Question

1. 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%.

1. Compute the payback period and the discounted payback period that you would communicate to the management.
2. 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
3. please solve by formula method and not by excel method

Answer 1

A ] Payback Period :

Year	Cash flow ($)	Cumulative Cash flow ($)
1	1	1
2	4	5
3	6	11
4	2	13
5	1	14

Initial Investment = $ 10

Payback Period = 2 years + 5 / 6 X 12month

= 2 years 10 monthB

B] Discounted Payback Period :

Year	Cash flow ($) ( I )	Present value factor @ 15 % (II)	Discounted cash flow($) ( I X II )	Cumulative Discounted cash flow ($)
1	1	0.870	0.87	0.87
2	4	0.756	3.02	3.89
3	6	0.658	3.95	7.84
4	2	0.572	1.14	8.98
5	1	0.497	0.50	9.48

Discounted Payback Period = From the above calculation by considering discounted cash flow company initial investment (Capital) will not come back with this 5 years.

Mangement communication : from the above calculation - without considering time value of money company can get back capital at the end of 3rd year and considering time value of money within 5 year capital will get back. Because after 3 year project not generating good cash flow (Profit).

C] Now If opportunity cost of capital will be @ 2% the discounted payback period =

Year	Cash flow ($) ( I )	Present value factor @ 2% (II)	Discounted cash flow($) ( I X II )	Cumulative Discounted cash flow ($)
1	1	0.980	0.98	0.98
2	4	0.961	3.84	4.82
3	6	0.942	5.65	10.47
4	2	0.924	1.85	12.32
5	1	0.906	0.91	13.23

Discounted Cash flow = 2 years + 5.18 / 5.65 X 12 month

= 2 years + 11 month

= 2 years 11 month

Management communication : If the scenario will change and any negative benchmark ratesand if opportunity cost will be @ 2% then discounted payback period will be 2 years 11 month as comparing with payback period not big difference in come back to diployed capital.