A DCF discounts at 10% and capitalizes terminal forward NOI at 8%. Why can the rates differ?
Correct Answer
A) They serve distinct discounting and terminal-income capitalization functions.
The yield (discount) rate converts each dated cash flow, including the reversion, to present value over the holding period; the terminal capitalization rate converts one year of forward NOI into an estimated resale price. Because they serve different functions and reflect different expectations, they need not be equal. USPAP does not require any particular relationship between them, such as terminal rate below discount rate or terminal rate equal to yield minus growth.
Why This Is the Correct Answer
Option A is correct because the discount rate and the terminal capitalization rate serve distinct functions. The yield rate discounts each dated cash flow, including the reversion, to present value, while the terminal rate converts one year of forward NOI into an estimated resale price. Because they do different jobs and reflect different expectations, they need not be equal.
Why the Other Options Are Wrong
Option B: USPAP requires the terminal capitalization rate to be set below the discount rate.
Option B says USPAP requires the terminal capitalization rate to be set below the discount rate. USPAP does not prescribe any particular numerical relationship between these rates; their levels depend on market evidence and assumptions.
Option C: Both serve an identical function but only one may apply to income.
Option C says both rates serve an identical function but only one may apply to income. They serve different functions, one discounting the cash-flow series and the other capitalizing terminal NOI, and both are used in the same analysis.
Option D: USPAP sets the terminal rate equal to the yield minus growth.
Option D says USPAP sets the terminal rate equal to the yield minus growth. USPAP does not set that or any formula for the terminal rate; any such relationship holds only under particular compatible assumptions.
Two rates, two jobs
The discount rate brings money back to today; the terminal rate turns future income into a future sale price.
How to use: Use this when a question asks why a DCF uses more than one rate.
Exam Tip
Be skeptical of answers that claim USPAP sets specific numerical rate relationships; USPAP sets performance standards rather than rate formulas.
Common Mistakes to Avoid
- -Assuming the discount rate and terminal rate must be equal
- -Believing USPAP dictates rate relationships
- -Confusing the terminal rate's role with the discount rate's role
Concept Deep Dive
Analysis
This question tests why a discount rate and a terminal capitalization rate can differ in a discounted cash flow analysis. The discount rate converts each dated cash flow to present value, while the terminal rate converts one year of forward NOI into a resale price. Different functions and expectations allow different rates.
Background Knowledge
A discounted cash flow analysis forecasts income over a holding period and a resale at the end. The resale price is often estimated by capitalizing the next year's NOI at a terminal rate, and all cash flows are then discounted at a yield rate.
Real-World Application
An appraiser builds a ten-year DCF for an office building, discounting cash flows at 10% based on investor surveys. The resale is estimated by capitalizing year-eleven NOI at 8%, a rate supported by sales of similar buildings.
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How does a holding-period yield differ from an overall capitalization rate?
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A client is under contract to buy a triplex for $480,000. The appraiser's stabilized NOI is $36,000, and sales of similar triplexes indicate an overall rate of 7.5%. The client then learns that the owner must begin paying for trash collection at $200 per month, and rents will not change. The client's planned loan carries annual debt service of $24,000. At what overall rate would the revised NOI support the contract price?