CHAPTER 12 Cash Flow Estimation and Risk Analysis SOURCE: Andre Jenny/Unicorn Stock Photos 46 HO M E D E P OT KEEPS GROWING $ HOME DEPOT H ome Depot Inc has grown phenomenally over the through the Internet Third, new stores could past decade, and it shows no sign of slowing “cannibalize,” that is, take sales away from, existing down At the beginning of 1990, it had 118 stores This last point was made in the July 16, 1999, stores, and its annual sales were $2.8 billion By early issue of Value Line: 2001, it had more than 1,000 stores, and its annual sales were in excess of $45 billion Despite concerns of The retailer has picked the “low-hanging fruit;” it a slowing economy, the company expects to open has already entered the most attractive markets To another 200 stores in fiscal 2001 avoid “cannibalization” — which occurs when Home Depot recently estimated that it costs, on duplicative stores are located too closely together — average, $16 million to purchase land, construct a new the company is developing complementary formats store, and stock it with inventory (The inventory costs For example, Home Depot is beginning to roll out its about $5 million, but about $2 million of this is Expo Design Center chain, which offers one-stop sales financed through accounts payable.) Each new store and service for kitchen and bath and other thus represents a major capital expenditure, so the remodeling and renovation work company must use capital budgeting techniques 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, store sales might be less than projected if the economy weakens Second, some of Home Depot’s customers might in the future 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 Companies such as Home Depot use these techniques on a regular basis to evaluate capital budgeting decisions I bypass it altogether and buy directly from manufacturers 547 The basic principles of capital budgeting were covered in Chapter 11 Given a project’s expected cash flows, it is easy to calculate its payback, discounted payback, NPV, IRR, and MIRR 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 this chapter, we first develop procedures for estimating cash flows associated with capital budgeting projects Then, we discuss techniques used to measure and take account of project risk Finally, we introduce the concept of real options and discuss some general principles for determining the optimal capital budget I E S T I M AT I N G C A S H F L O W S The most important, but also the most difficult, step in capital budgeting is estimating projects’ cash flows — the investment outlays and the annual net cash inflows after a project goes into operation 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 knowledge 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, production experts, personnel specialists, purchasing agents, and so forth It is difficult to accurately forecast the costs and revenues associated with a large, complex project, so forecast errors can be quite large For example, when several major oil companies decided to build the Alaska Pipeline, the original cost estimates were in the neighborhood of $700 million, but the final cost was closer to $7 billion Similar (or even worse) miscalculations are common in forecasts of product design costs, such as the costs to develop a new personal computer Further, as difficult as plant and equipment costs are to estimate, sales revenues and operating costs over the project’s life are even more uncertain For example, several years ago, Federal Express developed an electronic delivery service system (ZapMail) It used the correct capital budgeting technique, NPV, but it incorrectly estimated the project’s cash flows: Projected revenues were too high, projected costs were too low, and virtually no one was willing to pay the price required to cover the project’s costs As a result, cash flows failed to meet the forecasted levels, and Federal Express ended up losing about $200 million on the venture This example demonstrates a basic truth — 548 CHAPTER 12 I C A S H F L O W E S T I M AT I O N A N D R I S K A N A LY S I S if cash flow estimates are not reasonably accurate, any analytical technique, no matter how sophisticated, can lead to poor decisions Because of its financial strength, Federal Express was able to absorb losses on the project, but the ZapMail venture could have forced a weaker firm into bankruptcy The financial staff’s role in the forecasting process includes (1) obtaining information from various departments such as engineering and marketing, (2) ensuring that everyone involved with the forecast uses a consistent set of economic assumptions, and (3) making sure that no biases are inherent in the forecasts This last point is extremely important, because managers often become emotionally involved with pet projects and also develop empire-building complexes, both of which lead to cash flow forecasting biases that make bad projects look good — on paper It is almost impossible to overstate the problems one can encounter in cash flow forecasts It is also difficult to overstate the importance of these forecasts Still, observing the principles discussed in the next several sections will help minimize forecasting errors SELF-TEST QUESTIONS What is the most important step in a capital budgeting analysis? What departments are involved in estimating a project’s cash flows? What is the financial staff’s role in the forecasting process for capital projects? I D E N T I F Y I N G T H E R E L E VA N T C A S H F L O W S Relevant Cash Flows The specific cash flows that should be considered in a capital budgeting decision The starting point in any capital budgeting analysis is identifying 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 avoid mistakes: (1) Capital budgeting decisions must be based on cash flows, not accounting income (2) Only incremental cash flows are relevant Recall from Chapter that free cash flow is the cash flow available for distribution to investors In a nutshell, the relevant cash flow for a project is the additional free cash flow that the company expects if it implements the project, that is, the cash flow above and beyond what the company could expect if it doesn’t implement the project The following sections discuss the relevant cash flows in more detail PROJECT CASH FLOW VERSUS ACCOUNTING INCOME Recall that free cash flow is calculated as follows: Free cash flow ϭ ϭ After-tax Capital ϩ Depreciation Ϫ Ϫ operating income expenditures EBIT(1ϪT) ϩ Depreciation Ϫ Change in net operating working capital ⌬ Current assets Ϫ Capital Ϫ c d expenditures ⌬ Spontaneous liabilities I D E N T I F Y I N G T H E R E L E VA N T C A S H F L O W S 549 Just as a firm’s value depends on its free cash flows, the value of a project depends on its free cash flow We illustrate the estimation of project cash flow later in the chapter with a comprehensive example, but it is important for you to understand that project cash flow differs from accounting income Costs of Fixed Assets Most projects require assets, and asset purchases represent negative cash flows Even though the acquisition of assets results in a cash outflow, accountants 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 Note that the full costs of fixed assets include any shipping and installation costs When a firm acquires fixed assets, it often must incur substantial costs for shipping and installing the equipment These charges are added to the price of the equipment when the project’s cost is being determined Then, the full cost of the equipment, including shipping and installation costs, is used as the depreciable basis when depreciation charges are being calculated For example, if a company bought a computer with an invoice price of $100,000 and paid another $10,000 for shipping and installation, then the full cost of the computer (and its depreciable basis) would be $110,000 Note too that fixed assets can often be sold at the end of a project’s life If this is the case, then the after-tax cash proceeds represent a positive cash flow We will illustrate both depreciation and cash flow from asset sales later in the chapter Noncash Charges In calculating net income, accountants usually subtract depreciation from revenues So, while accountants not subtract the purchase price of fixed assets when calculating accounting income, they subtract a charge each year for depreciation 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 net income when estimating a project’s cash flow C h a n g e s i n N e t O p e r a t i n g Wo r k i n g C a p i t a l Change in Net Operating Working Capital The increased current assets resulting from a new project minus the spontaneous increase in accounts payable and accruals 550 CHAPTER 12 I Normally, additional inventories are required to support a new operation, and expanded sales tie additional funds up in accounts receivable However, payables and accruals increase spontaneously as a result of the expansion, and this reduces the cash needed to finance inventories and receivables The difference between the required increase in current assets and the spontaneous increase in current liabilities is the change in net operating working capital If this change is positive, as it generally 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 As a result, the investment in operating working capital will be returned by the end of the project’s life C A S H F L O W E S T I M AT I O N A N D R I S K A N A LY S I S 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 capital, and that the cost of capital is a weighted average of the costs of debt, preferred stock, and common equity (WACC), adjusted for the project’s risk Moreover, the WACC is the rate of return necessary to satisfy all of the firm’s investors — debtholders and stockholders The discounting process reduces the cash flows to account for the project’s capital costs If interest charges were first deducted and then the resulting cash flows were discounted, this would double count the cost of debt Therefore, you should not subtract interest expenses when finding a project’s cash flows Note that this differs from the procedures used to calculate accounting income Accountants measure the profit available for stockholders, so interest expenses are subtracted However, project cash flow is the cash flow available for all investors, bondholders as well as stockholders, so interest expenses are not subtracted All this is analogous to the procedures used in the corporate valuation model of Chapter 9, where the company’s free cash flows are discounted at the WACC.1 I N C R E M E N TA L C A S H F L O W S Incremental Cash Flow The net cash flow attributable to an investment project In evaluating a project, we focus on those cash flows that occur if and only if we accept the project These cash flows, called incremental cash flows, represent the change in the firm’s total cash flow that occurs as a direct result of accepting the project Three special problems in determining incremental cash flows are discussed next Sunk Costs Sunk Cost A cash outlay that has already been incurred and that cannot be recovered regardless of whether the project is accepted or rejected 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 To illustrate, in 2001, Northeast BankCorp was considering the establishment of a branch office in a newly developed section of Boston To help with its evaluation, Northeast had, back in 2000, hired a consulting firm to perform a site analysis; the cost was $100,000, and this amount was expensed for tax purposes in 2000 Is this 2000 expenditure a relevant cost with respect to the 2001 capital budgeting decision? The answer is no — the $100,000 is a sunk cost, and it will not affect Northeast’s future cash flows regardless of whether or not the new branch is built It often turns out that a particular project has a negative NPV when all the associated costs, including sunk costs, are considered However, on an incremental basis, An alternative approach to capital budgeting is to estimate the cash flows that are available for equity holders Although this produces the same NPV as our approach, we not recommend it because to apply it correctly requires that we determine the amount of debt and equity for every year of the project’s life I D E N T I F Y I N G T H E R E L E VA N T C A S H F L O W S 551 the project may be a good one because the incremental cash flows are large enough to produce a positive NPV on the incremental investment Opportunity Costs Opportunity Cost The return on the best alternative use of an asset, or the highest return that will not be earned if funds are invested in a particular project A second potential problem relates to opportunity costs, which are cash flows that could be generated from an asset the firm already owns provided it is not used for the project in question To illustrate, Northeast BankCorp already owns a piece of land that is suitable for the branch location When evaluating the prospective branch, should the cost of the land be disregarded because no additional cash outlay would be required? The answer is no, because there is an opportunity cost inherent in the use of the property In this case, the land could be sold to yield $150,000 after taxes Use of the site for the branch would require forgoing this inflow, so the $150,000 must be charged as an opportunity cost against the project Note that the proper land cost in this example is the $150,000 market-determined value, irrespective of whether Northeast originally paid $50,000 or $500,000 for the property (What Northeast paid would, of course, have an effect on taxes, hence on the after-tax opportunity cost.) Effects on Other Parts of the Firm: Externalities Externalities Effects of a project on cash flows in other parts of the firm Cannibalization Occurs when the introduction of a new product causes sales of existing products to decline The third potential problem involves the effects of a project on other parts of the firm, which economists call externalities For example, some of Northeast’s customers who would use the new branch are already banking with Northeast’s downtown office The loans and deposits, hence profits, generated by these customers would not be new to the bank; rather, they would represent a transfer from the main office to the branch Thus, the net income produced by these customers should not be treated as incremental income in the capital budgeting decision On the other hand, having a suburban branch would help the bank attract new business to its downtown office, because some people like to be able to bank both close to home and close to work In this case, the additional income that would actually flow to the downtown office should be attributed to the branch Although they are often difficult to quantify, externalities (which can be either positive or negative) should be considered When a new project takes sales from an existing product, this is often called cannibalization Naturally, firms not like to cannibalize their existing products, but it often turns out that if they not, someone else will To illustrate, IBM for years refused to provide full support for its PC division because it did not want to steal sales from its highly profitable mainframe business That turned out to be a huge strategic error, because it allowed Intel, Microsoft, Compaq, and others to become dominant forces in the computer industry Therefore, when considering externalities, the full implications of the proposed new project should be taken into account TIMING OF CASH FLOW We must account properly for the timing of cash flows Accounting income statements are for periods such as years or months, so they not reflect exactly when during the period cash revenues or expenses occur Because of the time 552 CHAPTER 12 I C A S H F L O W E S T I M AT I O N A N D R I S K A N A LY S I S value of money, capital budgeting cash flows should in theory be analyzed exactly as they occur Of course, there must be a compromise between accuracy and feasibility A time line with daily cash flows would in theory be most accurate, but daily cash flow estimates would be costly to construct, unwieldy to use, and probably no more accurate than annual cash flow estimates because we simply cannot forecast well enough to warrant this degree of detail Therefore, in most cases, we simply assume that all cash flows occur at the end of every year However, for some projects, it may be useful to assume that cash flows occur at mid-year, or even quarterly or monthly SELF-TEST QUESTIONS Why should companies use project cash flow rather than accounting income when finding the NPV of a project? How shipping and installation costs affect the costs of fixed assets and the depreciable basis? What is the most common noncash charge that must be added back when finding project cash flows? What is net operating working capital, and how does it affect projects’ costs in capital budgeting? How does the company get back the dollars it invests in net operating working capital? Explain the following terms: incremental cash flow, sunk cost, opportunity cost, externality, and cannibalization Give an example of a “good” externality, that is, one that makes a project look better E VA L U AT I N G C A P I TA L B U D G E T I N G P R O J E C T S New Expansion Project A project that is intended to increase sales Replacement Project A project that replaces an existing asset with a new asset Up until this point, we have discussed several important aspects of cash flow analysis, but we have not seen how they affect capital budgeting decisions Conceptually, these decisions are straightforward: A potential project creates value for the firm’s shareholders if and only if the net present value of the incremental cash flows from the project is positive In practice, however, estimating these cash flows can be difficult Incremental cash flows are affected by whether the project is a new expansion project or a replacement project A new expansion project is defined as one where the firm invests in new assets to increase sales Here the incremental cash flows are simply the project’s cash inflows and outflows In effect, the company is comparing what its value looks like with and without the proposed project By contrast, a replacement project occurs when the firm replaces an existing asset with a new one In this case, the incremental cash flows are the firm’s additional inflows and outflows that result from investing in the new asset E VA L U AT I N G C A P I TA L B U D G E T I N G P R O J E C T S 553 In a replacement analysis, the company is comparing its value if it acquires the new asset to its value if it continues to use the existing asset.2 Despite these differences, the basic principles for evaluating expansion and replacement projects are the same In each case, the cash flows typically include the following items: Initial investment outlay The initial investment includes the up-front cost of fixed assets associated with the project plus any increases in net operating working capital Operating cash flows over the project’s life These are the incremental cash inflows over the project’s economic life Annual operating cash flows equal after-tax operating income plus depreciation Recall (a) that depreciation is added back because it is a noncash expense and (b) that financing costs (including interest expense) are not included because they are accounted for in the discounting process Terminal year cash flows At the end of a project’s life, some extra cash flows are frequently received These include the salvage value of the fixed assets, adjusted for taxes if assets are not sold at their book value, plus the return of the net operating working capital For each year of the project’s life, the net cash flow is determined as the sum of the cash flows from each of the three categories These annual net cash flows are then plotted on a time line and used to calculate the project’s NPV and IRR We will illustrate the principles of capital budgeting analysis by examining a new project being considered by Brandt-Quigley Corporation (BQC), a large Atlanta-based technology company BQC’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 heating 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 Developments have now reached the stage where a decision must be made about whether or not to go forward with full-scale production BQC’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 The engineering department has reported that the firm would need additional manufacturing capability, and BQC 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, 2002, and for depreciation purposes it would fall into the MACRS 39-year class The necessary equipment would be purchased and installed late in 2002, and it would also be paid for on December 31, 2002 The equipment would fall into the MACRS 5-year class, and it would cost $8 million, including transportation For more discussion on replacement analysis decisions refer to the Concise web site or to Eugene F Brigham and Phillip R Daves, Intermediate Financial Management, 7th ed (Fort Worth, TX: Harcourt College Publishers, 2002), Chapter 12 554 CHAPTER 12 I C A S H F L O W E S T I M AT I O N A N D R I S K A N A LY S I S 13-1 QBE ϭ 500,000 13-2 30% debt and 70% equity 14-11 13-3 bU ϭ 1.0435 13-4 a(1) Ϫ$75,000 (2) $175,000 b QBE ϭ 140,000 13-5 a(1) Ϫ$60,000 b QBE ϭ 14,000 a b c e f g $6,000,000 $2.00; 25% $5,000,000 50% $1,000,000 $8,333,333 15-1 $3,000,000 A/R ϭ $59,500 13-6 a(2) $125,000 b QBE ϭ 7,000 15-2 15-3 kNom ϭ 75.26%; EAR ϭ 109.84% 13-7 a P0 ϭ $25 b P0 ϭ $25.81 15-4 EAR ϭ 8.49% 15-5 $7,500,000 13-8 a ROELL ϭ 14.6%; ROEHL ϭ 16.8% b ROELL ϭ 16.5% 15-6 13-9 No leverage: ROE ϭ 10.5%; ␴ ϭ 5.4%; CV ϭ 0.51; 60% leverage: ROE ϭ 13.7%; ␴ ϭ 13.5%; CV ϭ 0.99 a DSO ϭ 28 days b A/R ϭ $70,000 15-7 b 14.90% d 21.28% 13-10 ks ϭ 17% 13-12 a EPSOld ϭ $2.04; New: EPSD ϭ $4.74; EPSS ϭ $3.27 b 339,750 units c QNew, Debt ϭ 272,250 units 13-13 Debt used: E(EPS) ϭ $5.78; ␴EPS ϭ $1.05; E(TIE) ϭ 3.49ϫ Stock used: E(EPS) ϭ $5.51; ␴EPS ϭ $0.85; E(TIE) ϭ 6.00ϫ 13-14 a FCA ϭ $80,000; VA ϭ $4.80/unit; PA ϭ $8.00/unit 13-15 40% debt and 60% equity; WACC ϭ 11.45% 15-8 a 45.15% 15-9 Nominal cost ϭ 14.90%; Effective cost ϭ 15.89% 15-10 14.91% 15-11 a 32 days b $288,000 c $45,000 d(1) 30 (2) $378,000 15-12 a 83 days b $356,250 c 4.87ϫ 15-13 a 69.5 days b(1) 1.875ϫ (2) 11.25% c(1) 46.5 days (2) 2.1262ϫ (3) 12.76% 14-1 Payout ϭ 55% 14-2 P0 ϭ $60 14-3 P0 ϭ $40 15-14 14-4 14-5 $3,250,000 Payout ϭ 20% a ROET ϭ 11.75%; ROEM ϭ 10.80%; ROER ϭ 9.16% 15-15 a Feb surplus ϭ $2,000 14-6 14-7 14-8 14-9 Payout ϭ 52% D0 ϭ $3.44 Payout ϭ 31.39% a $1.44 b 3% c $1.20 d 33 1/3% 14-10 A-42 15-16 APPENDIX C I a $100,000 c(1) $300,000 (2) Nominal cost ϭ 37.24%; Effective cost ϭ 44.59% 15-18 14.35% 15-19 a(1) $3,960,000 (2) $4,800,000 (3) $9,360,000 (4) Regular ϭ $3,960,000; Extra ϭ $5,400,000 c 15% d 15% a Oct loan ϭ $22,800 15-17 a $300,000 15-20 a(1) $27,260 (3) $25,616 16-1 27.2436 yen per shekel 16-2 yen ϭ $0.00907 A N S W E R S TO E N D - O F - C H A P T E R P R O B L E MS 16-3 euro ϭ $0.68966 or $1 ϭ 1.45 euros 16-12 b $20,045.45 16-4 0.6667 pound per dollar 16-13 16-5 6.49351 krones 16-6 15 kronas per pound a $2,772,003 b $2,777,585 c $3,333,333 16-8 $468,837,209 16-14 b $1.6488 16-9 ϩ$250,000 16-15 kNom-U.S ϭ 4.6% 16-16 117 pesos 16-17 20 yen per euro, or 0.05 euro per yen 16-10 DOLLARS PER 1,000 UNITS OF: POUNDS CAN DOLLARS EUROS $1,442.80 $654.00 $891.70 YEN PESOS KRONAS $9.06 $106.10 $104.40 APPENDIX C I A N S W E R S TO E N D - O F - C H A P T E R P R O B L E MS A-43 APPENDIX D SELECTED EQUATIONS AND DATA CHAPTER Net cash flow ϭ Net income Ϫ Noncash revenues ϩ Noncash charges Net cash flow ϭ Net income ϩ Depreciation and amortization Net operating All current All current liabilities that ϭ Ϫ working capital assets not charge interest Net operating Cash and Accounts Accounts ϩ Inventories ¢ Ϫ a ϩ Accrualsb working ϭ ° marketable ϩ payable receivable capital securities Total operating capital ϭ Net operating working capital ϩ Net fixed assets NOPAT ϭ EBIT(1 Ϫ Tax rate) Operating cash flow ϭ NOPAT ϩ Depreciation Free cash flow ϭ Operating cash flow Ϫ Gross investment in operating capital Free cash flow ϭ NOPAT Ϫ Net investment in operating capital MVA ϭ Market value of stock Ϫ Equity capital supplied by shareholders ϭ [(Shares outstanding)(Stock price)] Ϫ Total common equity EVA ϭ NOPAT Ϫ After-tax dollar cost of capital used to support operations ϭ (EBIT)(1 Ϫ T) Ϫ (Operating capital)(After-tax percentage cost of capital) Equivalent pre-tax yield Muni yield ϭ on taxable bond 1ϪT INDIVIDUAL TAX RATES FOR APRIL 2001 Single Individuals IF YOUR TAXABLE INCOME IS Up to $26,250 YOU PAY THIS AMOUNT ON THE BASE OF THE BRACKET $ PLUS THIS PERCENTAGE ON THE EXCESS OVER THE BASE AVERAGE TAX RATE AT TOP OF BRACKET 15.0% 15.0% $26,250–$63,550 3,937.50 28.0 22.6 $63,550–$132,600 14,381.50 31.0 27.0 $132,600–$288,350 A-44 APPENDIX D I 35,787.00 36.0 31.9 Over $288,350 91,857.00 39.6 39.6 S E L E C T E D E Q U AT I O N S A N D D ATA Married Couples Filing Joint Returns YOU PAY THIS AMOUNT ON THE BASE OF THE BRACKET IF YOUR TAXABLE INCOME IS Up to $43,850 $ PLUS THIS PERCENTAGE ON THE EXCESS OVER THE BASE AVERAGE TAX RATE AT TOP OF BRACKET 15.0% 15.0% $43,850–$105,950 6,577.50 28.0 22.6 $105,950–$161,450 23,965.50 31.0 25.5 $161,450–$288,350 41,170.50 36.0 30.1 Over $288,350 86,854.50 39.6 39.6 Corporate Tax Rates IT PAYS THIS AMOUNT ON THE BASE OF THE BRACKET IF A CORPORATION’S TAXABLE INCOME IS Up to $50,000 $ PLUS THIS PERCENTAGE ON THE EXCESS OVER THE BASE 15.0% 15.0% $50,000–$75,000 7,500 25.0 18.3 $75,000–$100,000 13,750 34.0 22.3 $100,000–$335,000 22,250 39.0 34.0 113,900 34.0 34.0 3,400,000 35.0 34.3 $335,000–$10,000,000 $10,000,000–$15,000,000 AVERAGE TAX RATE AT TOP OF BRACKET $15,000,000–$18,333,333 5,150,000 38.0 35.0 Over $18,333,333 6,416,667 35.0 35.0 CHAPTER Current ratio ϭ Current assets Current liabilities Quick, or acid test, ratio ϭ Current assets Ϫ Inventories Current liabilities Inventory turnover ratio ϭ Sales Inventories DSO ϭ Days Receivables Receivables ϭ sales ϭ Average sales per day Annual sales/365 outstanding Fixed assets turnover ratio ϭ Sales Net fixed assets Total assets turnover ratio ϭ Sales Total assets Debt ratio ϭ D/E ϭ Total debt Total assets D/A D/E , and D/A ϭ Ϫ D/A ϩ D/E Debt ratio ϭ Ϫ Equity multiplier APPENDIX D I S E L E C T E D E Q U AT I O N S A N D D ATA A-45 Times-interest-earned (TIE) ratio ϭ EBITDA coverage ratio ϭ EBIT Interest charges EBITDA ϩ Lease payments Interest ϩ Principal payments ϩ Lease payments Net income available to common stockholders Profit margin on sales ϭ Sales Basic earning power ratio ϭ EBIT Total assets Net income available to common stockholders Return on total assets (ROA) ϭ Total assets ROA ϭ a Profit b (Total assets turnover) margin Return on common equity (ROE) ϭ Net income available to common stockholders Common equity ROE ϭ ROA ϫ Equity multiplier ϭa Profit Total assets Equity ba ba b margin turnover multiplier ϭa Net income Sales Total assets ba ba b Sales Total assets Common equity Return on investors' capital ϭ Price/earnings (P/E) ratio ϭ Price/cash flow ratio ϭ Book value per share ϭ Net income ϩ Interest Debt ϩ Equity Price per share Earnings per share Price per share Cash flow per share Common equity Shares outstanding Market/book (M/B) ratio ϭ Market price per share Book value per share EVA ϭ Net income Ϫ [(Cost of Equity Capital)(Equity Capital)] EVA ϭ (ROE Ϫ % Cost of Equity)(Dollars of Equity Capital) CHAPTER AFN ϭ (A*/S0)⌬S Ϫ (L*/S0)⌬S Ϫ MS1(RR) Full capacity sales ϭ A-46 APPENDIX D I Actual sales Percentage of capacity at which fixed assets were operated S E L E C T E D E Q U AT I O N S A N D D ATA Target FA/Sales ratio ϭ Actual fixed assets Full capacity sales Required level of FA ϭ (Target FA/Sales ratio) (Projected sales) CHAPTER k ϭ k* ϩ IP ϩ DRP ϩ LP ϩ MRP kRF ϭ k* ϩ IP I1 ϩ I2 ϩ # # # ϩ In n IPn ϭ CHAPTER Dollar return ϭ Amount received Ϫ Amount invested Percentage return ϭ Amount received Ϫ Amount invested Amount invested n ˆ Expected rate of return ϭ k ϭ a Piki iϭ1 n ˆ Variance ϭ ␴2 ϭ a (ki Ϫ k )2Pi iϭ1 ˆ a (ki Ϫ k ) Pi B iϭ1 n Standard deviation ϭ ␴ ϭ CV ϭ ␴ ˆ k n ˆ ˆ k p ϭ a wik i ˆ a (kpj Ϫ k p) Pj B iϭj iϭ1 n ␴p ϭ n b p ϭ a wibi iϭ1 SML ϭ ki ϭ kRF ϩ (kM Ϫ kRF)bi RPi ϭ (RPM)bi bϭ Y2 Ϫ Y1 ϭ Slope coefficient in kit ϭ a ϩ b kMt ϩ et X2 Ϫ X1 CHAPTER FVn ϭ PV(1 ϩ i)n ϭ PV(FVIFi,n) PV ϭ FVn a n b ϭ FVn(1 ϩ i)Ϫn ϭ FVn(PVIFi,n) 1ϩi APPENDIX D I S E L E C T E D E Q U AT I O N S A N D D ATA A-47 PVIFi,n ϭ FVIFi,n FVIFA i,n ϭ [(1 ϩ i)n Ϫ 1]/i PVIFA i,n ϭ [1 Ϫ (1/(1 ϩ i)n)]/i FVAn ϭ PMT(FVIFAi,n) FVAn (Annuity due) ϭ PMT(FVIFA i,n)(1 ϩ i) PVAn ϭ PMT(PVIFAi,n) PVAn (Annuity due) ϭ PMT(PVIFA i,n)(1 ϩ i) PV (Perpetuity) ϭ Payment Interest rate ϭ PMT i n t n PVUneven stream ϭ a CFt a b ϭ a CFt(PVIFi,t) 1ϩi tϭ1 tϭ1 n n FVUneven stream ϭ a CFt (1 ϩ i)nϪt ϭ a CFt(FVIFi,nϪt) tϭ1 FVn ϭ PVa1 ϩ iNom b m tϭ1 mn Effective annual rate ϭ a1 ϩ iNom m b Ϫ 1.0 m Periodic rate ϭ iNom/m iNom ϭ APR ϭ (Periodic rate)(m) FVn ϭ PV(ein) PV ϭ FVn(eϪin) CHAPTER N INT M VB ϭ a t ϩ (1 ϩ kd)N tϭ1 (1 ϩ kd) ϭ INT(PVIFAkd,N) ϩ M(PVIFkd,N) 2N INT/2 M INT (PVIFAkd/2,2N) ϩ M(PVIFkd/2,2N) VB ϭ a ϭ t ϩ 2N (1 ϩ kd/2) tϭ1 (1 ϩ kd /2) N Call price INT Price of callable bond ϭ a t ϩ (1 ϩ kd)N tϭ1 (1 ϩ kd) Current yield ϭ A-48 APPENDIX D I Annual interest Bond's current price S E L E C T E D E Q U AT I O N S A N D D ATA Accrued value at end of Year n ϭ Issue price ϫ (1 ϩ kd)n Interest in Year n ϭ Accrued valuen Ϫ Accrued valuenϪ1 Tax savings ϭ (Interest deduction)(T) CHAPTER ϱ Dt ˆ P0 ϭ PV of expected future dividends ϭ a (1 ϩ ks)t tϭ1 ˆ P0 ϭ D0(1 ϩ g) ks Ϫ g ϭ D1 ks Ϫ g D1 ˆ ks ϭ ϩ g P0 For a constant growth stock, Pn ϭ P0(1 ϩ g)n DNϩ1 ˆ Horizon value ϭ P N ϭ ks Ϫ g VCompany ϭ FCF1 (1 ϩ WACC)1 ϩ FCF2 (1 ϩ WACC)2 FCF ϭ EBIT(1 Ϫ T) ϩ Depreciation Ϫ Vp ϭ kp ϭ Dp kp Dp Vp ϩ ###ϩ FCFϱ (1 ϩ WACC)ϱ Change in Capital Ϫ net operating expenditures working capital CHAPTER 10 After-tax component cost of debt ϭ kd(1 Ϫ T) Component cost of preferred stock ϭ kp ϭ Dp Pp ˆ ks ϭ k s ϭ kRF ϩ RP ϭ D1/P0 ϩ g ks ϭ kRF ϩ (kM Ϫ kRF)bi ks ϭ Bond yield ϩ Risk premium ke ϭ D1 ϩ g P0(1 Ϫ F) N M(1 Ϫ F) ϭ a tϭ1 INT(1 Ϫ T) M ϩ t (1 ϩ kd) (1 ϩ kd)N g ϭ (Retention rate)(ROE) ϭ (1.0 Ϫ Payout rate)(ROE) REBreakpoint ϭ Addition to retained earnings Equity fraction APPENDIX D I S E L E C T E D E Q U AT I O N S A N D D ATA A-49 WACC ϭ wdkd(1 Ϫ T) ϩ wpkp ϩ wcks kp ϭ kRF ϩ (kM Ϫ kRF)bp CHAPTER 11 Payback ϭ Year before full recovery ϩ NPV ϭ CF0 ϩ CF1 ϩ (1 ϩ k)1 CF2 (1 ϩ k)2 Unrecovered cost at start of year Cash flow during year ϩ ###ϩ CFn (1 ϩ k)n n CFt ϭ a (1 ϩ k)t tϭ0 IRR: CF0 ϩ CF1 ϩ (1 ϩ IRR) CF2 (1 ϩ IRR) ϩ ###ϩ CFn ϭ0 (1 ϩ IRR)n n CFt a (1 ϩ IRR)t ϭ tϭ0 MIRR: PV costs ϭ PV terminal value n n COF a (1 ϩ k)t ϭ tϭ0 PV costs ϭ nϪt a CIFt(1 ϩ k) tϭ0 (1 ϩ MIRR)n TV (1 ϩ MIRR)n CHAPTER 12 Free cash flow ϭ EBIT(1 Ϫ T) ϩ Depreciation Ϫ Change in Capital Ϫ net operating expenditures working capital APPENDIX 12A Recovery Allowance Percentages for Personal Property CLASS OF INVESTMENT OWNERSHIP YEAR 3-YEAR 5-YEAR 7-YEAR 10-YEAR 33% 20% 14% 10% 45 32 25 18 15 19 17 14 12 13 12 11 9 6 7 9 10 11 A-50 APPENDIX D I S E L E C T E D E Q U AT I O N S A N D D ATA _ 100% _ 100% _ 100% 100% CHAPTER 13 Return on invested capital ϭ NOPAT Capital EBIT ϭ PQ Ϫ VQ Ϫ F QBE ϭ F PϪV EPS ϭ (S Ϫ FC Ϫ VC Ϫ I)(1 Ϫ T) (EBIT Ϫ I)(1 Ϫ T) ϭ Shares outstanding Shares outstanding b ϭ bU [1 ϩ (1 Ϫ T)(D/E)] bU ϭ b/[1 ϩ (1 Ϫ T)(D/E)] D/E ϭ D/A Ϫ D/A ks ϭ kRF ϩ Premium for business risk ϩ Premium for financial risk CHAPTER 14 g ϭ (Retention rate)(ROE) ϭ (1 Ϫ Payout rate)(ROE) Dividends ϭ Net income Ϫ [(Target equity ratio) (Total capital budget)] CHAPTER 15 Inventory conversion Inventory ϭ period Sales/365 Receivables Receivables collection ϭ DSO ϭ period Sales/365 Payables deferral period ϭ Payables Cost of goods sold/365 Inventory Receivables Payables Cash conversion ϩ collection Ϫ deferral ϭ conversion period period period cycle A/R ϭ Credit sales Length of ϫ per day collection period ADS ϭ Annual sales/365 ϭ (Units sold)(Sales price) 365 Receivables ϭ (ADS)(DSO) Nominal annual cost of payables ϭ 365 days Discount percent ϫ Discount Days credit is Discount Ϫ 100 Ϫ percent outstanding period APPENDIX D I S E L E C T E D E Q U AT I O N S A N D D ATA A-51 CHAPTER 16 Forward exchange rate Spot exchange rate ϭ Ph ϭ (Pf)(Spot rate) Spot rate ϭ A-52 APPENDIX D I Ph Pf S E L E C T E D E Q U AT I O N S A N D D ATA ϩ kh ϩ kf APR A/R b CAPM CF CV D DCF DRP DSO EAR EBIT EPS EVA F FVn FVAn FVIF FVIFA g i I INT IP IRR k ෆ k ˆ k k* kd ke kf kh kj kM kNom kp kRF ks Frequently Used Symbols Annual percentage rate Accounts receivable Beta coefficient, a measure of an asset’s riskiness Capital Asset Pricing Model Cash flow; CFt is the cash flow in Period t Coefficient of variation Dividend per share of stock (DPS); Dt is the dividend in Period t Discounted cash flow Default risk premium Days sales outstanding Effective annual rate, EFF% Earnings before interest and taxes ϭ net operating income Earnings per share Economic value added (1) Fixed operating costs (2) Flotation cost Future value for Year n Future value of an annuity for n years Future value interest factor for a lump sum Future value interest factor for an annuity Growth rate in earnings, dividends, and stock prices Interest rate; also referred to as k Interest rate key on some calculators Interest payment in dollars Inflation premium Internal rate of return (1) A percentage discount rate, or cost of capital; also referred to as i (2) Required rate of return “k bar,” historic, or realized, rate of return “k hat,” an expected rate of return Real risk-free rate of interest Cost of debt Cost of new common stock (outside equity) Interest rate in foreign country Interest rate in home country Cost of capital for an individual firm or security Cost of capital for “the market,” or an “average” stock Nominal rate of interest; also referred to as iNom (1) Cost of preferred stock (2) Project cost of capital (3) Portfolio’s return Rate of return on a risk-free security (1) Cost of retained earnings (2) Required return on a stock LP M M/B MCC MIRR MRP MVA N n NPV NOWC P Pf Ph PN P/E PMT PPP PV PVAn PVIF PVIFA Q r ROA ROE RP RPM RR S SML ⌺ ␴ ␴2 t T TIE V VB VC WACC YTC YTM Liquidity premium Maturity value of a bond Market-to-book ratio Marginal cost of capital Modified internal rate of return Maturity risk premium Market value added Calculator key denoting number of periods (1) Life of a project or investment (2) Number of shares outstanding Net present value Net operating working capital (1) Price of a share of stock; P0 ϭ price of the stock today (2) Sales price per unit of product sold Price of good in foreign country Price of good in home country A stock’s horizon, or terminal, value Price/earnings ratio Payment of an annuity Purchasing power parity Present value Present value of an annuity for n years Present value interest factor for a lump sum Present value interest factor for an annuity Quantity produced or sold Correlation coefficient Return on assets Return on equity Risk premium Market risk premium Retention rate Sales Security Market Line Summation sign (capital sigma) Standard deviation (lowercase sigma) Variance Time period Marginal income tax rate Times-interest-earned ratio Variable cost per unit Bond value Total variable costs Weighted average cost of capital Yield to call Yield to maturity ... Other Parts of the Firm: Externalities Externalities Effects of a project on cash flows in other parts of the firm Cannibalization Occurs when the introduction of a new product causes sales of existing... generating estimated rates of return and risk indexes 564 CHAPTER 12 I Monte Carlo simulation, so named because this type of analysis grew out of work on the mathematics of casino gambling, ties... example of a stable might be appropriate, given the stability of its basic company that uses a lot of debt financing Indeed, at business After all, the consumption of Cheerios and the end of 1999,