CHAPTER 11 VALUATION AND BUSINESS PERFORMANCE Throughout this book, we’ve stressed that managers must primarily focus their decision making about investments, operations, and financing on the creation of economic value for the company’s shareholders. Now let’s put shareholder value into a broader context by examining the key concepts of value and relating them to successful business performance. Earlier we discussed such categories as the recorded values reflected in a company’s financial statements, the economic values represented by the cash flows generated through capital investments, and the market value of shares or debt instruments. In each case, value was viewed in a specific context of analysis and assessment, but not necessarily against the full dynamics of management strategies and decisions that underlie the performance of any business. We’ll discuss the meaning of value in a variety of common situations where valuation is required. We’ll not only define several concepts of value in more pre- cise terms, but also once again use some of the now familiar analytical approaches that can be applied to the process of valuation. Foremost among these, of course, is the present value analysis of future cash flows (the main subject of Chapters 7 and 8), which is the common underpinning of modern valuation principles and shareholder value creation. In the final chapter we’ll integrate the various con- cepts into an overview of value-based management, returning to the systems ap- proach first discussed in Chapter 2 and using it to provide a consistent perspective of successful value creation. We’ll begin here with some basic definitions of value as found in business practice. Next, we’ll take the point of view of the investor assessing the value of the main forms of securities issued by a company, and the point of view of the creditor judging the value of the company’s obligations. Finally, we’ll discuss the key issues involved in valuing an ongoing business as the basis for determining whether shareholder value is being created—the principal objective of modern management. As we’ve emphasized throughout this book, the linkage between 357 hel78340_ch11.qxd 9/27/01 11:31 AM Page 357 Copyright 2001 The McGraw-Hill Companies, Inc. Click Here for Terms of Use. 358 Financial Analysis: Tools and Techniques cash flows and the creation of economic value is the ultimate expression of suc- cess or failure of business decisions on investment, operating, and financing. Recognition of this linkage spurred the wave of takeovers and restructuring activ- ities of the 1980s—essentially a reassessment of the effectiveness with which re- sources were employed by target companies—leading to redeployment of those resources in alternative ways expected to generate higher cash flows and returns to the shareholders. But the failure to recognize these linkages at the turn of the century led to the bubble and deflation in the dot.com business valuations as we discussed in Chapter 1. Definitions of Value It’ll be useful to refresh our memory briefly about the different types of value we’ve encountered so far, and to state as clearly as possible what they represent and for what purposes they might be appropriate. In this enumeration we’ll demonstrate that only some of these concepts are really useful for what we now understand to be the economic task of value creation in a business setting. Economic Value This concept, used throughout the book as the relevant term for shareholder value creation, relates to the basic ability of an asset—or a claim—to provide a stream of after-tax cash flows to the holder. Such cash flows can be generated through earnings, or contractual payments, and/or partial or total liquidation at a future point. As earlier chapters said, economic value is essentially a cash flow trade-off concept. The value of any asset is defined as the amount of cash a buyer is willing to give up now—its present value—in exchange for a pattern of future expected cash flows. Therefore, economic value is very much a future-oriented concept. It’s determined by estimating and assessing prospective future cash flows, including proceeds from the ultimate disposal of the asset itself. Remember that past costs and expenditures caused by prior decisions are sunk costs and thus irrelevant from an economic standpoint. As we’ll see, economic value underlies some of the other common concepts of value because it’s based on a trade-off logic that is quite natural to the process of investing. Calculating economic value is not without practical difficulties, how- ever. Recall that a representative discount rate (cost of capital or return standard) has to be selected and applied to the expected positive and negative cash flows over a defined period of time. The cash flows themselves are often difficult to es- timate, and they might also include specific assumptions about any recoverable cash from liquidation, or about any ongoing value remaining at the termination point of the analysis. The process in effect determines today’s equivalents of the cash flow amounts expected to occur in different parts of the time spectrum, based on a great deal of judgment. hel78340_ch11.qxd 9/27/01 11:31 AM Page 358 CHAPTER 11 Valuation and Business Performance 359 Recall also the need for risk assessment, both in determining the cash flow pattern itself and in setting the appropriate return standard. In other words, eco- nomic value isn’t absolute; it’s the result of the relative risk assessment of future expectations. In fact, economic value is closely tied to individual risk preferences, because different individuals will arrive at different valuation results due to their varying perceptions of risk. Yet, whether or not these aspects are made explicit in a given situation, the principle of economic value is at the core of all business decisions on investment, operating, and financing. Market Value Also referred to as fair market value, this is the value of any asset, or collection of assets, when traded in an organized market—or negotiated between private par- ties—in an unencumbered transaction without duress. The various securities and commodities exchanges are examples of organized markets, as are literally thou- sands of regional and local markets and exchanges that enable buyers and sellers to find mutually acceptable values for all kinds of tangible and intangible assets. Market value is, of course, also established through transactions between individ- uals when no organized market is conveniently available. Again, there’s nothing absolute in market value. Instead, it represents a mo- mentary consensus of two or more parties. In a sense, the parties to a transaction adjust their respective individual assessments of the asset’s economic value suffi- ciently to arrive at the consensus. The market value at any one time can therefore be subject to the preferences and even whims of the individuals involved, the psychological climate prevalent in an organized stock exchange, the heat of a takeover battle, significant industry developments, shifts in economic and politi- cal conditions, and so forth. Moreover, the volume of trading in the asset or secu- rity will influence the value placed on it by buyers and sellers. Despite its potential variability, market value is generally regarded as a rea- sonable criterion in estimating the current value of individual balance sheet assets and liabilities, as contrasted with their recorded value. It’s frequently used in in- ventory valuation and in capital investment analysis where future recovery values have to be estimated. On a larger scale, mergers and purchases of going concerns are also based on market values negotiated by the parties involved. As was the case with economic value, there are practical problems associated with establish- ing market value. A true market value can be found only by actually engaging in a transaction. Thus, unless the item is in fact traded, any market value assigned to it remains merely an estimate, which will tend to shift as conditions change and the perceptions of the parties are altered. But even if market quotations are readily available, certain judgments apply. For example, popular common stocks traded on the major exchanges have widely quoted market prices, yet frequently there are significant price fluctuations even within a day’s trading, and the volume of shares changing hands on a given day hel78340_ch11.qxd 9/27/01 11:31 AM Page 359 360 Financial Analysis: Tools and Techniques might vary greatly—affecting the relevance of the quotations for all other shares being held. Also, overall market movements will affect individual stocks. Thus, market value based on many similar transactions can be fixed only within a given range, which in turn, is tied to the trading conditions of the day, week, or month. For items that are traded infrequently or in relatively small numbers, estimating a realistic transaction value can become even more difficult. Yet the fact remains that market value is one of the most significant value concepts used in finan- cial/economic analysis. It is closely related to economic value, because it ulti- mately is based on the parties’ expectations about future cash flows to be derived from the asset or business involved. Book Value Recall from Chapter 2 that the book value of an asset or liability is the stated value as reflected on the balance sheet, which has been recorded and at times modified according to generally accepted accounting principles. While book value is han- dled consistently for accounting purposes, it usually bears little relationship to current economic value. It’s a historical value that, at one time, might have repre- sented market value, but the passage of time and changes in economic conditions increasingly distort it. Assets of a long-term nature are particularly subject to changes in economic value over time. The frequently quoted book value of com- mon shares, which represents the shareholder’s proportional claim on the com- posite net result of all past transactions in assets, liabilities, and operations, is especially subject to distortion. As a residual amount it is affected by all past and present accounting adjustments as well as value changes. Its usefulness for eco- nomic analysis is therefore questionable under most circumstances. Liquidation Value This value relates to the special condition when a company needs to liquidate part or all of its assets and claims. In essence, it’s an abnormal situation where time pressures and even duress distort the value assessments made by buyers and sell- ers. Under the cloud of impending business failure or intense pressure from cred- itors, management will find that liquidation values generally are considerably below potential market values. The setting for the negotiations is adversely af- fected by the known disadvantage under which the selling party must act in the transaction. As a consequence, liquidation value is really applicable only for the limited purpose intended. Nevertheless, it’s sometimes used to value assets of un- proved businesses as a more realistic basis for analysis than by estimating highly uncertain cash flow patterns when testing such aspects as creditworthiness. hel78340_ch11.qxd 9/27/01 11:31 AM Page 360 CHAPTER 11 Valuation and Business Performance 361 Breakup Value A variation of liquidation value, breakup value is related to corporate takeover and restructuring activities, as discussed later. On the assumption that the combined economic values of the individual segments of a multibusiness company exceed the company’s value as an entity—because of inadequate past management or current opportunities that were not recognized earlier—the company is broken up into salable components for disposal to other buyers. Any redundant assets, such as excess real estate, are also sold for their current values. Note that breakup value is usually realized on business segments with on- going operations, and less frequently through forced liquidation of individual as- sets supporting these business segments, as would be the case in a bankruptcy sale, for example. Any redundant assets not required for ongoing operations might, of course, be liquidated as such. Estimates of breakup value are a critical element in the analysis preceding takeover bids. Reproduction Value This is the amount that would be required to replace an existing fixed asset in kind. In other words, it’s the like-for-like replacement cost of a machine, facility, or other similar asset. Reproduction value is, in fact, one of several yardsticks used in judging the worth of the assets of an ongoing business. Determining reproduction value of specific assets is an estimate largely based on engineering judgments. There are several practical problems involved. The most important is whether the fixed asset in question could, or would, in fact be reproduced exactly as it was constructed originally. Most physical assets are subject to some pattern of technological obsolescence with the passage of time, in addition to physical wear and tear. There’s also the problem of estimating the currently applicable cost of actually reproducing the item in kind. For purposes of analysis, reproduction value often becomes just one checkpoint in assessing the market value of the assets of a going business. Collateral Value This is the value of an asset that is used as security for a loan or other type of credit. The collateral value is generally considered the maximum amount of credit that can be extended against a pledge of the asset. With their own security in mind, creditors usually set the collateral value lower than the market value of an asset. This provides a cushion of safety in case of default, and the risk preference of the individual creditor will determine the magnitude of the often arbitrary downward adjustment. Where no market value can be readily estimated, the col- lateral value is set on a purely judgmental basis, the creditor being in a position to hel78340_ch11.qxd 9/27/01 11:31 AM Page 361 362 Financial Analysis: Tools and Techniques allow for as much of a margin of safety as is deemed advisable in the particular circumstances. Assessed Value This value concept is established in local governmental statutes as the basis for property taxation. The rules governing assessment practices vary widely, and might or might not take market values into account. Use of assessed values is lim- ited to raising tax revenues, and therefore such values bear little relationship to the other value concepts. Appraised Value Appraised value is subjectively determined and used when the asset involved has no clearly definable market value. An effort is usually made to find evidence of transactions that are reasonably comparable to the asset being appraised. Often used in transactions of considerable size—especially in the case of commercial or residential real estate—appraised value is determined by an impartial expert ac- cepted by both parties to the transaction, whose knowledge of the type of asset in- volved can narrow the gap that might exist between buyer and seller, or at least establish a bargaining range. The quality of the estimate depends on the expertise of the appraiser and on the availability of comparable situations. Again, individ- ual ability and preference enter into the value equation. Only rarely will different appraisals yield exactly the same results, and ranges of value are used at times. Going Concern Value This concept applies economic valuation to a business in operation. A company viewed as a going concern is expected to produce a series of future cash flows that the potential buyer must value to arrive at a price for the business as a whole. Note that the same concept applies to valuing whole business segments of a company when its breakup value is established, as discussed earlier. Apart from the specific valuation techniques used, which we’ll discuss later, the concept requires that the business be viewed as a “living system” of investments, operations, and financing rather than a mere collection of assets and liabilities. Recall our earlier strong emphasis on the fact that economic value is created by a positive trade-off of future cash flows for present commitments and outlays. As we’ll see in Chapter 12, the going concern value is useful when comparative cash flow analyses, singly and in combination, are developed for setting value- based management goals and for acquisitions and mergers. Going concern value also enters the cash flow analysis as the final estimate at the end of the analysis period, where it represents the ongoing value of the business in relation to future performance. The continuing challenge to the analyst is to properly weigh this future value as well as the overall pattern of estimated cash flows. hel78340_ch11.qxd 9/27/01 11:31 AM Page 362 CHAPTER 11 Valuation and Business Performance 363 Shareholder Value As we’ve stated repeatedly, shareholder value is created when the returns gener- ated from existing and new investments consistently exceed the cost of capital of the company. It represents the total increase in the economic value of the business over time. This value in turn is reflected in the form of a growing periodic total re- turn to shareholders as measured by the combination of dividends and capital gains or losses achieved, which can be compared to overall market returns or the returns achieved by selected peer companies or industry groupings. Shareholder value, the ultimate expression of corporate success, is closely tied to cash flow trade-offs and return expectations that are the basis of economic value. We’ll dis- cuss the concept in more detail in Chapter 12. In summary, we’ve discussed a number of value definitions. Some were specialized yardsticks designed for specific situations. Many are directly or indi- rectly related to economic value. We’ve again defined economic value as the pre- sent value of future cash flows, discounted at the investor’s risk-adjusted standard. As we know, this value concept is broadly applicable as the underpinning of shareholder value creation, and we’ll use it extensively as we examine various decision areas where value measures are needed. Value to the Investor As in Chapters 6, 9, and 10, we’ll concentrate only on the three main types of cor- porate securities—bonds, preferred stock, and common stock—in discussing the techniques involved to assess value and yield. For our purposes here, value is de- fined as the current attractiveness of the investment to the investor in present value terms, while yield represents the internal rate of return (IRR) earned by the investor on the price paid for the investment. We’ll briefly discuss major provi- sions in the basic securities types insofar as they might affect their value and yield. The techniques covered should appear quite familiar to the reader because they closely relate to the various analytical approaches presented in earlier chapters. Bond Values Valuing a bond is normally fairly straightforward. A typical bond issued by a cor- poration is a simple debt instrument. Its basic provisions generally entail a series of contractual semiannual interest payments, defined as a fixed rate based on the bond’s stated par (face) value (usually $1,000). The legal contract, or indenture, promises repayment of the principal (nominal value) at a specified maturity date a number of years in the future. The two basic characteristics, defined interest payments and repayment stipulations, are encountered in most normal debt arrangements. Complicating aspects are sometimes found in provisions such as conversion into common stock at a predetermined exchange value, or payment of interest only when earned by the issuing company. We’ll review some of these specialized features later. hel78340_ch11.qxd 9/27/01 11:31 AM Page 363 364 Financial Analysis: Tools and Techniques A bond’s basic value rests on the investor’s assessment of the relative at- tractiveness of the expected stream of future interest receipts and the prospect for eventual recovery of the principal at maturity. Of course, there’s normally no obligation for the investor to hold the bond until maturity because most bonds can be traded readily in the securities markets. Still, the risk underlying the bond con- tract must be considered here in terms of the issuing company’s future ability to generate sufficient cash with which to pay both interest and principal. The collec- tive judgment of security analysts and investors about the issuing company’s prospects influences the price level at which the bond is publicly traded, which is further affected by prevailing interest rates in the economy. Also, the bond is likely to be rated by financial services like Moody’s and Standard & Poor’s and placed in a particular risk category relative to other bonds. To determine a bond’s value, we must first calculate the present value of the interest payments received up to the maturity date and add to this the present value of the ultimate principal repayment. You’ll recognize this method as com- parable with the process of calculating the present value of business investment expenditures shown in Chapter 7. The discount rate applied is the risk-adjusted interest rate that represents the investor’s own standard of measuring debt invest- ment opportunities within a range of acceptable risk. For example, an investor with an 8 percent annual interest return standard would value a bond with a coupon interest rate of 6 percent annually significantly lower than its par value. The calculation is shown in Figure 11–1. The investor’s annual standard of 8 percent is equivalent to a semiannual standard of 4 percent, a restatement for FIGURE 11–1 Bond Valuation Date of analysis: July 1, 2000 Face value (par) of bond: $1,000 Maturity date: July 1, 2014 Bond interest (coupon rate): 6% per year Interest receipts: $30 semiannually Present Total Value Cash Factors, Present Flow 4 Percent* Value 28 receipts of $30 over 14 years (28 periods) . . . . . . . . . . . . . . . . . . . . . . . . $ 840 16.663 (ϫ $30) $499.89 Receipt of principal 14 years hence (28 periods) . . . . . . . . . . . . . . . . . . . . . . . . 1,000 0.333 333.00 Totals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . $1,840 $832.89 *From Table 7–II and 7–I (end of Chapter 7), respectively. hel78340_ch11.qxd 9/27/01 11:31 AM Page 364 CHAPTER 11 Valuation and Business Performance 365 purposes of calculation that’s necessary to match the semiannual interest pay- ments paid by most bonds. The resulting value, $832.89, represents the maximum price our investor should be willing to pay—or the minimum price at which the investor should be willing to sell—if the investor normally expects a return (yield) of 8 percent from this type of investment. This particular bond should therefore be acquired only at a price considerably below (at a discount from) par. Note that the stated interest rate on the bond is relevant only for determining the semiannual cash receipts in absolute dollar terms. The actual valuation of the bond and the cash flows it represents therefore depends on the investor’s opportunity rate (return standard). In other words, the desired yield determines the appropriate price, and vice versa. This relationship also applies, of course, to the market quotations for publicly traded bonds. The quoted price, or value, is a function of the current yield collectively desired by the many buyers and sellers of these debt instruments, which in turn is based on gen- eral interest rate conditions. If our investor were for some unrealistic reason satisfied with the very low annual yield of only 4 percent from holding the same bond (equivalent to 2 per- cent per six-month period), the value to the investor would rise considerably above par, as shown in Figure 11–2. Under these assumed conditions, the investor should be willing to pay a premium of up to $212.43 for the $1,000 bond, because the personal return standard is lower than the stated interest rate. If the investor’s own standard and the coupon interest rate were to coincide precisely, the value of the bond would, of course, exactly match the par value of $1,000. In fact, the quoted market price of any bond will tend to approach the par value as it reaches maturity, because at that point, the only representative value will be the imminent repayment of the principal—assuming, of course, that the company is financially able to pay as the amount becomes due. FIGURE 11–2 Bond Valuation with Lower Return Standard (4 percent per year) Present Total Value Cash Factors, Present Flow 2 Percent* Value 28 receipts of $30 over 14 years (28 periods) . . . . . . . . . . . . . . . . . . . . . . . . $ 840 21.281 (ϫ $30) $ 638.43 Receipt of principal 14 years hence (28 periods) . . . . . . . . . . . . . . . . . . . . . . . . 1,000 0.574 574.00 Totals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . $1,840 $1,212.43 *From Tables 7–II and 7–I (end of Chapter 7), respectively. hel78340_ch11.qxd 9/27/01 11:31 AM Page 365 366 Financial Analysis: Tools and Techniques Bond Yields A related but common task for the analyst or investor is the calculation of the yield produced by various bonds, when quoted prices differ from par value. The key to this analysis again is the relationship of value and yield as discussed above, and the technique used is a present value calculation that in effect determines the internal rate of return (IRR) of the cash flow patterns generated by the bond over its remaining life. The method is identical to that used for assessing the cash flows of any busi- ness investment proposal. The key difference in the data is that the individual in- vestor’s calculations are based on pretax cash flows that must be adjusted in each case by the investor for his or her personal tax situation. Other minor differences are the cash incidence in a semiannual pattern, and the form in which bond prices (the net investment) are quoted. Published prices are normally stated as a per- centage of par. For example, a bond quoted at 103 3 ⁄8 has a price of $1,033.75. The change to decimal trading in process in early 2001 will make these quotations easier to handle. Bond yield tables have long been employed to determine a bond’s internal rate of return, or yield. While today’s computers and calculators have financial routines that make direct calculation routine, we’ll nevertheless take a quick look at a yield table, mainly to help the reader understand the examples by visual in- spection of the relationships. Bond yield tables are finely graduated present value tables that list the whole potential range of stated interest rates, subdivided into fractional progressions of as little as 1 ⁄32 of a point. They’re far more detailed than the present value tables used in Chapters 7 and 8. For example, Figure 11–3 is a small segment of such a yield table, in this case for a bond with a coupon interest rate of precisely 6 percent. The columns FIGURE 11–3 Bond Yield Table (sample section for a 6 percent rate) Price Given Years or Periods to Maturity Yield to 13 Years 13 1 ⁄2 Years 14 Years 14 1 ⁄2 Years 15 Years 15 1 ⁄2 Years Maturity (26 periods) (27 periods) (28 periods) (29 periods) (30 periods) (31 periods) 3.80% 1.224 043 1.230 661 1.237 155 1.243 528 1.249 782 1.255 919 3.85 1.218 284 1.224 709 1.231 012 1.237 196 1.243 263 1.249 215 3.90 1.212 559 1.218 793 1.224 907 1.230 904 1.236 787 1.242 557 3.95 1.206 868 1.212 913 1.218 841 1.224 654 1.230 354 1.235 944 4.00 1.201 210 1.207 068 1.212 812* 1.218 443 1.223 964 1.229 377 4.05 1.195 585 1.201 260 1.206 821 1.212 273 1.217 616 1.222 853 4.10 1.189 993 1.195 486 1.200 868 1.206 142 1.211 310 1.216 375 4.15 1.184 434 1.189 747 1.194 952 1.200 051 1.205 046 1.209 940 4.20 1.178 908 1.184 043 1.189 073 1.193 999 1.198 823 1.203 549 4.25 1.173 414 1.178 374 1.183 230 1.187 985 1.192 642 1.197 201 *This example was used in Figure 11–2 (slight difference due to rounding of present value factors). Note that prices are given in the form of a 7-digit multiplier, which is applied against a $1,000 par value. hel78340_ch11.qxd 9/27/01 11:31 AM Page 366 TEAMFLY Team-Fly ® [...]... hel78340_ch11.qxd 9/27/01 388 11: 31 AM Page 388 Financial Analysis: Tools and Techniques Key Issues The following is a recap of the key issues raised directly or indirectly in this chapter They are enumerated here to help the reader keep the techniques discussed within the perspective of financial theory and business practice 1 The concept of value is not independent of the purpose for which it is used, and. .. earlier in this chapter, rather than the recorded values on the balance sheet For example, if current interest rates are higher than the stated rates for the company’s debt, the value of the debt will be lower than recorded, and vice versa hel78340_ch11.qxd 9/27/01 11: 31 AM Page 386 386 Financial Analysis: Tools and Techniques F I G U R E 11 6 Present Value of Business Cash Flows and the Capital Structure... hel78340_ch11.qxd 9/27/01 11: 31 AM Page 372 372 Financial Analysis: Tools and Techniques In summary, the challenge of preferred stock valuation also goes beyond the simple techniques we have shown In the end, decisions should be made only after careful assessment of the relative attractiveness of the specific features and conditions surrounding a particular company’s preferred stock, and its place... after-tax earnings for noncash elements such as depreciation and amortization, and for deferred taxes, as we discussed in Chapters 4 and 7 The third step is to estimate the future investment outlays deemed necessary to support both the present level of earnings and any anticipated changes in hel78340_ch11.qxd 9/27/01 11: 31 AM Page 383 CHAPTER 11 Valuation and Business Performance 383 operations in line with... measure economic value creation for the company as a whole and for its hel78340_ch11.qxd 9/27/01 11: 31 AM Page 381 CHAPTER 11 Valuation and Business Performance 381 major businesses and reward the management team accordingly In this context, the business is periodically valued with various techniques to determine progress against planned performance, and to set the appropriate incentive compensation awards... claims, and assessments of general and specific risk, subject to economic and business conditions and the decisions of management and the board of directors It’s also affected by the breadth of trading in the security 5 Valuation techniques are essentially assessment tools that attempt to quantify available objective data and estimates Yet such quantification will always remain in part subjective, and. .. Values By its very nature, preferred stock represents a middle ground between debt and common equity ownership The security provides a series of cash dividend payments, but normally has no specific provision (or expectation) for repayment of hel78340_ch11.qxd 9/27/01 11: 31 AM 370 Page 370 Financial Analysis: Tools and Techniques the par value of the stock However, at times preferred stock carries a... also from earnings exceeding hel78340_ch11.qxd 9/27/01 11: 31 AM 382 Page 382 Financial Analysis: Tools and Techniques the cost of long-term financing used in the capital structure In fact, the common theme established early in the book was that the economic success of any company had to come from exceeding the weighted overall cost of capital in all of its present and future investments As we’ll see in... shortcut will always introduce some error, because it imperfectly simulates what is in fact a progressive present value structure As yield rates and the number of time periods increase, larger hel78340_ch11.qxd 9/27/01 11: 31 AM 368 Page 368 Financial Analysis: Tools and Techniques errors will result Yet the rough calculation provides a satisfactory result for use as an initial analytical check Had a premium... necessary to assume a declining cash flow pattern that reflects competitive and technological uncertainty, which would alter the formula above into adding the rate of decline to the cost of capital in the denominator, instead of subtracting the growth rate hel78340_ch11.qxd 9/27/01 11: 31 AM Page 384 384 Financial Analysis: Tools and Techniques The added difficulty of forecasting operations beyond the end . even within a day’s trading, and the volume of shares changing hands on a given day hel78340_ch11.qxd 9/27/01 11: 31 AM Page 359 360 Financial Analysis: Tools and Techniques might vary greatly—affecting. $1,840 $1,212.43 *From Tables 7–II and 7–I (end of Chapter 7), respectively. hel78340_ch11.qxd 9/27/01 11: 31 AM Page 365 366 Financial Analysis: Tools and Techniques Bond Yields A related but. between 357 hel78340_ch11.qxd 9/27/01 11: 31 AM Page 357 Copyright 2001 The McGraw-Hill Companies, Inc. Click Here for Terms of Use. 358 Financial Analysis: Tools and Techniques cash flows and the creation