Question

Citee Corp. has no debt but can borrow at 5.6 percent. The firm’s WACC is currently 9.4 percent, and the tax rate is 25 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 35 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 65 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 35 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 65 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

Part a:
Given that the company has no debt, so the firm is currently all equity.
WACC= Weight of equity*cost of equity+Weight of debt*Cost of debt
Given that WACC=9.4%
As weight of debt=0 and weight of equity=100%
WACC=100%*Cost of equity +0*cost of debt
=>9.4%=1*Cost of equity
=>Cost of equity=9.4%

Part b:
If the firm converts to 35% percent debt, the debt to equity ratio will be 35%/(100%-35%)=35%/65%=0.538461538
Note: As debt=35%, what remains is the equity. So, equity=100%-35%=65%

By using the Modigliani-Miller theorem we can get,
Cost of levered equity = Cost of unlevered equity +debt to equity ratio*(cost of unlevered equity - cost of debt)*(1 - tax rate)
Here,
Cost of unlevered equity=9.4%
Debt to equity ratio=0.538461538
Given that, the company can borrow at 5.6%. So, cost of debt=5.6%
Tax rate=25%
Cost of levered equity =9.4%+0.538461538*(9.4%-5.6%)*(1-25%)
=0.094+0.538461538*(0.038)*(0.75)
=0.094+0.015346154=0.109346154 or 10.93% (rounded up to two decimal places)

Part c:
If the firm converts to 65% percent debt, the debt to equity ratio will be 65%/(100%-65%)=.65/0.35=1.857142857
Now, cost of levered equity = Cost of unlevered equity +debt to equity ratio*(cost of unlevered equity - cost of debt)*(1 - tax rate)
Cost of unlevered equity=9.4%
Debt to equity ratio=1.857142857
Given that, the company can borrow at 5.6%. So, cost of debt=5.6%
Tax rate=25%
Substituting the values in the equation of cost of levered equity, we get:
Cost of levered equity=9.4%+1.857142857*(9.4%-5.6%)*(1-25%)
=0.094+1.857142857*(0.038)*(0.75)
=0.094+0.052928571
=0.146928571 or 14.69% (rounded up to two decimal places)

Part d-1:
Weight of debt=35%=.35, so weight of equity =1-35%=0.65
Weighted average cost of capital(WACC)=Weight of equity*Cost of equity +Weight of debt*Cost of debt*(1-tax rate)
Cost of equity=0.109346154
Cost of debt=5.6%
Tax rate=25%
=>WACC=0.65*0.109346154+0.35*5.6%*(1-25%)
=0.071075+0.35*5.6%*(0.75)
=0.071075+0.0147
0.085775 or 8.58%

Part d-2:
Weight of debt=65%, so weight of equity =1-65%=0.35
Weighted average cost of capital(WACC)=Weight of equity*Cost of equity +Weight of debt*Cost of debt*(1-tax rate)
Cost of equity=0.146928571
Cost of debt=5.6%
Tax rate=25%
WACC=0.35*0.146928571+0.65*5.6%*(1-25%)
=0.051425+0.65*5.6%*(0.75)
=0.051425+0.0273
0.078725 or 7.87%