What is the net present value of a project that has an upfront cash outlay of $30,000, and generates cash inflows of $15,000 in year 1, $20,000 in year 2, and $25,000 in year 3 assuming that the company’s cost of capital is 15% per year?
$14, 602
To calculate the net present value (NPV) of a project, we need to discount the future cash flows back to the present value and then subtract the initial cash outlay from it. The discount rate used in this calculation is the company's cost of capital, which in this case is given as 15% per year.
Let's break down the steps to calculate the NPV:
1. Calculate the present value factor for each year: To convert the future cash flows into their present value, we need to use the present value factor. The formula for calculating the present value factor is:
Present Value Factor = 1 / (1 + Discount Rate)^n
Where n represents the number of years.
For this project, the present value factors are as follows:
Year 1: 1 / (1 + 0.15)^1 = 0.8696
Year 2: 1 / (1 + 0.15)^2 = 0.7561
Year 3: 1 / (1 + 0.15)^3 = 0.6575
2. Calculate the present value of each cash inflow: Multiply the cash inflow for each year by its corresponding present value factor.
Year 1 cash inflow: $15,000 x 0.8696 = $13,044
Year 2 cash inflow: $20,000 x 0.7561 = $15,122
Year 3 cash inflow: $25,000 x 0.6575 = $16,438
3. Calculate the total present value of the cash inflows: Sum up the present value of each cash inflow.
Total present value of cash inflows = $13,044 + $15,122 + $16,438 = $44,604
4. Calculate the net present value (NPV): Subtract the upfront cash outlay from the total present value of the cash inflows.
NPV = Total present value of cash inflows - Upfront cash outlay
= $44,604 - $30,000
= $14,604
Therefore, the net present value (NPV) of the project is $14,604.