Question

# Alpha Industries is considering a project with an initial cost of \$7.5 million. The project will...

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

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