Question

An investment of $18,000 is expected to produce net cash flows of $5,000 in year 1, $6,000 in year 2, and $7,000 in years 3 and 4. What is the net present value of the investment if the relevant interest rate is 9 percent?

Answer 1

The net present value (NPV) of the investment is -$1,542.40 when the relevant interest rate is 9 percent.

Step-by-step explanation:

Net present value (NPV) is a financial calculation used to evaluate an investment by comparing the present value of its cash inflows to the present value of its cash outflows.

To calculate the NPV of the investment, we need to discount each cash flow to its present value using the relevant interest rate. Here is how to calculate the NPV:

1. Calculate the present value of each cash flow by dividing it by (1 + interest rate) to the power of the number of years. For example, the present value of the $5,000 cash flow in year 1 would be $5,000 / (1 + 0.09)^1.
2. Add up the present values of all the cash flows.
3. Subtract the initial investment from the total present values to find the NPV.

In this case, using the relevant interest rate of 9 percent:

1. The present value of the $5,000 cash flow in year 1 is $4,587.16.
2. The present value of the $6,000 cash flow in year 2 is $4,738.03.
3. The present value of the $7,000 cash flows in years 3 and 4 is $7,132.41.
4. The total present value of all the cash flows is $16,457.60.
5. Subtracting the initial investment of $18,000 from the total present values gives an NPV of -$1,542.40.

Therefore, the net present value of the investment is -$1,542.40.