Question

Calculate the NPV for the following projects. Round PVF values in intermediate calculation to four decimal places. Round answers to two decimal places. Use a minus sign to indicate a negative NPV.

1. An outflow of $7,000 followed by inflows of $3,000, $2,500, and $3,500 at one-year intervals at a cost of capital of 7%.
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2. An initial outlay of $35,400 followed by inflows of $6,500 for three years and then a single inflow in the fourth year of $18,000 at a cost of capital of 13%. (Recognize the first three inflows as an annuity in your calculations.)
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3. An initial outlay of $27,500 followed by an inflow of $3,000 followed by five years of inflows of $5,500 at a cost of capital of 9%. [Recognize the last five inflows as an annuity, but notice that it requires a treatment different from the annuity in part (b).]
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Answer 1

Answer a.

Cash Flows:
Year 0 = -$7,000
Year 1 = $3,000
Year 2 = $2,500
Year 3 = $3,500

Cost of Capital = 7%

Net Present Value = -$7,000 + $3,000 * PVF(7%, 1) + $2,500 * PVF(7%, 2) + $3,500 * PVF(7%, 3)
Net Present Value = -$7,000 + $3,000 * 0.9346 + $2,500 * 0.8734 + $3,500 * 0.8163
Net Present Value = $844.35

Answer b.

Cash Flows:
Year 0 = -$35,400
Year 1 = $6,500
Year 2 = $6,500
Year 3 = $6,500
Year 4 = $18,000

Cost of Capital = 13%

Net Present Value = -$35,400 + $6,500 * PVFA(13%, 3) + $18,000 * PVF(13%, 4)
Net Present Value = -$35,400 + $6,500 * 2.3612 + $18,000 * 0.6133
Net Present Value = -$9,012.80

Answer c.

Cash Flows:
Year 0 = -$27,500
Year 1 = $3,000
Year 2 = $5,500
Year 3 = $5,500
Year 4 = $5,500
Year 5 = $5,500
Year 6 = $5,500

Cost of Capital = 9%

Net Present Value = -$27,500 + $3,000 * PVF(9%, 1) + $5,500 * PVF(9%, 1) * PVFA(9%, 5)
Net Present Value = -$27,500 + $3,000 * 0.9174 + $5,500 * 0.9174 * 3.8897
Net Present Value = -$5,121.54