Question

Assume SFC requires all projects to have a payback period of 2.2 years or less with a cost of capital of 9%. Would the firm undertake the fertilizer project given the cash flow below under the payback period and discounted payback period rule?

Year	Cash Flow
0	-$28,000
1	12,000
2	15,000
3	11,000

Answer 1

First let us know the payback period;

initial investment to be recovered =>$28,000.

year	cash flow	cumulative cash flow
1	12,000	12,000
2	15,000	(15,000+12,000)=>27,000
3	11,000	(27,000+11,000)=>38,000

so $28,000 is recovered between year 2 and year 3.

payback period = year 2 + (initial investment - cumulative cash flow of year 2) / cash flow of year 3

=> year 2 + (28,000-27,000) / 11,000

=>year 2 + 1000/11000

=>year 2 +0.090909

=>2.09 years.

Since it is less than 2.2 years, the project can be accepted.

Now,

Discounted payback period

discounting factor = 1 /(1+r)^n

r = 9%

=>0.09.

year	cash flow	PV factor	PV factor * cash flow [discounted cash flow]	cumulative cash flow
1	12,000	1/(1.09)^1=>0.91743	(12,000*0.91743)=>11,009.16	11,009.16
2	15,000	1/(1.09)^2=>0.84168	(15,000*0.84168)=>12,625.20	(11009.16+12625.20)=>23,634.36
3	11,000	1/(1.09)^3=>0.77218	(11,000*0.77218)=>8,493.98	(23,634.36+8,493.98)=>32,128.34

so $28,000 is recovered between year 2 and year 3.

payback period = year 2 + (initial investment - cumulative cash flow of year 2) /discounted cash flow of year 3

=>year 2 + (28,000-23,634.36) / 8493.98

=>year 2 + 0.5139

=>2.51 years.

Since discounted payback period is greater than 2.2 years, the project cannot be accepted.