Two DCFs have identical positive projected operating cash flows and a positive terminal NOI, with no offsetting terminal costs. Model A uses a 6.0% discount rate and 5.5% terminal rate; B uses 7.2% and 6.8%. Which indicates more value?
Correct Answer
C) A: its lower discount rate raises present values and its lower terminal rate raises the reversion.
Both stated rate changes favor Model A: a lower discount rate increases present values of positive receipts, while a lower terminal capitalization rate increases value from the same positive terminal NOI. Neither effect offsets the other here. No claim about a dominant influence is needed.
Why This Is the Correct Answer
Option C is correct because Model A's 6.0% discount rate is lower than B's 7.2%, which increases the present value of the positive cash flows, and A's 5.5% terminal rate is lower than B's 6.8%, which produces a larger reversion from the same terminal NOI. Since neither effect offsets the other, Model A indicates more value.
Why the Other Options Are Wrong
Option A: B, because the higher terminal rate raises terminal value.
Option A says B is worth more because a higher terminal rate raises terminal value. That is backwards: dividing the same terminal NOI by a higher rate produces a smaller reversion, and B's higher discount rate also lowers present values.
Option B: The same value for both models, because the spread between the two rates is about the same in each case.
Option B says both models produce the same value because the spread between rates is similar. Value depends on the level of each rate, not just their spread; Model A's lower rates on both counts give it the higher value.
Option D: A only if its discount rate is lower than its terminal rate.
Option D says A is worth more only if its discount rate is below its terminal rate. That condition is not needed and does not even hold here (6.0% is above 5.5%), yet A still indicates more value because both of its rates are lower than B's.
Lower rate, higher value
Rates sit in the denominator, so lowering either the discount rate or the terminal cap rate raises value when the cash flows are positive.
How to use: Use this inverse relationship to compare DCF models quickly before doing any arithmetic.
Exam Tip
When comparing models, check whether the rate changes push value in the same direction; if they do, no detailed calculation is needed.
Common Mistakes to Avoid
- -Thinking a higher terminal cap rate increases resale value
- -Comparing only the spread between rates instead of their levels
- -Assuming the discount rate must be below the terminal rate for a model to be valid
Concept Deep Dive
Analysis
This question tests how discount rates and terminal capitalization rates affect DCF value. With identical positive cash flows, a lower discount rate raises the present value of each receipt, and a lower terminal cap rate raises the resale value from the same terminal NOI. Model A has both lower rates, so both effects point the same way.
Background Knowledge
In a discounted cash flow analysis, projected income and the reversion are discounted to present value at a discount rate. The reversion is often estimated by capitalizing a terminal-year NOI at a terminal capitalization rate; a lower rate in either place increases the indicated value, all else equal.
Real-World Application
A reviewer compares two DCF appraisals of the same office building with identical cash flow forecasts. Noticing that one report uses both a lower discount rate and a lower terminal rate, the reviewer recognizes why that report's value is higher and asks each appraiser for market support for the chosen rates.
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Previous Question
An appraiser finds a rented comparable that sold for a cash-equivalent price of $648,000 with monthly gross rent of $2,700. The subject has monthly gross rent of $2,450, measured on the same basis. Sales in the market area indicate the same price-to-rent ratio applies, and no other adjustments are required. What is the indicated value of the subject, rounded to the nearest dollar?
Next Question
The building on the subject site is known to be worth $1,800,000, and total annual NOI is $216,000. Market data indicate a 6% land capitalization rate and a 9% building capitalization rate. Using the land residual technique, what is the land value?