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 an environment, neither the stock price nor shareholders' wealth would be affected. In the real world Divido's management might be 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 interest payments will be $1.2 million per year (2.106.020=⨯) regardless the realised value of EBIT. The number of shares outstanding after exchanging debt for equity will be 800,000. EPS with debt is therefore

000

,8002.1debt

-=

EBIT EPS

The 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 frictionless financial 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 τ

Tango 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