Question

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Stern Associates is considering a project that has the following cash flow data. What is the...

Stern Associates is considering a project that has the following cash flow data. What is the project's payback? Show Work!

Year

0

1

2

3

4

5

Cash flows

-$1,000

$400

$410

$420

$430

$440

Solutions

Expert Solution

Answer: 2 years and 166 days ( 2.45 years)

Payback period

When the annual cash flows are not uniform, the cumulative cash inflows from operations must be calculated for each year. The payback period shall be corresponding period when total of cumulative cash inflows is equal to the initial capital investment. However, if exact sum does not match then the period in which it lies should be identified. After that we need to compute the fraction of the year.

Initial capital investment = $1,000

Cash flows

Year

Cash flow

Cumulative cash flow

1

$400

$400

2

$410

$810

3

$420

$1,230

4

$430

$1,660

5

$440

$2,100

Payback period in this case will lie between year 2 and year 3. Since up to 2 years a sum of $810 shall be recovered, balance of $190 shall be recovered in the part (Fraction) of 3rd year, Computation is as follows

            = (Balance recoverable ÷ Cash flow of year 3) * 365 days

= ($190 ÷ $420) * 365 days

            = 165.119 days

                = 166 days

(or in yeas = ($190 ÷ $420) = .45 years)

Payback period = 2 years and 166 days

Note:

$810 will be received in 2 years and cash flow of balance $190 will be received in 166 days(.45 year) . So Total payback period will be 2 years and 166 days (2.45 years)


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