第五次作业答案

第五次作业答案

第五次作业答案1.

a) In an M&M frictionless environment, where there are no taxes and contracts are costless to

make and enforce, the wealth of the shareholders is the same no matter what capital structure the firm adopts. In such anenvironment, neither the stock price nor shareholders' wealth would be affected. In the real world Divido's management mightbe able to create shareholder value by issuing debt and repurchasing shares in two ways:

- By reducing corporate taxes

- By reducing the free cash flow available to management and exposing itself to greater

market discipline.

b) The formula for EPS without debt is

000

,000,1equity

all EBIT EPS

=

If we assume the interest rate is 6% (conclusions will not change if you assume different interest rates), then the interestpayments will be $1.2 million per year (2.106.020=?) regardless the realised value of EBIT. The number of sharesoutstanding after exchanging debt for equity will be 800,000. EPS with debt is therefore

000

,8002.1debt

-=

EBIT EPSThe probability distribution of Divido's EBIT and EPS is as follows:

Although the shares of stock become riskier with debt financing, the expected earnings per share go up. In a frictionlessfinancial environment, the net effect is to leave the price of stock unchanged.

2.

a) The unlevered free cash flow for the Tango Shoes Division would be (in millions):

Sales: $10 Variable Costs $5.5 Depreciation: $1

Profit before Tax: $3.5 Taxes (@40%) $1.4 After-tax Profit: $2.1

Depreciation: $1 Investment: $1

Free Cash Flow:

$2.1 million

If unlevered, Tango is worth: 125.13$16

.01.2= million

b) If Tango issued $5 million debt, its total value would be:

125.1554.0125.13=?+=+=B V V c U L τTango equity: $10.125 million

c) The weighted average cost of capital (WACC) is given by (Bodie and Merton, p436)

125.151.2=WACC

125

.151.2=

WACC

And ()E

D D r E

D E r WACC D

c E +-++=τ1

()125

.155

10.04.01125

.15125.10125

.151.2?

-++

=E r ? %78.17=E r

(Alternatively, you can use equation 16.1 of Bodie and Merton, p435)

d) The expected net income is: ()8.1$510.06.01.2=??- million

The value of equity: 125.10$%

78.178.1= million

3.

a) Current price per share:

25.26$5

.0125.13=

b) Amount to borrow: 40% of $13.125 million = $5.25 million

PV of tax shield: 1.2$25.54.0=? million Value of levered firm: 13.125 + 2.1 = $12.225 million Value of equity: 15.225 - 5.25 =$9.975 million The number of shares repurchased:

2.025

.2625.5= million

c) Foxtron's management must trade off the tax saving due to additional debt financing against

the costs of financial distress that rise with the degree of debt financing. 4．

The valuation process involves four steps:

Step 1: Calculating the present value of unlevered cash flows for 1989-93. The unlevered cash flows for 1989-93 are shownin the last line of Table 1.

T ABLE 1. RJR Operating Cash Flows (in $millions)1989 1990 1991 1992 1993 Operating income

$2,620 $3,410 $3,645 $3,950 $4,310 Tax on operating income 891 1,142 1,222 1,326 1,448 After-tax operating income1,729 2,268 2,423 2,624 2,862 Add back depreciation 449 475 475 475 475 Less capital expenditures 522 512 525 538 551Less change in working capital (203) (275) 200 225 250 Add proceeds from asset sales 3,545 1,805 Unlevered cash flow(UCF)

$5,404

$4,311

$2,173

$2,336

$2,536

说明：这⾥给的是根据原始⽂献中的数据的计算结果。在原始⽂献中的“Change in working capital ”⼀项与作业中给出的值的符号是相反的。这是编辑此道题时出现的错误之⼀，在此表⽰歉意。These flows are discounted by the required asset return,r 0,which is 14 percent. The value as of the end of 1988 of theunlevered cash flows expected from 1989 through 1993 is

billion 224.12$14

.1536.214

.1336.214

.1173.214

.1311.414

.1404.55

4

3

2

=+

+

+

+

Step 2: Calculating the present value of the unlevered cash flows beyond 1993(i.e. unlevered terminal value) .

With the indications given in Table 4.3, it ’s easy to calculate the value, as of the end of 1993, which is:

b i l l i o n

746.23$03

.014.0)

03.1(536.2=- This translates to a 1988 value of

b i l l i o n

333.12$14

.1746.235

= Therefore, the total unlevered value of the firm is ($12.224+$12.333=) $24.557 billion. To calculate the total buyout value,we must add the interest tax shields expected to be realized by debt financing.Step 3: Calculating the present value of interest tax shields for 1989-93. It ’s easy to calculate interest tax shields for 1989-93according to Table 4.2:

T ABLE 2. T ax Shields for 1989-93 (in $millions)

The discounted value of these tax shields is :

b i l l i o n

877.3$135

.1184.1135

.1120.1135

.1058.1135

.1021.1135

.1151.15

4

3

2

=+

+

+

+

Step 4: Calculating the present value of interest tax shields beyond 1993.

Finally, we must calculate the value of tax shields associated with debt used to finance the operations of the company after1993. Since it ’s assumed that debt will be maintained at 25 percent of the value of the firm after 1993, it is appropriate to usethe W ACC method to calculate a terminal value for the firm at the target capital structure. This in turn can be decomposedinto an all-equity value and a value from tax shields. First, we can calculate its W ACC, which is: