Alpha Industries is considering a project with an initial cost of $8 million. The project will produce cash inflows of $1.49 million per year for 8 years. The project has the same risk as the firm. The firm has a pretax cost of debt of 5.61 percent and a cost of equity of 11.27 percent. The debt–equity ratio is .60 and the tax rate is 35 percent. What is the net present value of the project?

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TomShelby TomShelby · Answer 1 · 2019-07-26T00:19:02+02:00

Answer:

NPV = 1,003,046

Explanation:

NPV = Present value of income - investment

investment 8,000,000

1,490,000 income per year during 8 years at rate x

We need to calculate the WACC so we can know the rate

[tex]WACC = K_e(\frac{E}{E+D}) + K_d(1-t)(\frac{D}{E+D})[/tex]

equity-ratio = 0.40

[tex]\frac{E}{E+D} =0.40[/tex]

debt-equity ratio = 0.6

[tex]\frac{D}{E+D} =0.60[/tex]

[tex]K_e= 11.27\\0.1127 \times0.40 = 0.04508[/tex]

[tex]K_d = 5.61 \\0.0561\times (1-.35)\times 0.6 = 0.021879[/tex]

WACC 6.69590%

Now that we achieve the rate we solve for the present value of the cash flow

[tex]C * \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]

[tex]1.49* \frac{1-(1.06959)^{-8} }{0.06959} = PV\\[/tex]

PV 9,003,046

And finally get the answer

NPV 9,003,046 - 8,000,000 = 1,003,046