Question

Alpha Industries is considering a project with an initial cost of $7.5 million. The project will produce cash inflows of $1.55 million per year for 7 years. The project has the same risk as the firm. The firm has a pretax cost of debt of 5.46 percent and a cost of equity of 11.17 percent. The debt–equity ratio is .55 and the tax rate is 39 percent. What is the net present value of the project?

$263,559

$482,364

$463,811

$397,552

$417,430

Answer 1

Answer is Option 3. $463,811

NPV is the present value of all the cash flows discounted at t=0 by the discount rate, which is WACC or required rate of return on project. For this project, risk of the project is same as overall firm, hence we would use WACC as the discount rate.

Debt/Equity = 0.55 = 55/100

Weight of Debt = 55/(55 + 100) = 35.48%

Weight of Equity = 100/(55 + 100) = 64.52%

WACC = Weight of Debt * Pretax Cost of Debt * (1 - Tax rate) + Weight of Equity * Cost of Equity

WACC = [35.48% * 5.46% * (1- 39%)] + [64.52% * 11.17%]

WACC = 1.18% + 7.21% = 8.39%

Mapping the cashflows according by 8.39% discount rate. Remember to use the correct polarity or signs for cashflows. Negative sign for outflows and positive for outflows:

Year	Cashflow (in mil)	Discounting Cashflow @ 8.39%	Discounted Cashflow (in mil)
0	-7.5	= -7.5/(1 + 0.0839)^0	(7.500000)
1	1.55	= 1.55/(1 + 0.0839)^1	1.430021
2	1.55	= 1.55/(1 + 0.0839)^2	1.319329
3	1.55	= 1.55/(1 + 0.0839)^3	1.217206
4	1.55	= 1.55/(1 + 0.0839)^4	1.122987
5	1.55	= 1.55/(1 + 0.0839)^5	1.036062
6	1.55	= 1.55/(1 + 0.0839)^6	0.955865
7	1.55	= 1.55/(1 + 0.0839)^7	0.881875

NPV of the project (in $ mil) = -7.5 + 1.430021 + 1.319329 + 1.217206 + 1.122987 + 1.036062 + 0.955865 + 0.881875

NPV of the project = $0.463,811 mil.

Hence NPV = 463,811