Question

Cash Payback Method (Even cash flows)

Suppose that a particular investment required an up-front capital outlay of $100,000. This investment is expected to yield cash flows of $40,000 per year for 10 years. What is the payback period for this investment? If required, round your answer to two decimal places.

Cash Payback Period = $ / $ =  years

Payback Period (Uneven cash flows)

When the annual cash flows are unequal, the payback period is computed by adding the annual cash flows until such time as the original investment is recovered. If a fraction of a year is needed, it is assumed that cash flows occur evenly within each year.

The steps for determining the payback period with uneven cash flows is as follows:

1. Add the annual cash flows to one another until the investment is recovered.
2. For each full year's worth of cash flows consumed, add that year to your calculation for total payback years.
3. If you arrive at a point where only part of the year's cash flows are needed, only add the fraction of the year's cash flows relevant to recovering the initial investment to the total payback years.
4. If the unrecovered investment is greater than the annual cash flow, the payback period is "1". If the unrecovered investment is less than the annual cash flow the time needed for payback is computed by dividing the unrecovered investment by the annual cash flow for than year.

+ Explanation of Time Needed for Payback with uneven cash flows

Note: For each year in which the unrecovered investment meets or exceeds the annual cash flow, this is 1. For years in which the annual cash flow exceeds the unrecovered investment, this is the unrecovered investment divided by the annual cash flow for that year.

If				Then
Unrecovered Investment	≥	Annual Cash Flow		Time Needed for Payback	=	1 year
Unrecovered Investment	<	Annual Cash Flow		Time Needed for Payback	=	Unrecovered Investment
						Annual Cash Flow for the Year

Compute the time needed for payback for the following example assuming the investment required an up-front capital outlay of $100,000 and the uneven annual cash flows for each year are provided in the table. If an amount is zero, enter "0". For the time needed for payback, enter your answer to one decimal place, if less than one year (i.e. 0.2, 0.5, etc.).

Year	Unrecovered Investment (Beginning of year)	Annual Cash Flow		Time Needed for Payback
1	$100,000	$50,000		1 year
2		30,000
3		40,000
4		20,000
5		10,000

Total time needed for payback (to the nearest tenth of a year) = years

Answer 1

Cash payback Method (even cash flows)=Initial Investment /Expected annul cash flow

Initial Outlay =$100,000

Expected inflow =$40,000 per year for 10 years

Payback period =$100,000/$40,000=2.50 years

Payback period (Uneven cash flows)

Payback period =Years until payback+un recovered investment/Annual cash flow for the year

Initial Outlay =$100,000 Inflow year 1 $50,000 year 2 $30,000 year 3 $40,000 year 4 $20,000 year 5 $10,000

After 2 years the un recovered investment =$20,000 Year 3 cash flow =$40,000

So payback occurs some time between years 2 and 3

Payback period =2+$20,000/$40,000=2.5 years

Year	Unrecovered investment beginning of the year	Annual Cash flow	Time Needed for Payback
1	($100,000)	$50,000	1 year
2	($50,000)	30,000	1 year
3	($20,000)	40,000	20/40=0.5 years
4	0	$20,000	0
5	0	$10,000	0

Total Time needed for payback =1+1+.5 =2.5years