This chapter introduces two additional methods of capital budgeting, neither of which use time value of money as part of the process. These are the payback period method and the accounting rate of return method. These methods are often considered to be simplified methods as they are easier to calculate because they both ignore the time value of money. Even when an investment appears to be acceptable based on the results of one of these two methods, it is always advisable to evaluate under a method that utilizes the time value of money.
Payback Period Method
The payback period method (PBP) of capital budgeting calculates the time it takes to recover the initial cost of an investment. There are two approaches--the short cut method and the unequal cash flow method---both of which base their calculations on annual net cash flows (cash outflows minus cash inflows). As is true with NPV and IRR, each year may have different cash flow amounts.
Short Cut Method
When the amounts of annual operating cash flows expected from a potential capital asset acquisition are equal each year, the following short cut calculation can be used to determine the payback period:
|Payback period||=||Initial investment|
|Annual operating cash flow amount|
The payback period indicates how long it will take to recover the cash investment used to acquire the asset. The answer is expressed in years.
Unequal Cash Flows Method
When the dollar amount of operating cash flows are not expected to be the same amount each year, you must take a longer approach. In essence, you begin with the acquisition cost---the amount to be recovered, and subtract the expected cash flows for each year until you get to the point in time at which you have recovered all of the cash.
Begin with the amount of cash used to purchase the investment and subtract the cash inflows for the first year:
Amount to recover − Year 1 cash flows = Remaining cash to recover
If the amount of remaining cash flows to recover is greater than or equal to the cash flows of year 2, subtract the cash flows expected for year 2.
Continue subtracting projected operating cash flows for each subsequent year until the remaining cash flows not yet recovered are less than the cash flows expected for the next year. Determine the point during the next year that the remaining cash will be recovered. This is achieved by calculating the percentage portion of the next year that will pass at the point the final cash recovery is expected to occur. The portion of final recovery year is calculated as :
Portion of final year = Cash remaining to be recovered Cash to be received during the final year
The payback period is equal to the number of full years plus the portion of final recovery year.
Interpret the Payback Period
The payback period indicates how long it will take to recover the cash investment used to acquire the asset. It is expressed in years with two decimals, such as 4.25 years. In general, shorter payback periods are more attractive because the cash is recovered in a shorter period of time. If the cash is expected to be recovered in a time period shorter than the useful life of the investment, it is tentatively deemed acceptable. However, other capital budgeting methods should always be used in conjunction with the payback period method, because even when the PBP appears to be an acceptable investment, it may not be acceptable under a method that considers the time value of money.
If the shortcut method is used to calculate the PBP, the results may indicate a payback period that is greater than the useful life of the asset. It is not possible to have a useful life greater than the payback period because the 'end' of the useful life indicates the asset will no longer be used in the production of income. When it is no longer used, it no longer brings in economic resources. As such, when the numerical result using the shortcut method appears to have a payback period that exceeds the useful life, the interpretation is 'the investment will never be recovered.'
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 will consider years 1 and 2 since by the end of year 2, all $10,000 of the investment will be recovered. The cash flow in year 3 is ignored.
The second drawback of the payback period method is that it 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 evaluates both investments as equal options.
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. This capital budgeting method uses net income, not cash flows.
The accounting rate of return (ARR) method calculates the return generated from the average net income expected for each of the years the proposed capital investment is expected to be used in operations. It is much like the rate of return concept you learned in financial accounting, however this return is based on a single proposed asset acquisition, while the rate of return in financial accounting was based on the return generated by a company's total assets.
The calculation of accounting rate of return is calculated as:
|Accounting rate of return =||Average net income|
Average net income is calculated by dividing the number of years the investment is expected to generate economic resources into the total net income for these same years.
The average investment is based on the book value of the potential capital budgeting acquisition. The beginning book value and the ending book value are averaged to obtain the average investment. Beginning book value is the book value at the beginning of year 1 and ending book value is the book value at the end of the useful life of the proposed investment.
Average investment = [Book value beginning of year 1 + Book value 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's cost minus accumulated depreciation will equal the salvage value. When the asset is sold for the salvage value amount, there is no gain or loss on the sale.
Interpret the Accounting Rate of Return
The ARR is expressed as a percentage return with two decimals displayed, such as 6.93%. This amount tells you that the company is expected to earn almost 7 cents of profit 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 the investment is expected to generate a return that is less than the desired rate of return, it should be rejected. When comparing investments, the higher the ARR, the more attractive the investment.
Limitations of the Accounting Rate of Return
ARR ignores the time value of money in its computations. By doing this, it views amounts generated in the first year to be equal to the amounts generated in the last year on a dollar per dollar basis. In essence, it ignores the timing of the cash flows within the useful life.
Walk Through Problem
BlueMan, Inc. wants to purchase of a new ice cream truck with a cost of $58,000. BlueMan has a cost of capital of 8.4% and a required rate of return of 12.4%. Its income tax rate is 30%. The acquisition is proposed for January 1, 2018. BlueMan expects it can sell the new truck for $10,000 at end of its useful life of 4 years. BlueMan predicts the new truck will generate net income of $6,000 and operating cash flows of $18,000 during 2018, with an increase of $500 each subsequent year. Calculate the payback period and the accounting rate of return.
Solution - Payback Period Method
Because the cash flow amounts are not the same for each of the 4 years of the investment, the short cut method cannot be used. Begin with the amount to recover of $58,000. During 2018 (year 1), $18,000 is expected to be recovered. The balance at the end of year 1 to recover is $58,000 minus $18,000, or $40,000. The expected recovery is expected to increase to $18,500 in 2019, still leaving $21,500 to recover ($40,000 - $18,500). After the expected cash flows in 2020, there is a balance to recover of $2,500.
|Amount to recover||58,000|
|Year 1 - 2018||-18,000|
|Year 2 - 2019||-18,500|
|Year 3 - 2020||-19,000|
|Balance at the end of year 3||2,500|
Because the balance at the end of year 3 ($2,500) is less than the anticipated cash flow in 2021 of $19,500, you must determine at what point during 2021 that the last dollar is expected to be recovered. Assuming cash flows are expected to be recovered equally throughout any year, the timing of the cash flow for year 4
|Portion of final year =||Final year cash to be recovered|
|Cash expected in final year|
At about 12.82% of the way through 2021, BlueMan expects to recover the final dollars invested. The payback period is:
3.00 years + 0.1282 years = 3.13 years
BlueMan expects to recover its entire cash investment in 3.13 years. Because this is less than the estimated life of 4 years, this investment is acceptable based solely on the payback period method.
Solution - Accounting Rate of Return
The accounting rate of return method uses net income instead of cash flows. The net income for the four years must be averaged. The $500 increase applies as well.
Accounting Rate of Return =
|Average net income|
|=||($6,000 + $6,500 + $7,000 + $7,500) / 4 years||
|($58,000 + $10,000) / 2|
The denominator averages the book value at the acquisition date with the book value at the end of the 4 year period. At the acquisition date, the cost is $58,000 and accumulated depreciation is zero, leaving a book value of $58,000. At the end of the useful life, the cost is still $58,000 but with 4 years of depreciation at $12,000 each, total accumulated depreciation will be $48,000. The book value at the end of the life is $58,000 less $48,000, or $10,000. The book value at the end of the useful life is always equal to the salvage value. The denominator is divided by 2 because 2 numbers are being averaged.
This investment is expected to generate a return of profit of almost 20% for each of the 4 years of the proposed asset's life.