Question

An investment project costs $10,000 and has annual cash flows of $2,920 for six years.

What is the discounted payback period if the discount rate is zero percent? (Do not round intermediate calculations. Enter 0 if the project never pays back. Round your answer to 2 decimal places, e.g., 32.16.)

Discounted payback period _____ years

What is the discounted payback period if the discount rate is 4 percent? (Do not round intermediate calculations. Enter 0 if the project never pays back. Round your answer to 2 decimal places, e.g., 32.16.)

Discounted payback period     _____       years

What is the discounted payback period if the discount rate is 21 percent? (Do not round intermediate calculations. Enter 0 if the project never pays back. Round your answer to 2 decimal places, e.g., 32.16.)

Discounted payback period      _____       years

Answer 1

Ans-

The discounted payback period (DPP) method is based on the discounted cash flows technique and is used in project valuation as a supplemental screening criterion. In simple words, it is the number of years needed to recover initial cost (cash outflows) of a project from its future cash inflows. To calculate it, we need consequentially add the discounted value of each future cash inflow as long as the initial cost will be recovered

Discounted payback period at 0%

At 0% the discount value is 1 for all year.

Year	cash flows	DF AT 0%	PV	cumulative Pv
1	2,920	1	2,920	2,920
2	2,920	1	2,920	5840
3	2,920	1	2,920	8,760
4	2,920	1	2,920	11,680
5	2,920	1	2,920	14,600
6	2,920	1	2,920	17,520
	Total		17,520

Discounted payback period - 3+ (10,000-8760)/2,920

= 3.425 years

Discounted payback period at 4%

Year	cashflows	DF AT 4%	PV	cumulative pv
1	2,920	0.962	2,809.94	2809.94
2	2,920	0.925	2,701	5,510.94
3	2,920	0.889	2,595.88	8,106.82
4	2,920	0.855	2,584.2	10,691.02
5	2,920	0.822	2,400.24	13,091.26
6	2,920	0.790	2,306.8	15,398.06
	Total		15,398.06

Discounted payback period at 4% = 3 +(10,000-8106.82)/2,920

= 3.65 years

Discounted payback period at 21% :

Year	cashflows	DF at 21%	PV
1	2,920	0.8264	2,413.09
2	2,920	0.6830	1994.36
3	2,920	0.5645	1648.34
4	2,920	0.4665	1,362.18
5	2,920	0.3855	1,125.66
6	2,920	0.3186	930.31
	Total		9,473.94

Discounted payback period at 21% = 0 because the project never pay back the initial investment when the discount rate is 21%