Alpha Industries is considering a project with an initial cost of $8.5 million. The project will produce cash inflows of $1.51 million per year for 9 years. The project has the same risk as the firm. The firm has a pretax cost of debt of 5.76 percent and a cost of equity of 11.37 percent. The debt–equity ratio is .65 and the tax rate is 40 percent. What is the net present value of the project?

$834,608 (Approx).

Explanation:

For computing the net present value first we have to determine the following calculations

After tax cost of debt

= Pre tax cost of debt × (1 - tax rate)

= 5.76% × (1 - 0.4)

= 3.456%

As we know that

Debt-equity ratio = debt ÷ equity

Therefore

Debt = 0.65 × equity

Let us assume the equity be $x

So,

Debt = $0.65 x

Total = $1.65x

Now

WACC = Respective costs × Respective weights

= (0.65x ÷ 1.65x × 3.456) + (x ÷ 1.65x × 11.37)

= 8.2523636%(Approx)

Now

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

= $1.51 × [1 - (1.082523636)^ -9] ÷ 0.082523636

= $1.51 × 6.18185982

= $9,334,608.33

Now

Net present value = Present value of  cash inflows - Present value of cash outflows

= $9,334,608.33 - $8,500,000

= $834,608 (Approx).

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