Question

1. value: 10.00 points An investment project costs $10,000 and has annual cash flows of $2,980 for six years. What is the discounted payback period if the discount rate is zero percent? (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? (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? (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

Discounted payback period = A + B/C

A = Last period having negative discounted cash flow

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

C = Value of discounted cash flow after period A

1.

Year	Cash Flow (C)	PV Factor computation	PV Factor (F)	Discounted Cash Flow C x F	Cumulative Discounted Cash Flow
0	-$10,000	1/ (1+0.0)0	1	-$10,000	-$10,000
1	$2,980	1/ (1+0.0)1	1	$2,980	-$7,020
2	$2,980	1/ (1+0.0)2	1	$2,980	-$4,040
3	$2,980	1/ (1+0.0)3	1	$2,980	-$1,060
4	$2,980	1/ (1+0.0)4	1	$2,980	$1,920
5	$2,980	1/ (1+0.0)5	1	$2,980	$4,900
6	$2,980	1/ (1+0.0)6	1	$2,980	$7,880

Discounted payback period = 3 + $1,060/$2,980 = 3 + 0.355704698 = 3.355704698 or 3.36 years

2.

Year	Cash Flow (C)	PV Factor computation	PV Factor (F)	Discounted Cash Flow C x F	Cumulative Discounted Cash Flow
0	-$10,000	1/ (1+0.04)0	1	-$10,000.0000	-$10,000.0000
1	$2980	1/ (1+0.04)1	0.961538462	$2,865.3846	-$7,134.6154
2	$2980	1/ (1+0.04)2	0.924556213	$2,755.1775	-$4,379.4379
3	$2980	1/ (1+0.04)3	0.888996359	$2,649.2091	-$1,730.2287
4	$2980	1/ (1+0.04)4	0.854804191	$2,547.3165	$817.0878
5	$2980	1/ (1+0.04)5	0.821927107	$2,449.3428	$3,266.4305
6	$2980	1/ (1+0.04)6	0.790314526	$2,355.1373	$5,621.5678

Discounted payback period = 3 + $1,730.2287/$2,547.3165 = 3 + 0.679235855 = 3.679235855 or 3.68 years

3.

Year	Cash Flow (C)	PV Factor computation	PV Factor (F)	Discounted Cash Flow C x F	Cumulative Discounted Cash Flow
0	-$10,000	1/ (1+0.21)0	1	-$10,000.0000	-$10,000.0000
1	$2,980	1/ (1+0.21)1	0.826446281	$2,462.8099	-$7,537.1901
2	$2,980	1/ (1+0.21)2	0.683013455	$2,035.3801	-$5,501.8100
3	$2,980	1/ (1+0.21)3	0.56447393	$1,682.1323	-$3,819.6777
4	$2,980	1/ (1+0.21)4	0.46650738	$1,390.1920	-$2,429.4857
5	$2,980	1/ (1+0.21)5	0.385543289	$1,148.9190	-$1,280.5667
6	$2,980	1/ (1+0.21)6	0.318630818	$949.5198	-$331.0468

Discounted payback period is 0 years.