The subject property is a four-unit apartment building. This year the owner paid an $8,100 premium for a three-year property insurance policy and no other insurance. Effective gross income is $48,000, and expenses other than insurance, including property taxes, are $18,000. Sales of similar properties indicate an 8% overall rate. What is the indicated value by direct capitalization?
Correct Answer
C) $341,250
Direct capitalization converts one year of income, so a three-year premium is annualized: $8,100 ÷ 3 = $2,700. NOI = $48,000 − $18,000 − $2,700 = $27,300, and $27,300 ÷ 0.08 = $341,250. Deducting the full premium gives $273,750, deducting the $5,400 prepaid balance gives $307,500, and leaving insurance out of NOI and then subtracting the $2,700 annual cost from value gives $372,300.
Why This Is the Correct Answer
Option C is correct because direct capitalization needs one year's cost, and $8,100 ÷ 3 = $2,700. NOI is $48,000 − $18,000 − $2,700 = $27,300, and $27,300 ÷ 0.08 = $341,250. The method spreads a cost over the years it covers even though the cash went out at once.
Why the Other Options Are Wrong
Option A: $273,750
Option A, $273,750, deducts the whole $8,100 in one year: ($48,000 − $18,000 − $8,100) ÷ 0.08 = $273,750. Capitalizing it that way assumes a three-year premium is paid each year; the annual cost is $2,700 and the value is $341,250.
Option B: $307,500
Option B, $307,500, deducts the $5,400 unexpired balance: ($48,000 − $18,000 − $5,400) ÷ 0.08 = $307,500. That balance is an accounting prepaid amount, not an annual cost; the annual cost of $2,700 gives $341,250.
Option D: $372,300
Option D, $372,300, leaves insurance out of NOI and then subtracts the annual cost from value: ($48,000 − $18,000) ÷ 0.08 − $2,700 = $372,300. Insurance is a continuing operating cost, so $2,700 a year comes out of NOI before capitalizing, giving $341,250.
One-year rate, one-year cost
A one-year income figure needs one-year costs. Divide a multi-year bill by the years it covers.
How to use: Use this when a statement shows a cost that pays for more than one year.
Exam Tip
Check whether the model is direct capitalization or discounted cash flow before treating an irregular cost. Direct capitalization annualizes; discounted cash flow generally records it when paid.
Common Mistakes to Avoid
- -Capitalizing a multi-year premium as a single year's expense
- -Using the unexpired prepaid balance as the annual cost
- -Subtracting an annual expense from value instead of from NOI
Concept Deep Dive
Analysis
The issue is matching the timing of a cost to the single year being capitalized. Cash paid this year covers three years, so the statement overstates this year's cost and understates the next two. Convert the premium to its annual cost, then process income as usual.
Background Knowledge
Direct capitalization values a property from a single year's income, so irregular expenses are annualized even if they are not paid annually. Discounted cash flow analysis treats timing differently, deducting the expenditure in the year it is forecast to occur. Knowing which model you are using tells you how to treat the cost.
Real-World Application
A small apartment building's statement shows insurance jumping this year and nothing the prior two years. The appraiser sees a three-year policy on the declaration page and deducts one-third of the premium in the stabilized statement.
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 five-year lease has face rent of $24 per square foot per year and six total free months. Ignoring discounting and other concessions, what is average annual rent per square foot over all 60 months, to two decimal places?
Next Question
The subject office building has annual potential base rent of $480,000. Tenants also pay the landlord potential expense reimbursements of $120,000 a year, which are not included in the base rent, and pay nothing directly to third-party suppliers. Combined vacancy and collection loss is 8% of both the rent and the reimbursements. What is the annual EGI?