Chapter 18

Payback Period Method and Accounting Rate of Return

Simplified Approaches to Capital Budgeting

Two additional methods of capital budgeting do not use time value of money as part of the evaluation process. These are:


    Payback period method, and

    Accounting rate of return method



Payback Period Method

The payback period method (PB) of capital budgeting calculates the time it takes to recover the initial cost of an investment. There are two approaches depending on whether the operating cash flows are equal for each year of the assets' expected period of benefits. Both methods base the calculations on net cash flows (cash outflows minus cash inflows) for each year. As was true with NPV and IRR, each year may have different cash flow amounts.


Equal Annual Cash Inflows

When the annual operating cash flows are equal each year, the following short cut calculation can be used to determine the payback period:

               Payback period  =         Initial investment_____

                                              Annual Cash Flow Amount

Unequal Annual Cash Inflows

When operating cash flows (CF) differ are not the same dollar amount each year, you must take a longer approach. Begin with the amount of cash used to purchase the investment and subtract the cash inflows for the first year:


        Amount to recover − Cash flows of year 1 = Remaining CF to recover 


If the remaining cash flows to recover is less than or equal to the CF of year 2, subtract the CF of year 2. 


If the remaining cash flow amount to recover as of the end of year 2 is less than or equal to the cash flows of year 3r, subtract the cash flows of year 3, and so on. 


When the remaining cash flows to recover is determined to be greater than the cash flows expected for the next year, you must determine at what point during the next year that the remaining cash will be recovered. You can do this most easily by finding what percentage portion of the next year will be passed when the final cash recovery occurs.


Portion of final recovery year:


Cash remaining to be recovered
Cash to be received during the final recovery year

The payback period is equal to the number of full years plus the portion of final recovery year.


Limitations of the Payback Period Method

The payback period method has some faults that create limitations on its usage. First, it does not consider the total stream of cash flows. It ignores those after the end of the recovery period. For example, if a potential investment of $10,000 is expect to generate $6,000 in year 1, $4,000 in year 2, and $3,000 in year 3, the payback period method would consider years 1 and 2 since by the end of year 2, all $10,000 of the investment would be recovered. The payback period method ignores the cash flow in year 3.


Second, the payback period method does not consider the time value of money in its calculations. Assume two potential investments, each with a cost of $10,000 and an estimated 3 year period of benefit. Investment A has recoveries of $8,000, $2,000, and $3,000, respectively for the three years, while investment B has recoveries of $2,000, $8,000, and $4,000, respectively for its three years of benefits. Both investments have a 2 year payback period since 100 percent of the cost will be recovered within two years. However, because money has value over time, investment A clearly brings in more cash earlier in its life (year 1) compared to investment B which brings in fewer dollars in year 1. The payback period method ignores the timing of the cash flows and rates both investments as equal options.



Interpret the Payback Period The calculation of the payback period method is expressed in years with two decimals, such as 4.25 years. The general rule is that shorter payback periods are more attractive because the cash is recovered in a shorter period of time.  


Accounting Rate of Return

A second simplified approach to capital budgeting is the accounting rate of return method. It is considered to be 'simplified' because it does not use time value of money in evaluating capital investments.


The accounting rate of return (ARR) approach to capital budgeting calculates the return generated from net income of the proposed capital investment. It is much like the rate or return concept you learned in financial accounting, however this return is based on the effect of one proposed asset, while the rate of return in financial accounting was the return generated by a company's total assets.


The calculation of accounting rate of return is:


Average net income
Average investment


The average investment is based on the book value of the potential capital budgeting acquisition. The beginning book value is and the ending book value are averaged to obtain the denominator. Beginning book value is the book value at the beginning of year 1 and ending book value is the end of useful life of the proposed investment.


        Average investment =  [Book value at beginning of year 1 + book value at end of useful life] /2


Recall that book value is the cost of a long-term asset minus the amount of accumulated depreciation. At the end of an asset's life, the asset account balance minus accumulated depreciation will equal the salvage value. When the asset is then sold for the salvage value amount, there is no gain or loss on the sale.



What Does ARR Tell Users?

The ARR is a percentage return, such as 6.93%. This amounts tell you that the company is expected to earn almost 7 cents out each dollar it will have tied up in the investment  If the ARR is equal to or greater than the required rate of return, the project is acceptable. If it is less than the desired rate it should be rejected.  When comparing investments, the higher the ARR, the more attractive the investment.



Limitations of ARR

ARR ignores the time value of money in its computations meaning no discounting occurs. By doing this, it views amounts generated in the first year to be equal to the amounts generated in the last year. In essence, it ignores the timing of the cash flows within the useful life.


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