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Q2. Assume you are considering investing in an apartment building with the following estimated financial characteristics:ffice ffice" />
- Net operating income (NOI) = $64,000.
- Net operating income growth rate = 4% per year.
- Tax depreciation = $25,000 per year.
- Annual interest expense = $32,000.
- Annual debt service expense = $35,000.
- Equity investors marginal income tax rate = 36%.
- Investment horizon = 2 years.
- Net purchase price = $500,000.
- Equity investment = 30%.
- Gross sale price = $650,000.
- Cost of sale = $50,000.
- Outstanding mortgage balance at time of sale = $385,000.
- The tax rate on recaptured depreciation = 28%.
- Long-term capital gains tax rate = 20%.
- Required after tax return on equity = 6%.
The net present value (NPV) and internal rate of return (IRR) for this investment are closest to:
NPV IRR
A) $61,095 27%
B) $51,977 19%
C) $99,994 47%
Correct answer is A)
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Taxes Payable Computation: |
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Year-1 |
Year-2 |
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NOI (g = 4%) |
$64,000 |
$66,560 |
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Less depreciation |
(25,000) |
(25,000) |
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Less interest |
(32,000) |
(32,000) |
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Taxable income |
7,000 |
9,560 |
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times tax rate |
0.36 |
0.36 |
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Income taxes payable |
$2,520 |
$3,442 |
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Cash flow after taxes (CFAT) Computation: |
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Year-1 |
Year-2 |
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NOI (g = 4%) |
$64,000 |
$66,560 |
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Less debt service |
(35,000) |
(35,000) |
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Before tax cash flow |
$29,000 |
$31,560 |
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Less taxes payable |
(2,520) |
(3,442) |
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CFAT |
$26,480 |
$28,118 |
Equity reversion after taxes (ERAT) = net selling price – mortgage balance – taxes.
First, compute taxes.
Recaptured depreciation = 2 × $25,000 = $50,000
Tax on recaptured depreciation = $50,000 × 0.28 = $14,000
Total gain on sale = net selling price – adjusted basis
Net selling price = sales price – cost of sale = $650,000 ? 50,000 = $600,000
Adjusted basis = cost - accumulated depreciation = $500,000 ? 50,000 = $450,000
Total gain = $600,000 ? 450,000 = $150,000.
Long-term capital gain tax = capital gains tax rate x (total gain - recaptured depreciation)
= 0.20 × (150,000 ? 50,000) = 0.20 × 100,000 = $20,000
Total taxes payable = tax on recaptured depreciation + long-term capital gains tax
= $14,000 + $20,000 = $34,000
ERAT = net selling price – mortgage balance – taxes.
= 600,000 ? 385,000 ? 34,000 = $181,000
Relevant Cash Flows
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Year |
0 |
1 |
2 |
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EI* |
-$150,000 |
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CFATt |
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$26,480 |
$28,118 |
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ERAT |
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$181,000 |
*Equity investment = 0.30 × 500,000 = $150,000
Using your TI BAII Plus:
[CF] [2nd] [CLR WORK]
-150,000 [+/–] [ENTER] [↓ ]
26,480 [ENTER] [↓] [↓]
209,118 [Enter] (Note: CF2 = 28,118 + 181,000)
[NPV] {6} [ENTER] [↓]
[CPT] = $61,095.41
[IRR] [CPT] = 27.23%
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发表于 2009-3-10 10:17
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