Question

Firm A has 1000 shares of stock

It has a Flat perpetual cash flow of $800 equal to annual EBIT

As an unlevered firm it has no debt and an unlevered beta of .8

Rf = 5% and market risk premium = 5%

Assume a 25% tax rate

a)     What is the firm’s unlevered stock currently worth per share

b)    The manager has vowed to never issue equity. But now, he is convinced to do the following. Assume the firm issues sufficient perpetual debt to repurchase stock with the end result being 20% debt and 80% equity financing of the total firm market value. If the debt is risk free with a required 5% return and the firm says it will keep the debt as is without adjustments forever and the market believes it:

i.               What is the new cost of equity? What is the new WACC

ii.              What is the new value of the firm (Debt + Equity)? What is the value of equity?

iii.       What is the new share price of the firm?

iv.            What is the number of shares repurchased? (hint: figure out what stock would trade for when debt issue is announced and about to be done when figuring price to buy back stock at)

Answer 1

Expected return from equity =Re

Risk free rate=Rf=5%

Expected market return=Rm

Market premium=Rm-Rf=5%

Beta=0.8

Re=Rf+Beta*(Rm-Rf)

Expected return from equity=Re=5+0.8*5=9%=0.09

Perpetual cash flow=$800

Worth of the firm=800/0.09=$8888.89

Number of shares outstanding=1000

.a) The firm’s unlevered stock currently worth per share=$8888.89/1000=$8.89

20% debt(D) and 80% equity(E) financing will give D/E ratio of 0.2/0.8=0.25

BL =Levered Beta

Bu=Un levered Beta=0.8

Tc=Tax Rate=0.25

Levered Beta=BL=Bu*(1+((1-Tc)*D/E))

BL=Levered Beta=0.8*(1+((1-0.25)*0.25))

BL=0.8*1.1875=0.95

Expected return with levered Beta= Rf+Beta*(Rm-Rf)=5+0.95*5=9.75%

. i) New Cost of equity=9.75%

.ii) New WACC(Weighted Average Cost of capital)=0.2*Cost of debt+0.8* cost of equity

Before tax Cost of Debt=5%

Tax rate=25%=0.25

After tax cost of debt=(1-Tax rate)*5%=0.75*5=3.75%

Cost of equity=9.75%

New WACC=0.2*3.75+0.8*9.75=8.55%

Total value of the firm=D+E

D=0.25E

Total Value=1.25E

Present Value of cash flow before interest and tax=800/0.0855=$9356.73

Total value of Debt=0.2*$9356.73= $ 1,871.35

Total Value of Equity=0.8*$9356.73= $ 7,485.38

.iv)Price of share=$8.89

Price of share after announcement of repurchase=0.8/new cost of equity=0.8/0.0975=$8.21

.Value of debt=$1871.35

Number of shares purchased=1871.35/8.21=228

.iii)Interest cost=0.05*1871.35=$93.57

Cash flow after interest=800-93.57= $ 706.43

Tax=0.25* $706.43 =$176.61

Earning after tax and interest=706.43-176.61=$529.82

Number of shares=1000-228=772

Earning per share after repurchase=529.82/772=$0.69

Cost of equity=0.0975

New Price per share after repurchase=0.69/0.0975= $ 7.08