An appraiser verifies two fourplex sales, each at an effective gross income multiplier of 8.0. Sale A has an operating expense ratio of 30% of EGI, and Sale B has an operating expense ratio of 45% of EGI. What overall rates do these sales indicate?
Correct Answer
D) Sale A 8.75%; Sale B 6.88%
The net income ratio is 70% for Sale A and 55% for Sale B, so the implied overall rates are 70% ÷ 8.0 = 8.75% and 55% ÷ 8.0 = 6.88%. Equal multipliers therefore do not mean equal net returns. Dividing the expense ratios by 8.0 gives 3.75% and 5.63%, ignoring expenses gives 12.50% for both, and matching the ratios to the wrong sales reverses the rates.
Why This Is the Correct Answer
Option D is correct because Sale A keeps 70% of EGI as net income and Sale B keeps 55%. Dividing by the 8.0 multiplier gives 8.75% and 6.88%, which shows that a gross multiplier can mask a real difference in net return.
Why the Other Options Are Wrong
Option A: Sale A 3.75%; Sale B 5.63%
Option A, showing 3.75% and 5.63%, divides the expense ratios by the multiplier: 30% ÷ 8.0 and 45% ÷ 8.0. An overall rate rests on net income, so the correct figures are 70% ÷ 8.0 = 8.75% and 55% ÷ 8.0 = 6.88%.
Option B: Sale A 12.50%; Sale B 12.50%
Option B, showing 12.50% for each sale, computes 1 ÷ 8.0 with no expense deduction. That is EGI divided by price, not an overall rate; net income gives 8.75% for A and 6.88% for B.
Option C: Sale A 6.88%; Sale B 8.75%
Option C, showing A at 6.88% and B at 8.75%, matches the net income ratios to the wrong sales. Sale A has the lower expense ratio and so keeps more net income, giving A 8.75% and B 6.88%.
Keep over multiple equals rate
What the property keeps (the net income ratio) divided by the multiplier gives the overall rate. More expense means less kept and a lower rate at the same multiplier.
How to use: Use this phrase when a question gives a multiplier and an expense ratio and asks for a rate.
Exam Tip
Convert an expense ratio to a net income ratio before dividing. A quick check is that a higher expense ratio lowers the implied rate when the multiplier is fixed.
Common Mistakes to Avoid
- -Dividing the expense ratio rather than the net income ratio by the multiplier
- -Assuming equal multipliers mean equal overall rates
- -Reading the reciprocal of a gross multiplier as an overall rate
Concept Deep Dive
Analysis
The problem connects gross and net measures. Price divided by EGI and NOI divided by price share the sale price, so the overall rate equals the net income ratio divided by the multiplier. Different expense burdens produce different overall rates even when the multipliers match.
Background Knowledge
An effective gross income multiplier stops above the expense line, whereas an overall rate is measured after operating expenses. Standard texts relate the two through the net income ratio, which is one minus the operating expense ratio.
Real-World Application
Two older apartment buildings sell at the same gross multiple, but one has far higher operating costs. The appraiser's net analysis shows that the buyer of the costly building accepted a much lower overall rate, which casts doubt on treating the two sales as equivalent.
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