Question

Consider the following two mutually exclusive projects: Year 0 Cash Flow (A) 2360,000 35,000 55,000 55,000 430,000 Cash Flow (B) $45,000 23,000 21,000 18,500 13,600 1 2 3 4 ces Whichever project you choose, if any, you require a return of 14 percent on your investment a-1 What is the payback period for each project? (Do not round Intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) years Project A Project B years

Answer 1

a-1

Year	Investment	Net annual cash flow	Cumulative net cash flow	Balance to be recovered
0	(360,000)		-	360,000.00
1		35,000	35,000	325,000.00
2		55,000	90,000	270,000.00
3		55,000	145,000	215,000.00
4		430,000	575,000	-
Capital is recovered fully in year 4
Pay back period is=	3 + 215000/430000	3.50

Project A payback period is 3.5 years

B

Year	Investment	Net annual cash flow	Cumulative net cash flow	Balance to be recovered
0	(45,000)		-	45,000.00
1		23,000	23,000	22,000.00
2		21,000	44,000	1,000.00
3		18,500	62,500	-
4		13,600	76,100	-
Capital is recovered fully in year 3
Pay back period is=	2 + 1000/18500	2.05

Project B payback period is 2.05 years

a-2

Year	Cash flow	× discount rate	Discounted cash flow	Cumulative present worth	Balance to be recovered
0	$      (360,000)	1.00000	$      (360,000.00)	$                         -	$      360,000.00
1	$          35,000	0.87719	$          30,701.75	$           30,701.75	$      329,298.25
2	$          55,000	0.76947	$          42,320.71	$           73,022.47	$      286,977.53
3	$          55,000	0.67497	$          37,123.43	$         110,145.90	$      249,854.10
4	$       430,000	0.59208	$        254,594.52	$         364,740.42	$                       -
Capital is recovered fully in year	4
Discounted pay back period is	3 + 249854.1 / 254594.52	3.98

Discounted payback period for A is 3.98 years

B

Year	Cash flow	× discount rate	Discounted cash flow	Cumulative present worth	Balance to be recovered
0	$        (45,000)	1.00000	$        (45,000.00)	$                         -	$         45,000.00
1	$          23,000	0.87719	$          20,175.44	$           20,175.44	$         24,824.56
2	$          21,000	0.76947	$          16,158.82	$           36,334.26	$           8,665.74
3	$          18,500	0.67497	$          12,486.97	$           48,821.23	$                       -
4	$          13,600	0.59208	$            8,052.29	$           56,873.52	$                       -
Capital is recovered fully in year	3
Discounted pay back period is	2 + 8665.74 / 12486.97	2.69

Discounted payback period for B is 2.69 years