Question

andes, Inc. is considering the purchase of robots for its fulfillment centers at a cost of $10 million. The use of robots is expected to generate annual savings in labor costs as shown below. MARR is 15% per year compounded annually.

End of Year 2 3 4 5 Annual savings $3 million $3 million $3 million $4 million $4 million a) (8 points) Compute the simple payback period for this replacement option. b) (12 points) Determine the discounted payback period (DPBP). It is enough if you determine in which year the DPBP falls.

Answer 1

a)

Year	Cash Flow ($ Million)	Initial Cost left to Reduce	Time lapsed (Years)
0		10	0
1	3	7	1
2	3	4	2
3	3	1	3
4	4	0.25	3.25
5	4

The cash outflow = Cost of the robot = $ 10 million

At the end of 3rd year, $ 1 Million is left to be covered so that the entire $10 Million is covered.

In the 4th year, $ 1 Million would be covered in ($ 1 Million)/($ 4 Million) = 0.25 Year

The simple payback period = 3 Year + ($10 million - ($ 3 Million + $ 3 Million + $ 3 Million)) /($ 4 Million) * 1

= 3 Year + (1/4)*12 month

= 3.25 Year

Hence, the simple payback period is 3.25 Year

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b)

Discounted Cashflow at MARR of 15% per year is:

Year	Cash Flow ($ Million)	Discounted Cash Flow ($ Million)
0	0	0
1	3	2.608696
2	3	2.268431
3	3	1.972549
4	4	2.287013
5	4	1.988707

To evaluate the discounted payback period, find the number of years in which the discounted cash flow would be enough to cover $ 10 million.

Year	Cash Flow ($ Million)	Discounted Cash Flow ($ Million)	Initial Cost left to Reduce ($ Million)	Time lapsed (Years)
0	0	0	10	0
1	3	2.608696	7.391304348	1
2	3	2.268431	5.122873346	2
3	3	1.972549	3.150324649	3
4	4	2.287013	0.863311666	4
5	4	1.988707	0.434107031	4.434107031

At the end of 4th year, $ 0.863311666 Million is left to be covered

In the 5th year, the discounted cash flow = $ 1.988707 Million

Thus, the time period required to cover $ 0.863311666 Million is ($ 0.863311666 Million/$ 1.988707 Million) = 0.434107031 Year

Thus, 4.434107031 Years is the discounted payback period.