Question

Sky Enterprises is considering an investment project with the following cash flows:

Year                   Cash Flow

0                      -$100,000

1                         30,000

2                         40,000

3                         60,000

4                         90,000

The company has a 7% cost of capital. What is the project’s discounted payback period?

A. 2.76 years
B. 1.86 years
C. 1.86 years
D. 1.67 years
E. more than 3 years

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:

= $ 30,000 / 1.07¹ + $ 40,000 / 1.07²

= $ 62,974.93231

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

= $ 30,000 / 1.07¹ + $ 40,000 / 1.07² + $ 60,000 / 1.07³

= $ 111,952.8049

It means that the discounted payback period lies between year 1 and year 3, since the initial investment of $ 100,000 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 + [ ($ 100,000 - $ 62,974.93231) / ( $ 60,000 / 1.07³) ]

= 2 years + $ 37,025.06769 / $ 48,977.87261

= 2.76 years Approximately

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