Problem 10-01 NPV A project has an initial cost of $42,750, expected net cash inflows of...

Problem 10-01 NPV A project has an initial cost of $42,750, expected net cash inflows of $11,000 per year for 8 years, and a cost of capital of 14%. What is the project's NPV? (Hint: Begin by constructing a time line.) Do not round your intermediate calculations. Round your answer to the nearest cent.

Solutions

Expert Solution

Net Present value (NPV) is the present value of future cash inflows minus the initial investment.

Here the cash inflows will be same every year, so it is an annuity. For calculating the present value of annuity, we will use the following formula:

PVA = P * (1 - (1 + r)-n / r)

where, P is the periodical amount = $11000, r is the rate of interest = 14% and n is the time period = 8

Now, putting these values in the above formula, we get,

PVA = $11000 * (1 - (1 + 14%)-8 / 14%)

PVA = $11000 * (1 - (1 + 0.14)-8 / 0.14)

PVA = $11000 * (1 - (1.14)-8 / 0.14)

PVA = $11000 * (1 - 0.35055905485) / 0.14

PVA = $11000 * (0.64944094515 / 0.14)

PVA = $11000 * 4.6388638939

PVA = $51027.50

Present value of future cash flows = $51027.50

Initial investment (given) = $42750

Net Present value (NPV) = Present value of future cash inflows - initial investment

Net Present value (NPV) = $51027.50 - $42750 = $8277.50

jeff jeffy answered 1 year ago

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