Question

You have been offered a unique investment opportunity. If you invest $15,000 today, you will receive $750 one year from now, $2,250 two years from now, and $15,000 ten years from now. a. What is the NPV of the investment opportunity if the interest rate is 10% per year? Should you take the opportunity? b. What is the NPV of the investment opportunity if the interest rate is 6% per year? Should you take the opportunity? a. What is the NPV of the investment opportunity if the interest rate is 10% per year? The NPV of the investment opportunity if the interest rate is 10% per year is $. (Round to the nearest dollar.) Should you take the investment opportunity (Select the best choice below.) O A. Reject it because the NPV is less than 0. B. Take it because the NPV is equal to or greater than 0. b. What is the NPV of the investment opportunity if the interest rate is 6% per year? The NPV of the investment opportunity if the interest rate is 6% per year is $ Should you take the investment opportunity (Select the best choice below.) A. Reject it because the NPV is less than 0. B. Take it because the NPV is equal to or greater than 0. (Round to the nearest dollar.)

Answer 1

To calculate the net present value (NPV) of the investment opportunity, we need to discount the future cash flows to their present values using the given interest rates. The NPV formula is:

NPV = CF₁ / (1 + r)¹ + CF₂ / (1 + r)² + ... + CFₙ / (1 + r)ⁿ - Initial Investment

Step-by-step explanation:

a. NPV at 10% per year:

The cash flows are $750, $2,250, and $15,000 received at the end of years 1, 2, and 10, respectively. The initial investment is $15,000.

NPV = $750 / (1 + 0.10)¹ + $2,250 / (1 + 0.10)² + $15,000 / (1 + 0.10)¹⁰ - $15,000

Calculating this expression gives us an NPV of approximately $7,258.49. Therefore, the NPV at 10% per year is $7,258.

Since the NPV is greater than 0, you should take the investment opportunity (Select choice B: Take it because the NPV is equal to or greater than 0).

b. NPV at 6% per year:

Using the same formula and cash flows, but with an interest rate of 6% per year:

NPV = $750 / (1 + 0.06)¹ + $2,250 / (1 + 0.06)² + $15,000 / (1 + 0.06)¹⁰ - $15,000

Calculating this expression gives us an NPV of approximately $9,234.45. Therefore, the NPV at 6% per year is $9,234.

Again, since the NPV is greater than 0, you should take the investment opportunity (Select choice B: Take it because the NPV is equal to or greater than 0).