Question

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)

a)=8,000,000

b)10,000,000

c)3,000,000

d)15%

e)The cost of equity capital for Corp R will also be 15% as both firms as the similar capital structures given in the information above

f) 15%

Then g) down I need help with. I think it should be this equation WACC R=(E/V) RE+(D/E) RD (1-T) but no one on here uses that formula. one person uses WACC R=(E/V) RE+(D/E) RD =0.09375 which does make sense as an answer however why does the (1-T) just go away? If I use the full formula 0.0585 which just seems way to low.

h) R will have a lower WACC so I can figure that out after

i)?

j)?

k)?(I can likely figure this out to once I have help with J)

*Please DO NOT use Excel*

Answer 1

i) What principle have you proven in this case?

Answer: EBIT (Earning Before Interest tax)

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?

Solution:

WACC of Q = 15% = 0.15

Post tax annual cash flows = $ 500,000 = 0.5 mn

Time frame = 3 years

NPV of this project for Q = - 1.15 + 0.5 / 1.15 + 0.5 / 1.15² + 0.5 / 1.15³ = - 0.0084

Since this project is NPV negative for Q, hence Q should not invest in this project.

WACC of R = 12% = 0.12

Post tax annual cash flows = $ 500,000 = 0.5 mn

Time frame = 3 years

NPV of this project for R = - 1.15 + 0.5 / 1.12 + 0.5 / 1.12² + 0.5 / 1.12³ = 0.0509

Since this project is NPV positive for R, hence R should 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.

Solution:

Leverage leads to interest which is tax deductible. This reduces the tax burden of the firm. This tax shield has a value for the firm. Thus, leverage leads to incremental value creation for the firm through the tax shields. Because of this we saw the earlier equation that

Value of a levered firm = value of an unlevered firm + PV of all the tax shields

Leverage brings down the overall cost of capital of the firm.

Thus leverage increases the value of the firms in future, however only till a point called optimal leverage. Indebtedness beyond that point can lead to cost of bankruptcy and financial distress that may actually eat away the benefit due to interest tax shield. This will then lead to decline in the value of the firm.

Thus, leverage increase the value of a firm till a certain point, after which increasing leverage can reduce the value of the firm after accounting for cost of bankruptcy and financial distress.