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You have been offered a unique investment opportunity. If you invest $7,078 today, you will receive $848 one year from now, $3,947 three years from now, and $12,448 ten years from now. If the interest rate is 11% 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 7,078today,youwillreceive7,078 today, you will receive 848 one year from now, 3,947threeyearsfromnow,and3,947 three years from now, and 12,448 ten years from now. If the interest rate is 11% per year, the NPV of this project is closest to (round to whole integer):

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Solution

Alright, let's break this down.

First, let's understand what Net Present Value (NPV) is. It's a way to figure out how much an investment is worth right now, considering the money you'll get in the future. But, because money today is worth more than the same amount in the future (due to inflation and the potential to earn interest), we need to "discount" those future amounts to their present values.

Here's how we do it:

  1. We start with the money you'll receive in the future. In this case, it's 848afteroneyear,848 after one year, 3,947 after three years, and $12,448 after ten years.

  2. We then "discount" these amounts to their present values using the formula: Future Value / (1 + interest rate) ^ number of years. The interest rate here is 11% or 0.11 in decimal form.

  3. So, the present value of 848receivedafteroneyearis:848 received after one year is: 848 / (1 + 0.11) ^ 1 = $763.96

  4. The present value of 3,947receivedafterthreeyearsis:3,947 received after three years is: 3,947 / (1 + 0.11) ^ 3 = $2,981.07

  5. The present value of 12,448receivedaftertenyearsis:12,448 received after ten years is: 12,448 / (1 + 0.11) ^ 10 = $4,568.35

  6. We then add up these present values: 763.96+763.96 + 2,981.07 + 4,568.35=4,568.35 = 8,313.38

  7. Finally, we subtract the initial investment of 7,078fromthistotaltogettheNPV:7,078 from this total to get the NPV: 8,313.38 - 7,078=7,078 = 1,235.38

So, the NPV of this investment, rounded to the nearest whole number, is 1,235.Thismeansthat,consideringthefuturemoneyyou′llreceiveandtheinterestrate,thisinvestmentisworth1,235. This means that, considering the future money you'll receive and the interest rate, this investment is worth 1,235 more than what you're paying for it today.

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