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Fill in the Blank QuestionFill in the blank question.A company is considering an investment opportunity with a cost of $5,000 that will provide future cash flows of $8,000. The cash flows for the investment for the next 4 years are: $1,000, $1,000, $2,000 and $4,000. Assume a required rate of return of 10%. The NPV is $ (rounded to nearest dollar).Present Value of 1RatePeriods10%10.909120.826430.751340.6830Present Value of an Annuity of 1RatePeriods10%43.1699

Question

Fill in the Blank QuestionFill in the blank question.A company is considering an investment opportunity with a cost of 5,000thatwillprovidefuturecashflowsof5,000 that will provide future cash flows of 8,000. The cash flows for the investment for the next 4 years are: 1,000,1,000, 1,000, 2,000and2,000 and 4,000. Assume a required rate of return of 10%. The NPV is $ (rounded to nearest dollar).Present Value of 1RatePeriods10%10.909120.826430.751340.6830Present Value of an Annuity of 1RatePeriods10%43.1699

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Solution

To calculate the Net Present Value (NPV), we need to discount each year's cash flow to its present value and then sum these values.

The formula for the present value is:

PV = CF / (1 + r)^n

where:

  • PV is the present value
  • CF is the cash flow for the year
  • r is the required rate of return
  • n is the year

Using the provided cash flows, rate of return, and the formula above, we can calculate the present value for each year:

Year 1: PV = 1,000/(1+0.10)1=1,000 / (1 + 0.10)^1 = 909.09 Year 2: PV = 1,000/(1+0.10)2=1,000 / (1 + 0.10)^2 = 826.45 Year 3: PV = 2,000/(1+0.10)3=2,000 / (1 + 0.10)^3 = 1,502.74 Year 4: PV = 4,000/(1+0.10)4=4,000 / (1 + 0.10)^4 = 2,732.05

Adding these values together, we get the total present value of the cash flows:

Total PV = 909.09+909.09 + 826.45 + 1,502.74+1,502.74 + 2,732.05 = $5,970.33

The NPV is then calculated by subtracting the initial investment from the total present value of the cash flows:

NPV = Total PV - Initial Investment = 5,970.335,970.33 - 5,000 = $970.33

Rounded to the nearest dollar, the NPV is $970.

This problem has been solved

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