Question

7.      Q Corporation and R Inc. are two companies with very similar characteristics. The only difference between the two companies is that Q Corporation is an unlevered firm, and R Inc. is a levered firm with debt of $3.5 million and cost of debt of 10%. Both companies have earnings before interest and taxes (EBIT) of $1.5 million and a marginal corporate tax rate of 35%. Q Corporation has a cost of capital of 15%.                                  (20 marks)

a. What is Q Corporation’s firm value?                                        (2 marks)

b. What is R Inc.’s firm value?                                                   (2 marks)

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

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

e. What is R Inc.’s cost of equity capital?                                    (2 marks)

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

g. What is R Inc.’s WACC?                                                         (3 marks)

h. Compare the WACC of the two companies. What is your conclusion? (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, that will yield after tax cash inflows of $500,000 per year for the next three years. Assume that this project has the same risk level as each individual firm’s assets. Should Q Corporation invest in this project? Should R Inc. invest in this project?    (5 marks)

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

Answer 1

Q's cost of capital = Q's cost of Equity (as there is no debt) = 15%

As R and Q are similar, Q's cost of Equity is also the Unlevered cost of equity of R

a) For Q,

EBIT = $1.5 million

Less : Interest = 0

EBT = $1.5 million

Less: Tax (@35%)= $0.525 million

PAT = $0.975 million

So, Value of Q's Equity = Value of firm Q= PAT/Cost of equity = 0.975/0.15 = $6.50 million

b) Value of Levered Firm = Value of unlevered firm + t*D  (as per Modigliani Miller)

where t is the tax rate and D is the debt

R Inc's firm Value = Q Inc's value + t*D

= $6.50 million + 0.35* $3.5 =$7.725 million

c) R Inc's equity value = R Inc's firm value - R Inc's Debt Value

= $7.725 - $3.5

= $4.225 million

d) Q's cost of Equity = Q's cost of capital (as there is no debt) = 15%