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Mastery Problem: Cash Payback and Average Rate of Return(Advanced)
Companies use capital investment analysis to evaluate long-terminvestments. Capital investment evaluation methods that do not usepresent values are (1) Average rate of return method and (2) Cashpayback method.
Methods that do not use present value
One category of capital investment evaluation methods does notuse present value. The primary difference between the category ofmethods that do use present value and this category is that thiscategory does not take the time value of money intoaccount. The basic premise of the time value of money is that adollar today is worth more than a dollar tomorrow.
True or False: Considering the fact that most firms use methodsfrom each category, it can be concluded that both categories havevalue.
True
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Cash Payback Method
This method identifies how long it will take (in years) torecover the initial investment . The particulars of the method varydepending on whether the cash flows from an investment are even oruneven.
Cash Payback Method (Even cash flows)
Suppose that a particular investment required an up-frontcapital outlay of $100,000. This investment is expected to yieldcash flows of $50,000 per year for 10 years. What is the paybackperiod for this investment? If required, round your answer to twodecimal places.
Cash Payback Period = $ / $ = years
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Payback Period (Uneven cash flows)
When the annual cash flows are unequal, the payback period iscomputed by adding the annual cash flows until such time as theoriginal investment is recovered. If a fraction of a year isneeded, it is assumed that cash flows occur evenly within eachyear.
The steps for determining the payback period with uneven cashflows is as follows:
- Add the annual cash flows to one another until the investmentis recovered.
- For each full year's worth of cash flows consumed, add thatyear to your calculation for total payback years.
- If you arrive at a point where only part of the year's cashflows are needed, only add the fraction of the year's cash flowsrelevant to recovering the initial investment to the total paybackyears.
- If the unrecovered investment is greater than the annual cashflow, the payback period is "1". If the unrecovered investment isless than the annual cash flow the time needed for payback iscomputed by dividing the unrecovered investment by the annual cashflow for than year.
+ Explanation of Time Needed for Payback with uneven cashflows Note: For each year in which the unrecoveredinvestment meets or exceeds the annual cash flow, this is 1. Foryears in which the annual cash flow exceeds the unrecoveredinvestment, this is the unrecovered investment divided by theannual 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 exampleassuming the investment required an up-front capital outlay of$100,000 and the uneven annual cash flows for each year areprovided in the table. If an amount is zero, enter "0". For thetime needed for payback, enter your answer to one decimal place, ifless 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 usepresent value and is commonly used in making capital investmentdecisions. Unlike the cash payback method, the average rate ofreturn 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 understraight-line depreciation. The revenues are as follows: Year 1 -$10,000, Year 2 - $20,000, Year 3 - $30,000, Year 4 - $40,000 andYear 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 Rate of Return = | |
= % |
