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Find the present values of the following cash flow streams. The appropriate interest rate is 10%. (Hint: It is fairly easy to work this problem dealing with the individual cash flows. However, if you have a financial calculator, read the section of the manual that describes how to enter cash flows such as the ones in this problem. This will take a little time, but the investment will pay huge dividends throughout the course.

Year     Cash Stream A Cash Stream B
1 $100 $300
2 400 400
3 400 400
4 400 400
5 300 100
     
Required:
What is the value of each cash flow stream at a 0 percent interest rate?

Sagot :

Answer:

a. The present value of Cash flow stream A at 10% interest rate is $1,181.50; while the present value of Cash flow streams B at 10% interest rate is $1,239.13.

b. Present value of Cash flow streams A and B at 0% interest rate are both equal to $1,600.

Explanation:

a. Calculations of the present values of Cash Flow Stream A and B at 10% interest rate

The present value (PV) for a particular year can be calculated using the following formula:

PV = FV / (1 + r)^n

Where:

PV = present value of a particular year

FV = Future value or cash stream of a particular year

r = interest rate = 10%

n = The particular year in focus

The present value of cash flow streams at a particular interest rate is the sum of the present values of Cash Stream for all years, and this can be calculated as follows:

Present value of Cash flow stream A at 10% interest rate = (100 / (1 + 10%)^1) + (400 / (1 + 10%)^2) + (400 / (1 + 10%)^3) + (400 / (1 + 10%)^4) + (300 / (1 + 10%)^5) = $1,181.50

Present value of Cash flow streams B at 10% interest rate = (300 / (1 + 10%)^1) + (400 / (1 + 10%)^2) + (400 / (1 + 10%)^3) + (400 / (1 + 10%)^4) + (100 / (1 + 10%)^5) = $1,239.13

b. Calculations of the present values of Cash Flow Stream A and B at 0% interest rate

The present value of cash flow streams at a 0% is simply the sum of Cash Flow Stream for all years, and this can be calculated as follows:

Present value of Cash flow stream A at 0% interest rate = $100 + $400 + $400 + $400 + $300 = $1,600

Present value of Cash flow streams B at 0% interest rate = $300 + $400 + $400 + $400 + $100 = $1,600

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