Question

An investment project costs $10,000 and has annual cash flows of $2,850 for six years.

  

a.	What is the discounted payback period if the discount rate is 0 percent? (Enter 0 if the project never pays back on a discounted payback basis. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b.	What is the discounted payback period if the discount rate is 5 percent? (Enter 0 if the project never pays back on a discounted payback basis. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
c.	What is the discounted payback period if the discount rate is 19 percent? (Enter 0 if the project never pays back on a discounted payback basis. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

a.

Year	Cash inflow	Present value factor @0%	Present value of cash inflows	Cumulative present value of cash inflows
1	2850	1	2850	2850
2	2850	1	2850	5700
3	2850	1	2850	8550
4	2850	1	2850	11400
5	2850	1	2850	14250
6	2850	1	2850	17100

Initial cost is 10000 and from the table of cumulative present value of cash inflows we can see that 10000 is getting fully recovered after 3rd year
Discounted payback period = year 3 + ( 10000-8550 ) / 2850	3.51	years

b.

Year	Cash inflow	Present value factor @5%	Present value of cash inflows	Cumulative present value of cash inflows
1	2850	0.95238	2714	2714
2	2850	0.90703	2585	5299
3	2850	0.86384	2462	7761
4	2850	0.82270	2345	10106
5	2850	0.78353	2233	12339
6	2850	0.74622	2127	14466

Initial cost is 10000 and from the table of cumulative present value of cash inflows we can see that 10000 is getting fully recovered after 3rd year
Discounted payback period = year 3 + ( 10000-7761 ) / 2345	3.95	years

c.

Year	Cash inflow	Present value factor @19%	Present value of cash inflows	Cumulative present value of cash inflows
1	2850	0.84034	2395	2395
2	2850	0.70616	2013	4408
3	2850	0.59342	1691	6099
4	2850	0.49867	1421	7520
5	2850	0.41905	1194	8714
6	2850	0.35214	1004	9718

Here, the project never pays back

Discounted payback period = 0