Question

1. A company is using the Payback method to determine which project should be selected. The choice is between two machines: Machine A and Machine B. The machines both have a useful life of 10 years. Which machine should be selected based on the following cash flows and what is its payback period?

   Year 1	Machine A	Machine B
   0	($500,000)	($500,000)
   1	$100,000	$ 25,000
   2	$ 95,000	$ 50,000
   3	$ 85,000	$ 75,000
   4	$ 75,000	$100,000
   5	$ 65,000	$125,000
   6	$ 55,000	$150,000
   7	$ 45,000	$175,000
   8	$ 35,000	$200,000
   9	$ 25,000	$225,000
   10	$ 15,000	$250,000

   	A.	Machine A should be selected. Payback is 4.68 years.
   	B.	Machine B should be selected. Payback is 5.83 years.
   	C.	Machine A should be selected. Payback is 6.12 years.
   	D.	Machine B should be selected. Payback is 6.60 years.

Answer 1

Payback period represents the time period in which the initial investment in a project is recovered.

Payback period of Machine A is computed as follows:

The cumulative cash inflow of year 1, 2, 3, 4, 5 and 6 is computed as follows:

= $ 100,000 + $ 95,000 + $ 85,000 + $ 75,000 + $ 65,000 + $ 55,000

= $ 475,000

The cumulative cash inflow of year 1, 2, 3, 4, 5, 6 and 7 is computed as follows:

= $ 100,000 + $ 95,000 + $ 85,000 + $ 75,000 + $ 65,000 + $ 55,000 + $ 45,000

= $ 520,000

It means that the initial investment of $ 500,000 is recovered between year 6 and year 7 and hence the payback period lies between year 6 and year 7 and is computed as follows:

= 6 years + Remaining investment to be recovered / Year 7 cash inflow

= 6 years + ( $ 500,000 - $ 475,000) / $ 45,000

= 6.56 years Approximately

Payback period of Machine B is computed as follows:

The cumulative cash inflow of year 1, 2, 3, 4, 5 is computed as follows:

= $ 25,000 + $ 50,000 + $ 75,000 + $ 100,000 + $ 125,000

= $ 375,000

The cumulative cash inflow of year 1, 2, 3, 4, 5 and 6 is computed as follows:

= $ 25,000 + $ 50,000 + $ 75,000 + $ 100,000 + $ 125,000 + $ 150,000

= $ 525,000

It means that the initial investment of $ 500,000 is recovered between year 5 and year 6 and hence the payback period lies between year 5 and year 6 and is computed as follows:

= 5 years + Remaining investment to be recovered / Year 6 cash inflow

= 5 years + ( $ 500,000 - $ 375,000) / $ 150,000

= 5.83 years Approximately

So, the correct answer is option B.

Feel free to ask in case of any query relating to this question

Payback period represents the time period in which the initial investment in a project is recovered.

Payback period of Investment A is computed as follows:

The cumulative cash inflow of year 1, 2 and 3 is computed as follows:

= $ 25,000 + $ 15,000 + $ 30,000

= $ 70,000

The cumulative cash inflow of year 1, 2, 3 and 4 is computed as follows:

= $ 25,000 + $ 15,000 + $ 30,000 + $ 30,000

= $ 100,000

It means that the initial investment of $ 95,000 is recovered between year 3 and year 4 and hence the payback period lies between year 3 and year 4 and is computed as follows:

= 3 years + Remaining investment to be recovered / Year 4 cash inflow

= 3 years + ( $ 95,000 - $ 70,000) / $ 30,000

= 3.83 years Approximately