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Mastery Problem: Cash Payback and Average Rate of Return (Advanced)

Companies use capital investment analysis to evaluate long-term investments. Capital investment evaluation methods that do not use present values are (1) Average rate of return method and (2) Cash payback method.

Methods that do not use present value

One category of capital investment evaluation methods does not use present value. The primary difference between the category of methods that do use present value and this category is that this category does not  take the time value of money into account. The basic premise of the time value of money is that a dollar today is worth more than  a dollar tomorrow.

True or False: Considering the fact that most firms use methods from each category, it can be concluded that both categories have value.
True

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Cash Payback Method

This method identifies how long it will take (in years) to recover the initial investment . The particulars of the method vary depending on whether the cash flows from an investment are even or uneven.

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 $50,000 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

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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	$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

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Average Rate of Return

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

a	Calculation of Payback Period
Yr	Un recovered Investment	Annual Cash Flow	Cumulative Cash Flow	Time Needed for payback
	beginning of yr
1	$100,000	$10,000	$10,000	1 yr
2		$20,000	$30,000	2 yr
3		$30,000	$60,000	3 yr
4		$40,000	$100,000	4 th yr is the payback period	Initial Investment/Cumulative Cash Flows
5		$50,000	$150,000
b	Calculation of Average Rate of Return
	Calculation of Net Income
	Yr	Revenue	Expenses	Net Income
	1	$10,000	$20,000	($10,000)
	2	$20,000	$20,000	$0
	3	$30,000	$20,000	$10,000
	4	$40,000	$20,000	$20,000
	5	$50,000	$20,000	$30,000
		Total Earnings		$50,000
		Estimated life		$5
		Average Net Income	Total Earnings/Estimated Life	$10,000
		ARR	(Annual Average Net Earnings after Tax /Average Investment over the life of the project)*100	20%
			$10000/$50000*100
		Average Investment	(Initial Investment-salvage value)/2
			$100000/2
			$50,000
	Calculation of Depreciation
	Depreciation	Initial Outlay -Salvage value/no of yrs
	Straight Line Basis	($100000-0)/5
		$20,000