The subject property is a single-tenant retail building under a lease with exactly three years remaining and no renewal option. NOI at the contract rent is $100,000, and NOI at market rent would be $120,000; the difference is all rent, on identical expense terms. Sales of similar buildings leased at market rent indicate an overall rate of 8%. The market discount rate for the rent shortfall is 10%, with each year's shortfall taken at the end of the year. What is the indicated value of the leased fee interest, to the nearest dollar?
Correct Answer
B) $1,450,263
Market NOI capitalized at the market-rent rate gives $120,000 ÷ 0.08 = $1,500,000. The tenant's $20,000 annual rent advantage for three years at 10% has a present value of $49,737, and the leased fee is $1,500,000 − $49,737 = $1,450,263. Deducting the undiscounted $60,000 gives $1,440,000. Stopping at $1,500,000 values the fee simple, and adding the present value gives $1,549,737, the treatment for an above-market lease.
Why This Is the Correct Answer
Option B is correct because the market-rent rate is applied to market NOI: $120,000 ÷ 0.08 = $1,500,000. The $20,000 annual shortfall for three years at 10% has a present value of $20,000 × 2.48685 = $49,737. Deducting it gives $1,500,000 − $49,737 = $1,450,263.
Why the Other Options Are Wrong
Option A: $1,440,000
Option A shows $1,440,000, which is $1,500,000 − ($20,000 × 3). It deducts the shortfall at face value, although future dollars are worth less today; discounted at 10%, the shortfall is $49,737, and the value is $1,450,263.
Option C: $1,500,000
Option C shows $1,500,000, which is $120,000 ÷ 0.08. That is the value at market rent, and it ignores the three years of below-market rent that the owner of the leased fee has to accept; deducting the $49,737 present value gives $1,450,263.
Option D: $1,549,737
Option D shows $1,549,737, which is $1,500,000 + $49,737. Adding the present value fits a lease above market; this contract rent is below market, so the amount is deducted, giving $1,450,263.
Market value, less the gap
Capitalize market NOI, then subtract today's value of the rent the lease withholds until it ends.
How to use: Use this when a lease with a known remaining term has rent below market.
Exam Tip
Match the rate to the income: a rate from market-rent sales goes with market NOI. On an HP-12C, enter n, i and PMT, solve for PV, and subtract that amount for a below-market lease.
Common Mistakes to Avoid
- -Applying a market-rent rate to the depressed contract NOI
- -Deducting the rent shortfall without discounting it
- -Adding the present value of a below-market lease instead of deducting it
Concept Deep Dive
Analysis
This tests how a below-market lease enters a leased fee valuation. The 8% rate comes from market-rent sales, so it belongs with market NOI. The temporary rent shortfall is then valued separately as a present value and deducted, which keeps the temporary loss from being capitalized as if it lasted indefinitely.
Background Knowledge
When contract rent is below market, the leased fee is worth less than the fee simple. The size of the difference depends on the rent gap and the remaining lease term. It can be estimated by discounting the difference between market and contract rent over that term to a present value.
Real-World Application
A lender needs the leased fee value of a retail building whose tenant has three years left at an old rent. The appraiser finds that sales leased at market rent indicate the overall rate. The appraiser capitalizes market NOI and makes a lump-sum deduction for the discounted rent shortfall.
More Income Approach Questions
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Previous Question
Annual potential rent is $480,000. Apply 8% combined loss to rent only. Other collectible real-estate income is already effective at $15,000, with no further loss. What total EGI results? Do not include unrelated business receipts.
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