CHAPTER 20
Income Taxation and Value
Test Problems
1. Taxable income from the rental of actively managed depreciable real estate is
classified as:
2. Under current federal income tax law, what is the shortest cost recovery period
available to investors purchasing commercial rental property?
3. If an investor is a “dealer” with respect to certain real estate, that real estate is
classified (by the IRS) as being held:
4. When a property is sold for less than its adjusted basis, its depreciation (wear and
tear) was:
5. For tax purposes, a substantial real property improvement (CAPX) made after the
initial purchase is:
6. What percent of the income from residential rental property must be derived from
the leasing of units occupied by tenants as housing in order for the entire
depreciable basis to be depreciated using a 27 ½ year cost recovery period?
7. In 2012 you purchased a small office building for $450,000, which you financed
with a $337,500 fixed-rate, 25 year mortgage. Up-front financing costs totaled
$6,750. How much of this upfront financing expense could be written off against
ordinary income in 2012?
8. If the investor is in the 33% income tax bracket, how much will a tax credit of
$2,000 save the investor in taxes?
9. Which of the following best describes the taxation of gain and losses from the sale
of Section 1231 assets?
10. Which of the following statements is false?
d. Net passive activity losses can be used to offset dividend income from a real
Study Questions
1. Why do investors generally care whether the IRS classifies cash expenditures as
operating expenses rather than capital expenditures?
Solution: Operating expenses are generally deductible for income tax purposes in
the year they are paid. Capital expenditures are added to the tax basis of a
2. How are the discount points associated with financing an income property
handled for tax purposes?
Solution: All up-front financing costs are amortized over the life of the loan used
to finance the purchase. If the loan is prepaid before the end the loan term, the
3. What will be the taxes due on sale? Assume 6% selling costs, 33% percent
ordinary income tax rate, a 15 percent capital gains tax rate, and a 25 percent
recapture rate.
Solution:
Annual depreciation deduction = $750,000 x (1/27.5) = $27,272.73
Sale Price $1,270,000
Net Sale Proceeds 1,193,800
Taxable Gain 330,164
Capital Gain 193,800
Taxes Due on Sale $63,161
4. What will be the after-tax equity reversion (cash flow) from the sale?
Solution:
Net Sale Proceeds $1,193,800
Before-Tax Equity Reversion 555,665
After-Tax Equity Reversion $492,504
*(N=25*12, I=7/12, PV=-700,000, and FV=0) results in a monthly payment of
$4,947.45 and a yearly payment of $59,369 ($4,947.45 x 12). The remaining loan
5. Over the entire five-year holding period, how much were your taxes from rental
operations reduced by the annual depreciation deductions? Ignore the increased
taxes due on sale.
Solution: The amount of taxes saved from the annual tax depreciation is the total
6. What are the four classifications of real estate holdings for tax purposes? Which
classifications of property can be depreciated for tax purposes?
Solution: The four classes of real estate holdings for tax purposes are (1) real
estate held as a personal residence; (2) real estate held for sale to others, or dealer
7. What is your annual depreciation deduction? Ignore the mid-month convention.
Solution: The annual depreciation deduction is $36,364.64 (adjusted basis of
8. If you never sold the property, what would be the present value of the annual tax
savings from depreciation?
Solution: The present value of the annual tax savings from depreciation is
9. If you sold the property at the end of five years, what would be the present value
of the depreciation deductions, net of all taxes due on sale?
Solution:
After-tax value of annual depreciation deduction = $36,364.64 x 0.28 = $10,182
Total depreciation over 5 years = 5 x $36,364.64 = $181,823
Depreciation recapture tax at end of year 5 = $181,823 x 0.25 = $45,456
The NPV of the depreciation deductions over 5-year holding period is $9,339
10. Black Acres Apartment, Inc needs to compute taxable income (TI) for the
preceding year and wants your assistance. The effective gross income (EGI) was
$52,000; operating expenses were $19,000; $2,000 was put into a fund for future
replacement of stoves and refrigerators; debt service was $26,662, of which
$25,126 was interest; and the deprecation deduction was $17,000. Compute the
taxable income from operations:
Solution:
Effective Gross Income $52,000
Less: Operating Expenses (19,000)
Net Operating Income 31,000
Add: CAPX 2,000
Taxable Income (Loss) $(9,126)
11. You are considering the purchase of a small apartment complex.
a. Calculate the mortgage payment, the interest deduction, the depreciation
deduction, and the amortized financing costs for the first year of
operations.
b. What will be your net equity investment at “time zero”?
c. Estimate the after-tax cash flow from the first year of operations.
Solution:
a. Annual mortgage payment: $65,575 (N=25, I=8, PV=-700,000, and FV=0)
Interest Deduction in year 1 = 0.08 x $700,000 = $56,000
b. The net equity investment at time zero is $325,000 (Down payment of
c. The after-tax cash flow is calculated below:
Tax Calculations
Gross Potential Income $175,000
Effective Gross Income 154,000
Less: Operating Expenses (36,000)
Net Operating Income 116,000
Add: Capital Expenditures 2,000
Taxable Income 33,727
x 35%
Cash Calculations
Net Operating Income 116,000
Before Tax Cash Flow 50,425
After-tax Cash flow 38,620
12. Compute the after-tax cash flow from the sale of the following nonresidential
property.
a. Compute the annual depreciation expense.
b. Compute the adjusted basis at the time of sale (after two years).
c. Compute the tax liability from sale.
d. Compute the after-tax cash flow (equity reversion) from sale.
Solution:
a. Annual depreciation expense: $9,807.69 (Depreciable Basis =
0.85 x
b. Total depreciation over 2-year holding period = 2 x $9,807.69 = $19,615
Adjusted basis at the time of sale: $460,385 ($450,000 acquisition price,
c. Computation of Tax Liability:
The book says the market value of the property increased to $472,500 over
the two year holding period and that selling costs at that time will be 6
Selling Price $510,000
Net Sale Proceeds 494,700
Taxable Gain 34,315
Capital Gain 14,700
Capital Gain Tax @ 15% 2,205
Total Taxes $7,109
d. After-tax cash flow:
Net Sale Proceeds $494,700
Before-Tax Equity Reversion 140,424
After-tax Equity Reversion $133,315
13. A real estate investor is considering the purchase of a small office building. The
following assumptions are made:
Answer the following questions for the first year of operations:
e. What is the equity (cash) down payment required at “time zero”?
f. What is the annual tax depreciation deduction?
g. What is the total debt service in year 1?
h. What is the estimated net operating income?
Solution:
a. The equity (cash) down payment required at “time zero” is $193,750 (0.25
b. The annual tax depreciation deduction is $14,904 (Depreciable basis of
c. The amount of the debt service is 4,682.51 per month, or 56,190 per year.
d. The estimated net operating income is $148,950.
Less: Vacancy and Collection Losses (51,000)
Effective Gross Income 289,000
Net Operating Income $148,950
14. Compute the after-tax cash flows and after-tax equity reversion for the holding
period.
Solution:
Year 1 Year 2 Year 3 Year 4 Year 5
PGI $50,000 $52,500 $55,125 $57,881 $60,775
EGI 50,000 52,500 55,125 57,881 60,775
Less: Operating Expenses (10,000) (10,500) (11,025) (11,576) (12,155)
Net Operating Income 40,000 42,000 44,100 46,305 48,620
Add: Capital Expenditures 0 0 0 0 0
Less: Interest (24,929) (24,310) (23,646) (22,934) (22,171)
Taxable Income 4,723 7,342 10,106 13,023 8,002
Net Operating Income 40,000 42,000 44,100 46,305 48,620
Before-Tax Cash Flow 6,507 8,507 10,607 12,812 15,127
After-tax Cash Flow $5,090 $6,305 $7,575 $8,905 $12,727
* includes amortization of remaining up-front financing costs
15. Assuming a two-year holding period, should the investor make this investment
given a required levered, after-tax, rate of return of 14 percent?
Solution: The after- tax cash flows are calculated below:
Year 1 Year 2 Year 3
PGI $105,100 $113,508 $122,589
EGI 97,700 105,562 114,007
Net Operating Income 46,170 51,971 58,273
Less: Depreciation (10,897) (10,897)
Taxable Income 5,272 11,339
Net Operating Income 46,170 51,971
Before-Tax Cash Flow 12,903 18,661
After-Tax Cash Flow $11,383 $15,486
Selling Price ( 58,273/0.10 Cap Rate) $582,730
Net Sale Proceeds 541,939
Taxable Gain 63,734
Capital Gain 41,939
Taxes Due on Sale $11,740
Before-Tax Equity Reversion 173,824
After-tax Equity Reversion $162,085
The cash flow stream is as follows:
Year
After-Tax
Cash Flows
After-Tax Equity
Reversion
Total Cash
Flow
0 (125,000) (125,000)
These cash flows are discounted at the levered, after-tax, required rate of