Question

Consider the following two mutually exclusive projects:

  

Year	Cash Flow (A)	Cash Flow (B)
0	–$261,339	–$15,269
1	25,300	4,848
2	52,000	8,223
3	54,000	13,542
4	406,000	9,270

  

Whichever project you choose, if any, you require a 6 percent return on your investment.

Required:

(a)	What is the payback period for Project A?

   

(b)	What is the payback period for Project B?

(c)	What is the discounted payback period for Project A?

Answer 1

a

Project A
Year	Cash flow stream	Cumulative cash flow
0	-261339	-261339
1	25300	-236039
2	52000	-184039
3	54000	-130039
4	406000	275961

Payback period is the time by which undiscounted cashflow cover the intial investment outlay

this is happening between year 3 and 4

therefore by interpolation payback period = 3 + (0-(-130039))/(275961-(-130039))

3.32 Years

b

Project B
Year	Cash flow stream	Cumulative cash flow
0	-15269	-15269
1	4848	-10421
2	8223	-2198
3	13542	11344
4	9270	20614

Payback period is the time by which undiscounted cashflow cover the intial investment outlay

this is happening between year 2 and 3

therefore by interpolation payback period = 2 + (0-(-2198))/(11344-(-2198))

2.16 Years

c

Project A			Discount rate=	9.00%
Year	Cash flow stream	Cumulative cash flow	Discounting factor	Discounted cash flows project	Cumulative discounted CF
0	-261339	-261339	1	-261339	-261339.00
1	25300	-236039	1.09	23211.00917	-238127.99
2	52000	-184039	1.1881	43767.35965	-194360.63
3	54000	-130039	1.295029	41697.90792	-152662.72
4	406000	275961	1.41158161	287620.6357	134957.91

Discounted payback period is the time by which discounted cashflow cover the intial investment outlay

this is happening between year 3 and 4

therefore by interpolation payback period = 3 + (0-(-152662.72))/(134957.91-(-152662.72))

3.53 Years

Where

Discounting factor =(1 + discount rate)^(corresponding year)

Discounted Cashflow=Cash flow stream/discounting factor