Question

An investment project costs $10,000 and has annual cash flows of $2,890 for six years. 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.) Discounted payback period years What is the discounted payback period if the discount rate is 4 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.) Discounted payback period years What is the discounted payback period if the discount rate is 21 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.) Discounted payback period years

Answer 1

Discounted Payback period = A + |B|/C

A = Last period with a negative discounted cumulative cash flow

|B| = Absolute value of discounted cumulative cash flow at end of period A

C = Discounted cash flow during the period after A

Discounted payback at 0%

		Rate = R =	0.000000000%
Year	Cash flows	Cumulative cash flow	Discount factor = Df = 1/(1+R)^Year	Present value = Df x Cash flows	Cumulative discounted cash flow
0	-$10,000.00	-$10,000.00	1.00000	-$10,000.00	-$10,000.00
1	$2,890.00	-$7,110.00	1.00000	$2,890.00	-$7,110.00
2	$2,890.00	-$4,220.00	1.00000	$2,890.00	-$4,220.00
3	$2,890.00	-$1,330.00	1.00000	$2,890.00	-$1,330.00
4	$2,890.00	$1,560.00	1.00000	$2,890.00	$1,560.00
5	$2,890.00	$4,450.00	1.00000	$2,890.00	$4,450.00
6	$2,890.00	$7,340.00	1.00000	$2,890.00	$7,340.00
			Total of Present Value = NPV=	$7,340.00

Discounted Payback period = 3 + 1330/2890

Discounted Payback period = 3.46 years

Discounted payback period at 4%

		Rate = R =	4.000000000%
Year	Cash flows	Cumulative cash flow	Discount factor = Df = 1/(1+R)^Year	Present value = Df x Cash flows	Cumulative discounted cash flow
0	-$10,000.00	-$10,000.00	1.00000	-$10,000.00	-$10,000.00
1	$2,890.00	-$7,110.00	0.96154	$2,778.85	-$7,221.15
2	$2,890.00	-$4,220.00	0.92456	$2,671.97	-$4,549.19
3	$2,890.00	-$1,330.00	0.88900	$2,569.20	-$1,979.99
4	$2,890.00	$1,560.00	0.85480	$2,470.38	$490.40
5	$2,890.00	$4,450.00	0.82193	$2,375.37	$2,865.77
6	$2,890.00	$7,340.00	0.79031	$2,284.01	$5,149.78
			Total of Present Value = NPV=	$5,149.78

Discounted Payback period = 3 + 1979.99/2470.38

Discounted Payback period = 3.80 years

Discounted payback period at 21%

		Rate = R =	21.000000000%
Year	Cash flows	Cumulative cash flow	Discount factor = Df = 1/(1+R)^Year	Present value = Df x Cash flows	Cumulative discounted cash flow
0	-$10,000.00	-$10,000.00	1.00000	-$10,000.00	-$10,000.00
1	$2,890.00	-$7,110.00	0.82645	$2,388.43	-$7,611.57
2	$2,890.00	-$4,220.00	0.68301	$1,973.91	-$5,637.66
3	$2,890.00	-$1,330.00	0.56447	$1,631.33	-$4,006.33
4	$2,890.00	$1,560.00	0.46651	$1,348.21	-$2,658.13
5	$2,890.00	$4,450.00	0.38554	$1,114.22	-$1,543.91
6	$2,890.00	$7,340.00	0.31863	$920.84	-$623.06
			Total of Present Value = NPV=	-$623.06

Project is not paying back on discounted payback basis.

As there is no recovery of or say NPV is negative at 21% hence,

Discounted Payback period = 0