Question

2. 10.00 points An investment project costs $10,000 and has annual cash flows of $2,800 for six years. What is the discounted payback period if the discount rate is zero percent? (Enter 0 if the project never pays back. Round your answer to 2 decimal places, e.g. 32.16.) Discounted payback period years What is the discounted payback period if the discount rate is 4 percent? (Enter 0 if the project never pays back. Round your answer to 2 decimal places, e.g., 32.16.) years Discounted payback period What is the discounted payback period if the discount rate is 21 percent? (Enter 0 if the project never pays back. Round your answer to 2 decimal places, e.g. 32.16.) years Discounted payback period Hints References eBook & Resources

Answer 1

a. The discounted payback period is computed as shown below:

= Investment / Annual cash flow

= $ 10,000 / $ 2,800

= 3.57 years Approximately

b. The discounted payback period is computed as shown below:

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

= $ 2,800 / 1.04¹ + $ 2,800 / 1.04² + $ 2,800 / 1.04³

= $ 7,770.254893

Cumulative discounted cash flows from year 1 to year 4 is computed as follows:

= $ 2,800 / 1.04¹ + $ 2,800 / 1.04² + $ 2,800 / 1.04³ + $ 2,800 / 1.04⁴

= $ 10,163.70663

It means that the discounted payback period lies between year 3 and year 4, since the initial investment of $ 10,000 is recovered between them. So, the discounted payback period will be computed as follows:

= 3 years + Balance investment to be recovered / Year 4 discounted cash flow

= 3 years + [ ($ 10,000 - $ 7,770.254893) / ( $ 2,800 / 1.04⁴) ]

= 3 years + $ 2,229.745107 / $ 2,393.451735

= 3.93 years Approximately

c. The discounted payback period is computed as shown below:

Cumulative discounted cash flow from Year 1 to Year 6 is computed as follows:

= $ 2,800 / 1.21¹ + $ 2,800 / 1.21² + $ 2,800 / 1.21³ + $ 2,800 / 1.21⁴ + $ 2,800 / 1.21⁵ + $ 2,800 / 1.21⁶

= $ 9,084.922431 Approximately

As can be seen the initial investment of $ 10,000 is not recovered, hence the discounted payback period will be never.

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