Credit-Scoring Models and the Valuation of Fixed-Income Securities and Commercial Loans

Transcription

1 Credit-Scoring Models and the Valuation of Fixed-Income Securities and Commercial Loans Edward I. Altman Max L. Heine Professor offinance Stern School ofbusiness New York University The trend toward securitization of bank loans, the new mark-to-market accounting requirements, and increased investor interestin distressed or defaulted loans has caused a need for improved pricing methodologies. Discounted cash flow analysis using historical default and recovery experience and credit-scoring models linked to capital markets can help fill this gap in the valuation process. The valuation techniques that fixed-income investors use and those that lenders use are often closely linked. The methodology in this presentation was first applied to commercial loans, but these techniques can easily be applied to other types of fixedincome instruments. 1 The studies of valuation techniques reported here were motivated by several factors. First, a trend was developing toward securitization ofbank loans, and investor interest in secondary-market trading of nonliquid claims such as bank loans and trade debt was growing. In the next two to three years, interest in securitization of bank loans will be even greater and investors will be able to buy pools ofbank loans more easily than today. Another reason for the study was to help financial institutions meet the new Statement of Financial Accounting Standards (SFAS) mark-to-market disclosure requirements for their assets. A third motivation was growing investor interest in distressed or defaulted loans and the need for a pricing methodology for those securities. Of the $250-$260 billion public high-yield market, perhaps $10-$15 billion is defaulted and another $20-$25 bil- IDetails of earlier studies can be found in articles by Edward 1. Altman and co-authors in The Journal of Commercial Lending (August 1993); The Journal offinance (September 1968); the Journal of Banking and Finance (June 1977); the Financial Analysts Journal (July/ August 1985 and May/June 1992); The Journal of Portfolio Management (Summer 1994); and a series of papers available from the Salomon Center, Stern School of Business, New York University. lion is considered distressed. Such loans trade at less than 80 cents on the dollar, or 10 percentage points above the risk-free rate. The market potential is even larger because morebank loans than publicly traded debt securities are outstanding. Mark-to-Market Accounting Rules SFAS 107 requires disclosure of the fair value of financial instruments in financial statements issued after December 15, Companies must put a fair value on financial assets using either a market price quoted in an active market or, for illiquid assets, the quoted market price of a similar instrument. The latter approach, commonly known as matrix pricing, is used by many of the pricing services. If neither of these methods is possible or if a financial institution does not have faith in the prices quoted for similar financial instruments, then SFAS 107 advocates using discounted present value (PV) analysis for this disclosure. SFAS 114, another standard effective for financial statements issued after December 15, 1994, deals with the way banks should account for impaired or nonaccruing loans or those that are not selling at par value. According to SFAS 114, the carrying value of a loan should equal the PV of its interest and principal cash flows, discounted at the loan's effective rate. When a loan is performing, that value is its original book value; when a loan becomes impaired, the car- 14

2 rying value should be adjusted to reflect changes in the timing and size of expected cash flows, but the loan's original contractual rate is still used as the discount rate. I strongly disagree with the aspect of SFAS 114 thatrequires the discountrate usedinthe PV analysis to be the loan's original contract rate. The assumption is that interest rate changes do not affect the rate on impaired loans, even though the analysis is performed when the asset becomes impaired two or three years later. The discount rate also should be adjusted to reflect changes in timing. The Valuation Process The valuation process discussed here has three stages: the credit-scoring procedure, use of the credit-scoring criteria to analyze historical default and recovery experience, and analysis of the discounted cash flow (DCF). This technique has been picked up by both Moody's Investors Service and Standard & Poor's Corporation (S&P) and has been modified, perhaps improved, in their calculations. Although Moody's and S&P perform their analyses of expected default and recovery experiences by market value, they analyze defaults primarily by number of issuers; for example, if lout of 100 issuers defaulted, that is a 1 percent default rate. Their way is particularly relevant for collateralized bond obligations (CBOs), in which equal dollar amounts are assumed to be invested in individual securities. The other difference between their method and mine is that Moody's and S&P lump all bonds in a particular rating class together regardless of whether they are new or seasoned (what is called "aged") issues, whereas I examine the bonds by date of issuance. S&P and Moody's go through a stress test when assigningbond ratings to CBOs orcollateralized loan obligations (CLOs). The test is based either on mortality rates or on aged default rates. The rating agencies "stress" the dataina fairly stringentwayinorder to be as conservative as possible from their standpoints. I have been among those trying to convince these agencies thatbeing conservative is fine butthat they should be at least within two standard deviations of expected values. These efforts in persuasion have been partially successful. TheC~tt~ringPr~u~ The most important aspect of a credit-scoring procedure, in addition to its accuracy, is its link to capital market risk ratings. Most banks today are either experimenting with new credit-scoring systems or have in place systems that rank loans from 1 to 9. If you ask employees using a typical bank system what a 2 or a 3 is in their rating system, they will be able to tell you that a 2 is better than a 3 and a 3 is better than a 4. Ifyou ask how much better, they will have difficulty coming up with an answer. The precise answer, however, is critical to pricing. Bond ratings, despite the fact that they havebeen much maligned by the press and by some practitioners, are an excellent basis for linking the credit-scoring system with publicly available credit information. Linking an internal rating system with capital market activity and performance of similar risk instruments allows investors to observe historical default rates and loss experience by bond-rating category. Most importantly, investors can measure the performance subsequent to those bond-rating equivalents. To develop our credit score, we use a discriminant analysis statistical technique to come up with a Z-score: whereal ~ an are discriminant coefficients (weights) and Xl ~ X n are discriminant variables (e.g., ratios). Developing the credit score is not limited to the Z-score technique. Traditional discriminant analysis, which we used when we first began this research more than 25 years ago, is not considered as much in vogue today as are chaos theory, neural network analysis, or option pricing. Nevertheless, it is still a venerable and reliable technique. A Z-score model can be used to examine a number of independent, or discriminant, variables, such as traditional liquidity, debt and earnings ratios, market values, and volatility. The variables are then weighted objectively according to some statistical criteria; the coefficients are multiplied by the variables and then summed. The result is an overall credit score that represents the risk profile of the issuing entity. We profile the issuer, not the bond itself, because even though bond characteristics (covenants, seniority, collateral) may change the ultimate loss in case of default, the basic risk of default or bankruptcy depends on company fundamentals. The discriminant analysis program then analyzes the population ofhealthy firms and risky firms and comes up with weightings for the various variables. Figure 1 displays an example of a two-variable case with the equity-to-debt ratio on one axis and return on assets (defined as earnings before interest and taxes [EBlT] to total assets) on the other. The diagonal roughly separates the risky firms (circles) from the healthy ones (squares). The statistical analysis determines the weightings for the variables. Oursecond-generation Z-score model, known as the ZETA -score model, uses seven financial indica- 15

3 Figure 1. Forecasting Distress with Discriminant Analysis ODD DO cj) Q).0 DO 0 cj) cj) DO.0 0 <::: 'ill 0 0 ;S "- o E-< DO r.li DO Equity/ Debt Source: Edward I. Altman. tors, many of which are standard variables in company analyses. (Seven is not a magic number; the model could have any number of variables.) The seven variables are return on assets (EBIT/ total assets), size (total tangible assets), interest coverage (EBIT/ total interest payments), liquidity (current assets/current liabilities), cumulative profitability (retained earnings/total assets), market capitalization (market value of equity/total capital), and stability of earnings (standard error of the estimate of a tenyear regression of EBIT/total assets). As few as five years can be used for this latter measure. ZETA-scores are importantindeterminingbondrating equivalents. This model can be used for both private and public companies to create credit scores, a single measure that captures a company's overall risk profile. Over the years, the model has been quite accurate. The original sample was 70 percentaccurate five years prior to bankruptcy and about 96 percent accurate one year prior; in subsequent testing, the model held its accuracy fairly well. Average ZETA-scores by S&P bond-rating cate- Table 1. Average ZETA-5cores by S&P Rating Category goryfor the period are presented in Table 1. For theperiodas a whole, the averageaaacompany (excluding finance companies and public utilities) had a ZETA-score of 8.7, the B-rated companies had negative scores, and the CCC companies had even more negative scores. Bond-Rating Equivalents Regardless of the technique used to come up with an overall assessment of a company's health, the ability to relate it to the public bond rating is critical. An importantissue is whether adjacentbond ratings are equally different incredit quality over the entire spectrum as are ZETA-scores. To examine this question, we ran a regression ofthe ZETA-scores for companies relative to bondratings, codified the bond ratings from 1 to 21 (counting pluses and minuses), and ended up with a very smooth relationship. We could say, for example, that a company ZETA-score of -2 is equivalent to the average B security or even finer-b+ or B-. The empirical results show that, although not exact, the differences in average scores between adjacent bond ratings are quite similar, on average ZETA-points. Historical Default Rates and Loss Experiences Step two ofthe valuation process is to observe the historical default rate and recovery experience of the bond-rating-equivalent loans by the credit-scoring criteria established in step one. The high-yield market has a long history of measurements of default and recoveryrates, startingwithhickman's classic study, which examined the risk and return experiences of publicly tradedbondsfrom 1900 to The default studyreportedhere updatesanoriginal studycarried out in 1985 using traditional methods of measuring default rates in the public bond market. These default-rate dataare easily available from sell-side firms 2Braddock Hickman, Corporate Bond Quality and Investor Experience (Princeton: Princeton University Press, 1958). Average Rating AAA a AA A BBB BB D.71 -D.86 -D.61 -D B D CCC Nonrated athe AAA industrial average (not including AAA public utilities) was in 1993, in 1992, and in Source: ZETA Services. 16

4 that have a high-yield desk. Some of them use our measures, and some of them generate their own. Incredibly, the default rates in 1990 and 1991 exceeded 10 percent of the high-yield market, as shownin Table 2, but they have been declining since Table 2. Value of Issues Outstanding and of Defaults and Default Rates (Straight Debt Only), Year 1994 b Par Value Outstanding a ($millions) $225, , , , , , , ,557 90,243 58,088 40,939 27,492 18,109 17,115 14,935 10,356 8,946 8,157 7,735 7,471 10,894 7,824 6,529 5,805 6,598 Arithmetic average default rate (standard deviations in parentheses) % (3.212) (3.013) (3.272) Weighted average default rated (standard deviations in parentheses) (3.464) (3.452) (3.423) Par Value Defaults ($millions) 1,245 2,287 5,545 18,862 18,354 8,110 3,944 7,486 c 3, Default Rates (%) 0.553% c aexcludes defaulted issues. bthrough September 30. C$1,841.7 million without Texaco, Inc., Texaco Capital, and Texaco N.V. The default rate is then percent. dweighted by par value of amount outstanding for each year. Source: Edward I. Altman and V. Kishore, "Returns and Defaults in the High-Yield Debt Market: Analysis from ," Salomon Center, Stern School of Business, New York University (1995). then-to 1.45 percent in During the period, 4.2 percent a year was the average annual default rate in the high-yield market; of course, this proportion is much lower as a percentage of the total corporate debt market. Many investors use these data inappropriately as global information for the market. Unless investors have a perfectly diversified portfolio that mirrors the overallmarket, theyshould be interested only in the default expectation relevant to their own portfolios. The methodology presented here can help investors and lenders determine that expectation. Today, analysts have good data on recovery rates, in the event of default, by seniority class. The average senior secured debt in the public market recovers 60 cents onthe dollar atdefault. The average senior unsecured debtrecovers 51 cents onthe dollar; the average senior subordinated debt, 36 cents; and the average junior unsubordinated debt, about 30 cents. For all bonds, the historical recovery rate is about 40 cents on the dollar. We recently examined the prices of defaulted bonds at the time the companies emerged from Chapter 11. So far in the 1990s, the senior secured debt has been selling slightly above par at the time a company emerges from bankruptcy, which takes an average of two years. The senior unsecured bonds are receiving about 80 cents on the dollar. The junior bonds, on average, do not sell upon restructuring for anymore than theywouldhave atthe time ofdefault. Another interesting measure is default rates and recoveries by individual bond rating. Bonds migrate up or down from the lower categories, but they can only go in one direction if they are AAA. So, assuming that a AAA bond will never migrate down in its credit rating is wrong; AAs and even AAAs default. Indeed,onlyabout68 percentofaaas are still AAAs five years after issuance. If investors hold bonds to maturity, therefore, they have credit migration risk as well as default risk to consider. Mortality Rates and Loss Measurements A mortality rate on a bond measures the extent to which age has any predictive value about a bond's default characteristics. The question is not whether the bond is going to default but when it is going to default and what will be the likely recovery, given its original bond rating and its original seniority. Formally, the model, borrowed from the insurance actuaries, is MMR _ Total value of defaulting debt in year t Total value of population at start of year t t -, where MMR is the marginal mortality rate, which is calculated in a way that is similar to the way a traditional bond analyst calculates default rates. The cal- 17

5 culation begins with the total value of defaulting debt by market value in any year relative to the population that was outstanding at the beginning of the year. In 1994, about $250 billion in debt was outstanding-$225-$230 billion, not counting defaults. If $3 billion defaulted in that year, we can calculate the default rate. One can measure the cumulative mortality rate (CMR) during a specific time period (1,2,..., t years) by subtracting the product of the surviving populations of each of the previous years from 1; that is, t CMRt = 1 - n SRt, t=1 where CMR T is the cumulative mortalityrate in t and SRt is the survival rate in t, or 1- (MMRh Going forward each year, the total value of the population for a specific cohort, such as a bond-rating category, is going to change-not only because of defaults but also because the CMR over time is taken from the actuarial calculation 1 minus the product of the survival rates. Think of mortality as going out of existence; that means the CMR calculation should adjust for factors that affect the population, such as maturities, calls, and sinking funds. As an example, if the mortality rate for a BBrated bond is 1 percent in the first year, the bond's survival rate is 99 percent. In the second year, if it is 2 percent, the survival rate will be 98 percent. Then, multiply the survival rates and subtract from 1 to get the CMR. Simply adding up the marginal mortality rates yields similar but not exact results; 1 percent + 2 percent is 3 percent cumulated for two years. In Table 3, CMRs are shownbybond-ratingclass from one to ten years after issuance. Calls and sinking funds are taken out of the total outstanding each year. This analysis includes all defaults for all corporate issues that have been rated since The Society of Actuaries has done a comparable study on private placements and mortgage loans for insurance companies from 1986 to 1989, which is now being updated through Investors can do the same thing with mortgages. For an example of how to interpret the Table 3 data, note that the expected mortality of a B-rated portfolio ten years after issuance is percent. This CMR does not necessarily mean that B-rated bonds are bad investments. Recovery rates (the percentage of the principal recovered) and returns have not been considered. The promised yield spreads on a B security have probably averaged 4-5 percent a year over Treasuries. Today's spread is lower, of course. All that the CMR determines is that, if you were a B investor, about a quarter of your portfolio defaulted in five years and a little more than onethird of your portfolio had defaulted by the tenth year. Notice that at Year 3 and after, according to Table 3, AA bonds have a higher default rate than As. The reason behind this anomaly is that Texaco had many AA-rated securities outstanding that defaulted. The analysis of recovery rates will adjust for this effect. Table 4 reports the cumulative mortality losses adjusted for the lost coupon, or the coupon an investor would have received at the default date. The fact that most companies default when a coupon is coming due represents an opportunity cost that must be factored in together with the recovery rate. This analysis assumes that the investor sells at the time of default rather than holding the bond until the company emerges from bankruptcy. Thus, for B-rated bonds, the five-year and ten-year averages go from 25 percent to 19 percent and from 36 percent to 29 percent, respectively. These data will be the basis for our valuation analysis. One important difference for CLOs is that most loans are senior securities; most bonds that default are junior securities. So, the expected recovery rate 3Gery J. Berry, in The Financial Dynamics of the Insurance Industry (Burr Ridge, Ill.:Irwin, 1994): Table 3. Cumulative Mortality Rates by Original Rating, 1971~ Years after Issuance AAA AA A BBB BB B CCC % 0.00% 0.00% 0.06% 0.00% 1.51% 1.51% NA NA NA NA = not available. Source: Altman and Kishore, "Returns and Defaults in the High-Yield Debt Market: Analysis from " 18

6 Table 4. Cumulative Mortality Losses by Original Rating, Years after Issuance AAA AA A BBB BB B CCC % 0.00% 0.00% 0.05% 0.00% 0.70% 1.20% NA NA NA NA NA = not available. Source: Altman and Kishore, "Returns and Defaults in the High-Yield Debt Market: Analysis from " in the corporate loan market might be quite different from the rate in the public bond market. To do this same analysis for bank loans, one would have to adjust for seniority. Application of Standard PV Procedures to Loan Valuation The last part of the analysis deals with applying standard DCF analysis to valuing the instruments. As an example, Table 5 traces a three-year loan for $1 million carrying an 11 percent coupon payable at year end. The loan type is "plain vanilla": It is unsecured and pays interest-only until maturity. Its ZETA-score is -1.8, equivalent to an S&P rating of B. The bank cost of funds used in Table 5, or the required rate of return for the investor, is 8 percent. Each bank would use its specific cost of capital, which is basically the cost of debt plus a small premium for the cost of equity, which would probably be 8-10 percent of a bank's total capital. The horizon in such an analysis does not have to be maturity; if this approach were used for a bond, the horizonwould be whenever the bond is expected to go outofexistence. With mostbonds in the market today, the time horizon would be the first call date. Investmentbanks will quote a yield-to-first-call ratio or a yield-to-worst ratio. Most people do not invest in a bond or make a loan if they expect it to fail, but for certain categories, a proportionofthebondsor loans will fail. Ifanalysts do not take that knowledge into consideration, they are obviously going to be sadly mistaken about their expected returns. Table 5 lists the proportions of the portfolio expected to default, adjusted for recoveries, based on the expected loss tables. The expected loss rates are 1.04 percent, 3.80 percent, and 8.97 percent for years 1 through 3. Remember that 1 minus the expected loss rate times the promised cash flow equals the expected cash flow. The expected cash flow is then discounted by the required rate of return-in this case, the bank's cost of capital. The result is the present value ofthe expected cash flows. This calculation is like any DCF analysis a company might use in capital budgeting or valuation analysis. For this particular loan, for which a 3 percent premium is charged over the bank's cost of capital, factoring in the expected default and loss causes a negativenetpresentvalue (NPV). In otherwords,the present value of the expected cash flows is less than the $1 million invested, the outflow. This analysis does not consider the effect of the loan on the bank's portfolio. If the bank wished to make the loan, it could raise the interest rate to reach at least zero NPV or itcould change the timing of the cash flows; the bank has some control over the loan terms. An investor's initial choice is simply to accept the investment or not. The investment banker has come to the investor with a certain deal. Should the inves- Table 5. Example of Valuation, Loss Reserves, and Pricing Promised Expected Expected Discount PV Expected Period Cash Flow Loss Rate Cash Flow Factor Cash Flow 0 -$1,000, % -$1,000, $1,000, , , , , , , ,110, ,010, ,081 Total -$ 6,410 Source: ZETA Services. 19

7 Figure 2. Decision Tree Example p Default Recovery Loan Amount P NO $1,000,000<: Year 1 Payment $456,000 Default Recovery $100,000 Default Recovery <0 Interest Payment Interest PNO and Principal Repayment Year $1,100,000 Year 3 Source: Edward 1. Altman. torbuy it or not? Based on the analysis here, this deal is not a good investment. The investor also could seek to change the terms of the investment, however-either require more collateral or go into the market and offer to buy at a different price. This type of negotiation goes on all the time. Decision Tree Analysis Decision tree analysis for loans or bonds builds on the probabilities of default and nondefault and the expected cash flow recoveries in each case. Figure 2 presents the model; Po is the marginal expected mortality one year, two years, and three years after issuance. The bottom part of the figure applies the model to the example loan discussed in the last section; the $100,000 is the loan's interest payment assuming no default, and the $456,000 is the average recovery amount on $1 million of bonds defaulted after three years. To complete the decision tree analysis, the probabilities are multiplied by the payoffs and the results are summed to calculate the internal rate of return. For the example loan, the internal rate of return is about 6.5 percent, less than the bank's 8 percent required rate of return, so this analytical approach also finds the loan to be not attractive. If the loan were marked to market, the value of the loan, if unimpaired and in light ofthe bank's cost of funds and the expected loss rates, could reasonably be stated at only $945,489, less than its book value. This valuation analysis can be done at any time during a loan's life, including origination. Conclusion Credit-scoring models linked to the capital markets combined withdefaultrates and recoveryexperience can be used in PV analysis to determine value. After a price is determined, itcanbeusedinthe negotiation process prior to making or purchasing a loan, for marking financial assets to market, or to determine expected returns on fixed-income or loan portfolios of all types. The techniques can be used in the valuation of publicly traded assets as well as illiquid assets, buttheyareperhapsmore usefulfor thelatter. Please keep in mind that the research and approaches discussed here are ongoing and should not be taken as definitive. 20

8 Question and Answer Session Edward I. Altman Question: Does SFAS 107 markto-market accounting apply only to new debt issues? Altman: No, it applies to an entire investment portfolio. Anything going forward from December 15, 1994, has to be marked to market. The requirement applies to all financial institutions, not banks alone. Most of the banks have already implemented the requirement for all securities for purposes of accounting disclosure. Today, such disclosure is probably a nonissue, but it may become more important as interest rates rise. Question: Are these valuation procedures necessary or applicable for all loans? Altman: For performing loans, use book value. You should apply the valuation procedures only for impaired loans. Question: Please comment on determining PV for floating-rate loans. Altman: The accounting requirements for floating-rate loans are sensible. For floating rates, the Financial Accounting Standards Board requires the use of today's rate because the original rate is obviously irrelevant. Question: Are there any statistics on default rates by industry? Altman: I have not seen default rates by industry. We have statistics on the number and dollar amounts of defaulting bonds by industry but not the total population of bonds by industry, which is necessary to calculate a default rate. Financial services, leisure, and general manufacturing have had the highest number of defaults during the past 20 years or so. Question: Does the default rate have anything to do with the overall performance of the economy? Altman: Studies by Blume and Keim took the historical default rate and adjusted it for the economic situation. 4 They were concerned only with the effect of a given economic situation on expected default rates for the highyield market, and they concluded that the economy does have an effect. My experience has been that a link between, say, GNP growth and default rates in the high-yield market is going to be tenuous. The timing is very subtle in terms of coincident or leading/lagging effects. Clearly, in a difficult overall economic scenario, default rates on average will be higher than in calmer times, but they may not be higher immediately. It takes time for a general economic decline to have an impact on a company's ability to make interest payments, so I would expect default rates to lag a change in the economy. The effect of the economy is also going to vary according to companies' leverage. The high default rates of 1991 did not occur mainly because of the economic recession that began at that time; they occurred more because of adverse leverage structures. Ifcompanies had gone into the recession with less leverage, the default rate would have been much lower. 4Seeissues ofthe Journal offinance and Financial Analysts Journal for Question: What do you think will happen in emerging market debt in the next ten years? Altman: Some people, includ ~g myself, believe that the emergmg markets are where the high-yield debt market was in 1984 or 1985 in terms of new issuance, potential growth, and investor appetite. If we are correct, emerging markets are going to be an explosive area-but one with risks of major stress. I urge my students to become proficient in emerging market debt and to un?erstand international accounting Issues as much as possible. Salomon Brothers Inc and I are working on building an emerging market credit model. We are addressing Latin American corporate debt, particularly in Mexico, Argentina, and Brazil. Our approach is to ask, first: If this company were located in the United States, what would be its bond-rating equivalent? Given the accounting and other differences in these countries, that question is not easy to answer. After we get a U.s. bond-rating equivalent, we adjust it up or down depending on the firm's unique characteristics, such as industry and competitive position. For example, a company that looks like a BBB company but is a monopoly or a quasi-monopoly in a growing market might be upgraded. We would also make upgrades or downgrades based on a company's ability to generate cash flows in the currency in which the bond is denominated. Most of these emerging market bonds are Eurobonds denominated in dollars, but you also have Mexican peso or Brazilian cruzeiro bonds with cash flows in the local currencies. 21

9 The next step, and the most controversial (although not difficult) one, is to decide how much of a "haircut" to give a bond's rating because of its country of origin. The simple way to approach this problem, and the way we are leaning, is to take the spread of, say, Mexican sovereign bonds over u.s. sovereign bonds. Then, take the risk-free rate in Mexico and add that to the implied spread from the first two steps. When this method is used, a number of emerging market corpo- rates are found actually to be selling richer than the sovereign bonds. If I am going to give a full haircut to the sovereign differential on top of the yield spread based on its bond-rating equivalent, I would not buy that bond if it is now selling richer or at a lower yield than the sovereign. This result concerns us, but we think it is the right way to look at the problem. Portfolio considerations are also relevant. For example, if only one Argentine telecommunications bond is available and if some mutual funds out there would love to buy a telecommunications bond in Argentina, that bond is going to be very attractive regardless of other considerations. This demand might cause the yield to be much lower than it would be if the company were a general manufacturing company. Then, we would adjust the implied yield spread for particular bond issues based on such factors as confidence, security, and so on. 22