An appraiser is valuing a newly built retail building that cost $1,100,000 to construct and is in lease-up. There is no cash flow in year 1. NOI is projected at $100,000 at the end of year 2 and $120,000 at the end of year 3, when net sale proceeds of $1,500,000 are also expected. The discount rate is 10%. What is the present value of these benefits?
Correct Answer
B) $1,299,775
Discount each amount from its own date: $100,000 ÷ 1.10^2 = $82,645 and $1,620,000 ÷ 1.10^3 = $1,217,130, for a total of $1,299,775. Dropping the year 2 income gives $1,217,130. Adding the NOI at face value and discounting the sale alone gives $1,346,972. Ignoring the empty first year, so that each amount moves one year earlier, gives $1,429,752. Construction cost is a past outlay, not a future benefit.
Why This Is the Correct Answer
Option B is correct because each amount is discounted from its actual date: $100,000 ÷ 1.10^2 = $82,645 and $1,620,000 ÷ 1.10^3 = $1,217,130. Their sum is $1,299,775.
Why the Other Options Are Wrong
Option A: $1,217,130
Option A, $1,217,130, counts year 3 alone: $1,620,000 ÷ 1.10^3 = $1,217,130. The year 2 NOI adds $82,645 of present value, for $1,299,775.
Option C: $1,346,972
Option C, $1,346,972, leaves the NOI at face value: $220,000 + $1,500,000 ÷ 1.10^3 = $1,346,972. Income received later is also worth less today, so the total is $1,299,775.
Option D: $1,429,752
Option D, $1,429,752, treats the first receipt as arriving in year 1: $100,000 ÷ 1.10 + $1,620,000 ÷ 1.10^2 = $1,429,752. With year 1 empty, the factors are for years 2 and 3, giving $1,299,775.
Date each dollar
Write a timeline with one line per year, including empty years. Each amount takes the factor for its own year.
How to use: Use a timeline whenever cash flows are uneven or begin after year 1.
Exam Tip
Treat a zero year as a real period on the timeline. It changes the exponent on later cash flows even though it adds no dollars.
Common Mistakes to Avoid
- -Skipping an empty year when counting periods
- -Adding undiscounted income to a discounted reversion
- -Leaving out one of the receipts in the final year
Concept Deep Dive
Analysis
Annuity shortcuts do not fit because the amounts differ and year 1 is empty. Each cash flow gets its own present value factor based on when it arrives. The empty year matters because it pushes later receipts further from today. The construction cost has already been spent and is not part of the future benefits.
Background Knowledge
The present value of variable cash flows is the sum of their individual present values, and this is the basis of discounted cash flow analysis. Yield capitalization accounts for the size, shape and duration of the income stream, which direct capitalization does not show explicitly.
Real-World Application
An appraiser values a just-completed building that will not produce net income until its second year. A DCF with an explicit lease-up period shows the delay, which a single-year capitalization would not reveal.
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 tells an appraiser that fourplexes in the market area are selling at 12.5 times NOI. A lender’s survey of the same market reports a 7.5% overall rate. What overall rate does the broker’s figure represent, and how does its value indication compare with that of the lender’s rate?
Next Question
The model applies loss to base rent only. Tenant reimbursements are separately forecast at already-effective collectible amounts; gross operating expenses include the reimbursed costs. How are recoveries included in EGI?