How risky are your capital expenditures? Here's how to incorporate risk into your NPV and...
What could possibly be new about net present value (NPV) and internal rate of return (IRR) analyses? For many decades, accounting and finance professionals have been using NPV and IRR measurements to evaluate capital expenditures. Typically, you develop estimates of future cash flows, time periods,
Let's take a look at how to accomplish this task.
GUIDANCE FROM FASB
The Financial Accounting Standards Board (FASB) provides us with guidance on how to estimate the range of possible cash flows. The FASB's Statement of Financial Accounting Concepts No. 7, "Using Cash Flow Information and Present Value in Accounting Measurements" (CON 7), shows us how to build risk into measuring the present value of estimated future cash flows using weighted cash flow estimates. According to CON 7, risk is built into the measurement system by evaluating each future cash flow estimate.
Let's compare a traditional future cash flow measurement model with a CON 7 future cash flow measurement model within a present value analysis framework. In a traditional future cash flow measurement, we'll assume a project has three years of estimated future cash inflows of $1,000 each. To compute present value, the best estimate of $1,000 for each year would be discounted at a specified discount rate based on the overall risk of the capital expenditure--the more risk there is, the highter the rate; less risk, less rate. This approach assumes the risk of the three years of estimated future cash flows is constant and can be captured in one discount rate--indeed a major assumption when the typical capital expenditure analysis incorporates several years and many different sources for estimated future cash inflows and outflows. Some estimates are reasonable, even concrete, while others can be soft and uncertain. Thus, it's unreasonable to assume that the discount rate can capture the risk associated with many estimates of future cash flows.
In contrast to the traditional NPV model, CON 7 builds risk into an analysis by weighting the possible range of cash flow estimates that may be applied in an investment decision. In our three-year project, let's give year one a 20% chance of receiving $800, a 50% chance of receiving $1,000, and a 30% chance of receiving $1,200 for a weighted average of $1,020, as shown in Table 1. Then we'll give years two and three weighted average amounts of $980 and $1,050, respectively.
Weighting the cash flows offers two distinct advantages. The first is that it introduces the expected range of estimated future cash flows into the model. The risk is captured in the range of cash flow estimates. The second is that you don't have to guess the discount rate. The discount rate used in a present value model, where the cash flows are weighted following CON 7, is the company's weighted average cost of debt and/or equity. That is, the discount rate isn't dependent upon the risk of individual projects. The rate can be set at a company-wide hurdle rate. As a result, you can use the same discount rate in all models, improving company-wide comparability.
CON 7 teaches us about weighting cash flows, significantly improving NPV analysis. CON 7 also shows that each estimated future cash flow must be evaluated on its own merits and adjusted for its possible range of outcomes. In doing so, the risk of each estimate is explicit, and evaluation of risk is at the source--the range of estimated cash flows. To make those risks explicit, CON 7 says to compute the weighted average of each estimated future cash flow. Although this approach seems reasonable, it doesn't provide a workable, dynamic tool to support business capital expenditure analysis because there will be only one outcome measure while you ideally want a range of possible outcomes in an NPV or IRR analysis.
ENHANCING THE CAPITAL EXPENDITURE MODEL
A useful approach in a capital expenditure analysis is to establish a best case to worst case range of possible outcomes. This can be done by building a workable spreadsheet that considers two or more estimates for each projected cash inflow or outflow. From this, you'll be able to run a dynamic NPV or IRR evaluation of a capital expenditure, observing the range of possible outcomes, as illustrated in Tables 2, 4, 5, and 6. (More advanced capital expenditure models are commercially available, requiring the user to estimate probability distributions. But the advantage of the model in this article is it accomplishes the same task with less complexity.)
Let us illustrate. Our capital expenditure is for an enterprise resource planning (ERP) system. We've chosen an ERP expenditure because of the challenges inherent in evaluating the costs and benefits of this type of procurement. We'll give cash flow estimates for the initial investment and for years one and five, as shown in Table 2. We jump from year one to five to illustrate the value of a dynamic capital expenditure analysis. The process begins by placing the most likely estimated future cash flow for each line item into the model. Next, we estimate the best and worst case outcomes, represented by the weights applied. By weighting the outcomes, the risk evaluation is at the source and is explicit in the analysis.
Some estimates are relatively easy to determine while others are more difficult. Easy estimates typically include the initial outlay and estimates for outlays in the early years of the project. For example, the initial outlay for hardware, which comes from the purchase order, is assigned a weight of 1.0 in the best case scenario, shown in Table 2. If you don't have direct experience knowing what a particular cash flow estimate is or aren't confident in your cash flow estimate, then your range between the best case and worst case weights should be much wider. For example, under ERP data conversion in Table 2, we have a best case weight of .8 and a worst case weight of 1.2. This signals that we are less certain about the $200,000 estimate for the conversion. We use a similar approach for estimating recurring costs and savings, making the risk associated with each cash flow explicit by weighing each estimate.
TYPE AND RANGE OF EXPENDITURES
Taking capital expenditure analysis still further, let's look at how to work with the type and range of cash flow estimates for our ERP expenditure.While in Table 2 we illustrated the weighting concept in an NPV calculation, in Table 3 we evaluate critical aspects of our ERP acquisition.
To begin, we list and rank estimated future cash inflows and outflows by the quality of the estimate, shown in Table 3. That is, estimated future cash flow savings and expenditures built on reliable information should be listed first, and the riskier estimations should follow. For example, cash flow estimates from an external contract or request for proposal shouldn't vary as the contract rolls out. Estimates based on a limited amount of information should reflect a wide range of possible outcomes. For example, cash flow estimates driven by management's response to information will be dependent upon how well the system works and several other controlled and uncontrolled variables and will likely vary as the contract rolls out. Thus, in reading and evaluating our ERP expenditure model, we expect to see a narrow range of outcomes in some estimates and a wide range in others. In addition, we should see a wider range in outcomes in later-year estimates in general because the ability to predict cash flows declines as the projection moves out into future periods.
Cost estimates in categories four and five in Table 3, market and information interaction and management's response to information, respectively, can be the most subjective. Certainly an accounting professional can generate information from data. But can senior management employ this information to capture market opportunities, such as increased sales from knowing how to better serve customers, or identify the most profitable customers, market segments, or product lines? The risk increases because capturing these benefits is dependent upon external market conditions that management may not control and by leveraging intangible and tangible company resources.
NPV AND IRR RESULTS
To make NPV and IRR a dynamic, what-if process, we begin designing a spreadsheet for the ERP expenditure by setting up four sheets: (1) a data section (Table 4), (2) best case scenario (Table 5), (3) worst case scenario (Table 6), and (4) a graph of corresponding NPVs and IRRs (Figure 1). (One of the authors of this article, Thomas L. Zeller, will give you this demonstration in an Excel spreadsheet if you e-mail him at tzeller@luc.edu and write in the subject line "NPV IRR analysis.")
[FIGURE 1 OMITTED]
In Table 4 we have the data for a typical NPV or IRR analysis of our ERP procurement, and we've added weights to incorporate risk for each estimated future cash flow.We suggest you pay particular attention to the larger dollar estimates throughout an analysis because they impact NPV and IRR the most. The listing of each category of future cash flows is by quality of estimate. For example, savings generated by reducing clerical staff is a more certain estimate than savings derived from warehouse efficiencies.
Noteworthy in Table 4 is the pattern of weights. Specifically, the weights begin to widen when moving from left to right and top to bottom. For example, observe how the weights in the row labeled "software" under recurring costs in years two and three both have a range of 1.0 to 1.1. This signals that the range of possible cash flows is relatively stable. Support for such a narrow and consistent range of estimated cash flows would be a purchase order or legal contract, which we noted previously. Now observe the weights in the row titled "Warehousing efficiencies" under "Savings." In year two the weights are best case of 1.1 and worst case of 0.8. The gap widens in year three to 1.1 and 0.7 because problems could occur and reduce savings opportunities, making the estimate riskier over time. If we were to estimate beyond year three, the gap between best case and worst case weights would logically widen still more.
We built two other features into Table 4: the cost of capital and depreciation tax savings. The cost of capital, 8%, is noted in the upper left; and depreciation tax savings is shown in the upper right box. All values from Table 4 are linked by cell reference to Tables 5 and 6. That is, Table 4 is the only location where data is inputted and/or changed. Tables 5 and 6 provide best case and worst case scenario NPVs and IRRs, respectively.
Finally, we graph the outcomes in Figure 1. The net present value ranges from the worst case scenario, a $1.6 million reduction in wealth, to a best case scenario of a $1.4 million increase in wealth. The internal rate of return for this illustration ranges from -23% to 21%. These graphs can be useful when working through the estimates with management or the workforce. You can simply split the screen and show the data section in one half and the graphs in the other. Because the entire document is cell referenced beginning at the data section, the results of estimate changes can be observed immediately, making for a rich and dynamic evaluation of a capital expenditure analysis. This can help facilitate meaningful discussions, challenges, critiques, and changes in estimates about such things as dollar amount, timing, best case weight, and worst case weight. The end result is a range of possible NPV and IRR outcomes driven by a critical analysis based on an interactive dynamic process.
Analyzing capital expenditures by building risk into individual elements that comprise estimated future cash flows is a much better way to evaluate and model potential outcomes. Theoretically, you don't have to guess at incorporating risk. Capital expenditure analysis is too complex to employ only one estimate as a valid risk measure. Our suggested framework makes the source of risk and the possible range of outcomes explicit. As a result, you can do a much better job serving your internal customers. Take the framework, sit with your team, and efficiently and effectively evaluate possible outcomes for estimates, showing them the graphical output when different ranges of cash flows are debated and put into the model. This framework provides immediate feedback for evaluation and decision making--an important tool because the complexity and risk associated with capital expenditures is increasing. Substantial dollars are at stake, and you need to combine tangible and intangible resources to create wealth.
Table 1: WEIGHTING CASH FLOWS
YEAR DESCRIPTION Year 1
Best estimate $1,000
Possible alternatives
A 20% $800 $160
B 50% 1,000 500
C 30% 1,200 360
Weighted average $1,020
YEAR DESCRIPTION Year 2
Best estimate $1,000
Possible alternatives
A 30% $800 $240
B 50% 1,000 500
C 20% 1,200 240
Weighted average $980
YEAR DESCRIPTION Year 3
Best estimate $1,000
Possible alternatives
A 20% $500 $100
B 50% 1,000 500
C 30% 1,500 450
Weighted average $1,050
Table 2: WEIGHTED CASH FLOW ESTIMATES FOR ACQUIRING
AN ENTERPRISE RESOURCE PLANNING (ERP) SYSTEM
WORST
BEST CASE CASE
WEIGHT WEIGHT
INITIAL OUTLAY COSTS
Hardware $2,000,000 1.0 1.0
Software 400,000 0.9 1.1
Conversion 200,000 0.8 1.2
Total initial cost $2,600,000
WORST
BEST CASE CASE
YEAR 1 WEIGHT WEIGHT
RECURRING COSTS
Hardware expansion $50,000 1.0 1.0
Communication charges 100,000 1.0 1.1
Software updates 300,000 1.0 1.0
Total recurring costs $450,000
SAVINGS
Clerical cost savings $600,000 1.0 0.8
Warehousing efficiencies 100,000 1.3 0.9
Total savings $700,000
WORST
BEST CASE CASE
YEAR 5 WEIGHT WEIGHT
RECURRING COSTS
Hardware expansion $260,000 0.7 1.4
Communication charges 160,000 0.8 1.2
Software updates 420,000 0.8 1.4
Total recurring costs $840,000
SAVINGS
Clerical cost savings $1,200,000 1.0 0.6
Warehousing efficiencies 500,000 1.1 0.7
Total savings $1,700,000
Table 3: EVALUATING ASPECTS OF AN ERP EXPENDITURE
QUALITY
CATEGORY AND TYPE OF THE
OF THE ESTIMATE ESTIMATE EXAMPLE
1. External contract or High * Legal contract with a locked-
request for proposal in price,such as physical
installation, hardware,
software, outsource, or
eliminated outsource
functions.
2. Wages and benefits High to * Additional information
(controlled by Medium technology professionals.
management)
* Fewer clerical staff for
3. Productive use of input, data management, and
working capital reporting.
resources (controlled
by management) * Fewer information technology
professionals.
* Inventory: reduce inventory
and increase turns with
better information and
logistics.
* Accounts receivable: identify
a higher caliber of customer,
and improve billing cycle.
* Accounts payable: take full
advantage of discount with
superior cash flow
management.
4. Market and information Medium * Increase sales and profits
interaction to Low with superior customer
service and interaction with
market planning and
advertising.
5. Management's response * Efficient and effective use
to information- of new, timely information,
dependent upon system such as what inventory to
and several other purchase, segment profita-
controlled and bility, performance reports,
uncontrolled and budget analysis.
variables.
Table 4: DATA FOR AN NPV AND IRR ANALYSIS OF A CAPITAL EXPENDITURE
Cost of Capital 8%
Investment Savings and Costs
BEST CASE WORST CASE
INITIAL OUTLAY COSTS WEIGHT WEIGHT
Hardware $90,000 1.0 1.0
Software 400,000 1.0 1.1
Training 200,000 0.9 1.3
Site preparation 200,000 1.0 1.2
Initial systems design 2,000,000 0.8 1.2
Conversion 200,000 0.9 1.3
Total initial outlays 5,000,000
Depreciation Tax Savings
Depreciation on initial investment of $3,750,000
Tax Rate: 33.3%
YEAR RATE DEPRECIATION TAX SAVINGS
1 33.3% $1,250,000 $312,500
2 33.3% 1,250,000 312,500
3 33.3% 1,250,000 312,500
WORST
BEST CASE CASE
YEAR 1 WEIGHT WEIGHT
RECURRING COSTS
Hardware expansion $-- 1.0 1.0
Software $-- 1.0 1.1
Systems maintenance 60,000 1.0 1.3
Personnel costs 500,000 1.0 1.2
Communication charges 100,000 1.0 1.1
Overhead 300,000 1.0 1.0
Total recurring costs $960,000
SAVINGS
Clerical cost savings $600,000 1.0 0.9
Working capital savings 900,000 1.1 0.9
Profits from sales increases -- 1.0 1.0
Warehousing efficiencies -- 1.0 1.0
Total savings $1,500,000
WORST
BEST CASE CASE
YEAR 2 WEIGHT WEIGHT
RECURRING COSTS
Hardware expansion $260,000 1.0 1.0
Software 150,000 1.0 1.1
Systems maintenance 120,000 0.9 1.3
Personnel costs 800,000 0.9 1.2
Communication charges 160,000 1.0 1.1
Overhead 420,000 1.0 1.0
Total recurring costs $1,910,000
SAVINGS
Clerical cost savings $1,200,000 1.1 0.8
Working capital savings 1,200,000 1.0 1.0
Profits from sales increases 500,000 1.1 0.8
Warehousing efficiencies 400,000 1.1 0.8
Total savings $3,300,000
WORST
BEST CASE CASE
YEAR 3 WEIGHT WEIGHT
RECURRING COSTS
Hardware expansion $300,000 1.0 1.0
Software 200,000 1.0 1.1
Systems maintenance 130,000 0.9 1.3
Personnel costs 900,000 0.9 1.2
Communication charges 180,000 0.8 1.1
Overhead 490,000 0.8 1.1
Total recurring costs $2,200,000
SAVINGS
Clerical cost savings $1,400,000 1.1 0.8
Working capital savings 1,500,000 1.0 0.8
Profits from sales increases 900,000 1.1 0.7
Warehousing efficiencies 800,000 1.1 0.7
Total savings $4,600,000
Table 5: BEST CASE NPV AND IRR ANALYSIS OF THE CAPITAL EXPENDITURE
INITIAL OUTLAY YEAR 1
INITIAL OUTLAY COSTS
Hardware $900,000
Software 400,000
Training 180,000
Site preparation 200,000
Initial systems design 1,600,000
Conversion 180,000
Total initial outlays 2,650,000
RECURRING COSTS
Hardware expansion $--
Software $--
Systems maintenance 60,000
Personnel costs 500,000
Communication charges 100,000
Overhead 300,000
Total costs 960,000
SAVINGS
Clerical cost savings 600,000
Working capital savings 990,000
Profits from sales increases --
Warehousing efficiencies --
Total savings 1,590,000
SAVINGS MINUS RECURRING COSTS 630,000
Less income taxes @ 25% (157,500)
Cash savings (net of tax) 472,500
Savings on taxes due to 312,500
depreciation deduction
Net savings 785,000
Present value of net saving 4,085,373 $726,852
Net present value $1,435,373
Internal rate of return 21%
YEAR 2 YEAR 3
INITIAL OUTLAY COSTS
Hardware
Software
Training
Site preparation
Initial systems design
Conversion
Total initial outlays
RECURRING COSTS
Hardware expansion $260,000 $300,000
Software 150,000 200,000
Systems maintenance 108,000 117,000
Personnel costs 720,000 810,000
Communication charges 160,000 144,000
Overhead 420,000 392,000
Total costs 1,818,000 1,963,000
SAVINGS
Clerical cost savings 1,320,000 1,540,000
Working capital savings 1,200,000 1,500,000
Profits from sales increases 550,000 990,000
Warehousing efficiencies 440,000 880,000
Total savings 3,510,000 4,910,000
SAVINGS MINUS RECURRING COSTS 1,692,000 2,947,000
Less income taxes @ 25% (423,000) (736,750)
Cash savings (net of tax) 1,269,000 2,210,250
Savings on taxes due to 312,500 312,500
depreciation deduction
Net savings 1,581,500 2,522,750
Present value of net saving $1,355,881 $2,002,640
Net present value
Internal rate of return
Table 6: WORST CASE NPV AND IRR ANALYSIS OF A CAPITAL EXPENDITURE
INITIAL OUTLAY YEAR 1
INITIAL OUTLAY COSTS
Hardware $90,000
Software 440,000
Training 260,000
Site preparation 240,000
Initial systems design 2,400,000
Conversion 260,000
Total initial outlays 3,690,000
RECURRING COSTS
Hardware expansion $--
Software $--
Systems maintenance 78,000
Personnel costs 600,000
Communication charges 110,000
Overhead 300,000
Total costs 1,088,000
SAVINGS
Clerical cost savings 540,000
Working capital savings 810,000
Profits from sales increases --
Warehousing efficiencies --
Total savings 1,350,000
SAVINGS MINUS RECURRING COSTS 262,000
Less income taxes @ 25% (65,500)
Cash savings (net of tax) 196,500
Savings on taxes due to 312,500
depreciation deduction
Net savings 509,000
Present value of net savings 2,062,795 $471,296
Net present value $(1,627,205)
Internal rate of return -23%
YEAR 2 YEAR 3
INITIAL OUTLAY COSTS
Hardware
Software
Training
Site preparation
Initial systems design
Conversion
Total initial outlays
RECURRING COSTS
Hardware expansion $260,000 $300,000
Software 165,000 220,000
Systems maintenance 156,000 169,000
Personnel costs 960,000 1,080,000
Communication charges 176,000 198,000
Overhead 420,000 539,000
Total costs 2,137,000 2,506,000
SAVINGS
Clerical cost savings 960,000 1,120,000
Working capital savings 1,200,000 1,200,000
Profits from sales increases 400,000 630,000
Warehousing efficiencies 320,000 560,000
Total savings 2,880,000 3,510,000
SAVINGS MINUS RECURRING COSTS 743,000 1,004,000
Less income taxes @ 25% (185,750) (251,000)
Cash savings (net of tax) 557,250 753,000
Savings on taxes due to 312,500 312,500
depreciation deduction
Net savings 869,750 1,065,500
Present value of net savings $745,670 $845,828
Net present value
Internal rate of return
Thomas L. Zeller, Ph.D., CPA, is a professor of accounting at Loyola University Chicago. You can reach Tom at (312) 915-7626 or tzeller@luc.edu.
Brian B. Stanko, Ph.D., CPA, is a professor of accounting at Loyola University Chicago. You can reach Brian at (312) 915-7106 or bstanko@luc.edu.
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