Question

# Alpha Industries is considering a project with an initial cost of \$8.4 million. The project will...

Alpha Industries is considering a project with an initial cost of \$8.4 million. The project will produce cash inflows of \$1.64 million per year for 8 years. The project has the same risk as the firm. The firm has a pretax cost of debt of 5.73 percent and a cost of equity of 11.35 percent. The debt–equity ratio is .64 and the tax rate is 39 percent. What is the net present value of the project?

After-tax cost of debt=5.73*(1-tax rate)

=5.73*(1-0.39)=3.4953%

Debt-equity ratio=debt/equity

Hence debt=0.64 equity

Let equity be \$x

Debt=\$0.64x

Total=\$1.64x

WACC=Respective costs*Respective weight

=(x/1.64x*11.35)+(0.64x/1.64x*3.4953)

=8.28475122%

Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate

=1.64[1-(1.0828475122)^-8]/0.0828475122

=\$1.64*5.685056762

=\$9.32 million

NPV=Present value of inflows-Present value of outflows

=\$9.32 million-\$8.4 million

=\$0.92 million(or \$923,493.09 approx).

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