Assuming that there is an unlevered firm and a levered firm. The basic information is given by the following table. Table1: Information of the firms Unlevered firmLevered firmEBIT1000010000Interest03200Taxable income  Tax (tax rate: 34%)  Net income  CFFA   Assuming that cost of debt =8%; unlevered cost of capital =10%; systematic risk of the asset is 1.5Fill in the blanksWhat is the present value of the tax shield?

Question
Asked Nov 26, 2019
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Assuming that there is an unlevered firm and a levered firm. The basic information is given by the following table.

 

Table1: Information of the firms

 

Unlevered firm

Levered firm

EBIT

10000

10000

Interest

0

3200

Taxable income

 

 

Tax (tax rate: 34%)

 

 

Net income

 

 

CFFA

 

 

 

Assuming that cost of debt =8%; unlevered cost of capital =10%; systematic risk of the asset is 1.5

  • Fill in the blanks
  • What is the present value of the tax shield?
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Expert Answer

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Step 1

The required values are mentioned in below table:

Unlevered firm
Levered firm
$10,000
$0
EBIT (A)
$10,000
$3,200
Interest (B)
Taxable income (C) = (A) - (B)
Tax (D) (C) x 34%
Net income (C)-(D).
$10,000
$3,400
$6,600
$0
$6,800
$2,312
$4,488
-$3,200
CFFA
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Unlevered firm Levered firm $10,000 $0 EBIT (A) $10,000 $3,200 Interest (B) Taxable income (C) = (A) - (B) Tax (D) (C) x 34% Net income (C)-(D). $10,000 $3,400 $6,600 $0 $6,800 $2,312 $4,488 -$3,200 CFFA

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Step 2

Unlevered firm will have zero tax shield as no interest on debt is paid.

In order to calculate the present value of tax shield, cost of capital should be known. Assume the weights for equity and debt is 50:50.

The cost of capital is calculated below:

Cost of equity x Equity percentage
+(Cost of debtx Debt percentage x (1-Tax rate)
Cost of capital
=[10%x 50%+8%x 50% x (1-34%)
= 5%+ 4% x 66%
= 5%+2.64%
= 7.64%
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Cost of equity x Equity percentage +(Cost of debtx Debt percentage x (1-Tax rate) Cost of capital =[10%x 50%+8%x 50% x (1-34%) = 5%+ 4% x 66% = 5%+2.64% = 7.64%

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Step 3

The present value of tax shiel...

Interest on debtx Tax rate
Present value of tax shield
(1+i)
$3,200 x 34%
(1+7.649%)
$1,088
1.0764
$1,010.78
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Interest on debtx Tax rate Present value of tax shield (1+i) $3,200 x 34% (1+7.649%) $1,088 1.0764 $1,010.78

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