Question

Consider the following two mutually exclusive projects: Year Cash Flow (A) Cash Flow (B) 0 –$ 343,000 –$ 50,000 1 52,000 24,700 2 72,000 22,700 3 72,000 20,200 4 447,000 15,300 Whichever project you choose, if any, you require a return of 16 percent on your investment. a-1 What is the payback period for each project? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

The payback period for each of the project is - project A = 3.33 and project B = 2.13

Explanation:

First of all the payback period means the amount of time it would take for  a company to recover its initial cost or investment which it has invested in the project .

Calculating the payback period for project A

Year   Cash flow      Cumulative    Discounting     Present    Discounted

                                 cash flow        factor              value        cumulative flow

( NOTE - Formula used for discounting factor = 1 / (1 + i)^n, where i = 16% which is the rate of return on the investment and n is the number of years.)

0   -$343,000       -$343,000          1                  -$343,000         -$343,000

1     $52,000         -$291,000          .86206         $44,828           -$298,172

2    $72,000          -$219,000         .74314            $53,508         -$244,665

3    $72,000          -$147,000         .64063            $46,127         -$198,537

4    $447,000         $300,000        .55226           $2,46,874        $48,337

Now we will in which year the cash flow was last negative and then in that we will add ( cumulative cash flow of the year it was last negative / cash flow of the next period ).

= 3 + $147,000 / $447,000

= 3.33 ( payback period for project A )

Calculating the payback period for project B

Year   Cash flow      Cumulative    Discounting     Present    Discounted                                                              

                                   cash flow       factor              value         cash flow

0        -$50,000         -$50,000         1                   -$50,000    -$50,000

1          $24,700          -$25,300         .86206        $21,293       -$28,707

2         $22,700          -$2600            .74314          $16,869      - $11,838

3         $20,200          $17,600           . 64063        $12,941        $1013

4         $15,300           $32,900          .55226         $8,450        $9463

Now we will in which year the cash flow was last negative and then in that we will add ( cumulative cash flow of the year it was last negative / cash flow of the next period ).

= 2 + 2600 / 20,200

= 2.13 ( payback period for project B)