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You have been offered a unique investment opportunity. If you invest $7,876 today, you will receive $827 one year from now, $3,852 three years from now, and $12,631 ten years from now. If the interest rate is 12% per year, the NPV of this project is closest to (round to whole integer):

Question

You have been offered a unique investment opportunity. If you invest 7,876today,youwillreceive7,876 today, you will receive 827 one year from now, 3,852threeyearsfromnow,and3,852 three years from now, and 12,631 ten years from now. If the interest rate is 12% per year, the NPV of this project is closest to (round to whole integer):

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Solution

To calculate the Net Present Value (NPV), we need to discount each future cash flow back to its present value and then sum them up. The formula to calculate the present value is:

PV = FV / (1 + r)^n

where:

  • PV is the present value
  • FV is the future value
  • r is the interest rate
  • n is the number of periods

Let's calculate the present value for each cash flow:

  1. For the cash flow received one year from now (827):PV1=827/(1+0.12)1=827): PV1 = 827 / (1 + 0.12)^1 = 738.39

  2. For the cash flow received three years from now (3,852):PV2=3852/(1+0.12)3=3,852): PV2 = 3852 / (1 + 0.12)^3 = 2,738.72

  3. For the cash flow received ten years from now (12,631):PV3=12631/(1+0.12)10=12,631): PV3 = 12631 / (1 + 0.12)^10 = 3,932.57

Now, let's sum up these present values and subtract the initial investment:

NPV = (PV1 + PV2 + PV3) - Initial Investment NPV = (738.39+738.39 + 2,738.72 + 3,932.57)−3,932.57) - 7,876 NPV = -$466.32

So, the NPV of this project, rounded to the nearest whole number, is -$466. This means that the project is not a good investment at a 12% interest rate, as it would result in a loss.

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