Question

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	$10,000		1 year
2		20,000
3		30,000
4		40,000
5		50,000

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

The average rate of return is another method that does not use present value and is commonly used in making capital investment decisions. Unlike the cash payback method, the average rate of return focuses on income rather than cash flow.

Assume that the investment involves an initial outlay of $100,000 with a five-year useful life and no salvage value under straight-line depreciation. The revenues are as follows: Year 1 - $10,000, Year 2 - $20,000, Year 3 - $30,000, Year 4 - $40,000 and Year 5 - $50,000.

Use the minus sign to indicate a net loss. If an amount is zero, enter "0".

Year		Revenues		Expenses		Net Income
Year 1 Net Income (loss)	=	$	-	$	=	$
Year 2 Net Income (loss)	=		-		=
Year 3 Net Income (loss)	=		-		=
Year 4 Net Income (loss)	=		-		=
Year 5 Net Income (loss)	=		-		=

Total Net Income (five years) = $

Average Net Income =

$

= $

Average Rate of Return =

$ $

=  %

Answer 1

Cash flow is calaculated as follows

Uneven Cash Flow = Initial Investment/Perodic cash flow

However is the cases of uneven cash follows

Payback can be calculated using the formula = Years before full recovery + Uncover cost start of the year dived by cash flow during the year

So Initial ivestment = 1,00,000

Years of cash Flow=10000+20000+ 30000+40000

Pay back period is   =4years

Average Net Inome= Total cash flow/no of years =150000/5= 3000=

Average Rate of Return +Total Net Profit /No of years /inital Cost *100

=150000/5/100000*100=30

ARR=30%