Question

If a project costs $100,000 and is expected to return $20,000 annually, how long does it take to recover the initial investment? What would be the discounted payback period at i = 15%? Assume that the cash flows occur continuously throughout the year. The payback period is 5 years. (Round to one decimal place.) The discounted payback period at i = 15% would be years. (Round to one decimal place.)

Answer 1

Project Cost = 100,000

Annual Return = 20,000

Interest Rate = 15%

a. Simple Payback Period

Simple Payback Period = Initial Cost ÷ Annual Return

Simple Payback Period = 100,000 ÷ 20,000 = 5 years

b. Discounted Payback Period

Year	CF	PV Factor	DCF	CCF
0	$-100,000	1	$-100,000	$-100,000
1	$20,000	0.87	$17,391.3	$-82,608.7
2	$20,000	0.76	$15,122.87	$-67,485.82
3	$20,000	0.66	$13,150.32	$-54,335.5
4	$20,000	0.57	$11,435.06	$-42,900.43
5	$20,000	0.5	$9,943.53	$-32,956.9
6	$20,000	0.43	$8,646.55	$-24,310.35
7	$20,000	0.38	$7,518.74	$-16,791.61
8	$20,000	0.33	$6,538.04	$-10,253.57
9	$20,000	0.28	$5,685.25	$-4,568.32
10	$20,000	0.25	$4,943.69	$375.37

Discounted Payback Period = 9 + [$-4,568.32 – 0 ÷ $-4,568.32 – ($375.37)] * 1 = 9.9 years