Question

Q4. (25 marks) Alina Smith is considering an investment which will cost her $120,000. The investment produces no cash flows for the first year. In the second year the cash inflow is $35,000. This inflow will increase to $55,000 and then $75,000 for the following two years before ceasing permanently. Alina requires a 10 % rate of return and has a required discounted payback period of three years. Calculate discounted payback period and comment whether the project should be accepted or not.

Answer 1

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Answer
Payback refers to the time taken by the project to recover its initial investment
We calculate cumulative cash flows for calculating the payback period

Cash flows are discounted at 10% .

Year	Cash flows	Discounted cash flows	Cumulative cash flows
0	-120000	-120000	-120000
1	0	0	0
2	35000	28925.62	-91074.4
3	55000	41322.31	-49752.1
4	75000	51226.01	1473.943

As we see the cumulative cash flows become positive between the end of 3rd and 4 th year .
D.P.B = 3 + (49752/51226.01)
= 3+ .97
= 3.97 years

The discounted payback period is greater than 3 years. The PROJECT SHOULD NOT BE ACCEPTED .