Question

1. Q Corporation and R Inc. are two companies with very similar characteristics. The only difference between the two companies is that Q Corp. is an unlevered firm, and R Inc. is a levered firm with debt of $5 million and cost of debt of 10%. Both companies have earnings before interest and taxes (EBIT) of $2 million and a marginal corporate tax rate of 40%. Q Corp. has a cost of capital of 15%.                         (20 marks total)

a. What is Q’s firm value?                                                                                     

b. What is R’s firm value?                                                                                      

c.   What is R’s equity value?                                                                         (1 mark)

d. What is Q’s cost of equity capital?                                                        (1 mark)

e. What is R’s cost of equity capital?                                                       .

f.   What is Q’s WACC?                                                                                     (1 mark)

g. What is R’s WACC?                                                                                  

h. Compare the WACC of the two companies. What do you conclude?       (1 mark)

i.    What principle have you proven in this case?                                                (1 mark)

j.   Both companies are now evaluating a project that requires an initial investment of $1.15 million and that will yield cash inflows of $500,000 per year for the next three years. Assume that this project has the same risk level as the individual firm’s assets. Should Q invest in this project? Should R invest in this project?                                                                                                                               

k. Based on your results for part (j), discuss the effects of leverage and its tax shields effects on the future value of the two firms.                                 (1 mark)

Answer 1

Firm Q corporation ( only equity )

Firm R Inc. ( Equity and debt )

EBIT = $2 million

Q corporation cost of capital = 15%

R Inc cost of debt = 10%

Value of debt = $5 million.

Tax rate = 40%

Question a.

Value of Q's firm = EBIT ( 1 - tax rate ) / Cost of capital

= $2 million ( 1 - .40 ) / 15%

= $8 million

Since it has all equity structure hence no interest expenses. Cost of capital is equal to cost of equity since firm is unleavered.

Question b.

Value of R's firm = ( Value of equity + Value of debt )

Value of debt = $5 million

Value of equity = ( EBIT - Interest expenses ) ( 1- tax rate ) / Cost of equity

Interest expenses = ( $5 million * 10% ) = $0.5 Million

Value of equity = ( $2 million - $0.5 million ) ( 1 - .40 ) / 15%

= $6 million

Value of firm = ( $6 million + $5 million )

= $11 million

Question c.

R equity value = $6 Million ( Calculated in above step )

Question d.

Q's cost of equity capital

Since Q's corporation is the all equity firm . Hence total cost of capital is equal to the cost of equity.

Cost of equity = 15%

Question e.

R's cost of equity capital is also 15%. Since both companies has same level of equity capital structure.