Question

XYZ firm is a technology firm operating in a sector which is highly competitive and disruptive. The management has identified an investment in a new technology that will result in substantial savings. The investment in the new project is $ 10 million. The project delivers the cash flow starting year 1 as follows for the next 5 years: $ 1, 4, 6, 2, and 1 million. You are in the board meeting and want to understand the time taken for the deployed capital to come back to you. The firm is operating in a country that has traditionally high discount rates. The opportunity cost of capital for the investors in this firm is 15%.

a. Compute the payback period and the discounted payback period that you would communicate to the management.

b. Suppose, in a country with negative benchmark rates, a similar investment would have an opportunity cost of capital of 2%.

Will there be any adjust- ments to the payback and discounted payback periods communicated to the management in such a scenario, why ?

Answer 1

A-
When opportunity cost and discount rate is 15%
Payback period					Discounted Payback period
Year	cash flow	cumulative cash flow			Year	cash flow	present value of cash flow = cash flow/(1+r)^n r =15%	cumulative cash flow
0	-10				0	-10	-10
1	1	1			1	1	0.869565	0.869565
2	4	5			2	4	3.024575	4.869565
3	6	5	amount to be recovered in year 3		3	6	3.945097	8.814663
4	2				4	2	1.143506	9.958169
5	1				5	1	0.497177	0.041831
Payback period in Years =year before final year of recovery+(amount to be recovered/cash flow of final year of recovery)	2+(5/6)	2.83			Discounted Payback period in Years =year before final year of recovery+(present value that to be recovered/present value of cash flow of final year of recovery)	4+(.0418/.4971)		4.08
B-
When opportunity cost and discount rate is 2%
Year	cash flow	cumulative cash flow			Discounted Payback period
0	-10				Year	cash flow	present value of cash flow = cash flow/(1+r)^n r =2%	cumulative cash flow
1	1	1			0	-10	-10
2	4	5			1	1	0.980392	0.980392
3	6	5			2	4	3.844675	4.980392
4	2				3	6	5.653934	5.019608
5	1				4	2	1.847691
Payback period in Years =year before final year of recovery+(amount to be recovered/cash flow of final year of recovery)	2+(5/6)	2.83			5	1	0.905731
					Discounted Payback period in Years =year before final year of recovery+(present value that to be recovered/present value of cash flow of final year of recovery)	2+(5.0196/5.6539)		2.89
This change will bring no change in payback period but discounted payback period will reduce to 2.89 year in B in comparison to 4.08 Years in Plan A