Question

Please answer only d-j

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?

d. What is Q Corporation’s cost of equity capital?

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

f.   What is Q Corporation’s WACC?

g. What is R Inc.’s WACC?

h. Compare the WACC of the two companies. What is your conclusion?

i.   What principle have you proven in this case.

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

Part (a)

Value of Q' corporation

Since "Q' corporation is an unlevered firm ,the value of firm is calculated by following formula

Which is =(EBIT x (1-tax rate))/the required rate of return

[ $ 1.5 x (1-0.35) ] /15%

0.975 /0.15

$ 6.5

Value of 'Q' corporation is = $ 6.5 million

Part (b)

Value of Q' corporation
Since "Q' corporation is an unlevered firm ,the value of firm is calculated by following formula
Which is =(EBIT x (1-tax rate))/the required rate of return
[ $ 1.5 x (1-0.35) ] /15%
0.975 /0.15
$ 6.5
Value of 'Q' corporation is = $ 6.5 million
Interest on debt @ 10%	$ 0.35 million
Tax savings on debt @ 35%	$ 1.225 million
Hence value of firm 'R' is ($ 6.5 + $ 1.225)	$ 7.725 million

Part (c)

Value of equity of 'R'corporation
Value of firm	$ 7.725 million
Value of debt	3.5 million
Hence equity value is(7.725- 3.5)	$ 4.225 million

Part (d)

Since 'Q' corporation is an unlevered firm ,its' cost of capital is 15%

Part (e)

Cost of equity of 'R ' corporation is same 15%

Part (f)

WACC of 'Q' corporation is 15%

Part (g)

WACC of 'R' corporation is as follows

Value of 'R' can be =Free cashflow for a firm /WACC

Value of 'R' = $ 7.725

FCFF = 0.975

which is 7.725 = (0.975/ WACC)

WACC is 12.62%

Part (h)

WACC of Q is 15% where as R is 12.62%,it means that ,firm Q needs to have 15% return on its capital to meet their financial needs,at the same time R needs only 12.62% rate of return,this is because R gets incremental tax savings on debt portion in its capital

Part (i)

Leverage can increase the value of a firm through incremental cash savings

Part (j)

Q' corporation
WACC of 'Q' =15%
Annual cashflow	500000
term	3 years
PVF @ 15% for 3 years	2.283
Discounted cashflow for 3 years
(500000*2.283)	1141500
In million (1141500 /1000000)	1.1415
Less:Initial investment	1.15 million
Net present value	-0.0085
R' corporation
WACC	12.62%
Annual cashflow	500000
term	3 years
PVF @ 12.62% for 3 years	2.3764
Discounted cashflow for 3 years
(500000*2.376)	1188200
In million (1188200 /1000000)	1.1882
Less:Initial investment	1.15 million
Net present value	0.0382
Since NPV is positive R should invest in this project

Part (k)

Leverage means including debt in the funding of a company,it leads to save tax on interest portion on debt
Thus leverage can create incremental value creation for the firm through tax savings