Question

There are two machine learning projects available to the Chief Information Officer (CIO). The IBM project requires a $10 million dollar investment today followed by $1.8 milion of ongoing support costs aver 4 years (assume end of year cash flows). The Google project requires a $11.5 million dollar investment today followed by $1.5 million of ongoing support costs over S years (assume end of year cash flows). Assuming that each project can be renewed again at the same costs for the same time period, which project should the CIO pick? The discount rate is 15%. Draw a timeline diagram to show the cash flows. What is the payback period for each project if they both support the same annual operating cash inflow of $10 million (assume end of year cash flows?

Answer 1

In order to make decison which machine project to chose we shall calculate the sum of present value of cash outflows

For IBM Project : Total cash outflow = $15.14 M ( calculated below)

Years	Cash outflow( a)	Discounting Factor = 1/(1+r)^n - (b)	Present Value (a*b)
0	10	1	10
1	1.8	0.869565217	1.565217391
2	1.8	0.756143667	1.361058601
3	1.8	0.657516232	1.183529218
4	1.8	0.571753246	1.029155842
Total Cash outflow at time= 0	15.13896105

For Google Project : Total cash outflow = $16.53 M ( calculated below)

Years	Cash outflow( a)	Discounting Factor = 1/(1+r)^n - (b)	Present Value (a*b)
0	11.5	1	11.5
1	1.5	0.869565217	1.304347826
2	1.5	0.756143667	1.134215501
3	1.5	0.657516232	0.986274349
4	1.5	0.571753246	0.857629868
5	1.5	0.497176735	0.745765103
Total Cash outflow at time= 0	16.52823265

CIO will pick IBM Project as IBM Project as lesses present value of cash outflows. Ie will cost less compared to Google.

Payback period = No of years in which initial investment is recovered

Years	Cash Inflows	Cummulative Cash Inflows
1	10	10
2	10	20
3	10	30
4	10	40
5	10	50

So for IBM payback period = 1 + ( 10 - 5.14) / 10 = 1 + 0.486 = 1.486 years

For Google Project , Payback period = 1 + ( 10 - 6.53) / 10 = 1 + 0.653 = 1.653 years.