Question

An investment project costs $17,200 and has annual cash flows of $4,200 for six years.

  

a. What is the discounted payback period if the discount rate is zero percent?

4.10 4.18 4.01 4.45 3.75

  

b. What is the discounted payback period if the discount rate is 3 percent?

4.44 4.53 4.35 4.79 4.09

  

c. What is the discounted payback period if the discount rate is 20 percent?

Never 1.02 3.98 3.35 4.35

Answer 1

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

= Investment / Annual cash flow

= $ 17,200 / $ 4,200

= 4.10 Approximately

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

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

= $ 4,200 / 1.03¹ + $ 4,200 / 1.03² + $ 4,200 / 1.03³ + $ 4,200 / 1.03⁴

= $ 15,611.81329

Cumulative discounted cash flows from year 1 to year 5 is computed as follows:

= $ 4,200 / 1.03¹ + $ 4,200 / 1.03² + $ 4,200 / 1.03³ + $ 4,200 / 1.03⁴ + $ 4,200 / 1.03⁵

= $ 19,234.77019

It means that the discounted payback period lies between year 4 and year 5, since the initial investment of $ 17,200 is recovered between them. So, the discounted payback period will be computed as follows:

= 4 years + Balance investment to be recovered / Year 5 discounted cash flow

= 4 years + [ ($ 17,200 - $ 15,611.81329) / ( $ 4,200 / 1.03⁵) ]

= 4 years + $ 1,588.18671 / $ 3,622.956894

= 4.44 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:

= $ 4,200 / 1.20¹ + $ 4,200 / 1.20² + $ 4,200 / 1.20³ + $ 4,200 / 1.20⁴ + $ 4,200 / 1.20⁵ + $ 4,200 / 1.20⁶

= $ 13,967.14 Approximately

As can be seen the initial investment of $ 17,200 is not recovered, hence the correct answer is option of Never.

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