Alpha Industries is considering a project with an initial cost of $9.1 million. The project will produce cash inflows of $1.84 million per year for 7 years. The project has the same risk as the firm. The firm has a pretax cost of debt of 5.94 percent and a cost of equity of 11.49 percent. The debt–equity ratio is .71 and the tax rate is 40 percent. What is the net present value of the project?

NPV = $1.22  million

Explanation:

The Net present value (NPV) is the difference between the Present value (PV) of cash inflows and the PV of cash outflows. A positive NPV implies a good investment decision and a negative figure implies the opposite.  

NPV of an investment:  

NPV = PV of Cash inflows - PV of cash outflow  

To work oit the NPV we would need to determine the discount rate i.e cost of capital as follows:

Cost of capital -discount rate -

WACC = We×Ke + Wd×Kd

After cost o debt = 5.94× (1-0.4)=3.56

WACC = (0.71×3.56 %)  + (0.29×11.49%)=5.86 %

PV of cash inflow = A× (1- (1+r)^(-n))/r

A- annul cash inflow, r- 5.86%, n- 7

PV of cash inflow= 1.84 million × (1- 1.0586^(-7))/0.0586 =10.32

Initial cost = 9.1 million

NPV = 10.32  - 9.1 =  1.22 million

NPV = $1.22  million

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