A landowner’s leased fee DCF contains ground rent for 40 years and a $3 million reversion at year 40. One 5% annual discount rate applies to both. How is the reversion treated?
Correct Answer
B) Discount the $3 million for 40 years and add it to the rent’s present value.
The landowner receives ground rent and the specified terminal reversion; this is a leased-fee DCF, not the tenant’s leasehold. At the single 5% discount rate, discount the $3 million terminal receipt for 40 years (÷1.05^40) and add it to the present value of the ground rents. A reversion is not excluded, is not treated as already present value, and is not capitalized as a perpetual annual payment.
Why This Is the Correct Answer
Option B is correct because the $3 million reversion is a single future payment received at year 40, so it is discounted for 40 years at 5% (÷ 1.05^40) and added to the present value of the ground rents. The leased fee interest includes both the right to receive the ground rent and the reversionary right at the end of the lease. Both benefits are discounted at the stated single rate.
Why the Other Options Are Wrong
Option A: Exclude it, because ground leases cannot have any reversion at all.
Option A says to exclude the reversion because ground leases cannot have any reversion, which is wrong. A leased fee includes the right to receive the property at the end of the lease term, so the reversion is a real benefit to the landowner.
Option C: Treat the year-40 amount as a present value today, with no discounting applied.
Option C treats the year-40 amount as a present value with no discounting, which overstates it greatly. A sum received 40 years from now is worth far less today and must be discounted.
Option D: Capitalize the reversion as if it were a perpetual annual rent payment.
Option D capitalizes the reversion as if it were a perpetual annual rent payment. The reversion is a single lump sum received once at year 40, not a recurring income stream, so it is discounted as a single payment.
Rent stream plus reversion
Leased fee value equals the present value of the rent stream plus the present value of the reversion.
How to use: Use this to structure any leased fee valuation.
Exam Tip
Treat a reversion as a single future payment: discount it for the full term with the present value of one factor.
Common Mistakes to Avoid
- -Omitting the reversion from a leased fee valuation
- -Adding the reversion at its future amount without discounting
- -Treating a lump-sum reversion as an annual income stream
Concept Deep Dive
Analysis
This question tests how a reversion is handled when valuing a leased fee under a ground lease. The landowner holds the right to receive rent and to get the property back at lease end. That year-40 lump sum is discounted for 40 years and added to the present value of the rent stream.
Background Knowledge
The leased fee is the lessor's interest: the right to contract rent plus the reversionary right when the lease ends. In valuing it, the rent stream is discounted as a series and the reversion as a single future payment.
Real-World Application
An appraiser values a parcel leased to a developer under a long-term ground lease. The analysis discounts the scheduled ground rents and the estimated value of the land at lease expiration to arrive at the leased fee value.
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 seven-year DCF forecasts operating income growing 3% annually and a terminal sale at the end of year 7. One 7.2% discount rate applies to every benefit. Which receipts in the seven-year model are discounted?
Next Question
Market vacancy for the area is 7%, but the subject has run 2% for a decade under long-term leases expiring in eight years. The vacancy allowance should reflect: