The traditional payback period technique that is used in capital budgeting analyses _____.

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The Payback Period Calculator can calculate payback periods, discounted payback periods, average returns, and schedules of investments.

Fixed Cash Flow

Irregular Cash Flow Each Year

Cash Flow

Cash flow is the inflow and outflow of cash or cash-equivalents of a project, an individual, an organization, or other entities. Positive cash flow that occurs during a period, such as revenue or accounts receivable means an increase in liquid assets. On the other hand, negative cash flow such as the payment for expenses, rent, and taxes indicate a decrease in liquid assets. Oftentimes, cash flow is conveyed as a net of the sum total of both positive and negative cash flows during a period, as is done for the calculator. The study of cash flow provides a general indication of solvency; generally, having adequate cash reserves is a positive sign of financial health for an individual or organization.

Discounted Cash Flow

Discounted cash flow (DCF) is a valuation method commonly used to estimate investment opportunities using the concept of the time value of money, which is a theory that states that money today is worth more than money tomorrow. Forecasted future cash flows are discounted backward in time to determine a present value estimate, which is evaluated to conclude whether an investment is worthwhile. In DCF analysis, the weighted average cost of capital (WACC) is the discount rate used to compute the present value of future cash flows. WACC is the calculation of a firm's cost of capital, where each category of capital, such as equity or bonds, is proportionately weighted. For more detailed cash flow analysis, WACC is usually used in place of discount rate because it is a more accurate measurement of the financial opportunity cost of investments. WACC can be used in place of discount rate for either of the calculations.

Discount Rate

Discount rate is sometimes described as an inverse interest rate. It is a rate that is applied to future payments in order to compute the present value or subsequent value of said future payments. For example, an investor may determine the net present value (NPV) of investing in something by discounting the cash flows they expect to receive in the future using an appropriate discount rate. It's similar to determining how much money the investor currently needs to invest at this same rate in order to get the same cash flows at the same time in the future. Discount rate is useful because it can take future expected payments from different periods and discount everything to a single point in time for comparison purposes.

Payback Period

Payback period, which is used most often in capital budgeting, is the period of time required to reach the break-even point (the point at which positive cash flows and negative cash flows equal each other, resulting in zero) of an investment based on cash flow. For instance, a $2,000 investment at the start of the first year that returns $1,500 after the first year and $500 at the end of the second year has a two-year payback period. As a rule of thumb, the shorter the payback period, the better for an investment. Any investments with longer payback periods are generally not as enticing.

Due to its ease of use, payback period is a common method used to express return on investments, though it is important to note it does not account for the time value of money. As a result, payback period is best used in conjunction with other metrics.

The formula to calculate payback period is:

As an example, to calculate the payback period of a $100 investment with an annual payback of $20:

Discounted Payback Period

A limitation of payback period is that it does not consider the time value of money. The discounted payback period (DPP), which is the period of time required to reach the break-even point based on a net present value (NPV) of the cash flow, accounts for this limitation. Unlike payback period, DPP reflects the amount of time necessary to break-even in a project based not only on what cash flows occur, but when they occur and the prevailing rate of return in the market, or the period in which the cumulative net present value of a project equals zero all while accounting for the time value of money. Discounted payback period is useful in that it helps determine the profitability of investments in a very specific way: if the discounted payback period is less than its useful life (estimated lifespan) or any predetermined time, the investment is viable. Conversely, if it's greater, the investment generally should not be considered. Comparing the DPP of different investments, ones with the relatively shorter DPPs are generally more enticing because they take less time to break-even.

The formula for discounted payback period is:

The following is an example of determining discounted payback period using the same example as used for determining payback period. If a $100 investment has an annual payback of $20 and the discount rate is 10%., the NPV of the first $20 payback is:

The NPV of the second payback is:

The next in the series will have a denominator of 1.103, and continuously as needed. For this particular example, the break-even point is:

The discounted payback period of 7.27 years is longer than the 5 years as calculated by the regular payback period because the time value of money is factored in.

Discounted payback period will usually be greater than regular payback period. Investments with higher cash flows toward the end of their lives will have greater discounting. Both payback period and discounted payback period analysis can be helpful when evaluating financial investments, but keep in mind they do not account for risk nor opportunity costs such as alternative investments or systemic market volatility. It can help to use other metrics in financial decision making such as DCF analysis, or the internal rate of return (IRR), which is the discount rate that makes the NPV of all cash flows of an investment equal to zero.

Capital investments are long-term investments in which the assets involved have useful lives of multiple years. For example, constructing a new production facility and investing in machinery and equipment are capital investments. Capital budgeting is a method of estimating the financial viability of a capital investment over the life of the investment.

Unlike some other types of investment analysis, capital budgeting focuses on cash flows rather than profits. Capital budgeting involves identifying the cash in flows and cash out flows rather than accounting revenues and expenses flowing from the investment. For example, non-expense items like debt principal payments are included in capital budgeting because they are cash flow transactions. Conversely, non-cash expenses like depreciation are not included in capital budgeting (except to the extent they impact tax calculations for “after tax” cash flows) because they are not cash transactions. Instead, the cash flow expenditures associated with the actual purchase and/or financing of a capital asset are included in the analysis.

Over the long run, capital budgeting and conventional profit-and-loss analysis will lend to similar net values. However, capital budgeting methods include adjustments for the time value of money (discussed in AgDM File C5-96, Understanding the Time Value of Money). Capital investments create cash flows that are often spread over several years into the future. To accurately assess the value of a capital investment, the timing of the future cash flows are taken into account and converted to the current time period (present value).

Below are the steps involved in capital budgeting.

1. Identify long-term goals of the individual or business.
2. Identify potential investment proposals for meeting the long-term goals identified in Step 1.
3. Estimate and analyze the relevant cash flows of the investment proposal identified in Step 2.
4. Determine financial feasibility of each of the investment proposals in Step 3 by using the capital budgeting methods outlined below.
5. Choose the projects to implement from among the investment proposals outlined in Step 4.
6. Implement the projects chosen in Step 5.
7. Monitor the projects implemented in Step 6 as to how they meet the capital budgeting projections and make adjustments where needed.

There are several capital budgeting analysis methods that can be used to determine the economic feasibility of a capital investment. They include the Payback Period, Discounted Payment Period, Net Present Value, Profitability Index, Internal Rate of Return, and Modified Internal Rate of Return.

Payback Period

A simple method of capital budgeting is the Payback Period. It represents the amount of time required for the cash flows generated by the investment to repay the cost of the original investment. For example, assume that an investment of $600 will generate annual cash flows of $100 per year for 10 years. The number of years required to recoup the investment is six years.

The Payback Period analysis provides insight into the liquidity of the investment (length of time until the investment funds are recovered). However, the analysis does not include cash flow payments beyond the payback period. In the example above, the investment generates cash flows for an additional four years beyond the six year payback period. The value of these four cash flows is not included in the analysis. Suppose the investment generates cash flow payments for 15 years rather than 10. The return from the investment is much greater because there are five more years of cash flows. However, the analysis does not take this into account and the Payback Period is still six years.

Three capital projects are outlined in Table 1. Each requires an initial $1,000 investment. But each project varies in the size and number of cash flows generated. Project C has the shortest Payback Period of two years. Project B has the next shortest Payback (almost three years) and Project A has the longest (four years). However, Project A generates the most return ($2,500) of the three projects. Project C, with the shortest Payback Period, generates the least return ($1,500). Thus, the Payback Period method is most useful for comparing projects with nearly equal lives.

Discounted Payback Period

The Payback Period analysis does not take into account the time value of money. To correct for this deficiency, the Discounted Payback Period method was created. As shown in Figure 1, this method discounts the future cash flows back to their present value so the investment and the stream of cash flows can be compared at the same time period. Each of the cash flows is discounted over the number of years from the time of the cash flow payment to the time of the original investment. For example, the first cash flow is discounted over one year and the fifth cash flow is discounted over five years.

To properly discount a series of cash flows, a discount rate must be established. The discount rate for a company may represent its cost of capital or the potential rate of return from an alternative investment.

The discounted cash flows for Project B in Table 1 are shown in Table 2. Assuming a 10 percent discount rate, the $350 cash flow in year one has a present value of $318 (350/1.10) because it is only discounted over one year. Conversely, the $350 cash flow in year five has a present value of only $217 (350/1.10/1.10/1.10/1.10/1.10) because it is discounted over five years. The nominal value of the stream of five years of cash flows is $1,750 but the present value of the cash flow stream is only $1,326.

In Table 3, a Discounted Payback Period analysis is shown using the same three projects outlined in Table 1, except the cash flows are now discounted. You can see that it takes longer to repay the investment when the cash flows are discounted. For example, it takes 3.54 years rather than 2.86 years (.68 of a year longer) to repay the investment in Project B. Discounting has an even larger impact for investments with a long stream of relatively small cash flows like Project A. It takes an additional 1.37 years to repay Project A when the cash flows are discounted. It should be noted that although Project A has the longest Discounted Payback Period, it also has the largest discounted total return of the three projects ($1,536).

Net Present Value

The Net Present Value (NPV) method involves discounting a stream of future cash flows back to present value. The cash flows can be either positive (cash received) or negative (cash paid). The present value of the initial investment is its full face value because the investment is made at the beginning of the time period. The ending cash flow includes any monetary sale value or remaining value of the capital asset at the end of the analysis period, if any. The cash inflows and outflows over the life of the investment are then discounted back to their present values.

The Net Present Value is the amount by which the present value of the cash inflows exceeds the present value of the cash outflows. Conversely, if the present value of the cash outflows exceeds the present value of the cash inflows, the Net Present Value is negative. From a different perspective, a positive (negative) Net Present Value means that the rate of return on the capital investment is greater (less) than the discount rate used in the analysis.

The discount rate is an integral part of the analysis. The discount rate can represent several different approaches for the company. For example, it may represent the cost of capital such as the cost of borrowing money to finance the capital expenditure or the cost of using the company’s internal funds. It may represent the rate of return needed to attract outside investment for the capital project. Or it may represent the rate of return the company can receive from an alternative investment. The discount rate may also reflect the Threshold Rate of Return (TRR) required by the company before it will move forward with a capital investment. The Threshold Rate of Return may represent an acceptable rate of return above the cost of capital to entice the company to make the investment. It may reflect the risk level of the capital investment. Or it may reflect other factors important to the company. Choosing the proper discount rate is important for an accurate Net Present Value analysis.

A simple example using two discount rates is shown in Table 4. If the five percent discount rate is used, the Net Present Value is positive and the project is accepted. If the 10 percent rate is used, the Net Present Value is negative and the project is rejected.

Profitability Index

Another measure to determine the acceptability of a capital investment is the Profitability Index (PI). The Profitability Index is computed by dividing the present value of cash inflows of the capital investment by the present value of cash outflows of the capital investment. If the Profitability Index is greater than one, the capital investment is accepted. If it is less than one, the capital investment is rejected.

A Profitability Index analysis is shown with two discount rates (5 and 10 percent) in Table 5. The Profitability Index is positive (greater than one) with the five percent discount rate. The Profitability Index is negative (less than one) with 10 percent discount rate. If the Profitability Index is greater than one, the investment is accepted. If it is less than one, it is rejected.

The Profitability Index is a variation of the Net Present Value approach to comparing projects. Although the Profitability Index does not stipulate the amount of cash return from a capital investment, it does provide the cash return per dollar invested. The index can be thought of as the discounted cash inflow per dollar of discounted cash outflow. For example, the index at the five percent discount rate returns $1.10 of discounted cash inflow per dollar of discounted cash outflow. The index at the 10 percent discount rate returns only 94.5 cents of discounted cash inflow per dollar of discounted cash outflow. Because it is an analysis of the ratio of cash inflow per unit of cash outflow, the Profitability Index is useful for comparing two or more projects which have very different magnitudes of cash flows.

Internal Rate of Return

Another method of analyzing capital investments is the Internal Rate of Return (IRR). The Internal Rate of Return is the rate of return from the capital investment. In other words, the Internal Rate of Return is the discount rate that makes the Net Present Value equal to zero. As with the Net Present Value analysis, the Internal Rate of Return can be compared to a Threshold Rate of Return to determine if the investment should move forward.

An Internal Rate of Return analysis for two investments is shown in Table 6. The Internal Rate of Return of Project A is 7.9 percent. If the Internal Rate of Return (e.g. 7.9 percent) is above the Threshold Rate of Return (e.g. 7 percent), the capital investment is accepted. If the Internal Rate of Return (e.g. 7.9 percent) is below the Threshold Rate of Return (e.g. 9 percent), the capital investment is rejected. However, if the company is choosing between projects, Project B will be chosen because it has a higher Internal Rate of Return.

The Internal Rate of Return analysis is commonly used in business analysis. However, a precaution should be noted. It involves the cash surpluses/deficits during the analysis period. As long as the initial investment is a cash outflow and the trailing cash flows are all inflows, the Internal Rate of Return method is accurate. However, if the trailing cash flows fluctuate between positive and negative cash flows, the possibility exists that multiple Internal Rates of Return may be computed.

Modified Internal Rate of Return

Another problem with the Internal Rate of Return method is that it assumes that cash flows during the analysis period will be reinvested at the Internal Rate of Return. If the Internal Rate of Return is substan­tially different than the rate at which the cash flows can be reinvested, the results will be skewed.

To understand this we must further investigate the process by which a series of cash flows are discounted to their present value. As an example, the third year cash flow in Figure 2 is shown discounted to the current time period.

However, to accurately discount a future cash flow, it must be analyzed over the entire five year time period. So, as shown in Figure 3, the cash flow received in year three must be compounded for two years to a future value for the fifth year and then discounted over the entire five-year period back to the present time. If the interest rate stays the same over the compounding and discounting years, the compounding from year three to year five is offset by the discounting from year five to year three. So, only the discounting from year three to the present time is relevant for the analysis (Figure 2).

For the Discounted Payback Period and the Net Present Value analysis, the discount rate (the rate at which debt can be repaid or the potential rate of return received from an alternative investment) is used for both the compounding and discounting analysis. So only the discounting from the time of the cash flow to the present time is relevant.

However, the Internal Rate of Return analysis involves compounding the cash flows at the Internal Rate of Return. If the Internal Rate of Return is high, the company may not be able to reinvest the cash flows at this level. Conversely, if the Internal Rate of Return is low, the company may be able to reinvest at a higher rate of return. So, a Reinvestment Rate of Return (RRR) needs to be used in the compounding period (the rate at which debt can be repaid or the rate of return received from an alternative investment). The Internal Rate of Return is then the rate used to discount the compounded value in year five back to the present time.

The Modified Internal Rate of Return for two $10,000 investments with annual cash flows of $2,500 and $3,000 is shown in Table 7. The Internal Rates of Return for the projects are 7.9 and 15.2 percent, respectively. However, if we modify the analysis where cash flows are reinvested at 7 percent, the Modified Internal Rates of Return of the two projects drop to 7.5 percent and 11.5 percent, respectively. If we further modify the analysis where cash flows are reinvested at 9 percent, the first Modified Internal Rate of Return rises to 8.4 percent and the second only drops to 12.4 percent. If the Reinvestment Rate of Return is lower than the Internal Rate of Return, the Modified Internal Rate of Return will be lower than the Internal Rate of Return. The opposite occurs if the Reinvestment Rate of Return is higher than the Internal Rate of Return. In this case the Modified Internal Rate of Return will be higher than the Internal Rate of Return.

Comparison of Methods

For a comparison of the six capital budgeting methods, two capital investments projects are presented in Table 8 for analysis. The first is a $300,000 investment that returns $100,000 per year for five years. The other is a $2 million investment that returns $600,000 per year for five years.

Both projects have Payback Periods well within the five year time period. Project A has the shortest Payback Period of three years and Project B is only slightly longer. When the cash flows are discounted (10 percent) to compute a Discounted Payback Period, the time period needed to repay the investment is longer. Project B now has a repayment period over four years in length and comes close to consuming the entire cash flows from the five year time period.

The Net Present Value of Project B is $275,000 compared to only $79,000 for Project A. If only one investment project will be chosen and funds are unlimited, Project B is the preferred investment because it will increase the value of the company by $275,000.

However, Project A provides more return per dollar of investment as shown with the Profitability Index ($1.26 for Project A versus $1.14 for Project B). So if funds are limited, Project A will be chosen.

Both projects have a high Internal Rate of Return (Project A has the highest). If only one capital project is accepted, it’s Project A. Alternatively, the company may accept projects based on a Threshold Rate of Return. This may involve accepting both or neither of the projects depending on the size of the Threshold Rate of Return.

When the Modified Internal Rates of Return are computed, both rates of return are lower than their corresponding Internal Rates of Return. However, the rates are above the Reinvestment Rate of Return of 10 percent. As with the Internal Rate of Return, the Project with the higher Modified Internal Rate of Return will be selected if only one project is accepted. Or the modified rates may be compared to the company’s Threshold Rate of Return to determine which projects will be accepted.

Conclusion

Each of the capital budgeting methods outlined has advantages and disadvantages. The Payback Period is simple and shows the liquidity of the investment. But it doesn’t account for the time value of money or the value of cash flows received after the payback period. The Discounted Payback Period incorporates the time value of money but still doesn’t account for cash flows received after the payback period. The Net Present Value analysis provides a dollar denominated present value return from the investment.

However, it has little value for comparing investments of different size. The Profitability Index is a variation on the Net Present Value analysis that shows the cash return per dollar invested, which is valuable for comparing projects. However, many analysts prefer to see a percentage return on an investment. For this the Internal Rate of Return can be computed. But the company may not be able to reinvest the internal cash flows at the Internal Rate of Return. Therefore, the Modified Internal Rate of Return analysis may be used.

Which capital budgeting method should you use? Each one has unique advantages and disadvantages, and companies often use all of them. Each one provides a different perspective on the capital investment decision.

Don Hofstrand, retired extension value added agriculture specialist,