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

Debt to Equity Ratio = 0.55

This means when Debt is $ 0.55, then the equity is $ 1

Hence, total capital = Debt + Equity = 0.55 + 1 = 1.55

Weight of Debt in Total Capital = 0.55 / 1.55 = 0.3548

Weight of Equity in Total Capital = 0.55 / 1.55 = 0.65

= 0.3548 * 5.46 % * ( 1 - 0.39 ) + 0.6451 * 11.17 %

= 1.18182 % + 7.20642 %

= 8.3883 %

= 8.38 %

where CF = cash inflows and t = number of year

NPV = $ 1,550,000 / ( 1 + 0.0838)¹ +  $ 1,550,000 / ( 1 + 0.0838)² +  $ 1,550,000 / ( 1 + 0.0838)³ +

$ 1,550,000 / ( 1 + 0.0838)⁴ +  $ 1,550,000 / ( 1 + 0.0838)⁵ +  $ 1,550,000 / ( 1 + 0.0838)⁶ +  

$ 1,550,000 / ( 1 + 0.0838)⁷ - $ 7,500,000

= $ 7,963,811 - $ 7,500,000

= $ 463,811