Question

PLEASE ANSWER J&K :) THANK YOU!

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

j. Calculating Equity for Q and R

Since, Q is unlevered firm therefore Debt = 0

Q corporation

EBIT = $2million

Debt = 0

Interest = 0

PBT = EBIT -I = $2 million

Tax @ 40% = 0.40*2 = $0.80 million

PAT = PBT -T = $1.2 million = Equity

R corporation

EBIT = $2million

Debt = $5 million

Interest = 0.10*5 = $0.5 million

PBT = EBIT -I = $2 -0.5 = 1.5 million

Tax @ 40% = 0.40*1.5 = $0.60 million

PAT = PBT -T = $0.9 million = Equity

Firm Value = Debt + Equity

Q firm value = $1.2 million

R firm Value = 5+0.9 = $5.9 million

Cost of Equity for firm R = Cost of Capita for firm Q = 15% ( both have same characteristics)

WACC = Cost of Debt*Portion of debt (1-T) + Cost of Equity* Portion of Equity

Q WACC = 15% ( given)

R WACC = 10%*(5/5.9)(1-0.40) + 15%*(0.9/5.9) = 7.37%

j. NPV for Q

NPV = -1150000 + 500000(P/A,15%,3)

NPV = -1150000 + 1141612.56

NPV = -$8387.44

NPV for R

NPV = -1150000 + 500000(P/A,7.37%,3)

NPV = -1150000 + 1303338.07

NPV = $153338.0

Since for Q NPV is negative and for R its positive , so R should accept the project and Q should reject the project

k. Since Q in unlevered , its debt is zero. As a result of debt, which is cheaper than equity and also the tax shield is obtained which reduces the overall taxable income and also further reduces the after tax WACC. This help the firm R to accept project since its WACC is low as compared to Q.