What Is a Fair Price to Pay? Direct Cap, DCF, Mortgages & Risk

Direct capitalization is most appropriate when the property's current or stabilized NOI is representative of a durable income stream and a market-supported cap rate can be observed. It works best when these conditions are present:

• Stabilized operations: the property is at or near sustainable market occupancy, with rents, concessions, and expenses that reasonably reflect normal operations. There is no major lease-up, renovation, redevelopment, or repositioning plan driving future income.
• Reliable comparable transactions: recent, similar, arm's-length sales are available to support the cap rate. Without relevant comps or other defensible cap-rate evidence, the valuation becomes much more judgmental.
• Screening or market pricing: the analyst needs a quick value estimate, pricing check, or acquisition screen before building a full DCF. Direct cap is often a useful first filter, especially for stabilized assets.

Where Direct Capitalization Fails

Direct capitalization compresses value into a single-year income measure and one cap rate. It works only when that single income measure is a reasonable proxy for the property's expected income stream. It becomes less reliable when the property has below-market leases rolling to market, major near-term capital expenditures, changing vacancy, unusual expense growth, temporary income disruption, material rent steps, or a business plan that changes the income profile over time. In those cases, a one-period valuation can hide the timing, risk, and cost of reaching the projected income.

For investment underwriting, where the objective is to estimate returns over a specific hold period, direct capitalization is usually not enough by itself. A discounted cash flow analysis is needed when timing, capital costs, lease rollover, debt, and exit value materially affect the investment outcome.

The Gordon Growth Model is not usually how practitioners directly value individual real estate acquisitions. Real estate investors typically rely on market-extracted cap rates, direct capitalization, and multi-year DCF models with an exit cap rate. Still, the Gordon Growth framework is useful because it explains the theoretical relationship between cap rates, required returns, and expected income growth. Under a simplified constant-growth perpetuity:

R = Y − g

Where R is the capitalization rate, Y is the required unlevered total return (or discount rate), and g is the expected long-term growth rate of income.

In real estate terms, this relationship helps explain what an exit cap rate is doing. When an investor applies a terminal cap rate to next year's NOI, the investor is effectively converting a future income stream into value. The terminal cap rate reflects the market's view of required return, income growth, risk, asset quality, lease durability, and capital-market conditions.

This decomposition also explains why a low cap rate does not automatically mean a property is overpriced. If the market requires an 8.0% unlevered return and expects long-term NOI growth of 3.5%, the implied cap rate is 8.0% − 3.5% = 4.5%. If the required return is still 8.0% but expected long-term NOI growth is only 1.0%, the implied cap rate is 8.0% − 1.0% = 7.0%. The first property is not necessarily overpriced: it may be pricing in stronger expected growth, lower risk, better asset quality, or stronger investor demand.

The formula also clarifies a common confusion: cap rates and discount rates are not the same thing. In the constant-growth framework, the cap rate is below the discount rate when expected income growth is positive. They converge only when expected growth is zero. If expected income growth is negative, the cap rate could theoretically exceed the discount rate. In practice, real estate cap rates are observed in the market rather than derived mechanically from the Gordon Growth Model, but the model provides the intuition: a terminal cap rate is not just a number. It is a compressed expression of risk, required return, and expected long-term income growth.

Cap rates are shaped by required returns, expected income growth, risk, and capital flows. They are not fixed characteristics of an asset class. A multifamily property does not "have" a 5.0% cap rate because it is multifamily; it trades at a cap rate based on the market's view of its income durability, growth prospects, risk, financing environment, and buyer demand. A useful way to organize the drivers is the Gordon Growth relationship, R = Y − g: cap rates tend to rise when required returns rise, all else equal, and tend to fall when expected income growth improves, all else equal.

Interest rates matter because Treasury yields influence the risk-free component of required returns. When Treasury yields rise, investors often require higher real estate returns, which can put upward pressure on cap rates. But the relationship is not one-for-one, and cap-rate spreads can tighten or widen depending on capital availability, credit conditions, investor risk appetite, property type, and expected NOI growth.

Capital flows also matter. Strong inflows from institutions, REITs, private equity, foreign investors, or lenders can compress cap rates even if property-level fundamentals have not improved proportionately. Conversely, weaker liquidity or tighter debt markets can push cap rates higher even when current NOI is stable.

Property type and asset quality create further dispersion. Industrial and multifamily assets have often traded at lower cap rates when investors expect stronger rent growth, deeper buyer demand, or more durable occupancy. Office assets have often traded at higher cap rates when investors perceive greater leasing risk, rollover risk, capital cost exposure, or uncertainty around long-term space demand. Retail cap rates vary widely by format, tenant quality, location, and sales productivity. Market data should be framed as a dated snapshot: survey data from late 2024, for example, showed meaningful dispersion across sectors, with lower cap rates generally observed for stronger industrial and multifamily assets and higher cap rates for many office assets because of elevated vacancy, leasing risk, and remote-work uncertainty.

A complete real estate DCF follows a disciplined sequence. The process connects the pro forma forecasting framework from Chapter 4 to the valuation and return analysis in this chapter.

Selling costs are often modeled as a percentage of gross sale price, commonly around 1.5% to 2.5%, but the appropriate assumption depends on market, asset size, brokerage costs, transfer taxes, and legal costs.

Consider a 60-unit multifamily property with Year 1 NOI of $1,500,000, growing at 3.0% annually. Capital reserves are $60,000 in Year 1, escalating at 2.0% annually. The unlevered discount rate is 8.0%, the exit cap rate is 6.25%, and selling costs are 2.0% of gross sale price.

Present values are computed from unrounded discount factors and then rounded for display; recomputing from the rounded factors shown may create small differences. PV of operating cash flows: $6,081,945.

Terminal Value Calculation

The exit cap rate is applied to forward NOI, not Year 5 CFBDS:

• Forward NOI, Year 6: $1,688,263 × 1.03 = $1,738,911
• Gross reversion: $1,738,911 ÷ 0.0625 = $27,822,578
• Less selling costs, 2.0%: ($556,452)
• Net sale proceeds: $27,266,126
• PV of net reversion: $27,266,126 ÷ (1.08)⁵ = $18,556,867

DCF Value: $6,081,945 + $18,556,867 = $24,638,813. Rounded, the indicated unlevered value is approximately $24.6 million.

In this example, the present value of the reversion is $18.6 million, or roughly 75% of total DCF value. This illustrates why terminal value assumptions are so important in real estate DCF analysis. A 25-basis-point increase in the exit cap rate, from 6.25% to 6.50%, would reduce the gross reversion by approximately $1.07 million and reduce the total DCF value by approximately $714,000, after selling costs and discounting.

The implied going-in cap rate provides a useful sanity check: $1,500,000 ÷ $24,638,813 = 6.1%. If comparable properties in the market trade at cap rates between 5.5% and 6.5%, the DCF result is within a reasonable range. If the DCF implied a 4.0% going-in cap while comparable properties traded around 6.0%, the analyst should re-examine the growth, discount rate, capital reserve, or exit assumptions. The 6.25% exit cap rate is modestly above the 6.1% implied going-in cap rate, which is directionally consistent with a conservative exit assumption, though the final exit cap should be supported by market evidence.

The discount rate is the investor's required total return: the annualized return needed to compensate for the time value of money, risk, illiquidity, and management burden of the investment. The correct discount rate depends on the cash flow being discounted. Pre-tax cash flows require a pre-tax discount rate. After-tax cash flows require an after-tax discount rate. Unlevered cash flows require an unlevered rate. Levered equity cash flows require an equity rate.

For an unlevered property DCF, the analyst discounts cash flow before debt service at an unlevered property discount rate. A practical real estate build-up formula is:

Y = R_f + RP_re + RA_property

Where Y is the unlevered property discount rate, R_f is the risk-free rate, RP_re is the real estate risk premium, and RA_property is the property-specific risk adjustment. The risk-free rate is often proxied by the 10-year U.S. Treasury yield. The real estate risk premium compensates for illiquidity, transaction costs, operating risk, leasing risk, capital-market risk, and valuation uncertainty. The property-specific adjustment reflects the asset's location, age, tenant credit, lease rollover, physical condition, income volatility, capital needs, and business-plan complexity.

This resembles the logic of CAPM, but it is not the same thing. In corporate finance, the Capital Asset Pricing Model estimates the required return on equity as R_e = R_f + β(R_m − R_f). CAPM compensates investors for systematic market risk, measured by beta, and works most cleanly for publicly traded securities with observable prices. Direct real estate is different: properties trade infrequently, are illiquid, require active management, and carry asset-specific risks such as tenant rollover, local supply, capital expenditures, and leasing execution. Those risks are not captured cleanly by a public-market beta, which is why real estate underwriting often uses a CAPM-like build-up approach rather than strict CAPM.

Where WACC fits. In corporate finance, after-tax WACC = D/V × R_d × (1 − Tax Rate) + E/V × R_e, used to discount unlevered after-tax free cash flow when valuing an entire company. The real estate equivalent is the unlevered property discount rate, but most property DCFs are built on pre-tax NOI and pre-tax cash flow before debt service, so analysts usually use a pre-tax property discount rate rather than after-tax corporate WACC. The interest tax shield is usually excluded from property-level valuation because income-tax treatment is investor-specific: a REIT, pension fund, taxable individual, private fund, and foreign investor may face different tax consequences. If the analyst builds a buyer-specific after-tax model, then tax effects can be modeled explicitly; they should not be mixed into a pre-tax property DCF.

Levered equity DCF. A levered equity DCF values the equity investor's claim, not the property as a whole. Start with cash flow before debt service; subtract annual debt service (interest and principal); the result is cash flow to equity during the hold. At sale, estimate the gross reversion, deduct selling costs, and repay the remaining loan balance; the remaining proceeds belong to equity. Discount those equity cash flows at the equity required return, or calculate levered IRR and equity multiple: Equity Value = CFTE₁ ÷ (1 + R_e)¹ + CFTE₂ ÷ (1 + R_e)² + … + Final Equity Proceeds ÷ (1 + R_e)ⁿ.

For a levered equity DCF, WACC is not the correct discount rate because the cash flows are already after debt service. The debt claim has been removed from the cash flow, and the remaining cash flow belongs to equity. Using WACC would double-count the debt benefit by including debt in both the cash flow and the discount rate.

Direct capitalization is useful, but it compresses value into one income measure and one cap rate. That works best for stabilized properties with durable income and normal capital needs. Investment analysis often requires more detail. A DCF is stronger when timing, growth, capital expenditures, lease rollover, financing, or exit assumptions materially affect value.

Direct capitalization remains valuable as a screening tool and as a sanity check on DCF results. For stabilized properties, direct capitalization and DCF should usually point to a broadly similar value range if the assumptions are consistent. If they diverge materially, the analyst should investigate why: the difference may come from growth assumptions, capital costs, lease rollover, discount rate, or exit pricing.

The Gordon Growth Model can also be used to estimate terminal value by treating the post-hold-period income stream as a growing perpetuity:

Terminal Value = Forward NOI ÷ (Y − g)

Where Y is the unlevered property discount rate and g is the expected long-term NOI growth rate. The formula should use forward NOI (the NOI for the first year after the hold period), and the discount rate and growth rate must be consistent with the cash flow being capitalized: if the model uses pre-tax NOI, the discount rate and growth rate should also be pre-tax, property-level assumptions.

For example, if Y = 8.0% and g = 2.0%, then Y − g = 6.0%. That 6.0% is the implied terminal cap rate. A property with $1,800,000 of forward NOI would have a terminal value of $1,800,000 ÷ 0.060 = $30,000,000. Under constant-growth assumptions, the Gordon Growth approach and the exit cap rate approach are mathematically equivalent because R = Y − g.

In practice, the exit cap rate method dominates real estate underwriting because it is simpler and more directly tied to observable market evidence. The Gordon Growth framework is still useful because it explains what an exit cap rate implies about required return and long-term income growth: it is a check on the logic behind the cap rate, not usually the primary method. The long-term growth rate must also be realistic: if g is too close to Y, the terminal value becomes inflated; if g exceeds Y, the formula breaks down. Long-term NOI growth should be supportable and sustainable.

Sensitivity Testing Is Non-Negotiable

Because terminal value often drives a large share of DCF value, sensitivity analysis around the exit cap rate is essential. A standard table varies the exit cap rate in 25-basis-point increments around the base case. Assume a property has $1,800,000 of forward NOI:

Moving 75 basis points below or above the base case, from 5.25% to 6.75%, creates a terminal value range of about $7.6 million, or more than 25% of the base-case terminal value. This is why experienced underwriters focus disproportionate attention on the exit cap rate assumption and why investment committees scrutinize it closely.

At any point in a fully amortizing or partially amortizing fixed-rate loan, the outstanding loan balance equals the present value of the remaining scheduled payments, discounted at the contract rate. This is one of the most useful identities in mortgage mathematics. There are two equivalent ways to calculate the balance: amortize forward month by month, splitting each payment into interest and principal, or discount the remaining payments back to the current date at the contract rate.

For the worked loan, the monthly payment is approximately $95,928, based on a 6.0% annual rate (0.5% per month) and a 30-year amortization schedule. After 60 payments, there are 300 scheduled amortization payments remaining, so the balance is the present value of 300 remaining monthly payments of $95,928 at 0.5% per month = $14,888,697.

The balloon payment is simply the remaining loan balance at maturity on a partially amortized loan. The loan matures after 10 years even though it was amortized over 30 years, so the borrower does not make the remaining 240 scheduled monthly payments; instead, the present value of those remaining payments becomes the balloon balance due at maturity.

This also explains why long-amortization loans pay down slowly at first. During the first 10 years, the borrower makes more than $11.5 million of scheduled payments, but only about $2.6 million of the original $16 million principal balance is repaid. Most of the early payments are interest. The identity matters at sale as well: if the property is sold at the end of Year 5, the equity investor receives net sale proceeds only after repaying the remaining loan balance of approximately $14,888,697, assuming no prepayment penalty, defeasance cost, yield maintenance charge, or exit fee.

The 6.0% note rate determines how interest accrues on the loan balance, but it does not fully describe the economics of the loan once fees and closing costs are included. Two related measures capture the all-in yield or cost, depending on whose perspective is being measured.

• Lender's yield: the internal rate of return on the lender's cash flows. The lender funds the loan but receives the origination fee at closing. In the worked loan, the lender disburses $16,000,000 but collects a $320,000 origination fee, so its net outlay is $15,680,000. If the loan is held to the Year 10 balloon, the scheduled payments and balloon repayment produce a lender's yield of approximately 6.29%.
• Effective borrowing cost (EBC): the internal rate of return on the borrower's cash flows. The borrower pays the origination fee plus third-party closing costs that the lender does not receive. In the worked loan, the borrower receives $16,000,000, pays $320,000 in points and $80,000 in third-party costs, and therefore has $15,600,000 of net usable proceeds while owing the full loan schedule. If the loan is held to maturity, the effective borrowing cost is approximately 6.36%.

The difference between lender's yield and EBC is the treatment of third-party costs. Origination fees paid to the lender affect both measures. Third-party costs affect the borrower's cost but not the lender's yield because the lender does not receive them.

On consumer residential loans, the Truth in Lending Act requires lenders to disclose an annual percentage rate, or APR. APR is similar in concept to EBC because it incorporates specified finance charges into an annualized cost of credit. However, APR is calculated under regulatory rules and may not include every cost a borrower considers economically relevant. It can also understate the realized cost for borrowers who repay early, because upfront costs are spread over the assumed loan term.

Prepayment changes the annualized economics because upfront costs are paid at closing. If the loan is repaid sooner, those costs are spread over fewer years. Assuming no prepayment penalty, if the worked loan is prepaid at the end of Year 5 by paying off the $14,888,697 remaining balance, the lender's yield rises to approximately 6.48% and the borrower's EBC rises to approximately 6.61%.

A lender holding a long-term fixed-rate loan has committed to receiving a stream of fixed payments. That position carries several risks: interest rate risk (if market rates rise, the value of the fixed-rate payment stream falls), default risk (the borrower may stop paying), prepayment risk (the borrower may repay or refinance when rates fall, just when the fixed-rate loan is most valuable to the lender), and reinvestment risk (principal repaid through amortization or prepayment must be reinvested at whatever rates are available).

Loan structure allocates these risks. A shorter term or balloon maturity reduces the lender's exposure to long-term interest rate movements by shortening the period during which the lender is locked into a fixed rate. Prepayment provisions (lockouts, yield maintenance, or defeasance) manage prepayment risk.

An adjustable-rate mortgage, or ARM, reallocates part of the interest rate risk from the lender to the borrower by resetting the loan's interest rate according to a defined formula. The mechanics are standard:

• Index: a published market interest rate used as the reference rate, such as SOFR or a Treasury rate. In most U.S. mortgage and commercial loan contexts, the index is an interest-rate benchmark, not an inflation index.
• Margin: the lender's fixed spread over the index, usually set for the life of the loan. The fully indexed rate equals the index plus the margin: a 4.10% index plus a 2.40% margin produces a 6.50% fully indexed rate.
• Initial or teaser rate: an introductory rate that may be below the fully indexed rate. When the first adjustment occurs, the loan may reset toward the index-plus-margin rate, subject to caps, even if the index has not changed.
• Adjustment interval: how often the rate resets after the initial fixed period. Many residential hybrid ARMs are fixed for an initial period, such as 3, 5, 7, or 10 years, and then adjust periodically, often annually or every six months.
• Caps and floors: contractual limits on how much the rate can change. A periodic cap limits the change at a reset date, while a lifetime cap limits total rate movement over the loan's life. A floor sets a minimum rate. Tighter caps reduce the borrower's exposure to rate increases and shift some risk back to the lender, which may affect pricing.

At each reset, the payment is usually recalculated based on the new interest rate, the remaining loan balance, and the remaining amortization period. Because the borrower bears more interest rate risk, ARMs often start with a lower rate than otherwise similar fixed-rate loans: that lower initial rate is the compensation for accepting future rate uncertainty. Commercial floating-rate loans use the same basic index-plus-spread logic, especially in bridge, construction, and transitional lending; they are often interest-only, may reset monthly, and may require interest-rate caps or hedges to limit the borrower's exposure.

A permanent loan is the long-term first mortgage on a stabilized, income-producing property. The worked loan's structure (a 30-year amortization schedule with a 10-year balloon maturity) is a common commercial mortgage format. Two features often distinguish permanent commercial debt from the residential mortgages most students know: recourse and prepayment restrictions.

Recourse. Commercial real estate borrowers often hold each property in a special-purpose entity, or SPE, such as an LLC or limited partnership created to own that asset alone. If the lender's claim is limited to the property and the lender cannot generally pursue the personal assets of the sponsor, the loan is nonrecourse. Nonrecourse does not mean the borrower has no obligations: lenders usually require "bad-boy" carve-outs that can create personal liability for fraud, misrepresentation, misapplication of funds, bankruptcy interference, environmental issues, or other specified bad acts. Some loans may also require partial recourse, repayment guarantees, completion guarantees, or other credit support.

Prepayment. Residential borrowers can often prepay without a major penalty. Commercial lenders frequently restrict prepayment because they priced the loan expecting a particular stream of interest and principal payments. Common protections: lockout (prepayment prohibited for a stated period); prepayment penalty (a fee, often a declining percentage of the balance, such as 5-4-3-2-1); yield maintenance (a make-whole amount compensating the lender for lost yield, typically comparing the contract rate to a Treasury benchmark); and defeasance (the borrower substitutes a portfolio of permitted securities, often Treasuries, designed to replicate the loan's remaining scheduled payments, common in CMBS loans). These provisions matter for underwriting: if a property is sold in Year 5 but the loan has a 10-year term, the borrower may not be able to repay at par. If a model assumes repayment at par, that assumption should be treated as a simplification.

Alternative Structures Finance What Permanent Debt Will Not

Floating-rate loans are commonly priced at an index plus a spread, similar to the ARM's index-plus-margin structure. Borrowers often purchase an interest-rate cap so a sharp rate increase does not overwhelm project cash flow or the development budget.

Above the first mortgage, two junior capital structures are often confused. A second mortgage is a junior lien on the real estate itself: if the borrower defaults, the second mortgage lender's remedy is against the property, but it stands behind the first mortgage lender. A mezzanine loan is usually secured by a pledge of the equity interests in the property-owning entity rather than by a mortgage lien on the property. If the borrower defaults, the mezzanine lender may foreclose on the pledged equity interests under the Uniform Commercial Code and step into the borrower's ownership position, subject to the first mortgage and the intercreditor agreement. This remedy can be faster than mortgage foreclosure. Mezzanine debt is common in larger institutional and securitized capital stacks because it can provide additional leverage without placing another mortgage lien directly on the property.

Two distribution mechanisms complete the picture. Loan syndication shares a large loan across multiple lenders: one lender usually leads, coordinates underwriting, and may act as administrative agent or servicer. The secondary mortgage market allows originators to sell whole loans or pool loans into commercial mortgage-backed securities. Whether a lender plans to hold the loan in portfolio or sell it affects documentation, servicing, reserves, prepayment provisions, and pricing: CMBS loans commonly use defeasance or yield maintenance because investors are buying a predictable stream of loan cash flows.

Investors accept additional risk only when they expect additional compensation. This relationship appears throughout the module. The built-up discount rate starts with a risk-free rate and adds premiums for real estate risk and property-specific risk. Cap rate dispersion across property types reflects differences in perceived risk, growth, liquidity, and capital demand. Equity return targets also rise as strategy risk increases: core strategies generally require lower returns than value-add or opportunistic strategies.

The discipline is to verify that the premium is real compensation, not just an attractive headline yield. A Class B office building offering a 200-basis-point cap rate spread over a Class A comparable is attractive only if the rollover schedule, capital needs, tenant credit, and leasing assumptions survive underwriting. Treat every above-market yield as a question: which risks am I being paid to hold, and is the payment sufficient?

Diversification Manages What Underwriting Cannot

Underwriting manages risks inside a deal. Diversification manages risks that no single deal can fully avoid. Modern portfolio theory shows that portfolio risk depends not only on how risky each asset is individually, but also on how the assets move together. Combining assets with less-than-perfect correlation can reduce portfolio volatility even when each asset remains risky on its own. In real estate, diversification operates across several dimensions:

• Property type: apartments, industrial, retail, and office respond differently to employment growth, interest rates, consumer behavior, e-commerce, remote work, and supply cycles.
• Geography: a portfolio concentrated in one metro is exposed to that metro's employment base, population trends, supply pipeline, weather risk, tax regime, and regulatory environment.
• Tenant and industry exposure: diversified tenants, industries, and lease maturities reduce the risk that one tenant, sector, or rollover year damages the entire income stream.
• Strategy and debt maturity: mixing core and value-add assets, and laddering loan maturities, can reduce exposure to a single capital-market window or refinancing event.

Real estate can also diversify a mixed-asset portfolio because its return patterns may differ from stocks and bonds. Specific correlation estimates vary by period, property type, leverage, appraisal methodology, and whether the exposure is public REITs or private real estate, so treat them as estimates, not constants. The practical limits are real: direct properties are large, capital-intensive, and slow to trade, so diversification through direct ownership requires scale. Smaller investors often obtain diversification through REITs, private funds, or commingled vehicles. Within a single property, diversification cannot solve the problem; underwriting, structure, and management controls must do the work.

Scenario analysis tests a few coherent cases, such as bull, base, and bear. Monte Carlo simulation generalizes that idea. Instead of selecting three input combinations by hand, the analyst assigns probability distributions to key inputs such as rent growth, vacancy, exit cap rate, interest rates, construction costs, or lease-up timing. The model then randomly draws values from those distributions, runs the DCF, records the result, and repeats the process thousands of times.

The output is a distribution of outcomes rather than a single point estimate. The analyst can estimate the probability that the deal loses money, the probability that IRR falls below the hurdle rate, the range containing most outcomes, or the downside tail. Monte Carlo simulation is useful for large portfolios, development projects, structured finance, and underwriting where downside risk matters as much as the average result. At this course level, the key idea is simple: Monte Carlo is scenario analysis at scale, producing probability statements instead of only a few hand-picked cases.

The method is only as good as its inputs. Distributions, correlations, and assumptions are still judgment calls. A simulation built on optimistic inputs will produce an optimistic output, even if it looks mathematically sophisticated.

The module's deal is now complete enough to measure equity returns. The investor buys the property at its $24,638,813 DCF value, finances it with the Part Five loan of $16,000,000 at a 6.0% fixed rate with 30-year amortization, and invests $8,638,813 of equity. This simplified example excludes acquisition costs beyond the loan assumptions already discussed.

The property performs exactly as forecast in Part Three. Each year, cash flow before debt service is reduced by annual debt service of $1,151,137 to calculate cash flow after debt service. At the end of Year 5, the property sells for $27,266,126 of net sale proceeds before debt repayment. The remaining loan balance of $14,888,697 is repaid, leaving $12,377,429 of net sale proceeds to equity. One simplification: the loan is assumed to be repaid at par with no prepayment cost. Part Five explains why a real 10-year permanent loan repaid in Year 5 might require yield maintenance, defeasance, or another prepayment cost.

The same equity cash flows produce three return measures: levered IRR 11.2%, equity multiple 1.65x, and Year 1 cash-on-cash 3.3%, rising to 5.5% by Year 5. The equity multiple is total equity distributions divided by initial equity invested: $288,863 + $332,663 + $377,789 + $424,281 + $472,180 + $12,377,429 = $14,273,205; $14,273,205 ÷ $8,638,813 = 1.65x.

The deal is positively levered on an IRR basis: the 11.2% levered IRR exceeds the 8.0% unlevered return implied by the purchase price. However, Year 1 cash-on-cash of 3.3% is below the property's Year 1 unlevered cash yield of $1,440,000 ÷ $24,638,813 = 5.8%. The reason is the mortgage constant: although the note rate is 6.0%, annual debt service equals 7.19% of the original loan amount because each payment includes both interest and scheduled principal repayment. That principal repayment reduces current cash flow but builds equity by lowering the loan balance. Over the first five years, the balance falls from $16,000,000 to $14,888,697, a principal reduction of $1,111,303. Combined with NOI growth and the sale proceeds, that amortization helps produce the higher levered IRR at exit.