Basics of Capital Budgeting
Don Hofstrand
retired Iowa State University Extension agricultural economist
agmrc@iastate.edu
Capital investments are long-term investments where 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.
Different than 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 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.
Most capital budgeting methods include adjustments for the time value of money (discussed in a companion document). 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.
- Identify long-term goals of the individual or business.
- Identify potential investment proposals for meeting the long-term goals identified in Step 1.
- Estimate and analyze the relevant cash flows of the investment proposal identified in Step 2.
- Determine financial feasibility of each of the investment proposals in Step 3 by using the capital budgeting methods outlined below.
- Choose the projects to implement from among the investment proposals outlined in Step 4
- Implement the projects chosen in Step 5.
- Monitor the projects implemented in Step 6 as to how they meet the capital budgeting projection and make adjustments where relevant.
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 investment. For example, assume that an investment of $600 will generate annual cash flows of $100 per year for ten 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 flows payments for fifteen years rather than ten. 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.
Table 1. Payback Period Analysis of Future Cash Flow Payments for Three Capital Projects.
Project A | Project B | Project C | ||||
---|---|---|---|---|---|---|
Year | Cash Flow | Cumulative | Cash Flow | Cumulative | Cash Flow | Cumulative |
0 | -$1,000 | -$1,000 | -$1,000 | |||
1 | $250 | $250 | $350 | $350 | $500 | $500 |
2 | $250 | $500 | $350 | $700 | $500 | $1,000 |
3 | $250 | $750 | $350 | $1,050 | $500 | $1,500 |
4 | $250 | $1,000 | $350 | $1,400 | ||
5 | $250 | $1,250 | $350 | $1,750 | ||
6 | $250 | $1,500 | ||||
7 | $250 | $1,750 | ||||
8 | $250 | $2,000 | ||||
9 | $250 | $2,250 | ||||
10 | $250 | $2,500 |
Payback Period Comparison
Project | Payback Period | Cash Return |
---|---|---|
A | 4 yrs. | $2,500 |
B | 3 (2.86) yrs. | $1,750 |
C | 2 yrs. | $1,500 |
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).
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 rate of return from an alternative investment.
The discounted cash flows for Project B in Table 1 are shown in Table 2. Assuming a ten percent discount rate, the $350 cash flow in year one has a present value of $318 because it is only discounted over one year. Conversely, the $350 cash flow in year five has a present value of only $217 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.
Table 2. Discounting a Series of Future Cash Flows (10% discount rate).
Year | Cash Flows | Present Value of Cash Flows |
---|---|---|
0 | ||
1 | $350 | $318 |
2 | $350 | $289 |
3 | $350 | $263 |
4 | $350 | $239 |
5 | $350 | $217 |
Total | $1,750 | $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 has the largest discounted total return of the three projects ($1,536).
Table 3. Discounting Payback Period Analysis of Three $1,000 Investments.
Project A | Project B | Project C | ||||
---|---|---|---|---|---|---|
Year | Cash Flow | Cumulative | Cash Flow | Cumulative | Cash Flow | Cumulative |
0 | -$1,000 | -$1,000 | -$1,000 | |||
1 | $227 | $227 | $318 | $318 | $455 | $455 |
2 | $207 | $434 | $289 | $607 | $413 | $868 |
3 | $188 | $622 | $263 | $870 | $376 | $1,244 |
4 | $171 | $792 | $239 | $1,109 | ||
5 | $155 | $948 | $217 | $1,326 | ||
6 | $141 | $1,089 | ||||
7 | $128 | $1,217 | ||||
8 | $117 | $1,334 | ||||
9 | $106 | $1,440 | ||||
10 | $96 | $1,536 |
Payback Period Comparison
Project | Payback | Cash Return |
---|---|---|
A | 6 (5.37) | $1,536 |
B | 4 (3.54) | $1,326 |
C | 3 (2.35) | $1,244 |
Time Difference between Payback Period and Discounted Payback Period
Project A | Project B | Project C | |
---|---|---|---|
Years | |||
Payback Period | 4.00 | 2.86 | 2.00 |
Discounted Payback Period | 5.37 | 3.54 | 2.35 |
Difference | 1.37 | .68 | .35 |
Net Present Value
The Net Present Value (NPV) method involves discounting a stream of future cash flows back to its present value. The cash flows can be either positive or negative. 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. The cash inflows and outflows over the life of the investment are then discounted back to their present value.
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 of the analysis.
Net Present Value = Present value of cash inflows – present value of cash outflows. Net Present Value Rule = Accept investments with a positive Net Present Value and reject investments with a negative Net Present Value. |
---|
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. So, choosing the proper discount rate is important for an accurate Net Present Value analysis.
Table 4. Net Present Value Analysis (5% and 10% discount rates)
Assume:
Capital expenditure = $10,000
Useful life of expenditure = 5 years
Annual return from expenditure = $2,000
Value of investment at the end of the analysis period = $1,000
Discount rate = 5% and 10%
Present Value of Cash Flows | |||||
---|---|---|---|---|---|
Year | Capital Investment & Ending Value | Annual Return | Net Cash Flows | 5% Discount | 10% Discount |
0 | -$10,000 | -$10,000 | -$10,000 | -$10,000 | |
1 | $2,000 | $2,000 | $1,905 | $1,818 | |
2 | $2,000 | $2,000 | $1,814 | $1,653 | |
3 | $2,000 | $2,000 | $1,728 | $1,503 | |
4 | $2,000 | $2,000 | $1,645 | $1,366 | |
5 | $3,000 | $2,000 | $2,000 | $3,918 | $3,105 |
Total | $1,010 | -$555 |
Net Present Value
5% Discount Rate = $1,010
10% Discount Rate = -$555
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 ten 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.
Profitability Index = Present Value of Cash Inflows Present Value of Cash Outflows Profitability Index Rule = Accept investments if the Profitability Index is greater than one and reject investments if the Profitability Index is less than one. |
---|
A Profitability Index analysis is shown with two discount rates (5% and 10%) 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 the ten percent discount rate. If the Profitability Index is greater than one, the investment is accepted. If it is less than one, it is rejected.
Table 5. Profitability Index Comparison Analysis (5% and 10% discount rates)
Present Value of Cash Flows | |||
---|---|---|---|
Year | Cash Flows | 5% Discount | 10% Discount |
0 | -$10,000 | -$10,000 | -$10,000 |
1 | $2,000 | $1,905 | $1,818 |
2 | $2,000 | $1,814 | $1,653 |
3 | $2,000 | $1,728 | $1,503 |
4 | $2,000 | $1,645 | $1,366 |
5 | $5,000 | $3,918 | $3,105 |
Total | $1,010 | -$555 |
Profitability Index (5%) = $11,010 = 1.101
$10,000
Profitability Index (10%) = $9,445 = .9445
$10,000
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 cash inflow per dollar of 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 ten percent discount rate returns only 94.5 cents of discounted cash inflow per dollar of discounted cash outflow.
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.
Internal Rate of Return = The discount rate that makes the Net Present Value equal to zero. Internal Rate of Return Rule = Accept investments if the Internal Rate of Return is greater than the Threshold Rate of Return and reject investments if the Internal Rate of Return is less than the Threshold Rate of Return. |
---|
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.
Table 6. Internal Rate of Return Analysis
Cash Flows | ||
---|---|---|
Year | Project A | Project B |
0 | -$10,000 | -$10,000 |
1 | $2,500 | $3,000 |
2 | $2,500 | $3,000 |
3 | $2,500 | $3,000 |
4 | $2,500 | $3,000 |
5 | $2,500 | $3,000 |
Total | $12,500 | $15,000 |
IRR | 7.9% | 15.2% |
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 flow 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 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.
Modified Internal Rate of Return = The Discount Rate that makes the Net Present Value equal to zero when a Reinvestment Rate of Return is included in the analysis. Modified Internal Rate of Return Rule = Accept investments if the Modified Internal Rate of Return is greater than the Threshold Rate of Return and reject investments if the Modified Internal Rate of Return is less than the Threshold Rate of Return. |
---|
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% 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 drops 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.
Table 7. Modified Internal Rate of Return Analysis of Future Cash Flows for Two $10,000 Investments.
Cash Flows | ||
---|---|---|
Year | Project A | Project B |
0 | -$10,000 | -$10,000 |
1 | $2,500 | $3,000 |
2 | $2,500 | $3,000 |
3 | $2,500 | $3,000 |
4 | $2,500 | $3,000 |
5 | $2,500 | $3,000 |
Total | $2,500 | $5,000 |
IRR | 7.9% | 15.2% |
MIRR (7% RRR) | 7.5% | 11.5% |
MIRR (9% RRR) | 8.4% | 12.4% |
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 thousand investment that returns $100 thousand per year for five years. The other is a $2 million investment that returns $600 thousand 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%) 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 thousand dollars compared to only $79 thousand 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 thousand dollars.
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.
Table 8. Comparison of Capital Budgeting Methods (10% discount rate and reinvestment rate of return)
Cash Flows | ||
---|---|---|
Year | Project A | Project B |
0 | -$300,000 | -$2,000,000 |
1 | $100,000 | $600,000 |
2 | $100,000 | $600,000 |
3 | $100,000 | $600,000 |
4 | $100,000 | $600,000 |
5 | $100,000 | $600,000 |
Total | $200,000 | $1,000,000 |
Payback Period | 3.00 yrs. | 3.33 yrs. |
Discounted Payback Period |
3.75 yrs. | 4.26 yrs. |
Net Present Value (10% discount rate) |
$79,079 | $274,472 |
Profitability Index (10% discount rate) |
1.26 | 1.14 |
Internal Rate of Return | 19.9% | 15.2% |
Modified Internal Rate of Return (10% reinvestment rate of return) |
15.3% | 12.9% |
Both projects have a high Internal Rate of Return (Project A the highest). If only one capital project is accepted, it 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 Rate of Return is 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 ten 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 above has advantages and disadvantages. So which one should you use? Companies often use all of the methods. Each one provides a different perspective on the capital investment decision.