Fourplex Math vs. a Broker's Cap Rate
A buyer is evaluating a four-unit apartment building listed at $400,000. The seller's records show effective gross income of $52,000 and operating expenses of $14,000, for NOI of $38,000. The buyer plans a $300,000 loan at 7.5% interest, 25-year amortization, and will pay $8,000 in closing costs. The lender requires a minimum 1.25 debt service coverage ratio and will lend up to 75% of appraised value. A broker tells the buyer the property is worth $475,000 because 'the market cap rate is 8%, so $38,000 divided by 8% equals $475,000.' The buyer asks whether the deal works under the lender's tests and what the cash-on-cash return would be.
1. Calculate the annual debt service, DSCR, and cash-on-cash return. Does the property meet the lender's tests?
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Debt service. Loan $300,000 at 7.5% annual, 25-year amortization. Monthly rate = 0.075/12 = 0.00625; n = 300. Payment factor = 0.00625 / (1 - 1.00625^-300) = about 0.007389. Monthly payment = $300,000 x 0.007389 = about $2,217. Annual debt service = about $26,600.
DSCR. NOI $38,000 / $26,600 = about 1.43. The lender's minimum is 1.25, so the property passes. The loan is 75% of the $400,000 purchase price ($300,000), so it also passes the LTV test at purchase. If the lender uses the lower of purchase price or appraisal, the $400,000 purchase price still supports the $300,000 loan.
Cash-on-cash. Cash invested = down payment $100,000 + closing costs $8,000 = $108,000. Annual cash flow before tax = NOI $38,000 - debt service $26,600 = $11,400. Cash-on-cash = $11,400 / $108,000 = about 10.6%.
2. Evaluate the broker's $475,000 valuation and explain how the buyer should use the appraisal and cap-rate evidence in the purchase decision.
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The broker's direct capitalization is arithmetically correct only if 8% is the right cap rate for this property and the NOI is sustainable. $38,000 / 0.08 = $475,000. But the buyer should verify comparable sales, vacancy and collection assumptions, reserves, and expense growth. A purchase price of $400,000 implies a 9.5% cap rate ($38,000 / $400,000), which may indicate a bargain or greater risk.
The appraisal is evidence for the lender, not a guarantee of value. The buyer should compare the appraiser's cap rate and comparables with the broker's assertion, confirm the lender will use the lower of purchase price or appraised value, and stress-test the NOI. If the 8% cap rate is not supported by comparable sales and the property's condition, the broker's $475,000 figure is an opinion, not a fact. The buyer should decide based on verified income, expenses, and financing, not on a single cap-rate calculation.