Year 11 NOI is projected at $385,000. Capitalize it at 7% to estimate a gross sale at the end of year 10. There are no selling costs. Discount that single reversion for 10 years at 8.5% annually. What is its present value, rounded to the nearest dollar?
Correct Answer
C) $2,432,570
385000÷0.07÷(1.085^10) = 2432569.7827. Common errors: not discounting the reversion gives $5,500,000; capitalizing year-11 NOI at the 8.5% discount rate gives $2,003,293; discounting for 11 years instead of 10 gives $2,242,000.
Why This Is the Correct Answer
Option C is correct because the reversion is $385,000 ÷ 0.07 = $5,500,000 at the end of year 10. Discounting it for 10 years at 8.5% gives $5,500,000 ÷ 1.085^10 = $2,432,570.
Why the Other Options Are Wrong
Option A: $2,003,293
Option A, $2,003,293, capitalizes year-11 NOI at the 8.5% discount rate instead of the 7% terminal rate: $385,000 ÷ 0.085 ÷ 1.085^10 = $2,003,293. The stated 7% terminal rate gives a $5,500,000 reversion and a present value of $2,432,570.
Option B: $2,242,000
Option B, $2,242,000, discounts the reversion for 11 years instead of 10: $5,500,000 ÷ 1.085^11 = $2,242,000. The sale occurs at the end of year 10, so it is discounted 10 periods, giving $2,432,570.
Option D: $5,500,000
Option D, $5,500,000, is the undiscounted reversion ($385,000 ÷ 0.07). It is received at the end of year 10, so it must be discounted at 8.5% for 10 years, giving $2,432,570.
Next year's NOI, this year's sale
Capitalize year 11 income to price the year 10 sale, then discount that sale back 10 years.
How to use: Use it to keep the reversion's timing and the discount periods aligned.
Exam Tip
Keep the terminal cap rate and the discount rate in their own roles: one prices the sale, the other discounts it.
Common Mistakes to Avoid
- -Leaving the reversion undiscounted
- -Capitalizing the reversion with the discount rate
- -Discounting for 11 periods because the NOI is from year 11
Concept Deep Dive
Analysis
This question tests valuing a reversion in a discounted cash flow. The year-11 NOI is capitalized at the terminal rate to estimate the sale price at the end of year 10, and that single amount is discounted back 10 years at the discount rate. Mixing up the terminal and discount rates or the number of periods produces the distractors.
Background Knowledge
In DCF analysis, the reversion is often estimated by capitalizing the following year's NOI at a terminal capitalization rate. That future sale price is then discounted to present value at the discount rate over the holding period.
Real-World Application
An appraiser preparing a 10-year DCF for an office building estimates the resale price by capitalizing projected year-11 NOI at a market-supported terminal rate. That reversion is then discounted back to the date of value along with the annual cash flows.
More Income Approach Questions
Which model describes yield capitalization of property benefits?
An appraiser is valuing a duplex. A market survey of recent duplex sales reports prices at 10.8 times potential gross income, with stabilized vacancy and credit loss of 10% of PGI and no other income. The subject's rent schedule is unavailable, but the property manager's records show collected income of $54,000 a year, in line with market rent and the 10% market loss. What value is indicated?
The subject property is a fourplex with annual EGI of $72,000 and operating expenses of $28,800. Of those expenses, $18,000 is fixed and $10,800 varies in direct proportion to EGI. The owner's annual mortgage payments are $21,000. An appraiser projects that EGI will fall 10% because of higher vacancy. What is the projected NOI?
Annual NOI available for debt service is $168,000 and total annual mortgage principal and interest debt service is $120,000. What is NOI ÷ debt service?
Annual PGI is $250,000 and combined vacancy and collection loss is explicitly 12% of that same PGI base. There is no other income. What annual EGI remains?
Annual PGI is $360,000 and combined vacancy and collection loss is explicitly 8% of that same PGI base. There is no other income. What annual EGI remains?
Annual PGI is $640,000. Combined vacancy and collection loss is 6.25% of PGI. There is no other income. What EGI remains?
An appraiser is updating a prior appraisal of a triplex with potential gross income of $60,000 and no other income. The prior appraisal used vacancy and credit loss of 5% of PGI, and a new survey of competing rentals indicates 8%. The operating expenses of $24,000 are property taxes, insurance and contract services that do not vary with occupancy, and the market overall rate remains 7.5%. By what percentages do effective gross income and indicated value decrease?
Annual potential rental income is $600,000 and vacancy loss alone is $36,000. What percentage of potential rent does that loss represent?
In the subject's market, lenders on fourplexes have lowered their typical loan-to-value ratio from 70% to 60%. The annual mortgage constant remains 5% and the equity dividend rate remains 10%. The subject's NOI has not changed. How does this affect the overall rate indicated by the band of investment and the indicated value?
People Also Study
Real Estate Market
13.6% of exam
Property Description
11.8% of exam
Land or Site Valuation
4.5% of exam
Sales Comparison Approach
16.4% of exam
Cost Approach
13.6% of exam
Previous Question
A broker reports the $2,160,000 cash-equivalent sale of a small retail building with “net income” of $118,800. Verification shows that this figure is after $54,000 of annual debt service on the seller’s loan. The subject property is a similar retail building with annual NOI of $156,000. What is the subject’s indicated value by direct capitalization?
Next Question
A discount rate for a DCF may be supported by: