# Solution: Loan Sizing

> Illustrative teaching case. Northgate Commons is not a real property, this is not a real transaction, and the term sheet is not a real financing quote. Every figure is fabricated for instruction.

## The input

Underwritten net operating income: **$1,090,004**.

Every test below runs on that figure. A student who ran the mechanics perfectly
on the seller's reported net operating income, or on the broker pro forma, gets
a wrong loan for a right reason, which is why net operating income is checkpoint
one and this is checkpoint two.

## The three tests

### Loan to value

65% of the purchase price.

    65% x $17,400,000 = $11,310,000

### Debt service coverage

The term sheet sizes on the greater of actual and fully amortizing debt service,
so the 30-year constant governs even though the first two
years are interest only.

Monthly payment factor at 6.35% over 30 years:

    i = 6.35% / 12 = 0.00529167
    factor = i / (1 - (1 + i)^-360) = 0.00622236
    annual constant = factor x 12 = 0.07466828

Maximum loan:

    $1,090,004 / (1.25 x 0.074668) = $11,678,361

### Debt yield

    $1,090,004 / 10.25% = $10,634,185

## The result

| Test | Maximum loan | Rank |
|---|---|---|
| Minimum debt yield of 10.25% | $10,634,185 | **Binds** |
| Maximum LTV of 65% | $11,310,000 | Second |
| Minimum DSCR of 1.25x | $11,678,361 | Loosest |

Proceeds are the lesser of the three, rounded down the way a lender quotes them.

> ## Supportable loan: $10,634,000
> ## Binding test: Minimum debt yield of 10.25%

## Why this is the interesting answer

The debt yield test is the one most often skipped, and here it is the one that
governs. It binds $675,815 below the next tightest test, so a student who ran
loan to value and coverage and stopped would have come away with
$11,310,000, over-levered by roughly
6.4%, and would
have built the rest of the model on an equity check that is too small.

The reason debt yield binds is worth understanding rather than memorizing. Debt
yield ignores the interest rate and the amortization schedule entirely. Coverage
does not: at a 6.35% rate the constant is
0.0747, and a 1.25x coverage
requirement against that constant is a fairly relaxed constraint. Loan to value
is a function of price, and the price here is not aggressive relative to the
comparables. Debt yield is the only one of the three that asks what the property
alone earns on the money lent, and on a normalized net operating income that has
absorbed a management fee and a tax reset, that answer is modest.

Two things follow. If the rate had been higher, coverage would have tightened and
might have bound instead. If the price had been higher, loan to value would have
loosened in dollar terms while debt yield stayed where it is, so the gap would
have widened rather than closed.

## Resulting metrics on the $10,634,000 loan

| Metric | Value | Threshold | Headroom |
|---|---|---|---|
| Loan to value | 61.11% | 65% maximum | 3.89% |
| Debt yield | 10.250% | 10.25% minimum | At the limit |
| Coverage on the amortizing constant | 1.373x | 1.25x minimum | 0.123x |
| Coverage on the actual year-one payment | 1.614x | Not tested | Interest only inflates this |
| Coverage in year 3, first amortizing year | 1.587x | 1.25x | 0.337x |

## Debt service and payoff

| Item | Amount |
|---|---|
| Interest-only annual debt service, years 1 and 2 | $675,259 |
| Fully amortizing annual debt service, years 3 to 5 | $794,023 |
| Origination fee at closing | $106,340 |
| Loan balance at the end of year 5 | $10,242,647 |

The payoff balance is lower than the original loan because the
24-month interest-only period is followed by 36 amortizing
payments before the term ends. Amortization on a
30-year schedule is slow in the early years, so the balance
falls by $391,353, which is
3.7% of the
original principal.

## Sources and uses

| Uses | Amount |
|---|---|
| Purchase price | $17,400,000 |
| Acquisition costs | $217,500 |
| Origination fee | $106,340 |
| **Total** | **$17,723,840** |

| Sources | Amount |
|---|---|
| Loan proceeds | $10,634,000 |
| Sponsor equity | $7,089,840 |
| **Total** | **$17,723,840** |

Renovation capital is funded from operations as it is spent rather than reserved
at closing, which is a modeling convention rather than a rule. Funding it at
closing would raise the equity check and lower the year-one levered cash flow,
and the effect on the levered IRR would be small either way.

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*Illustrative teaching case. Northgate Commons, the market, the broker, the lender, the comparables, and every figure in this packet are fabricated for instruction. Nothing here is a real property, a real transaction, or a real financing quote.*