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An investment project has annual cash inflows of $4,600, $3,700, $4,900, and $4,100, for the next four years, respectively. The discount rate is 13 percent.
A. What is the discounted payback period for these cash flows if the initial cost is $5,500?
B. What is the discounted payback period for these cash flows if the initial cost is $7,600?
C. What is the discounted payback period for these cash flows if the initial cost is $10,600?

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Answer:

A. What is the discounted payback period for these cash flows if the initial cost is $5,500?

$5,500 - $4,070.80 = $1,429.20

$1,429.20 / $2,897.64 = 0.49

discounted payback period = 1.49 years

B. What is the discounted payback period for these cash flows if the initial cost is $7,600?

$7,600 - $4,070.80 - $2,897.64 = $631.56

$631.56 / $3,395.95 = 0.19

discounted payback period = 2.19 years

C. What is the discounted payback period for these cash flows if the initial cost is $10,600?

$10,600 - $4,070.80 - $2,897.64 - $3,395.95 = $235.61

$235.61 / $2,514.61 = 0.09

discounted payback period = 3.09 years

Explanation:

year                 annual cash flows                discounted cash flows

1                         $4,600                            = $4,600/1.13 = $4,070.80

2                        $3,700                            = $3,700/1.13² = $2,897.64

3                        $4,900                            = $4,900/1.13³ = $3,395.95

4                        $4,100                             = $4,100/1.13⁴ = $2,514.61

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