Final answer:
The present value (PV) of a project with cash flows over three years at a discount rate of 12.5% can be calculated by discounting each cash flow to its present value and summing them. The PV of the first year's cash flow is $419.56, the second year's is $140.37, and the third year's is $592.23, resulting in a total PV of $1,152.16.
Step-by-step explanation:
The student is asking to calculate the present value (PV) of a project that produces cash flows over a three-year period with a cost of capital of 12.5%. The present value of cash flows can be calculated using the following formula:
PV = CF1 / (1 + r)1 + CF2 / (1 + r)2 + CF3 / (1 + r)3
Where CF1, CF2, and CF3 are the cash flows in years 1, 2, and 3, respectively, and 'r' is the discount rate (cost of capital). To solve this, first calculate the present value of each individual cash flow, then sum them up:
PV = $472 / (1 + 0.125)1 + $177 / (1 + 0.125)2 + $837 / (1 + 0.125)3
Next, compute these values to find the project's PV:
- PV of Year 1 = $472 / (1.125)1 = $419.56
- PV of Year 2 = $177 / (1.125)2 = $140.37
- PV of Year 3 = $837 / (1.125)3 = $592.23
Finally, add up all the present values to get the final PV of the project:
Total PV = $419.56 + $140.37 + $592.23 = $1,152.16