McCann Co. has identified an investment project with the following cash flows.

Year Cash Flow
1 $860
2 1,210
3 1,470
4 1,625

a. If the discount rate is 11 percent, what is the present value of these cash flows?
b. What is the present value at 16 percent?
c. What is the present value at 30 percent?

The present value at 11% is $3,902.13,$3,479.85  at 16% and $2,615.57  at 30%

Explanation:

The present value formula is given as :

PV=FV/(1+r)^n

Where FV is the future value of cash flows such as the ones given in the question

r is the rate of return at 11%,16% and 30%

n is the applicable time horizon relevant to each of the cash flow.

Find attached spreadsheet for detailed calculations.

Present values @ 11%

Years   Present Value

1               $775

2              $982

3              $1075

4              $1070

Present values @ 16%

Years   Present Value

1               $741

2              $899

3              $942

4              $897

c.

Present values @ 30%

Years   Present Value

1               $662

2              $716

3              $669

4              $569

Explanation:

Cash flows that will be received in future do not have same value as today, because if received today there is an opportunity to reinvest it and get some return. For this reason we calculate the present value of future cash flow.

Discounting method is used to calculate the present values. using following formula of discounting we calculate the PV.

PV  = FV / ( 1 + r )^n

a.

Present values @ 11%

Years   Cash Flows      Discounting       Present Value

1               $860         860 x ( 1 + 11%)^-1            $775

2              $1,210        1,210 x ( 1 + 11%)^-2         $982

3              $1,470        1,470 x ( 1 + 11%)^-3        $1075

4              $1,625        1,625 x ( 1 + 11%)^-4       $1070

b.

Present values @ 16%

Years   Cash Flows      Discounting       Present Value

1               $860         860 x ( 1 + 16%)^-1            $741

2              $1,210        1,210 x ( 1 + 16%)^-2         $899

3              $1,470        1,470 x ( 1 + 16%)^-3        $942

4              $1,625        1,625 x ( 1 + 16%)^-4       $897

c.

Present values @ 30%

Years   Cash Flows      Discounting       Present Value

1               $860         860 x ( 1 + 30%)^-1           $662

2              $1,210        1,210 x ( 1 + 30%)^-2         $716

3              $1,470        1,470 x ( 1 + 30%)^-3        $669

4              $1,625        1,625 x ( 1 + 30%)^-4       $569

As the discount rate increase the Present value of the cash flows  decreases because of discounting factor.

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