Question

Sisyphean Company is planning on investing in a new project. This will involve the purchase of some new machinery costing $450,000. The Sisyphean Company expects cash inflows from this project as detailed below:

Year One Year Two Year Three Year Four

$200,000 $225,000 $275,000 $200,000

the appropriate discount for this project is 12%

the discounted payback for this period is closest to

2.1

3.0

2.0

2.5

Answer 1

The discounted payback period is computed as shown below:

Cumulative discounted cash flows from year 1 to year 2 is computed as follows:

= $ 200,000 / 1.12¹ + $ 225,000 / 1.12²

= $ 357,940.051

Cumulative discounted cash flows from year 1 to year 3 is computed as follows:

= $ 200,000 / 1.12¹ + $ 225,000 / 1.12² + $ 275,000 / 1.12³

= $ 553,679.6192

It means that the discounted payback period lies between year 2 and year 3, since the initial investment of $ 450,000 is recovered between them. So, the discounted payback period will be computed as follows:

= 2 years + Balance investment to be recovered / Year 3 discounted cash flow

= 2 years + [ ($ 450,000 - $ 357,940.051) / ( $ 275,000 / 1.12³) ]

= 2 years + $ 92,059.949 / $ 195,739.5681

= 2.5 years Approximately

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