Question

An investment project has annual cash inflows of $4,400, $3,900, $5,100, and $4,300, for the next four years, respectively. The discount rate is 14 percent. a. What is the discounted payback period for these cash flows if the initial cost is $5,700? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. What is the discounted payback period for these cash flows if the initial cost is $7,800? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) c. What is the discounted payback period for these cash flows if the initial cost is $10,800? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

Discounted payback period shall be as follows:

a. 1 year 7.36 months

b. 2 years 3.27 months

c. 3 years 2.9 months

Explanation:

a. Payback period in case of cash outflow = $5,700

For calculating the pay back period we shall firstly discount the cash flows to present value @14 %.

Year         Cash Flow         PV Factor           PV of Cash Flow       Cumulative

                                                                                                            Cash Flow

0                 -  $5,700            1                             - $5,700                    -5,700

1                     $4,400         0.877                         $3,858.8                -$1,841.2

2                    $3,900         0.770                         $3,003                    $1,161.8

Since the cumulative cash flows are positive in 2nd year payback period =

1 + $\frac{1,841.2}{3,003} \times 12$ = 1 year and 7.36 months

b. Payback period in case of cash outflow = $7,800

For calculating the pay back period we shall firstly discount the cash flows to present value @14 %.

Year         Cash Flow         PV Factor           PV of Cash Flow       Cumulative

                                                                                                            Cash Flow

0                 -  $7,800            1                             - $7,800                    -7,800

1                     $4,400         0.877                         $3,858.8                -$3,941.2

2                    $3,900         0.770                         $3,003                    -$938.2

3                    $5,100          0.675                         $3,442.5                  $2,504.3

Since the cumulative cash flows are positive in 3rd year payback period =

2 + $\frac{938.2}{3,442.5} \times 12$ = 2 years and 3.27 months

b. Payback period in case of cash outflow = $10,800

For calculating the pay back period we shall firstly discount the cash flows to present value @14 %.

Year         Cash Flow         PV Factor           PV of Cash Flow       Cumulative

                                                                                                            Cash Flow

0               -  $10,800            1                          - $10,800                   -$10,800

1                   $4,400         0.877                         $3,858.8                 -$6,941.2

2                  $3,900         0.770                         $3,003                    -$3,938.2

3                  $5,100          0.675                         $3,442.5                   -$495.7

4                  $4,300          0.592                        $2,545.6                   $2,049.9

Since the cumulative cash flows are positive in 4th year payback period =

3 + $\frac{495.7}{2,049.9} \times 12$ = 3 years and 2.9 months

Final Answer

Discounted payback period shall be as follows:

a. 1 year 7.36 months

b. 2 years 3.27 months

c. 3 years 2.9 months