CHAPTER 8
Valuation Using the Income Approach
Test Problems
1. Which of the following expenses is not an operating expense?
d. Mortgage payment.
2. An overall capitalization rate (Ro) is divided into which type of income or cash flow
to obtain an indicated market value?
a. Net operating income (NOI).
3. Which of the following types of properties probably would not be appropriate for
income capitalization?
e. Public school.
4. Estimated capital expenditures
d. are subtracted to compute NOI in a below-line treatment.
5. An appraiser estimates that a property will produce NOI of $25,000 in perpetuity, yo
is 11 percent, and the constant annual growth rate in NOI is 2.0 percent. What is the
estimated property value?
a. $277,778.
6. If a comparable property sells for $1,200,000 and the effective gross income of the
property is $12,000 per month, the effective gross income multiplier (EGIM) is
b. 8.33
7. Which of the following statements regarding capitalization rates on commercial real
estate investments is the most correct?
b. Cap rates vary positively with the perceived risk of the investment.
8. The methodology of appraisal differs from that of investment analysis primarily
regarding
e. Point of view.
Use the following information to answer questions 9-10.
You have just completed the appraisal of an office building and have concluded that the
market value of the property is $2,500,000. You expect Potential Gross Income (PGI) in the
first year of operations to be $450,000; vacancy and collection losses to be 9 percent of PGI;
operating expenses to be 38 percent of Effective Gross Income (EGI), and capital
expenditures to be 4 percent of EGI.
9. What is the implied going-in capitalization rate?
10. What is the effective gross income multiplier (EGIM)?
Study Questions
1. Data for five comparable income properties that sold recently are shown below:
Property NOI Sale Price Overall Rate
A $ 57,800 $ 566,600 0.1020
B 49,200 496,900 0.0990
C 63,000 630,000 0.1000
D 56,000 538,500 0.1040
E 58,500 600,000 0.0975
What is the indicated overall rate (RO)?
Solution: The indicated overall cap rate of 10.05 percent is the simple average of the
2. Why is the market value of real estate determined partly by the lender’s requirements
and partly by the requirements of equity investors?
Solution: Real estate investments are frequently financed using a combination of
equity and mortgage debt. A real estate investment can be viewed as a joint
investment made by both the lender and equity investor, and therefore, both parties’
3. Assume a reserve for non-recurring capital expenditures is to be included in the pro
forma for the subject property. Explain how an above-line treatment of this
expenditure would differ from a below-line treatment.
Solution: In an above-line treatment, the reserve for non-recurring capital
expenditures would be taken out in the calculation of net operating income (i.e.,
4. Use the following property data:
Cash flow from operations:
Year 1 2 3 4 5
NOI $150,000 $150,000 $150,000 $150,000 $150,000
Debt Service $125,000 $125,000 $125,000 $125,000 $125,000
Cash Flow at sale:
Sale Price: $2,000,000
Cost of sale: $125,000
Mortgage balance: $1,500,000
a. Assuming the going-in capitalization rate is 8.00 percent, compute a value for the
property using direct capitalization.
b. Assuming the required yield/return on unlevered cash flows is 10 percent, and
that the property will be held by a buyer for five years, compute the value of the
property based on discounting unlevered cash flows.
Solution:
Sale Price: $2,000,000
c. Assuming the relevant required yield/return on levered cash flows is 15 percent,
and that the property will be held by a buyer for five years, what is the present
value of the levered cash flows?
Solution:
Year 1 2 3 4 5
NOI $150,000 $150,000 $150,000 $150,000 $150,000
Sale Price: $2,000,000
Net sale proceeds $1,875,000
Before-tax equity reversion $375,000
5. Given the following owner’s income and expense estimates for an apartment
property, formulate a reconstructed operating statement. The building consists of 10
units that could rent for $550 per month each.
Owner’s Annual Income Statement
Rental income (last year) $60,600
Less: Operating & capital expenses
Power $2,200
Heat 1,700
Janitor 4,600
Water 3,700
Maintenance 4,800
Reserve for capital expenditures 2,800
Management 3,000
Tax depreciation 5,000
Mortgage payments 6,300
Estimating vacancy and collection losses at 5 percent of potential gross income,
reconstruct the operating statement to obtain an estimate of NOI. Assume an
above-line treatment of CAPX. Remember, there may be items in the owner’s
statement that should not be included in the reconstructed operating statement. Using
the NOI and a Ro of 11.0 percent, calculate the property’s indicated market value.
Round your answer to the nearest $1,000.
Solution:
Reconstructed Operating Statement
PGI: (10 units x $550 x 12) $66,000
Less: Vacancy Loss (at 5 percent) (3,300)
EGI: 62,700
Less: Operating Expenses
Power $2,200
Heat 1,700
Note: Mortgage payments and depreciation are not included in the calculation of the
property’s NOI.
The indicated value of the property is $362,727 ($39,900 / 0.11), which rounds to
$363,000.
6. You have been asked to estimate the market value of an apartment complex that is
producing annual net operating income of $44,500. Four highly similar and
competitive apartment properties within two blocks of the subject property have sold
in the past three months. All four offer essentially the same amenities and services as
the subject. All were open-market transactions with similar terms of sale. All were
financed with 30-year fixed-rate mortgages using 70 percent debt and 30 percent
equity. The sale prices and estimated first-year net operating incomes were as
follows:
Comparable 1: Sale price $500,000; NOI $55,000
Comparable 2: Sale price $420,000; NOI $50,400
Comparable 3: Sale price $475,000; NOI $53,400
Comparable 4: Sale price $600,000; NOI $69,000
What is the indicated value of the subject property using direct capitalization?
Solution:
The abstracted going-in capitalization rates from the four properties are listed below:
Comparable 1: 0.110
Comparable 2: 0.120
The simple average of the four comparable cap rates is 0.114. Thus, the indicated
7. You are estimating the value of a small office building. Suppose the estimated NOI
for the first year of operations is $100,000.
a. If you expect that NOI will remain constant at $100,000 over the next 50 years and
that the office building will have no value at the end of 50 years, what is the present
value of the building assuming a 12.2% discount rate? If you pay this amount, what
is the indicated initial cap rate?
Solution: The present value, using a financial calculator, is $817,078.
The initial (going-in) cap rate is $100,000/$817,078 = 12.24%
b. If you expect that NOI will remain constant at $100,000 forever, what is the value
of the building assuming a 12.2% discount rate? If you pay this amount, what is the
indicated initial cap rate?
Solution: The value of the building with NOI remaining constant at $100,000 is
calculated using the formula for a perpetuity, which is $100,000/0.122, or $819,672.
c. If you expect the initial $100,000 NOI will grow forever at a 3% annual rate, what
is the value of the building assuming a 12.2% discount rate? If you pay this amount,
what is the indicated initial cap rate?
Solution: The capitalization rate consists of a required IRR on equity and a growth
rate. Applying the general constant-growth formula and assuming that the growth
8. Describe the conditions under which the use of effective gross income multipliers to
value the subject property is appropriate.
Solution: The use of gross income multipliers is predicated on two primary
assumptions. First, it is assumed that the operating expense percentage of the subject
9. In what situations or for which types of properties might discounted cash flow
analysis be preferred to direct capitalization?
Solution: Direct capitalization is dependent on information obtained from sales of
properties that are deemed to be comparable to the subject property. Identifying
comparable properties is particularly difficult with commercial real estate
10. What is the difference between a fee simple estate and a leased fee estate?
Solution: A fee simple estate is the highest form of property ownership. It is complete
ownership of a property without regard to leases. A leased fee estate is ownership of a
11. What is the difference between contract rent and market rent? Why is this distinction
more important for investors purchasing existing office buildings than for investors
purchasing existing apartment complexes?
Solution: Contract rent refers to the actual rent paid under existing lease contracts
executed between owners and tenants. Market rent refers to the potential rental
income a property could receive on the open market as of the effective date of an
12. Estimate the market value of the following small office building. The property has
10,500 square feet of leasable space that was leased to a single tenant on January 1,
four years ago. Terms of the lease call for rent payments of $9,525 per month for the
first five years, and rent payments of $11,325 per month for the next five years. The
tenant must pay all operating expenses.
During the remaining term of the lease, there will be no vacancy and collection
losses; however, upon termination of the lease it is expected that the property will be
vacant for three months. When the property is released under short-term leases, with
tenants paying all operating expenses, a vacancy and collection loss allowance of 8
percent per year is anticipated.
The current market rental for properties of this type under triple net leases is $11 per
square foot, and this rate has been increasing at a rate of 3 percent per year. The
market discount rate for similar properties is about 11 percent, the “going-in” cap rate
is about 9 percent, and terminal cap rates are typically 1 percentage point above
going-in cap rates.
Prepare a spreadsheet showing the rental income, expense reimbursements, NOIs, and
the net proceeds from the sale of the property at the end of an 8-year holding period.
Then use the information provided to estimate the market value of the property.
Solution: The fifth year of the 10-year lease is the first year of analysis. The problem
calls for an 8-year analysis–one for the last year of the 1st 5-year period, five for the
second 5-year period, one to allow the vacancy and collection loss to achieve a
Yr. 1 Yr. 2 Yr. 3 Yr. 4 Yr. 5 Yr. 6 Yr. 7 Yr. 8 Yr. 9
Contract Rent 114,300 135,900 135,90
0
135,90
0
135,900 135,90
0
Market Rent 115,500 118,965 122,534 126,21
0
129,996 133,89
6
137,913 142,05
0
146,311
0
0
0
6
Sale price at the end of Yr. 8: = [NOI (yr9) / Terminal cap rate]
Cash Flows: CF1 = 114,300
CF2 = 135,900
CF3 = 135,900
PV of Cash Flows @ 11 percent = $1,246,090