Final answer:
The NPV of a project with an initial cash outflow of $42,600 and cash inflows for 3 years at a discount rate of 12 percent is calculated by discounting each cash inflow to present value, summing them up, and subtracting the initial investment. The result is an NPV of $161.71.
Step-by-step explanation:
To calculate the net present value (NPV) of a project with an initial cash outflow of $42,600 and cash inflows of $17,680 in year 1, $19,920 in year 2, and $15,670 in year 3 at a discount rate of 12 percent, we must discount each of the cash inflows back to their present value and then sum these values while subtracting the initial investment.
The present value (PV) for each year can be calculated using the formula PV = Cash Inflow / (1 + r)t, where 'r' is the discount rate and 't' is the time period in years. Calculating the present values for the cash inflows at a 12 percent discount rate:
- Year 1: PV = $17,680 / (1 + 0.12)1 = $15,785.71
- Year 2: PV = $19,920 / (1 + 0.12)2 = $15,839.29
- Year 3: PV = $15,670 / (1 + 0.12)3 = $11,136.71
The NPV is then the sum of these present values minus the initial investment: NPV = ($15,785.71 + $15,839.29 + $11,136.71) - $42,600.
Calculating this gives an NPV of $42,761.71.
So, the NPV at a 12 percent discount rate is $42,761.71 - $42,600 = $161.71.