Question

1. Roger Inc. is currently an all equity firm that has 500,000 shares of stock outstanding at a market price of $20 a share. EBIT is $1,500,000 and is constant forever. The required annual rate of return on the share is 12%. The corporate tax is 35%. The firm is proposing borrowing an additional $2 million in debt and uses the proceeds to repurchase stock. If it does so, the cost of debt will be 10%. What will be the WACC after the capital structure changes?

2. Consider Asset A and B, which asset has higher systematic risk? Which one has higher total risk? Show your calculations. Assume the market risk premium is 8 percent, the risk-free rate is 4 percent, and the capital asset pricing model holds. (Rounding your answers to four decimal places)

3. State of Economy	Probability of State of Economy	Rate of Return if State Occurs
   		Asset A	Asset B
   Recession	0.10	0.02	-0.25
   Normal	0.70	0.25	0.09
   Irrational exuberance	0.20	0.05	0.40

Answer 1

Roger Inc.

Now, Equity= 100%

After debt issue & repurchase of stock,

No.of shares repurchased= Debt amt./Market price per share, ie.2000000/20=

100000

EPS (all equity)=EBIt*(1-Tax Rate)/No.of shares

ie.(1500000*(1-35%))/500000

1.95

P/E ratio= Market price/Earnings per share=

20/1.95=

10.25641

EPS (Debt+equity)=(EBIT-Debt Interest)*(1-Tax Rate)/No.of shares

ie.((1500000-200000)*(1-35%)))/(500000-100000)=

2.11

Using the above P/E ratio,

market price of equity=

2.11*10.25641=

21.6410251

so, total market value of equity=

(500000-100000)shares*21.64103=

8656412

Total D+E= 2000000+8656412=

10656412

so, wt. of equity= 8656412/10656412=

81.23%

wt. of debt=2000000/10656412=

18.77%

So, the WACC of the restuructured firm will be

(wt.e*ke)+(wt.d*kd*(1-Tax rate)

ie.(81.23%*12%)+(18.77%*10%*(1-35%)=

10.97%

Expected return of asset A=Sum( Probability*Return)

ie. (0.1*0.02)+(0.7*0.25)+(0.2*0.05)=

18.70%

With this expected return for asset A, we will find the Beta, which is the systematic -risk quotient

using the CAPM equation,

Expected return=RFR+(Beta*market risk premium)

ie.18.70%=4%+B*8%

Solving the above, we get the beta for tha asset as

1.8375

Expected return of asset B=Sum( Probability*Return)

ie. (0.1*-0.25)+(0.7*0.09)+(0.2*0.04)=

4.60%

With this expected return for asset B, we will find the Beta, which is the systematic -risk quotient

using the CAPM equation,

Expected return=RFR+(Beta*market risk premium)

ie.4.60%=4%+B*8%

Solving the above, we get the beta for tha asset as

0.075

Asset A has higher systematic risk

Beta > 1, asset A is more volatile than market as a whole

Beta <1, asset B is less volatile than market as a whole

Total risk is measured by standard deviation of the returns

ie. Std. devn.=Sq.rt. Of the( sum of Prob.(Return-Expected return)^2)

for asset A

((0.1*(0.02-0.187)^2)+(0.7*(0.25-0.187)^2)+(0.2*(0.05-0.187)^2))^(1/2)=

9.65%

for asset B

((0.1*(-0.25-0.046)^2)+(0.7*(0.09-0.046)^2)+(0.2*(0.04-0.046)^2))^(1/2)=

10.06%

Asset B has higher total risk

as its dispersion of returns from the mean is greater.