Given the following cash flows for a capital project, calculate its payback period and discounted payback period. the required rate of return is 8%. the discounted payback period is: year 0 1 2 3 4 5 cash flow –50,000 15,000 15,000 20,000 10,000 5,000 a. 0.16 years longer than the payback period. b. 0.51 years longer than the payback period. c. 1.01 years longer than the payback period.

Ans. c) Discounted period is 1.01 years longer than payback period.

Explanation:

Hi, the payback period is the time that takes for the initial invesment to return to the investor (regardless of the time value of money), so we add the cash flow for every period until the result is zero.

The discounted payback period is almost the same, here we do take into account the time value of money. let´s check out the math to this.

Payback period

PeriodCash FlowAdding cash flows  CoefficientPayback

0        -$50,000.00         -$50,000.00                                3

1         $15,000.00         -$35,000.00            1  

2         $15,000.00         -$20,000.00            1  

3         $20,000.00          $-                                    1  

4         $10,000.00    

5          $5,000.00    

Payback period = 3

Discount rate  8%    

PeriodCash FlowPresent ValueAdding CashCoefficient          

0      -$50,000.00  -$50,000.00    -$50,000.00              

1  $15,000.00            $13,888.88          -$36,111.11           1  

2  $15,000.00             $12,860.08         -$23,251.03           1  

3  $20,000.00             $15,876.64         -$7,374.38           1  

4  $10,000.00             $7,350.29         -$24.09                   1  

5  $5,000.00             $3,402.91                                0.01  

Discounted payback period = 4.01

The only thing here that needs some further explanation is the 0.01, this is by doing the following calculation.

This is the fraction of the year that will turn those $24.09 in zero (taking into account the cash flow of period 5 which is 3402.91)

So, discounted payback period - Payback period= 4.01 - 3 = 1.01

Best of luck.

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