Question

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%.                                      

a.   What is Q Corporation’s firm value?                   

b.   What is R Inc.’s firm value?                                

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?              

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

g.   What is R Inc.’s WACC?                                     

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?         

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.

Answer 1

a]	Q Corporation's firm value [Unlevered value - Vu] = EBIT*(1-t)/rsu = 1500000*(1-35%)/15% =	$   6,500,000
	[rsu = Unlevered cost of equity]
b]	R Inc's value = Value of levered firm [Vl] = Vu+B*t = 6500000+3500000*35% =	$   7,725,000
	[B = borrowings and t = tax rate]
c]	R Inc's equity value = Value of the firm-Value of debt = 7725000-3500000 =	$   4,225,000
d]	Q Corporation's cost of equity capital [given]	15.00%
e]	R Inc's cost of equity capital - rsl [Cost of levered equity] = rsu+(rsu+rd)*(1-t)*D/E = 15%+(15%-10%)*(1-35%)*3500000/4225000 =	17.69%
f]	Q Corporation's WACC = Cost of unlevered equity =	15.00%
g]	R Inc's WACC = 10%*(1-35%)*3500000/7725000+17.69%*4225000/7725000 =	12.62%
h]	The levered company has lower WACC.
i]	The proof is that leverage lowers the WACC and increases
	the value of the firm.
j]	NPV for Q Corporation = -1150000+500000*(1.15^3-1)/(0.15*1.15^3) =	$         (8,387)
	Q Corporation should not invest in the project as it has negative NPV.
	NPV for R Corporation = -1150000+500000*(1.1262^3-1)/(0.1262*1.1262^3) =	$         38,236
	R Corporation should invest in the project as it has positive NPV.
k]	Leverage increases the value of the firm as the debt provides interest tax shield, whose PV will add to the value of the firm.