Question

Shadow Corp. has no debt but can borrow at 6.8 percent. The firm’s WACC is currently 9.2 percent and the tax rate is 22 percent.

  

a.	What is the company’s cost of equity? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
b.	If the firm converts to 20 percent debt, what will its cost of equity be? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
c.	If the firm converts to 50 percent debt, what will its cost of equity be? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
d-1.	If the firm converts to 20 percent debt, what is the company’s WACC? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
d-2.	If the firm converts to 50 percent debt, what is the company’s WACC? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

    

Answer 1

A)The formula to calculate WACC (weighted cost of capital) is -

WACC = [(D/D+E)*Kd*(1-Tax)] + [(E/(D+E)*Ke]

Where D - Total Debt

E - Total Equity

Kd - Cost of debt for company which is cost of raising debt

Ke - Cost of equity for company which is cost of raising equity

Given that WACC = 9.2% , Tax = 22%, Kd = 6.%, Debt = 0

Thus we can calculate Ke using the formula above as;

WACC = [(D/D+E)*Kd*(1-Tax)] + [(E/(D+E)*Ke]

Ke  = 9.20%. Thus Cost of equity is 9.20%

B) According to Modigliani-Miller Proposition 2, we have the following formula:

Where Ra = unlevered cost of equity

Re = levered cost of equity

Rd = cost of debt

D/E = Debt to equity ratio

Here Ra = 9.2% (because this is the WACC when there was no leverage), Rd = 6.8% (given), Tax = 22% , D/E = 0.2/0/8 = 0.25

thus we can find levered cost of equity using the formula given above,

Re = 9.67%

C)Here given 50% debt which means D/E = 1. Using the same approach as in previous question we can get Re as

Re = 11.07%

D1) For 20% debt we have already calculate Ke = 9.67%. Also WACC = [(D/D+E)*Kd*(1-Tax)] + [(E/(D+E)*Ke]

Using the above formula and values calculated in part B, we can get WACC as

WACC = [(0.2/0.2+0.8)*6.8*(1-.22)] + [(0.8/(0.2+0.8)*9.67]

WACC = 8.7968%

D1) For 50% debt we have already calculate Ke = 11.07%. Also Using the same approach, we can calculate WACC as

WACC = [(D/D+E)*Kd*(1-Tax)] + [(E/(D+E)*Ke]

WACC = [(0.5/0.5+0.5)*6.8*(1-0.22)] + [(0.5/0.5+0.5)*11.07]

WACC = 8.188%