$59,051
4. −$11,463
5. $68,651

Related Week 5 deck

Project NPV with a terminal asset sale

Hard (6/8)

P026 · New quantitative practice

A project costs $350,000 today. Its year-end operating free cash flows are $120,000, $150,000, and $190,000 in Years 1–3. At the end of Year 3, it also generates $45,000 from an asset sale, stated after all taxes and selling costs. Use a 14% annual discount rate. The operating cash flows exclude the sale proceeds; there are no other flows. What is NPV today, rounded to the nearest dollar?

1. $43,928
2. −$1,072
3. $29,302
4. $379,302
5. $155,000

Related Week 5 deck

Annualized return from one exit

Medium (3/8)

P029 · New quantitative practice

An investor pays $1.6 million today and receives a single $4.4 million distribution exactly 5 years later. There are no interim distributions, fees, taxes, or follow-on investments. The company reports a 40% revenue growth rate over the first year. What is the investor’s annual IRR, expressed as a percentage and rounded to one decimal place?

1. 40.0%
2. 28.8%
3. 22.4%
4. 35.0%
5. 175.0%

Related Week 5 deck

Incremental value of the larger project

Hard (6/8)

P030 · New quantitative practice

Two mutually exclusive projects have the same three-year life and risk. Project A costs $0.75 million today and pays $0.32 million at each of the next three year-ends. Project B costs $1.15 million today and pays $0.49 million at each year-end. Capital is available for either project, and there are no later cash flows. Use a 12% opportunity cost of capital. What is NPV(B) minus NPV(A), expressed in millions and rounded to three decimal places?

1. −$0.008 million
2. $0.110 million
3. $0.408 million
4. $0.027 million
5. $0.008 million

Related Week 5 deck

Incremental NPV of an advance payment

Hard (7/8)

P031 · New quantitative practice

A service company can collect $190,000 at each year-end for 4 years, or collect the entire undiscounted contract price today less a 16% prepayment discount. Prepayment alone creates a $12,500 administration cost today. Service delivery costs $42,000 at each year-end under either option. Use 19% as the appropriate annual opportunity cost of capital. Service obligations are identical, all cash is collected as scheduled, and there are no taxes or other cash flows. What is incremental NPV of prepayment over annual billing, rounded to the nearest dollar?

1. −$134,100
2. $13,748
3. $137,069
4. −$124,569
5. $124,569

Related Week 5 deck

Project NPV with a terminal asset sale

Hard (6/8)

P032 · New quantitative practice

A project costs $420,000 today. Its year-end operating free cash flows are $135,000, $180,000, and $225,000 in Years 1–3. At the end of Year 3, it also generates $55,000 from an asset sale, stated after all taxes and selling costs. Use a 16% annual discount rate. The operating cash flows exclude the sale proceeds; there are no other flows. What is NPV today, rounded to the nearest dollar?

1. $175,000
2. $29,297
3. −$25,703
4. $9,533
5. $429,533

Related Week 5 deck

Annualized return from one exit

Medium (3/8)

P035 · New quantitative practice

An investor pays $2.1 million today and receives a single $6.3 million distribution exactly 6 years later. There are no interim distributions, fees, taxes, or follow-on investments. The company reports a 40% revenue growth rate over the first year. What is the investor’s annual IRR, expressed as a percentage and rounded to one decimal place?

1. 24.6%
2. 33.3%
3. 20.1%
4. 200.0%
5. 40.0%

Related Week 5 deck

Incremental value of the larger project

Hard (6/8)

P036 · New quantitative practice

Two mutually exclusive projects have the same three-year life and risk. Project A costs $0.90 million today and pays $0.39 million at each of the next three year-ends. Project B costs $1.30 million today and pays $0.55 million at each year-end. Capital is available for either project, and there are no later cash flows. Use a 14% opportunity cost of capital. What is NPV(B) minus NPV(A), expressed in millions and rounded to three decimal places?

1. $0.029 million
2. $0.080 million
3. −$0.023 million
4. $0.371 million
5. −$0.029 million

Related Week 5 deck

Terminal value and the equity bridge

Hard (6/8)

P037 · New quantitative practice

A DCF forecasts cash flows through Year 3. The present value today of all Year 1–3 FCFF is $4.6 million. FCFF in Year 4, the first year after the explicit forecast, is expected to be $2.8 million and then grow at 3.0% annually forever. WACC is 13.0%. Excess cash today is $1.1 million and debt today is $3.5 million, with no other claims. What is equity value today, expressed in millions and rounded to two decimal places?

1. $24.01 million
2. $19.37 million
3. $30.20 million
4. $21.61 million
5. $22.19 million

Related Week 5 deck

Full DCF with restricted cash

Hard (7/8)

P038 · New quantitative practice

Year-end FCFF in Years 1–3 is $-1.6, $0.8, and $3.1 million, respectively. Beginning in Year 4, FCFF grows at 3% annually forever from the Year 3 level. Use a constant 15% WACC. Current cash is $2.3 million, of which $0.7 million is restricted and must remain in operations; only the rest is excess. Current debt is $4.1 million. There are no other claims. What is current equity value, expressed in millions and rounded to two decimal places?

1. $20.35 million
2. $17.64 million
3. $16.25 million
4. $25.36 million
5. $16.95 million

Related Week 5 deck

Exit-multiple DCF

Hard (6/8)

P039 · New quantitative practice

The present value today of a company’s Year 1–4 FCFF is $6.4 million. At the end of Year 4, the business is assumed to sell for 8 times Year 4 EBITDA of $5.5 million. This multiple yields enterprise value. Use a 14% WACC. Current excess cash is $1.6 million and current debt is $6.2 million. Explicit FCFF excludes sale proceeds. What is current equity value, expressed in millions and rounded to two decimal places?

1. $27.85 million
2. $31.50 million
3. $32.45 million
4. $45.80 million
5. $21.45 million

Related Week 5 deck

PEG from compound EPS growth

Medium (4/8)

P040 · New quantitative practice

A company trades at $96.00 per share. Current annual EPS is $4.00; forecast annual EPS three years from now is $6.912. Revenue is expected to grow 30% per year, and the peer median P/E is 19×. For this question, use the company’s current EPS in P/E and annual compound growth from current EPS to the Year 3 EPS forecast in PEG. Enter growth as percentage points, such as 20 for 20%. What is PEG, rounded to two decimals?

1. 0.99
2. 0.69
3. 0.95
4. 0.80
5. 1.20

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PEG after forecast share dilution

Hard (7/8)

P041 · New quantitative practice

A firm trades at $84.00 per share. Current net income available to common shareholders is $160 million and current diluted shares are 50 million. Three years from now, forecast common net income is $280 million and diluted shares are 56 million. Use current diluted EPS for P/E and three-year compound diluted-EPS growth for PEG; enter growth in percentage points. What is PEG, rounded to two decimals?

1. 0.47
2. 1.64
3. 163.66
4. 1.05
5. 1.28

Related Week 5 deck

Normalized EBITDA and comparable value

Medium (4/8)

P042 · New quantitative practice

A company reports EBITDA of $4.20 million. This includes a one-time legal expense of $0.60 million and a nonrecurring gain of $0.35 million. Treat both as nonrecurring for this exercise. Apply a 7.5× EV/EBITDA multiple to normalized EBITDA. Excess cash is $1.2 million and debt is $4.0 million, with no other claims. What is indicated equity value, expressed in millions and rounded to two decimal places?

1. $30.58 million
2. $28.70 million
3. $33.38 million
4. $35.82 million
5. $21.57 million

Related Week 5 deck

Consistent revenue basis in comparable valuation

Medium (4/8)

P043 · New quantitative practice

Comparable-company analysis supports 4.5× next-twelve-month revenue for the subject’s risk and growth profile. The subject has trailing-twelve-month revenue of $6.1 million and next-twelve-month revenue of $7.8 million. The multiple yields enterprise value. Excess cash is $2.1 million and debt is $5.8 million. No other claims exist. What is indicated current equity value, expressed in millions and rounded to two decimal places?

1. $38.80 million
2. $43.00 million
3. $35.10 million
4. $23.75 million
5. $31.40 million

Related Week 5 deck

VC pricing after future dilution

Hard (7/8)

P044 · New quantitative practice

A VC invests $5 million today. At the end of Year 5, projected exit enterprise value is $110 million, exit debt is $14 million, and exit excess cash is $4 million. The investor targets a 30% annual return and expects a future financing to reduce its percentage ownership by 25% relative to its post-investment stake today. Assume no interim distributions, preferences, or other dilution. What current pre-money equity value is consistent with these assumptions, expressed in millions and rounded to two decimal places?

1. $21.93 million
2. $20.20 million
3. $17.22 million
4. $15.20 million
5. $25.00 million

Related Week 5 deck

Terminal value and the equity bridge

Hard (6/8)

P045 · New quantitative practice

A DCF forecasts cash flows through Year 3. The present value today of all Year 1–3 FCFF is $5.3 million. FCFF in Year 4, the first year after the explicit forecast, is expected to be $3.2 million and then grow at 3.5% annually forever. WACC is 14.5%. Excess cash today is $1.4 million and debt today is $4.2 million, with no other claims. What is equity value today, expressed in millions and rounded to two decimal places?

1. $21.88 million
2. $22.56 million
3. $24.68 million
4. $31.59 million
5. $19.43 million

Related Week 5 deck

Full DCF with restricted cash

Hard (7/8)

P046 · New quantitative practice

Year-end FCFF in Years 1–3 is $-1.9, $1.1, and $3.6 million, respectively. Beginning in Year 4, FCFF grows at 3% annually forever from the Year 3 level. Use a constant 16% WACC. Current cash is $2.6 million, of which $0.8 million is restricted and must remain in operations; only the rest is excess. Current debt is $4.7 million. There are no other claims. What is current equity value, expressed in millions and rounded to two decimal places?

1. $17.66 million
2. $16.86 million
3. $21.56 million
4. $18.50 million
5. $27.11 million

Related Week 5 deck

Exit-multiple DCF

Hard (6/8)

P047 · New quantitative practice

The present value today of a company’s Year 1–4 FCFF is $7.2 million. At the end of Year 4, the business is assumed to sell for 9 times Year 4 EBITDA of $6.2 million. This multiple yields enterprise value. Use a 16% WACC. Current excess cash is $1.9 million and current debt is $7.1 million. Explicit FCFF excludes sale proceeds. What is current equity value, expressed in millions and rounded to two decimal places?

1. $25.62 million
2. $57.80 million
3. $37.75 million
4. $38.02 million
5. $32.82 million

Related Week 5 deck

PEG from compound EPS growth

Medium (4/8)

P048 · New quantitative practice

A company trades at $132.00 per share. Current annual EPS is $6.00; forecast annual EPS three years from now is $9.585. Revenue is expected to grow 28% per year, and the peer median P/E is 19×. For this question, use the company’s current EPS in P/E and annual compound growth from current EPS to the Year 3 EPS forecast in PEG. Enter growth as percentage points, such as 20 for 20%. What is PEG, rounded to two decimals?

1. 1.10
2. 0.79
3. 0.81
4. 1.12
5. 1.30

Related Week 5 deck

PEG after forecast share dilution

Hard (7/8)

P049 · New quantitative practice

A firm trades at $108.00 per share. Current net income available to common shareholders is $210 million and current diluted shares are 60 million. Three years from now, forecast common net income is $350 million and diluted shares are 70 million. Use current diluted EPS for P/E and three-year compound diluted-EPS growth for PEG; enter growth in percentage points. What is PEG, rounded to two decimals?

1. 0.72
2. 1.66
3. 1.71
4. 2.44
5. 244.42

Related Week 5 deck

Normalized EBITDA and comparable value

Medium (4/8)

P050 · New quantitative practice

A company reports EBITDA of $5.30 million. This includes a one-time legal expense of $0.80 million and a nonrecurring gain of $0.40 million. Treat both as nonrecurring for this exercise. Apply a 8.0× EV/EBITDA multiple to normalized EBITDA. Excess cash is $1.5 million and debt is $5.0 million, with no other claims. What is indicated equity value, expressed in millions and rounded to two decimal places?

1. $38.90 million
2. $42.10 million
3. $29.30 million
4. $48.50 million
5. $45.60 million

Related Week 5 deck

Consistent revenue basis in comparable valuation

Medium (4/8)

P051 · New quantitative practice

Comparable-company analysis supports 5.0× next-twelve-month revenue for the subject’s risk and growth profile. The subject has trailing-twelve-month revenue of $7.4 million and next-twelve-month revenue of $9.6 million. The multiple yields enterprise value. Excess cash is $2.7 million and debt is $6.9 million. No other claims exist. What is indicated current equity value, expressed in millions and rounded to two decimal places?

1. $52.20 million
2. $32.80 million
3. $48.00 million
4. $57.60 million
5. $43.80 million

Related Week 5 deck

VC pricing after future dilution

Hard (7/8)

P052 · New quantitative practice

A VC invests $7 million today. At the end of Year 4, projected exit enterprise value is $140 million, exit debt is $18 million, and exit excess cash is $6 million. The investor targets a 28% annual return and expects a future financing to reduce its percentage ownership by 20% relative to its post-investment stake today. Assume no interim distributions, preferences, or other dilution. What current pre-money equity value is consistent with these assumptions, expressed in millions and rounded to two decimal places?

1. $34.72 million
2. $40.68 million
3. $41.30 million
4. $31.15 million
5. $38.15 million

Related Week 5 deck

Issued and fully diluted ownership

Medium (4/8)

W6-S005 · Source slide 5

A founder owns 3.6M of 6M issued shares. The agreed fully diluted count also includes 0.6M granted options and a separate 1.4M ungranted reserve. Which ownership pair is correct?

1. 60% of issued shares and 60% on the fully diluted basis
2. 45% of issued shares and 45% on the fully diluted basis
3. 60% of issued shares and 45% on the fully diluted basis
4. 45% of issued shares and 60% on the fully diluted basis
5. 60% of issued shares and 54.55% on the fully diluted basis

Related Week 6 deck

Financing price and share count

Medium (3/8)

W6-S008 · Source slide 8

Assumptions: The pricing model has 6M issued shares plus 2M included option rights and reserve shares. Total authorization is 10M. Use the stated fully diluted pricing basis.

A company is worth $12 million in equity value and has 8 million fully diluted shares. What is the per-share price?

1. $0.67
2. $2.00
3. $1.20
4. $1.50
5. $6.00

Related Week 6 deck

Issued and fully diluted ownership

Hard (7/8)

W6-S011 · Source slide 11

Before a financing, a company has the following capitalization:

The charter authorizes 20 million shares. The parties price a $5 million primary investment at a $20 million pre-money valuation using all five rows in the fully diluted denominator. Count each instrument at its stated share amount. Ignore any cash the company could receive from exercising options or warrants; do not reduce their share counts for such proceeds.

No existing instrument is exercised or converted at closing, and no pool change occurs. New investors receive newly issued shares, each representing one common-equivalent share. For issued ownership, use common-equivalent issued shares only.

What are the price per new share and the founders' post-financing fully diluted and issued ownership percentages?

1. Price: $2.50; founder ownership: 50.00% fully diluted and 60.00% issued.
2. Price: $1.00; founder ownership: 24.00% fully diluted and 46.15% issued.
3. Price: $2.00; founder ownership: 57.14% fully diluted and 48.00% issued.
4. Price: $2.00; founder ownership: 48.00% fully diluted and 57.14% issued.
5. Price: $2.00; founder ownership: 60.00% fully diluted and 75.00% issued.

Related Week 6 deck

Ownership and board rights

Medium (4/8)

W6-S014 · Source slide 14

Founders own 70% of the shares. They designate two directors, investors designate two, and one is independent. A budget requires three of five director votes and no separate stockholder consent. The founder nominees vote yes and investor nominees vote no. Which conclusion follows?

1. The independent director's vote determines whether the budget has enough board support.
2. The founders' 70% ownership supplies majority approval despite the split among directors.
3. The two investor votes block approval even if the independent director votes yes.
4. The budget must go to stockholders because founder and investor nominees are tied.
5. The independent director may vote only after each stockholder group approves the budget.

Related Week 6 deck

Two preferred series

Medium (4/8)

W6-S017 · Source slide 17

Assumptions: No debt, fees, dividends, or other claims. Series B closed after Series A.

Series A has a $2M preference claim and Series B a $1M claim. Both stay preferred. The charter ranks them equally and allocates insufficient proceeds in proportion to their preference claims. How should $2.4M available to equity be allocated?

1. Series A receives $2.0M and Series B receives $0.4M.
2. Series A receives $1.4M and Series B receives $1.0M.
3. Series A receives $1.2M and Series B receives $1.2M.
4. Series A receives $1.6M and Series B receives $0.8M.
5. Series A receives $2.0M and Series B receives $1.0M.

Related Week 6 deck

Participation and common proceeds

Easy (0/8)

W6-S020 · Source slide 20

Assumptions: Compare ordinary uncapped participating and nonparticipating preferred with the same investment, ownership, and 1x preference.

How does participating preferred differ from nonparticipating preferred for the common holders?

1. Participating preferred receives only its ownership percentage of the total exit.
2. Participating preferred takes its preference instead of sharing any remaining proceeds.
3. Participating preferred shares the residual after common first recovers invested capital.
4. Participating preferred increases its preference automatically when the next valuation rises.
5. Participating preferred receives its preference and then shares the remaining proceeds.

Related Week 6 deck

Participating exit proceeds

Medium (4/8)

W6-S023 · Source slide 23

Assumptions: The $20M is available to equity after other claims. One preferred series, uncapped participation, common owns the remaining 75%, and no dividends.

A $5M investor holds 25% via 1x participating preferred. At a $20M exit, what do common holders receive?

1. $15.00M
2. $10.00M
3. $11.25M
4. $8.75M
5. $3.75M

Related Week 6 deck

Capped participating preferred

Hard (6/8)

W6-S026 · Source slide 26

An investor paid $4 million for preferred shares representing 25% ownership on an as-converted basis. The shares have a 1× participating liquidation preference, with total proceeds under the preferred payout capped at 2× the original investment.

After the investor receives its initial preference, it participates in the remaining proceeds at 25% until the total payout cap is reached. The investor may instead convert fully to common and receive 25% of the entire equity distribution; the participation cap does not apply after conversion.

Consider two independent exits: one leaves $20 million available to equity and the other leaves $44 million. Both amounts are after debt, transaction costs, and all other claims. There are no other preferred securities.

What payout will the investor elect at each exit?

1. At the $20 million exit: $8.00 million; at the $44 million exit: $8.00 million.
2. At the $20 million exit: $8.00 million; at the $44 million exit: $14.00 million.
3. At the $20 million exit: $5.00 million; at the $44 million exit: $11.00 million.
4. At the $20 million exit: $5.00 million; at the $44 million exit: $14.00 million.
5. At the $20 million exit: $8.00 million; at the $44 million exit: $11.00 million.

Related Week 6 deck

A delayed priced round

Easy (1/8)

W6-S029 · Source slide 29

A company issued a convertible note and an unmodified YC post-money SAFE. The note reaches its contractual maturity before the next priced financing. Which assessment is correct?

1. Both instruments require repayment once the next priced financing is delayed beyond note maturity.
2. Both instruments extend automatically until the company completes its next priced equity financing.
3. Only the SAFE accrues interest while the company waits for another priced financing.
4. Both instruments automatically convert at their caps when the note reaches contractual maturity.
5. The note's maturity terms need review. The SAFE has no maturity deadline.

Related Week 6 deck

Cap versus discount

Medium (3/8)

W6-S032 · Source slide 32

A note uses the lower of its cap price and discounted round price. The new-round price is $2.00, the discount is 25%, and the cap price is $1.80. Which conversion price follows the agreement?

1. $1.80
2. $1.65
3. $1.35
4. $2.00
5. $1.50

Related Week 6 deck

SAFE financing sequence

Medium (4/8)

W6-S035 · Source slide 35

A company issues a second YC-style post-money valuation-cap SAFE and later raises a priced equity round. The cap price governs both SAFEs, and the option pool does not change. Which sequence correctly describes dilution?

1. The later SAFE dilutes earlier SAFEs. The priced round dilutes only founders.
2. The later SAFE dilutes current stockholders. The priced round dilutes both SAFE holders.
3. Both steps dilute only current stockholders because the SAFE ownership percentages remain fixed.
4. Both steps dilute founders and existing SAFE holders proportionately from their previous stakes.
5. The later SAFE leaves all modeled ownership unchanged until the priced round occurs.

Related Week 6 deck

Post-money SAFEs

Hard (7/8)

W6-S038 · Source slide 38

Founders initially own all of a company's shares. It then issues two post-money SAFEs:

SAFE A: $600,000 invested at a $6 million post-money valuation cap.

SAFE B: $400,000 invested at an $8 million post-money valuation cap.

Both SAFEs convert at their valuation caps. The share count used to apply each cap includes shares from both SAFE conversions, but excludes the new priced-round shares and the later option reserve. Neither SAFE has a discount or interest. No other securities or option reserve exist before these transactions.

The priced-round investor then receives newly issued shares representing 20% of the company immediately after that investment. Afterward, a new option reserve is created equal to 10% of the final fully diluted capitalization, diluting every then-existing holder proportionately.

What are the founders', SAFE A's, and SAFE B's final fully diluted ownership percentages?

1. Founders: 61.20%; SAFE A: 7.20%; SAFE B: 3.60%.
2. Founders: 68.00%; SAFE A: 8.00%; SAFE B: 4.00%.
3. Founders: 59.50%; SAFE A: 7.00%; SAFE B: 3.50%.
4. Founders: 62.61%; SAFE A: 6.26%; SAFE B: 3.13%.
5. Founders: 61.20%; SAFE A: 10.00%; SAFE B: 5.00%.

Related Week 6 deck

Convertible-note conversion

Hard (7/8)

W6-S043 · Source slide 43

A company has 4 million founder shares and 1 million seed-investor shares, all on a 1:1 common-equivalent basis. It has no options, warrants, or other convertibles except the note described below.

A financing raises $3 million at a fixed price of $3.00 per share. The price was negotiated using a $15 million valuation of the existing 5 million shares and excludes the converting note; it will not be recalculated after conversion.

At closing, the note has been outstanding for 18 months. It has $900,000 principal and accrues 8% annual simple interest; no interest has been paid in cash. Principal and accrued interest both convert at the lower of:

A 20% discount to the financing price; or

A $10 million valuation cap divided by the existing 5 million shares.

The discount is not applied again to the cap price. All newly issued and converting shares count one-for-one as common-equivalent shares.

How many shares does the note receive, and what is the founders' ownership percentage immediately after both the note conversion and the new investment?

1. Note conversion: 450,000 shares; founder ownership: 62.02%.
2. Note conversion: 504,000 shares; founder ownership: 61.50%.
3. Note conversion: 420,000 shares; founder ownership: 62.31%.
4. Note conversion: 630,000 shares; founder ownership: 60.33%.
5. Note conversion: 486,000 shares; founder ownership: 61.67%.

Related Week 6 deck

Preference amount and denominator

Medium (3/8)

W6-S046 · Source slide 46

Assumptions: The note contains $500K original principal and $40K accrued interest. Measure the effective preference multiple against original cash invested.

A $500K note converts to 360,000 shares priced at $1.50, but those shares carry a $2.00 liquidation preference. What is the effective preference multiple?

1. 1.08x
2. 0.75x
3. 2.00x
4. 1.33x
5. 1.44x

Related Week 6 deck

Conversion terms and preference

Medium (4/8)

W6-S049 · Source slide 49

Founders want to preserve a note holder's agreed conversion share count but limit its aggregate liquidation preference to the converting balance. Which negotiated term accomplishes both?

1. Set preference per share equal to the converting balance divided by converted shares.
2. Reduce converted shares until their full-price preference equals the converting balance.
3. Keep the full-price preference and cap the investor's later common conversion proceeds.
4. Use the original cash principal as the denominator when reporting the preference.
5. Keep the full-price preference but remove participation in the remaining exit proceeds.

Related Week 6 deck

Option-pool pricing

Medium (4/8)

W6-S053 · Source slide 53

Assumptions: Hold pre-money valuation and new cash fixed. Include the pool increase in the pricing capitalization. No convertibles or special protection rights alter the allocation.

An investor requires the new option pool to be created pre-money. What is the effect on the founders?

1. Founders and the new investor share the increase according to their post-round ownership.
2. Founder ownership changes only when employees later exercise options granted from the reserve.
3. Existing pre-money holders absorb the increase before the new investor's shares are priced.
4. The reserve replaces planned investor shares and preserves the founders' original ownership percentage.
5. The added reserve raises the investor's share price and reduces the shares it purchases.

Related Week 6 deck

The option-pool top-up

Hard (7/8)

W6-S057 · Source slide 57

A startup has the following pre-financing fully diluted capitalization:

The proposed financing has three terms:

New investment: $6 million at an $18 million pre-money valuation.

The ungranted reserve alone must equal 12.5% of fully diluted shares immediately after closing. Granted options do not count toward this target.

Any additional reserve is created before the investment and included in the share count used to price the new shares.

All shares and options count one-for-one as common-equivalent shares. There are no other securities, conversions, exercises, or transactions. The listed amounts remain unchanged except for the required reserve increase.

How many additional shares must be added to the ungranted reserve, and what will the founders' fully diluted ownership percentage be after closing? Round ownership to two decimal places.

1. Additional reserve: 714,286 shares; founder ownership: 46.32%.
2. Additional reserve: 600,000 shares; founder ownership: 46.88%.
3. Additional reserve: 1,000,000 shares; founder ownership: 46.15%.
4. Additional reserve: 1,200,000 shares; founder ownership: 44.12%.
5. Additional reserve: 1,800,000 shares; founder ownership: 41.67%.

Related Week 6 deck

Ownership after new cash

Hard (6/8)

W6-S061 · Source slide 61

Before a priced round, the agreed capitalization contains 9M common equivalents excluding one SAFE, including 5M founder shares. A $1M YC-style post-money SAFE has a $10M cap, which governs conversion. New cash investors receive 20% of post-closing ownership. With no other capitalization changes, what do founders and SAFE holders own after closing?

1. Founders: 44.44%. SAFE holders: 8.00%.
2. Founders: 40.00%. SAFE holders: 8.00%.
3. Founders: 40.00%. SAFE holders: 10.00%.
4. Founders: 41.67%. SAFE holders: 8.33%.
5. Founders: 30.00%. SAFE holders: 8.00%.

Related Week 6 deck

Full-ratchet adjustment

Easy (0/8)

W6-S064 · Source slide 64

Assumptions: The lower-price issuance triggers the full-ratchet clause. No exception or waiver applies.

In a down round, how does full-ratchet antidilution treat the earlier investor's conversion price?

1. It keeps the old price until new financing exceeds the previous round's size.
2. It weights the old and new prices using the number of shares issued.
3. It resets the conversion price to the new lower price for the covered issuance.
4. It reduces the liquidation preference amount while leaving the conversion price unchanged.
5. It reduces the conversion price by the percentage decline in headline company valuation.

Related Week 6 deck

A small down round

Medium (4/8)

W6-S067 · Source slide 67

Assumptions: Compare separate otherwise identical cases. No waiver or exception applies.

An earlier preferred series has a $2 conversion price. A small covered financing issues only 10,000 shares at $1. How does full ratchet differ from weighted-average protection?

1. Neither adjusts the conversion price because the new issuance is too small.
2. Both reset to $1 because they respond only to the lower price.
3. Full ratchet makes a smaller adjustment than weighted average for small issuances.
4. Full ratchet resets to $1. Weighted average also considers the issuance size.
5. Weighted average resets to $1. Full ratchet also considers the issuance size.

Related Week 6 deck

An unused pro-rata right

Easy (1/8)

W6-S070 · Source slide 70

An investor has a pro-rata purchase right but no financing veto. The company makes the required offer, and the investor declines before the offer expires. What follows?

1. Its percentage is preserved through additional shares issued without further payment.
2. Its percentage can fall because the right offered a chance to invest.
3. The company must cancel the financing because the investor declined its allocation.
4. Its liquidation preference increases automatically to compensate for the smaller ownership percentage.
5. It can buy the missed allocation later at the previous financing's price.

Related Week 6 deck

A pro-rata check changes the round size

Medium (4/8)

W6-S073 · Source slide 73

An existing investor owns 15% on the agreed fully diluted basis. New outside investors will contribute exactly $3.4m in a primary round. The existing investor may invest an additional amount at the same share price to preserve its 15%. No options, conversions, or other capitalization changes occur.

How much must the existing investor contribute?

1. $0.510 million.
2. $0.600 million.
3. $0.690 million.
4. $0.400 million.
5. $3.910 million.

Related Week 6 deck

Sale approvals

Medium (4/8)

W6-S076 · Source slide 76

A sale requires board approval and consent from holders of a majority of preferred shares. The drag-along activates only after both. The board votes 4–1 for the sale, including the preferred investor's nominee. No preferred-stockholder vote or written consent has occurred. What remains necessary before invoking the drag-along?

1. Obtain consent from holders of the required majority of preferred shares.
2. Record the preferred nominee's board vote as the required preferred-holder consent.
3. Invoke the drag-along so it supplies the preferred consent after board approval.
4. Obtain common-holder majority approval in place of the separate preferred-holder consent.
5. Certify the 4–1 board vote as satisfying both majority approval requirements.

Related Week 6 deck

Vesting after the cliff

Medium (4/8)

W6-S079 · Source slide 79

A founder receives 4.8M shares. Vesting is 25% at month 12, then 1/48 of the original grant each month. The founder leaves immediately after month 18 vesting. The company exercises its right to repurchase all unvested shares at cost. No acceleration applies. How many shares does the founder retain?

1. 1.2M shares
2. 4.8M shares
3. 0.6M shares
4. 3.0M shares
5. 1.8M shares

Related Week 6 deck

Restricted stock election

Easy (0/8)

W6-S082 · Source slide 82

A founder receives eligible substantially nonvested stock today. The first vesting date is next year. Which action and effect correctly describe a section 83(b) election?

1. File within 30 days of transfer to choose current compensation-income treatment.
2. File within 30 days of first vesting to fix the original share value.
3. File with the next tax return to have every unvested share treated as vested.
4. File before the eventual sale to qualify automatically for a capital-gains exclusion.
5. File within 30 days of transfer to eliminate the agreement's repurchase provision.

Related Week 6 deck

Founder exit proceeds

Hard (7/8)

W6-S084 · Source slide 84

Founders own all of a company before choosing between two financing offers. Each investor provides $4 million of new primary capital.