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    Investment Proposal: Calculating NPV for Varying Costs of Capital

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    Question: Dane Cosmetics is evaluating a new fragrance-mixing machine. The machine requires an initial investment of $24,000 and will generate after-tax cash inflows of $5,000 per year for 8 years. For each of the costs of capital listed, 1) calculate the net present value (NPV), 2) indicate whether to accept or reject the machine, 3) explain your decision.

    a. The cost of capital is 10%
    b. The cost of capital is 12%

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    Solution Preview

    Case a.
    The cost of capital is 10%

    1. For calculating NPV, let us calculate PV of cash inflows. In this case cash flows are the same in each year. We can find PV of cash inflows by finding out the present value of ordinary annuity (C=$5000, r=10%, n=8 years).
    PV of ordinary annuity = C/r*(1-1/(1+r)^n) = 5000/10%*(1-1/(1+10%)^8) = $26674.63
    PV of cash ...

    Solution Summary

    This solution describes the steps required to calculate NPV for a given investment proposal at two different costs of capital. This is all completed in about 220 words and all the required steps are outlined.