Question

An investment project has annual cash inflows of $3,200, $4,100, $5,300, and $4,500, and a discount rate of 14 percent. What is the discounted payback period for these cash flows if the initial cost is $5,900?

Answer 1

initial cost = $5,900.

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

here,

r= 14%=>0.14.

year	cash flow	discounting factor	cash flow * discount factor	cumulative cash flow
1	3200	1/(1.14)^1=>0.87719	(3200*0.87719)=>2807.008	2807.008
2	4100	1/(1.14)^2=>0.76947	(4100*0.76947)=>3154.827	2807.008+3154.827=>5,916.835
3	5300	1/(1.14)^3=>0.67497	(5300*0.67497)=>3,577.341	not needed since 5900 is recovered
4	4500	1/(1.14)^4=>0.59208	(4500*0.59208)=>2,664.36	not needed since 5900 is recovered

we can see that initial cost of 5900 has been recovered by end of second year.

precise discounted payback period = 1 year + (initial cost - cumulative cash flow of previous year) / (discounted cash flow of current year)

=>1 year + (5900-2807.008) / (3154.827)

=>1 +0.98

=>1.98 years.