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chapter 12
Cash Flow Estimation and Risk Analysis
H
ome Depot Inc. grew phenomen- ally during the 1990s, and it is still growing rapidly. At the beginning of 1990, it had 118 stores and annual sales of $2.8 billion. It now (mid-2006) has more than 2,065 stores and sales of more than $ billion. The stock has also performed quite well—a $10,000 investment in 1990 would now be worth about $129,200, for an annual return of more than 17%! For a typical new store, Home Depot spends around $20 million to purchase land, construct a new store, and stock it with inventory. Each new store thus repre- sents a major capital expenditure, so the company must use capital budgeting tech- niques to determine if a potential store’s expected cash flows are sufficient to cover its costs. Home Depot uses information from its existing stores to forecast new stores’ expected cash flows. Thus far, its forecasts have been outstanding, but there are always risks that must be considered.
First, sales might be less than projected if the economy weakens. Second, some of Home Depot’s customers might in the future bypass it altogether and buy directly from manufacturers through the Internet or from competitors such as Lowe’s. Third, new stores could take sales away from existing stores, or “cannibalize” them. To broaden its customer base from do-it- yourself customers and professional con- tractors, Home Depot also operates its Expo Design Center chain, which provides deco- rating advice, materials, and installation for middle- and upper-income customers. The decision to expand requires a detailed assessment of the forecasted cash flows, including the risk that the forecasted level of sales might not be realized. In this chapter, we describe techniques for estimating a project’s cash flows and their associated risk. As you read this chapter, think about how Home Depot might use these techniques to evaluate its capital budgeting decisions.
416 Chapter 12 (^) Cash Flow Estimation and Risk Analysis
The basic principles of capital budgeting were covered in Chapter 11. Given a project’s expected cash flows, it is easy to calculate its NPV, IRR, MIRR, PI, pay- back, and discounted payback. Unfortunately, cash flows are rarely just given— rather, managers must estimate them based on information collected from sources both inside and outside the company. Moreover, uncertainty surrounds the cash flow estimates, and some projects are riskier than others. In the first part of this chapter, we develop procedures for estimating the cash flows associated with cap- ital budgeting projects. Then, in the second part, we discuss techniques used to measure and take account of project risk.
12.1 Estimating Cash Flows
The most important, but also the most difficult, step in capital budgeting is esti- mating project cash flows. Many variables are involved, and many individuals and departments participate in the process. For example, the forecasts of unit sales and sales prices are normally made by the marketing group, based on their knowl- edge of price elasticity, advertising effects, the state of the economy, competitors’ reactions, and trends in consumers’ tastes. Similarly, the capital outlays associated with a new product are generally obtained from the engineering and product development staffs, while operating costs are estimated by cost accountants, pro- duction experts, personnel specialists, purchasing agents, and so forth. A proper analysis includes (1) obtaining information from various depart- ments such as engineering and marketing, (2) ensuring that everyone involved with the forecast uses a consistent set of realistic economic assumptions, and (3) making sure that no biases are inherent in the forecasts. This last point is extremely important, because some managers become emotionally involved with pet projects, and others seek to build empires. Both problems cause cash flow fore- cast biases which make bad projects look good—on paper! It is vital to identify the relevant cash flows, defined as the specific set of cash flows that should be considered in the decision at hand. Analysts often make errors in estimating cash flows, but two cardinal rules can help you minimize mis- takes: (1) Capital budgeting decisions must be based on cash flows , not accounting income. (2) Only incremental cash flows are relevant. Recall from Chapter 3 that free cash flow (FCF) is the cash flow available for distribution to investors. In a nutshell, the relevant cash flow for a project is the
Corporate Valuation, Cash Flows, and Risk Analysis
You can calculate the free cash flows (FCF) for a proj- ect in much the same way as for a firm. When the proj- ect’s expected free cash flows are discounted at the
project’s appropriate risk-adjusted rate, r, the result is the project’s value. This chapter focuses on how to estimate the size and risk of a project’s cash flows.
The textbook’s Web site contains an Excel file that will guide you through the chapter’s calculations. The file for this chapter is FM12 Ch 12 Tool Kit.xls, and we encourage you to open the file and fol- low along as you read the chapter.
NPV c
FCF 1 11 r 21
FCF 2 11 r 22
FCF 3 11 r 23
p^
FCFN 11 r 2 N^
d Initial cost.
418 Chapter 12 (^) Cash Flow Estimation and Risk Analysis
where all cash flows are after taxes and the sign of the cash flow indicates whether it is an inflow or outflow. The project’s free cash flows are also sometimes called net cash flow, and we will use the terms interchangeably. It is worth mentioning that project analysis focuses on expected cash flows, not accounting net income. Accounting net income is based on the depreciation rate the firm’s accountants choose, not necessarily the depreciation rates allowed by the IRS. Also, net income is measured after the deduction of interest expenses, whereas net cash flow focuses on operating cash flow. Moreover, the investment in working capital is not deducted from accounting income. For these and other reasons, net income is generally different from cash flow. Each has a role in finan- cial management, but for capital budgeting purposes it is the project’s net cash flow, not its accounting net income, that is relevant.
What is the most important step in a capital budgeting analysis? What are the major components of a project’s free cash flows?
SELF-TEST
12.2 Project Analysis: An Example
We illustrate the principles of capital budgeting analysis by examining a new proj- ect being considered by Regency Integrated Chips (RIC), a large Nashville-based technology company. This is a new expansion project, defined as one where the firm invests in new assets to increase sales. Following is some background infor- mation on the project.
Background on the Project RIC’s research and development department has been applying its expertise in microprocessor technology to develop a small computer designed to control home appliances. Once programmed, the computer will automatically control the heat- ing and air-conditioning systems, security system, hot water heater, and even small appliances such as a coffee maker. By increasing a home’s energy efficiency, the computer can cut costs enough to pay for itself within a few years. Development has now reached the stage where a decision must be made about whether or not to go forward with full-scale production. RIC’s marketing vice president believes that annual sales would be 20,000 units if the units were priced at $3,000 each, so annual sales are estimated at $60 million. RIC expects no growth in unit sales, and it believes that the unit price will rise by 2% each year. The engineering department has reported that the project will require additional manufacturing space, and RIC currently has an option to purchase an existing building, at a cost of $12 million, which would meet this need. The building would be bought and paid for on December 31, 2008. RIC bases depreciation on the Modified Accelerated Cost Recovery System (MACRS), which we explain in a later section. For depreciation purposes, the building falls into the MACRS 39-year class. The necessary equipment would be purchased and installed in late 2008, and it would also be paid for on December 31, 2008. The equipment falls into the MACRS 5-year class. The equipment would cost $7.8 million and would require $0.2 million for shipping and installation. The depreciable basis under MACRS is equal to the purchase price of an asset plus any shipping and installation costs.
Project Analysis: An Example 419
The basis is not adjusted for salvage value (which is the estimated market value of the asset at the end of its useful life), so the depreciation basis for the building is $7.8 $0.2 $8 million.^1 The project’s estimated economic life is 4 years. At the end of that time, the building is expected to have a market value of $7.5 million and a book value of $10.908 million, whereas the equipment would have a market value of $2 million and a book value of $1.36 million. The production department has estimated that variable manufacturing costs would be $2,100 per unit and that fixed overhead costs, excluding depreciation, would be $8 million a year. They expect variable costs to rise by 2% per year, and fixed costs to rise by 1% per year. Depreciation expenses would be determined in accordance with MACRS rates. RIC’s marginal federal-plus-state tax rate is 40%; its cost of capital is 12%; and, for capital budgeting purposes, the company’s policy is to assume that operating cash flows occur at the end of each year. Because the plant would begin operations on January 1, 2009, the first full year of operating cash flows would end on December 31, 2009. Several other points should be noted: (1) RIC is a relatively large corpora- tion, with sales of more than $4 billion, and it takes on many investments each year. Thus, if the computer control project does not work out, it will not bank- rupt the company—management can afford to take a chance on the computer control project. (2) If the project is accepted, the company will be contractually obligated to operate it for its full 4-year life. Management must make this com- mitment to its component suppliers. (3) Returns on this project would be posi- tively correlated with returns on RIC’s other projects and also with the stock market—the project should do well if other parts of the firm and the general economy are strong. Assume that you have been assigned to conduct the capital budgeting analy- sis. For now, assume that the project has the same risk as an average project and use the corporate weighted average cost of capital, 12%.
Estimation of the Cash Flows
Most projects are analyzed using a spreadsheet program such as Excel , and this one is no exception. The analysis is shown in Table 12-1 and is divided into five parts: (1) Input Data, (2) Depreciation Schedule, (3) Net Salvage Values, (4) Projected Net Cash Flows, and (5) Key Output. Note that numbers in the printed table are rounded from the actual numbers in the spreadsheet, although the spreadsheet uses the unrounded number for all calculations.
Input Data (Part 1) Part 1 of Table 12-1, the Input Data section, provides the basic
data used in the analysis. The inputs are really “assumptions”—thus, in the analy- sis we assume that 20,000 units can be sold at a price of $3 per unit (the sales price is actually $3,000, but for convenience we show all dollars in thousands). Some of the inputs are known with near certainty—for example, the 40% tax rate is not likely to change. Others are more speculative—units sold and the variable cost percentage are in this category. Obviously, if sales or costs are different from the assumed
See FM12 Ch 12 Tool Kit.xls at the textbook’s Web site for all calculations.
(^1) Regardless of whether accelerated or straight-line depreciation is used, the basis is not adjusted by the salvage value when calculating the depreciation that is used to determine taxable income.
Project Analysis: An Example 421
Depreciation Schedule (Part 2) Rows 38 and 42 give the yearly MACRS deprecia-
tion rates for the building and equipment; a later section explains why these are the appropriate rates, but for now we will just use them. Rows 39 and 43 give the annual depreciation expense, calculated as the depreciation rate multiplied by the asset’s depreciable basis. Rows 40 and 44 show the book values at the end of each year, found by subtracting the accumulated annual depreciation from the depreciable basis.
Net Salvage Values (Part 3) See Part 3 of Table 12-1 for the calculation of after-tax
salvage cash flows. Row 53 shows the salvage values for the building and equip- ment, which are the prices the company expects to receive when it sells the assets at the end of the project’s life. Row 54 shows the book values at the end of Year 4; these values are calculated in Part 2. Row 55 shows the expected gain or loss, defined as the difference between the sale price and the book value. For tax pur- poses, gains and losses on depreciable assets are treated as ordinary income, not capital gains or losses. RIC expects to sell the equipment for $2,000 even though it has a book value of only $1,360. To the IRS, this signifies that the depreciation rates were too high during the project’s life, which allowed the company to shield too much of its ear- lier income from taxes. Therefore, the gain is called “depreciation recapture” by the IRS and is taxed as ordinary income. RIC’s $640 gain on the sale of the equip- ment will be taxed at RIC’s 40 percent corporate tax rate, resulting in a tax liabi- lity of $640(0.40) $256, as shown in Row 56. Thus, RIC’s net after-tax cash flow from the sale of the equipment is the salvage price minus the tax: $2,000 $256 $1,744. As shown in Row 54, RIC’s building will have a book value of $10,908 at the time of salvage, but the company expects to realize only $7,500 when it is sold. This would result in a loss of $3,408. This indicates that the building should have been depreciated at a faster rate—only if depreciation had been $3,408 larger would the book and market values have been equal. To compensate for the fact that not enough depreciation was charged during the building’s life, the Tax Code stipulates that losses on the sale of operating assets can be used to reduce taxable ordinary income, just as depreciation reduces income. RIC expects to sell the building for $7,500 and receive a tax credit of $3,408(0.4) $1,363. The resulting net after-tax cash flow is $7,500 $1,336 $8,863, as shown in Row 57.^2 Thus, RIC expects to net $8,863 from the sale of the building and $1,744 from the equipment, for a total of $10,607.^3
Projected Net Cash Flows (Part 4) This section of Table 12-1 uses the information
developed in Parts 1, 2, and 3 to find the projected cash flows over the project’s life. Five periods are shown, from Year 0 to Year 4, in Columns E through I. The initial investment outlays for long-term assets are shown as negative cash flows in Cells E75 and E76 for Year 0. Had there been additional fixed assets pur- chased during the project’s life, their cash flows also would have been shown. Rows 79 through 90 show the calculations for the operating cash flows. We begin with sales revenues, found as the product of units sold and the sales price. Next, we subtract variable costs, which were assumed to be $2.10 per unit. We then deduct fixed operating costs and depreciation to obtain taxable operating
(^2) The formula in the spreadsheet subtracts the expected tax, but since the expected tax is negative, this is equivalent to adding a tax credit to the sales price. 3 Note that if an asset is sold for exactly its book value, there will be no gain or loss, hence no tax liability or credit.
422 Chapter 12 (^) Cash Flow Estimation and Risk Analysis
income, or EBIT, in Row 86. When taxes (at a 40% rate) are subtracted, we are left with net operating profit after taxes, or NOPAT, in Row 88. We add back depreci- ation to obtain annual values for operating cash flow, as shown in Row 90. RIC must purchase raw materials and replenish them each year as they are used. In Part 1 we assume that RIC must have an amount of NOWC on hand equal to 10% of the upcoming year’s sales. For example, sales in Year 1 are $60,000, so RIC must have $6,000 in NOWC at Year 0, as shown in Cell E93. Because RIC had no NOWC prior to Year 0, it must make a $6,000 investment in NOWC at Year 0, as shown in Cell E94. Sales increase to $61,200 in Year 2, so RIC must have $6,120 of NOWC at Year 1. Because it already had $6,000 in NOWC on hand, its net investment at Year 1 is just $120, shown in Cell F94. Note that RIC will have no sales after Year 4, so it will require no NOWC at Year 4. Thus, it has a positive cash flow of $6,367 at Year 4 as working capital is sold but not replaced. When the project’s life ends, the company will receive the “Salvage Cash Flows” as shown in the column for Year 4 in Rows 97 and 98.^4 Thus, the total sal- vage cash flow amounts to $10,607 as shown in Row 99.
Analysis of a New (Expansion) Project: Part 4 (Dollars in Thousands)
Table 12-
(^4) These after-tax cash flows were estimated previously in Part 3.
424 Chapter 12 (^) Cash Flow Estimation and Risk Analysis
Purchase of Fixed Assets and Noncash Charges Most projects require assets, and asset purchases represent negative cash flows. Even though the acquisition of assets results in a cash outflow, accountants do not show the purchase of fixed assets as a deduction from accounting income. Instead, they deduct a depreciation expense each year throughout the life of the asset. Depreciation shelters income from taxation, and this has an impact on cash flow, but depreciation itself is not a cash flow. Therefore, depreciation must be added to NOPAT when estimating a project’s operating cash flow. Depreciation is the most common noncash charge, but there are many other noncash charges that might appear on a company’s financial statements. Just as with depreciation, all other noncash charges should be added back when calculat- ing a project’s net cash flow.
Changes in Net Operating Working Capital Normally, additional inventories are required to support a new operation, and expanded sales tie up additional funds in accounts receivable. However, payables and accruals increase as a result of the expansion, and this reduces the cash needed to finance inventories and receivables. The difference between the required increase in operating current assets and the increase in operating current liabilities is the change in net operating working capital. If this change is positive, as it gen- erally is for expansion projects, then additional financing, over and above the cost of the fixed assets, will be needed. Toward the end of a project’s life, inventories will be used but not replaced, and receivables will be collected without corresponding replacements. As these changes occur, the firm will receive cash inflows, and as a result, the investment in net operating working capital will be returned by the end of the project’s life.
Interest Expenses Are Not Included in Project Cash Flows Recall from Chapter 11 that we discount a project’s cash flows by its cost of capi- tal and that the cost of capital is a weighted average (WACC) of the costs of debt, preferred stock, and common equity, adjusted for the project’s risk. This WACC is the rate of return necessary to satisfy all of the firm’s investors, both stockholders and debtholders. A common mistake made by many students and financial man- agers is to subtract interest payments when estimating a project’s cash flows. This is a mistake because the cost of debt is already embedded in the WACC, so sub- tracting interest payments from the project’s cash flows would amount to double- counting interest costs. If someone subtracted interest (or interest plus principal payments) from the project’s cash flows, then they would be calculating the cash flows available to the equity holders, and these cash flows should be discounted at the cost of equity. This technique can give the correct answer, but in order for it to work you must be very careful to adjust the amount of debt outstanding each year in order to keep the risk of the equity cash flows constant. This process is very complicated, and we do not recommend it. Here is one final caution: If someone subtracts inter- est, then it is definitely wrong to discount the resulting cash flows by the WACC, and no amount of care can correct that error. Therefore, you should not subtract interest expenses when finding a project’s cash flows.
Issues in Project Analysis 425
Sunk Costs
A sunk cost is an outlay that has already occurred, hence is not affected by the decision under consideration. Since sunk costs are not incremental costs, they should not be included in the analysis. For example, RIC spent $100,000 in 2007 for R&D to develop the technology for the integrated chips project. Is this 2007 expenditure a relevant cost with respect to the 2008 capital budgeting decision? The answer is no—the $100,000 is a sunk cost , and it will not affect future cash flows regardless of whether or not the new project is implemented. It often turns out that a particular project has a negative NPV if all the associated costs, includ- ing sunk costs, are considered. However, on an incremental basis, the project may be a good one because the future incremental cash flows are large enough to produce a positive NPV on the incremental investment.
Opportunity Costs
Opportunity costs are cash flows that could be generated from an asset the firm already owns, provided the asset is not used for the project in question. Instead of buying a new building, suppose that RIC already owns a building that could be used for the project. If RIC’s managers decided to use this building rather than buy a new one, RIC would not incur the $12 million cash outlay to buy a new building. Would this mean that we should delete the $12 million expenditure from the analysis, which would obviously raise the estimated NPV well above the $5.8 million we found in Table 12-1? The answer is that we should remove the cash flows related to the new build- ing, but we should include the opportunity cost associated with the existing build- ing as a cash cost. For example, if the building had a market value, after taxes and brokerage expenses, of $14 million, then RIC would be giving up $14 million if it used the building for the computer project. Therefore, we should charge the proj- ect the $14 million that would be forgone as an opportunity cost.
Effects on Other Parts of the Firm: Externalities
Economists define externalities as the effects a project has on other parts of the firm or on the environment. For example, Apple’s introduction of the iPod nano caused some people who were planning to purchase a regular iPod to switch to a nano. The nano project generates positive cash flows, but it also reduces some of the company’s current cash flows. This type of externality is called a cannibal- ization effect, because the new business eats into the company’s existing busi- ness. The lost cash flows should be charged to the new project. However, it often turns out that if the one company does not produce a new product, some other company will, so the old cash flows would be lost anyway. In this case, no charge should be assessed against the new project. All this makes determining the can- nibalization effect difficult, because it requires estimates of changes in sales and costs, and also the timing of when those changes will occur. Still, cannibalization can be important, so its potential effects should be considered. Note that externalities can be positive as well as negative. For example, Apple’s introduction of the nano has helped spur music sales at Apple’s Music Store. When Apple was evaluating the nano project, it should have increased the project’s cash flows by the expected cash flows due to additional music sales. It often turns out that a project’s direct cash flows are insufficient to produce a
Depreciation 427
stockholder reporting, one normally takes the cost of the asset, subtracts its esti- mated salvage value, and divides the net amount by the asset’s useful economic life. For example, consider an asset with a 5-year life that costs $100,000 and has a $12,500 salvage value; its annual straight-line depreciation charge is ($100,000 $12,500)/5 $17,500. Note, however, as we stated earlier, salvage value is a fac- tor in financial reporting but it is not considered for tax depreciation purposes. For tax purposes, Congress changes the permissible tax depreciation methods from time to time. Prior to 1954, the straight-line method was required for tax pur- poses, but in 1954 accelerated methods (double-declining balance and sum-of- years’-digits) were permitted. Then, in 1981, the old accelerated methods were replaced by a simpler procedure known as the Accelerated Cost Recovery System (ACRS). The ACRS system was changed again in 1986 as a part of the Tax Reform Act, and it is now known as the Modified Accelerated Cost Recovery System (MACRS); a 1993 tax law made further changes in this area. Note that U.S. tax laws are very complicated, and in this text we can only pro- vide an overview of MACRS designed to give you a basic understanding of the impact of depreciation on capital budgeting decisions. Further, the tax laws change so often that the numbers we present may be outdated before the book is even published. Thus, when dealing with tax depreciation in real-world situa- tions, current Internal Revenue Service (IRS) publications or individuals with expertise in tax matters should be consulted. For tax purposes, the entire cost of an asset is expensed over its depreciable life. Historically, an asset’s depreciable life was set equal to its estimated useful economic life; it was intended that an asset would be fully depreciated at approx- imately the same time that it reached the end of its useful economic life. However, MACRS totally abandoned that practice and set simple guidelines that created several classes of assets, each with a more-or-less arbitrarily prescribed life called a recovery period or class life. The MACRS class lives bear only a rough relationship to assets’ expected useful economic lives. A major effect of the MACRS system has been to shorten the depreciable lives of assets, thus giving businesses larger tax deductions early in the assets’ lives, and thereby increasing the present value of the cash flows. Table 12-2 describes the types of property that fit into the different class life groups, and Table 12-3 sets forth the MACRS recovery allowance percentages (depreciation rates) for selected classes of investment property. Consider Table 12-2, which gives the MACRS class lives and the types of assets that fall into each category. Property in the 27.5- and 39-year categories (real estate) must be depreciated by the straight-line method, but 3-, 5-, 7-, and 10-year
Major Classes and Asset Lives for MACRS
Table 12-
Class Type of Property
3-year Certain special manufacturing tools 5-year Automobiles, light-duty trucks, computers, and certain special manufacturing equipment 7-year Most industrial equipment, office furniture, and fixtures 10-year Certain longer-lived types of equipment 27.5-year Residential rental real property such as apartment buildings 39-year All nonresidential real property, including commercial and industrial buildings
428 Chapter 12 (^) Cash Flow Estimation and Risk Analysis
property (personal property) can be depreciated either by the accelerated method set forth in Table 12-3 or by the straight-line method.^5 As we saw earlier in the chapter, higher depreciation expenses result in lower taxes in the early years, hence a higher present value of cash flows. Therefore, since a firm has the choice of using straight-line rates or the accelerated rates shown in Table 12-3, most elect to use the accelerated rates.
Recovery Allowance Percentage for Personal Property
Table 12-
Class of Investment
Ownership Year 3-Year 5-Year 7-Year 10-Year
1 33% 20% 14% 10% 2 45 32 25 18 3 15 19 17 14 4 7 12 13 12 5 11 9 9 6 6 9 7 7 9 7 8 4 7 9 7 10 6 11 3
100% 100% 100% 100%
Notes: a (^) We developed these recovery allowance percentages based on the 200% declining balance method prescribed by MACRS, with a switch to straight-line depreciation at some point in the asset’s life. For example, consider the 5-year recovery allowance percentages. The straight-line percentage would be 20% per year, so the 200% declining balance multiplier is 2.0(20%) 40% 0.4. However, because the half-year convention applies, the MACRS percentage for Year 1 is 20%. For Year 2, there is 80% of the depreciable basis remaining to be depreciated, so the recovery allowance percentage is 0.40(80%) 32%. In Year 3, 20% 32% 52% of the depreciation has been taken, leaving 48%, so the percentage is 0.4(48%) 19%. In Year 4, the percentage is 0.4(29%) 12%. After 4 years, straight-line depreciation exceeds the declining balance depreciation, so a switch is made to straight-line (this is permitted under the law). However, the half-year convention must also be applied at the end of the class life, and the remaining 17% of depreciation must be taken (amortized) over 1.5 years. Thus, the percentage in Year 5 is 17%/1.5 11%, and in Year 6, 17% – 11% 6%. Although the tax tables carry the allowance percentages out to two decimal places, we have rounded to the nearest whole number for ease of illustration. b (^) Residential rental property (apartments) is depreciated over a 27.5-year life, whereas commer- cial and industrial structures are depreciated over 39 years. In both cases, straight-line depreci- ation must be used. The depreciation allowance for the first year is based, pro rata, on the month the asset was placed in service, with the remainder of the first year’s depreciation being taken in the 28th or 40th year. A half-month convention is assumed; that is, an asset placed in service in February would receive 10.5 months of depreciation in the first year.
(^5) The Tax Code currently (for 2006) permits companies to expense, which is equivalent to depreciating over 1 year, up to $108,000 of equipment; see IRS Publication 946 for details. This is a benefit primarily for small companies. Thus, if a small company bought one asset worth up to $108,000, it could write the asset off in the year it was acquired. This is called “Section 179 expensing.” We shall disregard this provision throughout the book. Also, Congress enacted the Job Creation and Worker Assistance Act of 2002 following the terrorist attacks on the World Trade Center and Pentagon. This act, among other things, temporarily changed how depreciation is charged for property acquired after September 10, 2001, and before September 11, 2004, and put in service before January 1,
- We shall disregard this provision throughout the book as well.
430 Chapter 12 (^) Cash Flow Estimation and Risk Analysis
For example, if the real cost of capital is 7% and the inflation rate is 5%, then 1 rNOM (1.07)(1.05) 1.1235, so rNOM 12.35%.^7 Now if net cash flows increase at the rate of i percent per year, and if this same inflation premium is built into the firm’s cost of capital, then the NPV would be calculated as follows:
Since the (1 i)t^ terms in the numerator and denominator cancel, we are left with
Thus, if all costs and also the sales price, hence annual cash flows, are expected to rise at the same inflation rate that investors have built into the cost of capital, then the inflation-adjusted NPV as determined using Equation 12-5 is the same whether you discount nominal cash flows at a nominal rate or real cash flows at a real rate. For example, the PV of a real $100 at Year 5 at a real rate of 7% is $71.30 $100/(1.07)^5. The PV of a nominal $127.63 at Year 5 at a nominal rate of 12.35% is also $71.30 $127.63/(1.1235)^5. However, some analysts mistakenly use base year, or constant (unadjusted), dollars throughout the analysis—say, 2008 dollars if the analysis is done in 2008— along with a cost of capital as determined in the marketplace as we described in Chapter 10. This is wrong: If the cost of capital includes an inflation premium, as it typ- ically does, but the cash flows are all stated in constant (unadjusted) dollars, then the cal- culated NPV will be lower than the true NPV. The denominator will reflect inflation, but the numerator will not, and this will produce a downward-biased NPV.
Making the Inflation Adjustment There are two ways to adjust for inflation. First, all project cash flows can be expressed as real (unadjusted) flows, with no consideration of inflation, and then the cost of capital can be adjusted to a real rate by removing the inflation premi- ums from the component costs. This approach is simple in theory, but to produce an unbiased NPV it requires (1) that all project cash flows, including depreciation, be affected identically by inflation, and (2) that this rate of increase equals the inflation rate built into investors’ required returns. Because these assumptions do not necessarily hold in practice, this method is not commonly used. The second method involves leaving the cost of capital in its nominal form, and then adjusting the individual cash flows to reflect expected inflation. This is what we did earlier in our RIC example as summarized in Table 12-1. There we assumed that sales prices and variable costs would increase at a rate of 2% per year,
NPV (^) a
N
t 0
RCFt 11 rr 2 t^
NPV 1 with inflation 2 (^) a
N
t 0
NCFt 11 rNOM 2 t^
(^) a
N
t 0
RCFt 11 i 2 t 11 rr 2 t^11 i 2 t
(^7) To focus on inflation effects, we have simplified the situation somewhat. The actual project cost of capital is made up of debt and equity components, both of which are affected by inflation, but only the debt component is adjusted for tax effects. Thus, the relationship between nominal and real costs of capital is more complex than indicated in our discussion here.
(12-5)
(12-6)
Project Risk Analysis: Techniques for Measuring Stand-Alone Risk 431
fixed costs would increase by 1% per year, and that depreciation charges would not be affected by inflation. One should always build inflation into the cash flow analy- sis, with the specific adjustment reflecting as accurately as possible the most likely set of circumstances. With a spreadsheet, it is easy to make the adjustments. Our conclusions about inflation may be summarized as follows. First, infla- tion is critically important, for it can and does have major effects on businesses. Therefore, it must be recognized and dealt with. Second, the most effective way of dealing with inflation in capital budgeting analyses is to build inflation estimates into each cash flow element, using the best available information on how each ele- ment will be affected. Third, since we cannot estimate future inflation rates with precision, errors are bound to be made. Thus, inflation adds to the uncertainty, or risk, of capital budgeting as well as to its complexity.
What is the best way of handling inflation, and how does this procedure eliminate the potential bias?
SELF-TEST
12.6 Project Risk Analysis: Techniques for
Measuring Stand-Alone Risk
Recall from Chapter 10 that there are three distinct types of risk: stand-alone risk, corporate risk, and market risk. Why should a project’s stand-alone risk be impor- tant to anyone? In theory, this type of risk should be of little or no concern. However, it is actually of great importance for two reasons:
- It is easier to estimate a project’s stand-alone risk than its corporate risk, and it is far easier to measure stand-alone risk than market risk.
- In the vast majority of cases, all three types of risk are highly correlated—if the general economy does well, so will the firm, and if the firm does well, so will most of its projects. Because of this high correlation, stand-alone risk is gener- ally a good proxy for hard-to-measure corporate and market risk.
The starting point for analyzing a project’s stand-alone risk involves deter- mining the uncertainty inherent in its cash flows. To illustrate what is involved, consider again Regency Integrated Chips’ appliance control computer project that we discussed above. Many of the key inputs shown in Part 1 of Table 12-1 are sub- ject to uncertainty. For example, sales were projected at 20,000 units to be sold at a net price of $3,000 per unit. However, actual unit sales will almost certainly be somewhat higher or lower than 20,000, and the sales price will probably turn out to be different from the projected $3,000 per unit. In effect, the sales quantity and price estimates are really expected values based on probability distributions, as are many of the other values that were shown in Part 1 of Table 12-1. The distributions could be relatively “tight,” reflecting small standard deviations and low risk, or they could be “wide,” denoting a great deal of uncertainty about the actual value of the vari- able in question and thus a high degree of stand-alone risk. The nature of the individual cash flow distributions, and their correlations with one another, determine the nature of the NPV probability distribution and, thus, the project’s stand-alone risk. In the following sections, we discuss three techniques for assessing a project’s stand-alone risk: (1) sensitivity analysis, (2) scenario analysis, and (3) Monte Carlo simulation.
Project Risk Analysis: Techniques for Measuring Stand-Alone Risk 433
NPV ($) 40,
30,
20,
10,
0
10,
20,
30, 30 15 0 15 30 Deviation from Base-Case Value (%)
Sales price
Growth rate
Units sold
WACC Fixed cost
Variable cost
Evaluating Risk: Sensitivity Analysis (Dollars in Thousands)
Figure 12-
NPV At Different Deviations From Base
Deviation from Variable Growth Year 1 Fixed Base Case Sales Price Cost/Unit Rate Units Sold Cost WACC
30% ($27,223) $29,404 ($ 4,923) ($ 3,628) $10,243 $9, 15 (10,707) 17,607 (115) 1,091 8,026 7, 0 5,809 5,809 5,809 5,809 5,809 5, 15 22,326 (5,988) 12,987 10,528 3,593 4, 30 38,842 (17,785) 21,556 15,247 1,376 3, Range $66,064 $47,189 $26,479 $18,875 $ 8,867 $6,
NPV Breakeven Analysis (Dollars in Thousands)
Table 12-
Input Input Value that Produces Zero NPV
Sales price $2. Variable cost/unit $2. Growth rate 14.7% Year 1 units sold 16, Fixed cost $11, WACC 20.1%
434 Chapter 12 (^) Cash Flow Estimation and Risk Analysis
project’s NPV is highly sensitive to changes in the sales price and the variable cost per unit. Those sensitivities suggest that the project is risky. Suppose, however, that Home Depot or Circuit City was anxious to get the new computer product and would sign a contract to purchase 20,000 units per year for 4 years at $3, per unit. Moreover, suppose Intel would agree to provide the principal compo- nent at a price that would ensure that the variable cost per unit would not exceed $2,100. Under these conditions, there would be a low probability of high or low sales prices and input costs, so the project would not be at all risky in spite of its sensitivity to those variables. We see, then, that we need to extend sensitivity analysis to deal with the prob- ability distributions of the inputs. In addition, it would be useful to vary more than one variable at a time so we could see the combined effects of changes in the vari- ables. Scenario analysis provides these extensions—it brings in the probabilities of changes in the key variables, and it allows us to change more than one variable at a time. In a scenario analysis, the financial analyst begins with the base case, or most likely set of values for the input variables. Then, he or she asks marketing, engineering, and other operating managers to specify a worst-case scenario (low unit sales, low sales price, high variable costs, and so on) and a best-case scenario. Often, the best case and worst case are set so as to have a 25% probability of con- ditions being that good or bad, and a 50% probability is assigned to the base-case conditions. Obviously, conditions could actually take on other values, but param- eters such as these are useful to get people focused on the central issues in risk analysis. The best-case, base-case, and worst-case values for RIC’s computer project are shown in Table 12-5, along with a plot of the NPVs. If the product is highly successful, then the combination of a high sales price, low production costs, high first year sales, and a strong growth rate in future sales will result in a very high NPV, $146 million. However, if things turn out badly, then the NPV will be –$37 million. The graph shows a very wide range of possibilities, indicating that this is indeed a very risky project. If the bad conditions materialize, this will not bankrupt the company—this is just one project for a large company. Still, losing $37 million would certainly not help the stock price or the career of the project’s manager. The scenario probabilities and NPVs constitute a probability distribution of returns like those we dealt with in Chapter 6, except that the returns are measured in dollars instead of percentages (rates of return). The expected NPV (in thousands of dollars) is $30,135:^8
Expected NPV (^) a
n
i 1
Pi 1 NPVi 2
See FM12 Ch 12 Tool Kit.xls for a scenario analysis using Excel’s Scenario Manager.
(^8) Note that the expected NPV, $30,135, is not the same as the base-case NPV, $5,809 (in thousands). This is because the two uncertain variables, sales volume and sales price, are multiplied together to obtain dollar sales, and this process causes the NPV distribution to be skewed to the right. A big number times another big number produces a very big number, which, in turn, causes the average, or expected value, to increase.
