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Reading 45: Investment Analysis-LOS c 习题精选

Session 13: Alternative Asset Valuation
Reading 45: Investment Analysis

LOS c: Calculate the after-tax cash flow and the after-tax equity reversion from real estate properties.

 

 

 

Assume you are considering investing in an apartment building with the following estimated financial characteristics:

  • Net operating income (NOI) = $60,000.
  • Net operating income growth rate = 5% per year.
  • Tax depreciation = $10,000 per year.
  • Annual interest expense = $9,000.
  • Annual debt service expense = $12,000.
  • Equity investors marginal income tax rate = 36%.
  • Investment horizon = four years.

The year-2 and year-3 cash flow after taxes is closest to:

A)
CFAT2 = $31,600 and CFAT3 = $33,400.
B)
CFAT2 = $33,240 and CFAT3 = $37,176.
C)
CFAT2 = $35,160 and CFAT3 = $37,176.



 

Taxes Payable Computation:

 

 

 

 

 

Year-1

Year-2

Year-3

Year-4

NOI (g = 5%)

$60,000

$63,000

$66,150

$69,458

Less depreciation

(10,000)

(10,000)

(10,000)

(10,000)

Less interest

(9,000)

(9,000)

(9,000)

(9,000)

Taxable income

41,000

44,000

47,150

50,458

times tax rate

′0.36

′0.36

′0.36

′0.36

Income taxes payable

$14,760

$15,840

$16,974

$18,165

 

 

 

 

 

CFATt Computation:

 

 

 

 

 

Year-1

Year-2

Year-3

Year-3

NOI (g = 5%)

$60,000

$63,000

$66,150

$69,458

Less debt service

(12,000)

(12,000)

(12,000)

(12,000)

Before tax cash flow

$48,000

$51,000

$54,150

$57,458

Less taxes payable

(14,760)

(15,840)

(16,974)

(18,165)

CFAT

$33,240

$35,160

$37,176

$39,293

Assume you are considering investing in an apartment building with the following estimated financial characteristics:

  • 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)

$51,977

19%

B)

$61,095

27%

C)

$99,994

47%




Taxes Payable Computation:

 

Year-1

Year-2

NOI (g = 4%)

$64,000

$66,560

Less depreciation

(25,000)

(25,000)

Less interest

(32,000)

(32,000)

Taxable income

7,000

9,560

times tax rate

0.36

0.36

Income taxes payable

$2,520

$3,442

 

 

 

Cash flow after taxes (CFAT) Computation:

 

Year-1

Year-2

NOI (g = 4%)

$64,000

$66,560

Less debt service

(35,000)

(35,000)

Before tax cash flow

$29,000

$31,560

Less taxes payable

(2,520)

(3,442)

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

Year

0

1

2

EI*

-$150,000

CFATt

 

$26,480

$28,118

ERAT

$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%

TOP

Suppose you are evaluating an investment opportunity in an office building for which you have estimated the following financial characteristics:

  • First year net operating income (NOI) = $75,000.
  • Growth rate in net operating income = 5% per year.
  • Tax depreciation = $10,000 per year.
  • Annual interest expense = $9,000.
  • Annual total debt service expense = $12,000.
  • Equity investors marginal income tax rate = 36%.
  • Investment horizon = four years.

The cash flows after taxes for years one and four are closest to:

A)
CFAT1 = $51,480 and CFAT4 = $50,766.
B)
CFAT1 = $42,840 and CFAT4 = $50,406.
C)
CFAT = $42,840 and CFAT4 = $47,760.



Taxes Payable Computation:

 

 

 

 

 

Year-1

Year-2

Year-3

Year-4

NOI (g = 5%)

$75,000

$78,750

$82,688

$86,822

Less depreciation

(10,000)

(10,000)

(10,000)

(10,000)

Less interest

(9,000)

(9,000)

(9,000)

(9,000)

Taxable income

$56,000

$59,750

$63,688

$67,822

times tax rate

′0.36

′0.36

′0.36

′0.36

Income taxes payable

$20,160

$21,510

$22,928

$24,416

 

 

 

 

 

CFATt Computation:

 

 

 

 

 

Year-1

Year-2

Year-3

Year-3

NOI (g = 5%)

$75,000

$78,750

$82,688

$86,822

Less debt service

(12,000)

(12,000)

(12,000)

(12,000)

Before tax cash flow

$63,000

$66,750

$70,688

$74,822

Less taxes payable

(20,160)

(21,510)

(22,928)

(24,416)

CFAT

$42,840

$45,240

$47,760

$50,406

TOP

A property was purchased for $550,000 and sold after six years for $850,000. Costs associated with the sale were $65,000 and the tax depreciation in each year was $20,000. At the time of the sale, $320,000 remained outstanding on the mortgage. The tax rate on recaptured depreciation is 28% and the long-term capital gains tax rate is 20%. The equity reversion after taxes for this property is closest to:

A)
$384,400.
B)
$365,600.
C)
$449,400.



Equity reversion after taxes (ERAT) = net selling price – mortgage balance – taxes.

First, compute taxes.

Recaptured depreciation = 6 × $20,000 = $120,000

Tax on recaptured depreciation = $120,000 ′ 0.28 = $33,600

Total gain on sale = net selling price – adjusted basis

Net selling price = sales price – cost of sale= $850,000 - 65,000 = $785,000

Adjusted basis = cost - accumulated depreciation = $550,000 - 120,000 = $430,000

Total gain = $785,000 - 430,000 = $355,000.

long-term capital gains tax

= capital gains tax rate × (total gain - recaptured depreciation) = 0.20 × (355,000 – 120,000) = 0.20 × 235,000 = $47,000

Total taxes payable

= tax on recaptured depreciation + tax on long-term capital gains = $33,600 + $47,000 = $80,600

ERAT = net selling price – mortgage balance – taxes = 785,000 - 320,000 - 80,600 = $384,400

TOP

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