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Discounted cash flows applicationsNet present Value calculations have a broad range of applications in finance.Calculate the NPV of the project based on the information below.Initial investment: $20,000Cash flow generated each year: $5,000Total period: 5 YearsDiscount rate: 6%

Question

Discounted cash flows applicationsNet present Value calculations have a broad range of applications in finance.Calculate the NPV of the project based on the information below.Initial investment: 20,000Cashflowgeneratedeachyear:20,000Cash flow generated each year: 5,000Total period: 5 YearsDiscount rate: 6%

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Solution

To calculate the Net Present Value (NPV), we need to discount each year's cash flow and then subtract the initial investment. Here's how to do it:

  1. Calculate the present value (PV) of each year's cash flow. The formula for this is:

    PV = Cash flow / (1 + r)^n

    where r is the discount rate (6% or 0.06 in this case) and n is the year.

    Year 1: PV = 5,000/(1+0.06)1=5,000 / (1 + 0.06)^1 = 4,716.98 Year 2: PV = 5,000/(1+0.06)2=5,000 / (1 + 0.06)^2 = 4,448.10 Year 3: PV = 5,000/(1+0.06)3=5,000 / (1 + 0.06)^3 = 4,197.26 Year 4: PV = 5,000/(1+0.06)4=5,000 / (1 + 0.06)^4 = 3,962.89 Year 5: PV = 5,000/(1+0.06)5=5,000 / (1 + 0.06)^5 = 3,743.92

  2. Add up all the present values:

    Total PV = 4,716.98+4,716.98 + 4,448.10 + 4,197.26+4,197.26 + 3,962.89 + 3,743.92=3,743.92 = 21,069.15

  3. Subtract the initial investment from the total present value to get the NPV:

    NPV = Total PV - Initial investment = 21,069.15−21,069.15 - 20,000 = $1,069.15

So, the NPV of the project is 1,069.15.Thismeansthattheprojectisexpectedtogenerateaprofitof1,069.15. This means that the project is expected to generate a profit of 1,069.15 in today's dollars, after taking into account the time value of money.

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