The net present value is the present value of all cash flows after Year 0 (positive and negative) less the initial investment. To calculate the present value of the cash flows after year 0, you could discount each individual cash flow amount by the appropriate present value of $1 factor. However, that is not the most time-effective way to do it. If you recognize that all the annual cash flow amounts contain an amount such as $100,000 and $100,000 is the exact amount of the cash flow for at least two of the years, you can save time by calculating first the present value of an annuity for the $100,000; then calculating the present value of $1 individually for any amounts over the $100,000 amount. In this case, we have 5 years of $100,000 cash flows, and the discount factor given for the PV of an annuity for 5 years is 3.36. We also have $60,000 to be discounted for one year and $40,000 to be discounted for two years using the appropriate present value of $1 factors. Thus, the present value of the cash inflows is ($100,000 × 3.36) + ($60,000 × .87) + ($40,000 × .76) = $418,600. The net present value is $418,600 less the initial investment of $400,000, or $18,600.
An answer of a negative $14,000 results from using the net earnings amounts instead of the after-tax cash flow amounts in the net present value analysis.
An answer of a negative $64,000 NPV results from using annual cash flows of $100,000, and forgetting to discount the additional cash flows of $60,000 in Year 1 and $40,000 in Year 2.
An answer of $200,000 results from subtracting the initial investment from the total of the undiscounted cash inflows.
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The net present value of this investment is: