Accrual Accounting and Valuation: Pricing Earnings

Transcription

1 Security, Third Chapter Six LINKS Accrual Accounting and : Pricing Earnings Link to previous chapter Chapter 5 showed how to price book values in the balance sheet and calculate intrinsic price-to-book ratios. This chapter This chapter shows how to price earnings in the income statement and calculate intrinsic price-earnings ratio. Link to next chapter Chapter 7 begins the financial statement analysis that is necessary to carry out the price-to-book and price-earnings valuations discussed in Chapters 5 and 6. How are are price-earnings returns calculated? ratios determined? How is a firm valued from forecasts of earnings growth? When should an investor not pay for growth? How do valuation methods protect the investor from paying too much for earnings growth? How does the analyst infer the market's forecast of earnings growth? The last chapter showed how to anchor valuations on the book value, the bottom line of the balance sheet. This chapter shows how to anchor valuations on earnings, the bottom line of the income statement. By anchoring on book value, the analyst develops the price-to-book ratio (P/B). By anchoring on earnings, the analyst develops the price-earnings ratio (P/E). So, while the last chapter asked how much one should pay per dollar of book value, this chapter asks how much one should pay per dollar of earnings. Link to Web page The Web page supplement has more applications of the techniques in this chapter.

2 Security, Third Chapter 6 Accrual Accounting and 199 The Analyst s Checklist After reading this chapter you should understand: What abnormal earnings growth is. How forecasting abnormal earnings growth yields the intrinsic P/E ratio. What is meant by a normal P/E ratio. The difference between ex-dividend earnings growth and cum-dividend earnings growth. The difference between a Case 1 and Case 2 abnormal earnings growth valuation. The advantages and disadvantages of using an abnormal earnings growth valuation and how the valuation compares with residual earnings valuation. How dividends, share issues, and share repurchases affect abnormal earnings growth. How abnormal earnings growth valuation protects the investor from paying too much for earnings growth. How abnormal earnings growth valuation protects the investor from paying for earnings that are created by accounting methods. How to use the abnormal earnings growth model in reverse engineering. What a PEG ratio is. After reading this chapter you should be able to: Calculate cum-dividend earnings. Calculate abnormal earnings growth. Calculate the value of equities from forecasts of earnings and dividends. Calculate intrinsic forward P/E and trailing P/E ratios. Calculate continuing values for the abnormal earnings growth model. Convert an analyst s EPS forecast to a valuation. Calculate implied earnings growth rates from the market price of a stock. Evaluate a PEG ratio. THE CONCEPT BEHIND THE PRICE-EARNINGS RATIO P/B ratios differ from 1.0 because accountants do not measure the full value of the equity in the balance sheet. However, the missing value is ultimately realized in the future earnings that assets produce, and these earnings can be forecasted: A price-to-book ratio is determined by expected earnings that have not yet been booked to book value, and the higher the future earnings relative to book value, the higher the P/B ratio. A parallel idea lies behind the P/E ratio. Whereas book value is a measure of the stock of value, earnings is a measure of the change in value. In Chapter 2 we appreciated that, just as book value is an imperfect measure of the stock of value, earnings is also an imperfect measure of the value added for shareholders. Current earnings measure value added from current sales, whereas share prices change in anticipation of value to be added in earnings from future sales as well. So the P/E ratio compares the value of expected future earnings (in the numerator) to current earnings (in the denominator). Therein lies the concept of the P/E ratio. Just as the P/B ratio is based on expected earnings that have not yet been booked to book value, the P/E ratio is based on expected earnings that have not yet been recognized. So P/E ratios are high when one forecasts considerably higher future earnings than current earnings, and P/E ratios are low when future earnings are forecasted to be lower than current earnings. In short, the P/E ratio prices earnings growth.

3 Security, Third 200 Part One Financial Statements and PROTOTYPE VALUATION This chapter supplies the formal valuation model to implement this concept of the P/E ratio rigorously, as well as the mechanics to apply the model faithfully. The formality is warranted, for one can pay too much for earnings growth if one is not careful. Beware of Paying Too Much for Earnings Growth Historically, high P/E stocks so-called growth stocks have been rewarding investments during bubble periods: Investors, excited about growth, push up prices and momentum trading takes over to yield yet higher prices and yet higher P/E ratios. But history shows that, overall, growth expectations are not realized: High P/E stocks have earned lower returns than low P/E stocks, and lower returns than broad indexes. Chapter 5 came with a warning: Beware of earnings growth and use valuation methods that build in protection from paying too much for earnings growth. This warning sets the stage for this chapter: A sound P/E valuation prices earnings growth but does not price growth that does not add value. In anchoring a valuation on earnings rather than book values, you need to appreciate that earnings is a measure of change in value a flow rather than a stock. To convert flows to stocks, we simply capitalize the flow. The stock of value implied by earnings is: Stock of value Earnings = Required return This earnings capitalization was explained in Box 3.6 in Chapter 3. The way to think about anchoring value on earnings is as follows: Value = Capitalized earnings + Extra value for forecasted earnings growth To value earnings we always start with the anchor of capitalized earnings, and then ask what extra value must be added for anticipated earnings growth. A savings account is easy to value, so we will begin with this simple asset as a prototype for valuing equities. Exhibit 6.1 presents the same savings account as in Exhibit 5.1 in Chapter 5 (and Box 2.2 in Chapter 2). The account involves $100 invested in 2005 to earn a 5 percent rate each year, from 2006 and thereafter. Two dividend payout scenarios are presented, full payout and no payout. In both cases, expected residual earnings are zero, so the asset is valued at its book value of $100 in 2005 using the residual earnings model. However, the asset also can be valued by capitalizing forward 2006 earnings of $5: Forward Earnings Value of savings account = Required return = $ 5. = $ Thus the savings account can be valued not only from its book value, but also by capitalizing forward earnings. For the savings account, there is no extra value for anticipated earnings growth. However, you will notice that, while the earnings growth rate in the full-payout scenario is zero, it is 5 percent per year in the no-payout scenario. Yet the value of the account is the same in both cases. According to our calculations, we will not pay for the 5 percent growth. The growth of 5 percent comes from reinvesting earnings, but the reinvested earnings earn only the required return. The equivalent valuations for the two accounts demonstrate the principle that one does not pay for growth that comes from an investment that earns only the required return, for such an investment does not add value.

4 Security, Third Chapter 6 Accrual Accounting and 201 EXHIBIT 6.1 Forecasts for a Savings Account with $100 Invested at the End of 2005, Earning 5% per Year Forecast Year Earnings withdrawn each year (full payout) Earnings Dividends Book value Residual earnings Earnings growth rate Cum-dividend earnings Cum-dividend earnings growth rate 5% 5% 5% 5% No withdrawals (zero payout) Earnings Dividends Book value Residual earnings Earnings growth rate 5% 5% 5% 5% Cum-dividend earnings Cum-dividend earnings growth rate 5% 5% 5% 5% A little more formalism captures this idea and protects us from paying too much for growth. The earnings growth rates in the two scenarios look different, but in fact they are not. The earnings from the full-payout account are actually understated, for the dividends from the account can be reinvested in an identical account to earn 5 percent. So, for example, the $5 withdrawn in 2006 can be reinvested to earn 5 percent, or $0.25 in 2007, so that the total expected earnings for 2007 are $5.25, the same as the zero-payout account. Earnings from an asset arise from two sources, earnings earned by the asset and earnings earned from reinvesting dividends in another asset. So, by reinvesting dividends for all years, the earnings in the two payout scenarios here are the same; in the no-payout case, earnings are reinvested in the same account that is, earnings are retained and in the full-payout case, earnings can be reinvested in a different account, in both cases earning 5 percent. The total earnings from an investment are referred to as cum-dividend earnings, that is, earnings with the dividend. Earnings without the reinvestment of dividends are called ex-dividend earnings. Value is always based on expected cum-dividend earnings and the P/E ratio is always based on cum-dividend earnings growth, for we must keep track of all sources of earnings from the investment. For any period, t Cum-dividend earnings t = Earnings t + (ρ 1)dividend t 1 where ρ is (as before) 1 plus the required return. So, for the full-payout savings account, cum-dividend earnings for 2007 are Earnings (0.05 Dividend 2006 ) = $5 + (0.05 $5) = $5.25. On a cum-dividend basis, earnings growth in the two scenarios is the same, 5 percent per year, as you can see from Exhibit 6.1. However, in both cases, the earnings growth is not growth that we will pay for. We only pay for earnings growth that is greater than the required return. Earnings that are due to growth at the required return are called normal earnings. For any period, t Normal earnings t =ρearnings t 1

5 Security, Third A Riddle 6.1 P/E RATIOS AND EARNINGS GROWTH FOR THE S&P 500 The historical average forward P/E ratio for the S&P 500 is about 13 (and the average trailing P/E ratio is about 14). The historical average earnings per share growth rate is about 8.5 percent per year. If the required return for stocks in general is 10 percent, the normal forward P/E ratio is 10. These numbers present a riddle: If the growth rate is 8.5 percent, less than the required return of 10 percent, the forward P/E should be below the normal of 10, not above it at 13. The riddle is solved as follows. Firms in the S&P 500 pay dividends; indeed, the historical dividend payout ratio has been about 45 percent of earnings (though it has been declining over the last 20 years). The 8.5 percent growth rate is an ex-dividend growth rate. The cum-dividend growth rate with 45 percent payout is about 13 percent. So, historically, earnings have really grown 13 percent per year, cum-dividend, above the assumed required return of 10 percent. That puts the forward P/E ratio above the normal of 10, which indeed it has been. So, for the savings account, normal earnings in 2007 = 1.05 $5 = $5.25, that is, the prior year s earnings growing at 5 percent. The part of cum-dividend earnings for which we will pay is the cum-dividend earnings growth over these normal earnings, that is, the abnormal earnings growth: Abnormal earnings growth t = Cum-dividend earnings t Normal earnings t = [Earnings t + (ρ 1)dividend t 1 ] ρearnings t 1 As cum-dividend earnings for the savings account in 2007 are $5.25, and as normal earnings also are $5.25, abnormal earnings growth is zero. And so for years 2008 and beyond. We will not pay for growth because, while we forecast growth, we do not forecast abnormal growth. With these basic concepts in place, we now can move from the simple prototype to the valuation of equities. Here is a summary of the concepts we carry with us: 1. An asset is worth more than its capitalized earnings only if it can grow cum-dividend earnings at a rate greater than the required return. This recognizes that one pays only for growth that adds value. 2. When forecasting earnings growth, one must focus on cum-dividend growth. Ex-dividend growth ignores the value that comes from reinvesting dividends. 3. Dividend payout is irrelevant to valuation, for cum-dividend earnings growth is the same irrespective of dividends. Box 6.1 solves a riddle about earnings growth. The Normal Forward P/E Ratio You will remember from Chapter 3 that the forward or leading P/E is price relative to the forecast of next year s earnings. For the savings account, the forward P/E ratio in 2005 is $100/$5 = 20. This is a particularly special P/E, referred to as the normal forward P/E: Normal forward P/E 1 = Required return That is, the normal forward P/E is just $1 capitalized at the required return. For the savings account, the forward P/E is 1/0.05 = 20. The normal P/E embeds a principle that applies to all assets, including equities. If one forecasts no abnormal earnings growth (as with the savings account), the forward P/E ratio must be 1/required return. That is, a normal P/E implies that normal earnings growth is expected. For a required (normal) return of 10 percent, the normal forward P/E is 1/0.10, or 10. For a required return of 12 percent, the normal forward P/E is 1/0.12 = If one 202

6 Security, Third Chapter 6 Accrual Accounting and 203 forecasts cum-dividend earnings to grow at a rate greater than the required return, the P/E must be above normal: One pays extra for growth. If one forecasts cum-dividend earnings to grow at a rate lower than the required return, the P/E ratio must be lower than normal: One discounts for low growth. The Normal Trailing P/E Ratio Chapter 3 distinguished the trailing P/E the multiple of current earnings from the forward or leading P/E the multiple of earnings forecasted one year ahead. Having calculated the value of the savings account from forecasts of forward earnings and earnings growth, it is, of course, straightforward to calculate the trailing P/E: Just divide the calculated value by the earnings reported in the last income statement. But there is an adjustment to make. For the savings account in Exhibit 6.1, suppose that $100 were invested in the account at the beginning of 2005 to earn 5 percent. Earnings for 2005 would be $5 and, if these earnings were paid out as dividends, the value of the account at the end of 2005 would still be $100. So it would appear that the trailing P/E is $100/$5 = 20, the same as the forward P/E. However, this is incorrect. How could the value of one more year of earnings be the same? Suppose the $5 earnings for 2005 were not paid out, so that the value in the account was $105. The P/E ratio then becomes $105/$5 = 21. The latter is the correct trailing P/E. The amount that $1 of earnings is worth the P/E multiple should not depend on dividends. The $5 of earnings for a savings account produces $105 in value for the owner of the account the $100 at the beginning of the period that produced the earnings, plus the $5 of earnings. If she leaves the earnings in the account, the owner has $105; if she withdraws the earnings, she still has $105, with $100 in the account and $5 in her wallet. The trailing P/E is 21. Thus the trailing P/E must always be based on cum-dividend prices: Trailing P/E = Price + Dividend Earnings This measure is the dividend-adjusted P/E introduced in Chapter 3. The adjustment is necessary because dividends reduce the price (in the numerator) but do not affect earnings (in the denominator). The adjustment is not necessary for the forward P/E because both prices and forward earnings are reduced by the current dividend. P/E ratios published in the financial press do not make this adjustment. If the dividend is small, it matters little, but for high-payout firms, published P/E ratios depend on dividends as well as the ability of the firm to grow earnings. Whereas the normal forward P/E is 1/Required return, the normal trailing P/E is: Normal trailing P/E = (1 + Required return) Required return For the savings account, the normal trailing P/E is $1.05/$0.05 = 21 (compared with 20 for the forward P/E). For a required return of 10 percent, the normal trailing P/E is $1.10/$0.10 = 11 (compared with 10 for the forward P/E), and for a required return of 12 percent, it is $1.12/$0.12 = 9.33 (compared with 8.33 for the forward P/E). The normal forward P/E and the normal trailing P/E always differ by 1.0, representing one current dollar earning at the required return for an extra year. Just as a normal forward P/E implies that forward earnings are expected to grow, cumdividend, at the required rate of return after the forward year, so a normal trailing P/E implies that current earnings are expected to grow, cum-dividend, at the required rate of return after the current year. So the trailing P/E for the savings account is 21 because the expected cum-dividend earnings growth rate is the required rate of 5 percent.

7 Security, Third 204 Part One Financial Statements and A Poor P/E Model The following model for valuing equities from forward earnings is quite common: Value of equity = Earn 1 g where g is (1 plus) the forecasted earnings growth rate. (You perhaps have seen this model with the letter r used to indicate the required return rather than ρ.) The model looks as if it should value earnings growth. The formula modifies the capitalized earnings formula (which worked for a savings account) for growth; indeed, the model is simply the formula for a perpetuity with growth that was introduced in Chapter 3. With this model, the forward P/E ratio is 1/(ρ g). This model is simple, but it is wrong. First, it is applied with forecasts of ex-dividend growth rates rather than cum-dividend growth rates. Ex-dividend growth rates ignore value from reinvesting dividends. Therefore, the higher the dividend payout, the higher the omitted value calculated by the formula; the lower the ex-dividend growth rate, the lower the value calculated by the formula. Second, the formula clearly does not work when the earnings growth rate is greater than the required return, for then the denominator is negative. You could apply the formula with cum-dividend growth rates rather than ex-dividend growth rates, but then you would be likely to have a negative denominator. For the savings account, the required return is 5 percent, but the expected cum-dividend growth rate is also 5 percent, so the denominator of this formula is zero (and the value of a savings account is infinite!). For equities, the cum-dividend growth rate is often higher than the required return, resulting in a negative denominator: This is the case for the S&P 500 in Box 6.1, for example. A growth rate slightly lower than the required return would have you paying a very high price and overpaying for growth. This is a poor model; it leads you into errors. The denominator problem is a mathematical problem, but behind this mathematical problem lurks a conceptual problem. We need a valuation model that protects us from paying too much for growth. A MODEL FOR ANCHORING VALUE ON EARNINGS The model for valuing earnings growth anchors the valuation on capitalized earnings and then adds value from anticipated growth: Value of equity = Capitalized forward earnings + Extra value for abnormal cum-dividend earnings growth V E Earn = E + AEG AEG AEG L 2 3 ρ 1 ρe 1 ρe ρe ρe 1 AEG2 AEG3 AEG4 = Earn L (6.1) 2 3 ρe 1 ρe ρe ρe where AEG is abnormal (cum-dividend) earnings growth. (The ellipses indicate that forecasts continue on into the future, for equities are going concerns.) You see from the first version of the formula here that the discounted value of abnormal earnings growth supplies the extra value over that from forward earnings. The discounting calculates the value at the end of Year 1 of growth from Year 2 onward, and the value is then capitalized (to convert the value of flows to a stock of value). As both the value of growth and forward earnings are capitalized, the second version of the formula simplifies the calculation. So, to value a ρ E

8 Security, Third Chapter 6 Accrual Accounting and 205 FIGURE 6.1 Calculation of Equity Value Using the Abnormal Earnings Growth Model Abnormal earnings growth is the difference between cum-dividend earnings and normal earnings. The present value of abnormal earnings growth for Year 2 and beyond is added to forward earnings for Year 1, and the total is then capitalized to calculate equity value. Abnormal earnings growth t = Cum-dividend earnings t Normal earnings t Cum-dividend earnings t = Earnings t + (ρ E 1) dividend t 1 Normal earnings t = ρ E Earnings t 1 Forecasts Year 1 ahead Year 2 ahead Year 3 ahead Year 4 ahead Forward earnings 1 Cumdividend earnings 2 Normal earnings 2 Cumdividend earnings 3 Normal earnings 3 Cumdividend earnings 4 Normal earnings 4 + Abnormal earnings 2 Abnormal earnings 3 Abnormal earnings 4 PV of AEG 2 Discount by + PV of AEG 3 Discount by 2 + PV of AEG 4 Discount by Current value Capitalize Total earnings plus growth share, proceed through the following steps: 1. Forecast one-year-ahead earnings. 2. Add the present value (at the end of Year 1) of expected abnormal earnings growth for Year 2 ahead and onward. 3. Capitalize the total of forward earnings and the value of abnormal earnings growth. Figure 6.1 directs you through these three steps. As with residual earnings valuation, earnings must be comprehensive earnings, otherwise value is lost in the calculation. Simply stated, the model says that value is based on future earnings, but with earnings from normal growth subtracted. The forward P/E is obtained by dividing through by forward earnings, Earn 1 : V0 E 1 1 AEG2 AEG3 AEG4 = E 1 + ρ ρe 1 ρe ρe ρe Earn L / Earn 1 (6.2)

9 Security, Third 206 Part One Financial Statements and So the forward P/E is calculated by capitalizing $1 plus the value of abnormal earnings growth relative to forward earnings. If no abnormal earnings growth is forecasted, and the P/E is normal: V0 E Earn = 1 ρ 1 E V0 E 1 = Earn 1 ρ E 1 The P/E in model (6.2) is the normal P/E plus a premium for growth. This model is referred to as the abnormal earnings growth model, or the Ohlson- Juettner model after its architects. 1 Measuring Abnormal Earnings Growth As for the savings account, abnormal earnings growth (AEG) is earnings (with dividends reinvested) in excess of earnings growing at the required return: Abnormal earnings growth t = Cum-dividend earn t Normal earn t = [Earn t + (ρ E 1)d t 1 ] ρ E Earn t 1 (6.3) Calculations can be made on a per-share basis or on a total dollar basis. When working on a per-share basis, dividends are dividends per share; when working on a total dollar basis, dividends are net dividends (dividends plus share repurchases minus share issues). Here are calculations of abnormal earnings growth for 2005 for two firms, Dell, Inc. and Nike, Inc. Dell has a required return of 11 percent, Nike 10 percent. Dell, Inc. Nike, Inc. EPS 2005 $1.18 $4.45 DPS 2004 $0.00 $0.74 Earnings on reinvested dividends Cum-dividend earnings Normal earnings from 2004: Dell: ; Nike: Abnormal earnings growth (AEG) Dell s EPS for 2005 was $1.18, up from $1.03 for Dell paid no dividends, so its EPS is cum-dividend EPS. Assuming Dell had a required equity return of 11 percent, normal earnings for 2005 were 1.11 $1.03 = $1.143, that is, 2004 earnings growing at 11 percent. So abnormal earnings growth for 2005 was $1.18 $1.143 = $ Nike, Inc., a firm that pays dividends, earned $4.45 per share for its fiscal 2005 year against $3.59 in It paid a dividend of $0.74 in 2004, so the cum-dividend earnings for a shareholder in 2005 (after reinvesting the 2004 dividend) was $ (0.10 $0.74) = $4.524, assuming a 10 percent shareholders required return. So, with normal earnings of 1.10 $3.59 = $3.949, abnormal earnings growth was $4.524 $3.949 = $0.575 per share. 1 See J. A. Ohlson and B. E. Juettner-Nauroth, Expected EPS and EPS Growth as Determinants of Value, Review of Accounting Studies, July September, 2005, pp

10 Security, Third Chapter 6 Accrual Accounting and 207 Abnormal earnings growth can be expressed in terms of growth rates relative to required rates: Abnormal earnings growth t = [G t ρ E ] Earnings t 1 (6.3a) where G t is 1 plus the cum-dividend earnings growth rate for the period. That is, AEG is the dollar amount by which a prior year s earnings grow, cum-dividend, relative to the required rate. If G t is equal to the required rate, there is no abnormal earnings growth. With EPS of $1.18 for 2005 (and no dividends), Dell s cum-dividend earnings growth rate was $1.18/1.03 = percent (plus 1). So, with a required return of 11 percent, Dell s AEG for 2005 was $1.03 ( ) = $0.037 per share, as before. With cum-dividend EPS of $4.524 in 2005, a growth rate of percent over 2004 EPS of $3.59, Nike s AEG for 2005 was $3.59 ( ) = $0.575 per share, as before. You can see from these calculations that the higher the expected abnormal earnings growth is after the forward year, the higher the forward P/E ratio will be. The calculation in equation 6.3a shows that AEG is determined by expected cum-dividend earnings growth rates, G t. Figure 6.2 plots forward P/E ratios for the S&P 500 firms at the end of 2000 price at the end of 2000 divided by earnings forecasts for 2001 on cum-dividend earnings growth rates for 2002 (two years ahead), using analysts consensus forecasts at the time. You see indeed that forward P/E ratios are related to forecasts of subsequent earnings growth. But there is considerable variation around the regression line representing the average relationship. The analyst tries to explain this variation. FIGURE 6.2 The Relationship between Forward P/E Ratios and Subsequent Earnings Growth Rates The figure plots forward P/E ratios for S&P 500 firms at the end of 2000 on cum-dividend earnings growth rates for Forward P/E is price per share at the end of 2000 divided by analysts consensus EPS forecast for Cum-dividend growth rates are those based on analysts forecasts for The regression line gives the relationship between forward P/E ratios and two-year-ahead earnings growth. Source: Prices are from Standard & Poor s COMPUSTAT. Analysts earnings forecasts are from Thomson Financial I/B/E/S database Earnings Growth Rate on Forward P/E Ratio Earnings Growth Rate (2002) Forward P/E Ratio (2000)

11 Security, Third 208 Part One Financial Statements and A Simple Demonstration Exhibit 6.2 applies the abnormal earnings growth model to the simple prototype firm used in Chapter 5. This firm has a required return of 10 percent and its earnings are expected to grow at 3 percent a year. A 3 percent growth rate looks low, but looks can be deceiving because the firm has a high payout ratio (76 percent of earnings). Based on the earnings and dividend forecasts and the future book values they imply, residual earnings for the firm are forecasted to grow at a 3 percent rate, as indicated in the exhibit. So the firm can be valued with a Case 3 residual earnings valuation by capitalizing Year 1 residual earnings at this growth rate, as in Chapter 5: = = million V E EXHIBIT 6.2 Forecasts for a Firm with Expected Earnings Growth of 3 Percent per Year In millions of dollars. Required return is 10 percent per year. Forecast Year Residual earnings forecasts: Earnings Dividends Book value Residual earnings (RE) RE growth rate 3% 3% 3% 3% Abnormal earnings growth forecasts: Earnings Dividends Earnings on reinvested dividends Cum-dividend earnings Normal earnings Abnormal earnings growth (AEG) Abnormal earnings growth rate 3% 3% 3% 3% Cum-dividend earnings growth rate 10.57% 10.57% 10.57% 10.57% 10.57% Normal earnings growth rate 10.0% 10.0% 10.0% 10.0% 10.0% The Calculations: Earnings on reinvested dividends refers to the prior year s dividend earning at the required return. So, for Year 2, earnings on reinvested dividends = Cum-dividend earnings adds earnings on reinvested dividends to the ex-dividend earnings forecasted. So, cum-dividend earnings for Year 2 are ( ) = Normal earnings is the prior year s earnings growing at the required return. So, for Year 2, normal earnings are = Abnormal earnings growth is cum-dividend earnings normal earnings. So, for Year 2, AEG = = Abnormal earnings growth is also the prior year s earnings multiplied by the spread between the cum-dividend growth rate and the required rate. So, for Year 2, AEG is ( ) = Allow for rounding errors.

12 Security, Third Chapter 6 Accrual Accounting and 209 The exhibit also forecasts abnormal earnings growth (AEG), in order to apply the abnormal earnings growth model. Abnormal earnings growth each year is cum-dividend earnings less normal earnings. Calculations are described at the bottom of the exhibit using both the equation (6.3) and (6.3a) methods. You see that AEG is growing at 3 percent after Year 1. So, the AEG for Year 2 can be capitalized with this growth rate: V E 0 1 million =. + = (Allow for rounding errors.) The forward P/E ratio is /12.36 = 10.82, higher than the normal P/E of 10. You will notice at the bottom of the exhibit that the cum-dividend earnings growth rate is percent, higher than the required return of 10 percent, and accordingly the P/E ratio is greater than the normal P/E. You also will notice that the cumdividend earnings growth rate is considerably higher than the 3 percent rate forecasted for (ex-dividend) earnings. 2 And you will notice that the RE model and the AEG model give us the same valuation. Anchoring on Current Earnings The valuation in this example prices forward earnings so, strictly speaking, it anchors on forecasted earnings rather than the current earnings in the financial statements. The value can be calculated by anchoring on current earnings: Capitalize current earnings, and then add the value of forecasted AEG from Year 1 onward. That is, shift the application of the model one period back in time. So, for the example in Exhibit 6.2, 110. VE 0 d =. +. =. + = million The value obtained is the cum-dividend value (price plus dividend) appropriate for valuing current earnings. The trailing P/E is $142.80/$12.00 = 11.90, higher than the normal trailing P/E of 11 (for a required return of 10 percent). The $12.00 here is earnings for Year 0 and the $0.069 is forecasted AEG for Year 1, which is expected to grow at a 3 percent rate. The capitalization rate is 1.10/0.10, the normal trailing P/E, rather than 1/0.10, the normal forward P/E. The formal model for the calculation is: VE ρe AEG1 AEG2 AEG3 0 + d0 = Earn L (6.4) 2 3 ρe 1 ρe ρe ρe Clearly, with no AEG after the current year, the trailing P/E is normal. Anchoring valuation on current earnings anchors on actual earnings in the financial statements rather than a forecast of earnings. However, there is a good reason to apply the model to forward earnings rather than current earnings. As we will see when we come to analyze financial statements, current earnings often contain nonsustainable components unusual events and one-time charges, for example that do not bear on the future. By focusing on forward earnings and using current earnings as a base for the forecast, we 2 Strictly, cum-dividend earnings for any year ahead are earnings for that year plus earnings from all dividends paid and reinvested from Year 1 up to that year. So, for Year 3, cum-dividend earnings are the $13.11 EPS for that year, plus the Year 2 dividend invested for one year, plus the earnings from the reinvested Year 1 dividend. However, as dividends earn at the required return and earnings at the required return are subtracted in the AEG calculation, it makes no difference to the valuation and is certainly simpler if we just include the earnings on the prior year s dividends in cum-dividend earnings.

13 Security, Third 210 Part One Financial Statements and effectively focus on the sustainable portion of current earnings that can grow. Indeed, the financial statement analysis of Part Two of the book aims to identify sustainable earnings that are a sound anchor for forecasting forward earnings. The Web page for this chapter provides a spreadsheet to help you develop abnormal earnings growth pro formas. APPLYING THE MODEL TO EQUITIES The example in Exhibit 6.2 is similar to our prototype savings account example, except that this firm has some abnormal earnings growth whereas the savings account had none. The firm is somewhat special because AEG is forecasted to grow at a constant rate. The model (6.1) requires infinite forecasting horizons, so, to value equities, we need continuing values to truncate the forecast horizon. In the simple example, this occurs just one year ahead. There are two types of continuing value calculations. Case 1 applies when one expects subsequent abnormal earnings growth to be zero. Case 2 applies when one expects subsequent abnormal earnings to grow at a constant rate. Case 1 is illustrated using General Electric Company with a required return of 10 percent. The EPS and DPS numbers in Case 1 are GE s actual numbers for , the same numbers used to value GE using residual earnings methods in the last chapter. As in the last chapter, we treat the numbers as forecasts and value GE s shares at the end of Recall that we attempted to value GE using discounted cash flow techniques in Chapter 4 but ran into difficulties. However, we found we could value it with residual earnings methods. The AEG valuation here produces the same $13.07 per share value as the RE valuation in Chapter 5. The Case 1 valuation is based on a forecast that AEG will be zero after While the analyst forecasts positive AEG for 2004, he notes that the average AEG is close to zero over and so forecasts zero AEG subsequently. Zero AEG implies, of course, that cum-dividend earnings are expected to grow after 2004 at the required rate of return, just like the savings account. The total AEG over , discounted to the end of 2000, is $0.017 per share. Added to forward earnings for 2000 of $1.29 yields $1.307, which when capitalized at the 10 percent rate, yields the valuation of $13.07 per share. CASE 1 General Electric Co. (GE) In this case, abnormal earnings growth is expected to be zero after Required rate of return is 10 percent. Forecast Year DPS EPS DPS reinvested (0.10 DPS t 1 ) Cum-dividend earnings (EPS + DPS reinvested) Normal earnings (1.10 EPS t 1 ) Abnormal earnings growth (AEG) Discount rate (1.10 t ) Present value of AEG Total PV of AEG Total earnings to be capitalized Capitalization rate Value per share Note: Allow for rounding errors.

14 Security, Third Chapter 6 Accrual Accounting and 211 CASE 2 Dell Computer Corp. (Dell, Inc.) In this case, abnormal earnings are expected to grow at a 6.5 percent rate after Required rate of return is 11 percent. Forecast Year DPS EPS DPS reinvested (0.11 DPS t 1 ) Cum-dividend earnings Normal earnings (1.11 EPS t 1 ) Abnormal earnings growth Discount rate (1.11 t ) Present value of AEG Total PV of AEG Continuing value (CV) PV of CV Total earnings to be capitalized Capitalization rate Value per share The continuing value calculation: CV = = Present value of CV = = Note: Allow for rounding errors. A Case 2 valuation is demonstrated using Dell Computer (Dell, Inc.) with a required rate of return of 11 percent. The EPS and DPS up to 2005 are the same as those in Chapter 5 where we valued the firm using residual earnings methods with a continuing value based on a forecast that residual earnings after 2005 would grow at 6.5 percent. The EPS for 2006 here is that for that would result from this growth rate. Dell pays no dividends, so cum-dividend earnings are the same as earnings. Case 2 differs from Case 1 because AEG is expected to grow after the forecast horizon, so the valuation adds a continuing value that incorporates this growth rate. With the forecasted AEG for 2006 expected to grow at a rate of 6.5 percent after 2006, the continuing value for Dell at the end of 2005 is per share. Adding the present value of this continuing value at the end of 2001 to the total present value of AEG up to the end of 2005 ($ 0.062) and the forward earnings for 2001 ($0.84) yields $1.354 of earnings to be capitalized, resulting in a value of $12.31 per share. This is the same value calculated with residual earnings methods in Chapter 5. Converting Analysts Forecasts to a In Chapter 5 we converted analysts forecasts for Nike to a valuation using residual earnings methods. Here we do the same for Reebok, Nike s rival, but using abnormal earnings growth methods. In Table 6.1 analysts consensus EPS forecasts for 2005 and 2006, made at the end of 2004, were $3.43 and $3.81 and a DPS of $0.30 was indicated for Analysts also forecasted a consensus 14 percent five-year growth rate, the same as for Nike, and the EPS for in the table are based on this growth rate.

15 Security, Third 212 Part One Financial Statements and TABLE 6.1 Converting Analysts Forecasts to a : Reebok International Ltd. (RBK) Analysts forecast EPS two years ahead ($3.43 for 2005 and $3.81 for 2006) and also give a five-year EPS growth rate of 14 percent. Forecasts for apply this consensus growth rate to the 2006 estimate. Dividends per share (DPS) are set at the 2005 indicated payout rate of 8.7 percent of earnings. Required rate of return is 10 percent. 2004A 2005E 2006E 2007E 2008E 2009E DPS EPS DPS reinvested (0.10 DPS t 1 ) Cum-dividend earnings Normal earnings (1.10 EPS t 1 ) Abnormal earnings growth Cum-div EPS growth rate 11.95% 14.78% 14.93% 15.00% Discount rate (1.10 t ) Present value of AEG Total PV of AEG 0.54 Continuing value (CV) PV of CV 2.94 Total earnings to be capitalized 6.91 Capitalization rate Value per share 010. $69.10 The continuing value calculation: CV = = Present value of CV = = Note: Allow for rounding errors. The calculations in the table show that analysts are forecasting abnormal earnings growth after the forward year, 2005, apparent also from cum-dividend earnings growth rates that are greater than the required return on 10 percent. Analysts do not provide forecasts more than five years ahead, so the continuing value here is based on a 4 percent longterm growth rate, the typical GDP growth rate. The calculated value is $69.10 per share. Reebok traded at $41 at the time, so this value is well in excess of the market s valuation. Analysts five-year growth rates are typically optimistic. This could be so here; alternatively, the market price is cheap. We will return to the issue when we reverse engineer the market price at the end of the chapter. FEATURES OF THE ABNORMAL EARNINGS GROWTH MODEL Box 6.2 lists the advantages and disadvantages of the abnormal earnings growth model. Compare it to similar summaries for the dividend discount model (in Chapter 4), the discounted cash flow model (in Chapter 4), and the residual earnings model (in Chapter 5). We have emphasized that AEG valuation, like the residual earnings valuation, protects us from paying too much for earnings growth. In this section we will discuss some other features of the model. Buy Earnings The abnormal earnings growth model adopts the perspective of buying earnings. It embodies the idea that the value of a firm is based on what it can earn. As earnings represent

16 Security, Third Abnormal Earnings Growth Analysis 6.2 ADVANTAGES Easy to understand: Uses accrual accounting: Investors think in terms of future earnings; investors buy earnings. Focuses directly on the most common multiple used, the P/E ratio. Embeds the properties of accrual accounting by which revenues are matched with expenses to measure value added from selling products. Versatility: Can be used under a variety of accounting principles (Chapter 16). Aligned with what people forecast: Analysts forecast earnings and earnings growth. DISADVANTAGES Accounting complexity: Concept complexity: Sensitive to the required return estimate: Application to strategy: Suspect accounting: Forecast horizon: Requires an understanding of how accrual accounting works. Requires an appreciation of the concept of cum-dividend earnings; that is, value is based on earnings to be earned within the firm and from earnings from the reinvestment of dividends. As the value derives completely from forecasts that are capitalized at the required return, the valuation is sensitive to the estimate used for the required return. Residual earnings valuations derive partly from book value that does not involve a required return. Does not give an insight into the drivers of earnings growth, particularly balance sheet items; therefore, it is not suited to strategy analysis. Relies on earnings numbers that can be suspect. Should be implemented along with an earnings quality analysis. (Chapter 17). Forecast horizons can be shorter than those for DCF analysis and more value is typically recognized in the immediate future. But the forecast horizon does depend on the quality of the accrual accounting (Chapter 16). value to be added from selling products and services in markets, the model anticipates the value to be added from trading with customers, after matching revenues from those customers with the values given up, in expenses, to generate the revenue. The AEG model embraces the language of the analyst community. P/E ratios are more often referred to than P/B ratios. Analysts talk of earnings and earning growth, not residual earnings and residual earnings growth. So, converting an analyst s forecast to a valuation is more direct with this model than with the residual earnings model. (The language of the (Wall) street does not recognize how dividends affect growth, however; analysts talk of ex-dividend earnings growth rates, not cum-dividend rates.) Abnormal Earnings Growth and Residual Earnings On the other hand, the AEG model does not give as much insight into the value creation as the residual earnings model. Firms invest in assets and add value by employing these assets in operations. The residual earnings (RE) model explicitly recognizes the investment in assets, then recognizes that value is added only if that return is greater that the required return. The residual earnings model is a better lens on the business of generating value, the cycle of investment and return on investment. Accordingly, we have not proposed the AEG model as a model for strategy analysis (as we did with the RE model), for strategy analysis involves investment. The central question in strategy analysis is whether the investment will add value. 213

17 Security, Third Comparing the Abnormal Earnings Growth Model with the Residual Earnings Model 6.3 The AEG model and the RE model look different but are really quite similar. Both require forecasts of earnings and dividends, although the RE model adds the extra mechanical step of calculating book value forecasts from these forecasts. So the two models have the same forecasts as inputs. Structurally, the two models are similar. The RE starts with book value as an anchor and then adds value by charging forecasted earnings by the required return applied to book value. The AEG model starts with capitalized earnings as an anchor and then adds value by charging forecasted (cumdividend) earnings by the required return applied to prior earnings, rather than book value. This structural difference is just a different arrangement of the inputs. A little algebra underscores the point. Abnormal earnings growth can be written in a different form: AEG t = [Earn t + (ρ E 1)d t 1 ] ρ E Earn t 1 = Earn t Earn t 1 (ρ E 1)(Earn t 1 d t 1 ) Using the stocks and flows equation for accounting for the book value of equity (Chapter 2), B t 1 = B t 2 + Earn t 1 d t 1, so Earn t 1 d t 1 = B t 1 B t 2. Thus, AEG t = Earn t Earn t 1 (ρ E 1)(B t 1 B t 2 ) = [Earn t (ρ E 1)B t 1 ] [Earn t 1 (ρ E 1)B t 2 ] = RE t RE t 1 So, abnormal earnings growth is always equal to the change in residual earnings. You can see this by comparing the changes in residual earnings with the AEG for the prototype firm in Exhibit 6.2: Residual earnings Change in residual earnings Abnormal earnings growth You can also test this relationship by comparing the abnormal earnings growth for General Electric and Dell Computer (Dell, Inc.) in this chapter with the residual earnings for the two firms in Chapter 5. For example, GE s residual earnings for 2003 are $0.855, an increase of $0.011 over the $0.844 for 2002, and that increase is equal to its abnormal earnings growth for So, forecasting that there will be no abnormal earnings growth is the same as forecasting that residual earnings will not change. Or, as abnormal earnings growth of zero means that (cum-dividend) earnings are growing at the required rate of return, forecasting this normal growth rate is the same as forecasting that residual earnings will not change. Correspondingly, forecasting cum-dividend earnings growth above normal is the same as forecasting growth in residual earnings. Accordingly, one set of forecasts give us both measures. The rearrangement of the inputs leads to the different anchors and different definitions of adding value to the anchors. Yet the underlying concepts are similar. AEG valuation enforces the point that a firm cannot add value from growing earnings unless it grows earnings at a rate greater than the required rate of return. Only then does it increase its P/E ratio. But that is the same as saying that the firm must grow residual earnings to increase its P/B ratio. That is, added value comes from investing to earn a return greater than the required return, and that added value has its manifestation in both growth in residual earnings and growth in cum-dividend earnings over a normal growth rate. If abnormal earnings growth is always equal to the change in residual earnings, then the abnormal earnings growth model 6.1 can be restated as 1 RE RE RE L V E = Earn1 ρ 2 3 E 1 ρe ρe ρe where RE is the change in residual earnings. So, to value equities, one forecasts residual earnings. For residual earnings valuation (to determine intrinsic P/B ratios), one uses these residual earnings forecasts in the calculation. For abnormal earnings growth valuation (to determine intrinsic P/E ratios), one uses changes in residual earnings. So the same pro forma is used for both valuations, as we will see. The RE model and AEG model always yield the same valuation. Box 6.3 shows, indeed, that the concepts underlying the two models are not very different: Abnormal earnings growth is always equal to the change in residual earnings. Abnormal Earnings Growth Is Not Affected by Dividends, Share Issues, or Share Repurchases We saw in Chapter 5 that residual earnings valuation is not sensitive to expected dividend payout or share issues and share repurchases. Such is also the case with the AEG model. 214

18 Security, Third Chapter 6 Accrual Accounting and 215 With respect to dividends, you can prove this to yourself using the simple example in Exhibit 6.2. Rather than paying a dividend, reinvest the dividends in the firm at the 10 percent rate. Subsequent earnings within the firm will increase by the amount of the reinvested dividends. Cum-dividend earnings the amount of earnings earned in the firm plus that earned by reinvesting the dividends outside the firm will be exactly the same as if the shareholder reinvested the dividends in a personal account (as in the exhibit). AEG will not change, nor will the valuation. This simulates the earnings for an investor who receives the dividend but uses the cash to buy the stock, which is priced to yield a 10 percent required return. He effectively undoes the dividend, with no effect on value. The same logic applies if the payouts in Exhibit 6.2 are from stock repurchases rather than dividends. Accounting Methods and The residual earnings model accommodates different accounting principles. As we saw in Chapter 5, this is because book values and earnings work together. Firms may create higher future earnings by the accounting they choose, but to do so they must write down book values. When the higher earnings are combined with the lower book values (in a residual earnings valuation), value is unaffected. The AEG model, at first glance, looks as if it might not have this feature. A manager can create higher future earnings by writing down book values, and the AEG model values future earnings without carrying book values as a correcting mechanism. We do not want to pay for growth that does not add value, and accounting methods can create growth in earnings that we do not want to pay for. As it happens, the AEG model, like the residual earnings model, provides protection against paying for growth that is created by accounting. Box 6.4 explains. Make sure you read the section titled A Lesson for the Analyst in Box 6.4. The trailing P/E indicates expected earnings from sales in the future relative to the earnings recognized from current sales. To measure the value added from sales, accounting methods match expenses with revenues. If that matching underestimates current expenses (by underestimating bad debts, for example), current earnings are higher. However, future earnings are lower earnings are borrowed from the future. Because more current earnings are recognized and less future earnings are expected (and value is not affected), the trailing P/E is lower. With lower future earnings, the forward P/E is higher. The converse is true if a firm recognizes more expenses in current earnings. REVERSE ENGINEERING THE MODEL FOR ACTIVE INVESTING Like the residual earnings model, the AEG model can be reverse engineered. Consider the simple example in Exhibit 6.2, where a value of $ million was calculated. Suppose that the equity for this firm were trading at $ million and you forecast one-yearahead earnings of $12.36 million, and two-year-ahead earnings of $12.73 million. With a 10 percent required return, these forecasts imply AEG of $0.071 for two years ahead, as in the exhibit. Reverse engineering sets up the following problem and solves for g: 1 P = $. million = g With a value of $ million, g = You have converted the market price into a forecast: the market s implied abnormal earnings growth rate is 3 percent. You have done so by reverse engineering the AEG model. Rather than forecasting a growth rate and

19 Security, Third Abnormal Earnings Growth s When Earnings Are Created by Accounting 6.4 Exhibit 6.2 presented pro forma earnings and earnings growth for valuing the equity of a prototype firm. Suppose the manager of this firm has decided to create more earnings for Year 1 by writing down inventory by $8 in Year 0. This accounting adjustment changes the accounting numbers, but it should not affect the value. Here is the revised pro forma: Creating Earnings with Accounting: Modifying Exhibit 6.2 for a Write-Down Forecast Year Earnings Dividends Book value Earnings on reinvested dividends Cum-dividend earnings Normal earnings Abnormal earnings growth (8.729) Abnormal earnings growth rate 3% 3% EFFECT ON VALUATION As a result of the $8 write-down, the $12 reported for Year 0 earnings is now $4 (and the book value is $92 instead of $100). Correspondingly, Year 1 forward earnings increase by $8 to $20.36 because cost of goods sold is lower by $8. Cumdividend earnings for Year 2 are not affected but, because those earnings are now compared to normal earnings of $22.396, on the high base of $20.36 for Year 1, abnormal earnings growth for Year 2 is (a decline of) $ Subsequent years are unaffected. The AEG valuation at the end of Year 0 is V E = =. This is the same as the value before the accounting change. While forward Year 1 earnings have increased, the higher earnings of $20.36 mean higher normal earnings for Year 2 and consequently lower earnings growth of $ The net effect is to leave the value unchanged. EFFECT ON P/E RATIOS While valuations are not affected by accounting methods, P/E ratios certainly are. The forward P/E for this firm is now $133.71/$20.36 = 6.57, down from The trailing (dividend-adjusted) P/E is now ($ $9.09)/$4.00 = 35.70, up from Shifting income from current earnings to forward earnings increases the trailing P/E; there is now more anticipated earnings growth next year and the P/E prices growth. However, shifting income to the future decreases the forward P/E there is now less anticipated growth after the forward year, and the value of the earnings (in the numerator) does not change. A LESSON FOR THE ANALYST There is a lesson here. The diligent analyst distinguishes growth that comes from accounting from growth that comes from real business factors. If growth is induced by the accounting, he changes the P/E ratio, but he does not change the valuation. Applying the AEG model (or indeed the residual earnings model) protects him from making the mistake of pricing earnings that are due to accounting methods. We opened this chapter with the caveat that we do not want to pay for growth that does not add value. We do not want to pay for earnings growth from added investment that earns only the required return. But we also do not want to pay for growth that is created by accounting methods. Using the residual earnings model or the abnormal earnings growth model protects us from both dangers. converting that forecast to a valuation, you have converted the market s valuation into a forecast of the growth rate. Suppose now that the equity were trading at $147.2 million. We would then calculate g = 1.07 (rounded). You have reverse engineered the residual earnings model to conclude that the market is forecasting an abnormal earnings growth rate of 7 percent per year. If, as a result of an analysis of the firm, you conclude that the growth rate can be no higher than 3 percent, you would conclude that the market price of $147.2 million is too high: sell. But you might also turn the analysis on yourself: Is there something the market knows that I don t know? 216

20 Security, Third Chapter 6 Accrual Accounting and 217 Reverse engineering can also extract the implied expected return. Suppose you were very firm in your belief that the growth rate can be no higher than 3 percent. Then you can set up the following problem and solve for ρ: AEG $. million. ρ ρ P 0 = = + AEG 2 involves the required return for reinvesting dividends, so set AEG 2 = [ (ρ 1) 9.36] (ρ 12.36). The reverse-engineered amount for ρ is ; that is, the market is forecasting a 9.36 percent rate of return from buying this stock. This is the market s implied expected return. If you require 10 percent, you would say the stock is too expensive. The formula for reverse engineering the expected return looks a little complicated, but there are just a few numbers to plug in: ρ= Earn1 Earn2 Earn1 A A + ( g 1) P Earn 0 1 (6.5) 1 Div1 where A = g P0 Rather than screening stocks on the too-simple P/E ratio, the active investor might screen stocks on these implied expected returns: Buy stocks with high expected returns and sell those with low expected returns. This requires some analysis, of course, for we must have some sense of the AEG growth rate. Part Two of the book builds the analysis. Reverse Engineering the S&P 500 At the end of 2003, the S&P 500 index stood at The chief economist of a leading Wall Street investment bank was forecasting 2004 earnings for the S&P stocks of $53.00 and $58.20 for These earnings estimates are in the same units as the index, so the economist s forward P/E ratio for the index was $1,000/$53 = The payout ratio for the S&P 500 was 31 percent at the time and the economist estimated a market risk premium of 5 percent over the 10-year Treasury rate of 4 percent. With a beta of 1.0 for this market portfolio, these rates imply a CAPM required return of 9 percent. The normal forward P/E for a 9 percent required return is 1/0.09 = 11.11, so the market, with a P/E of 18.87, is expecting some abnormal earnings growth. The payout ratio implies expected dividends of $ = $16.43 in 2004, and with the reinvestment of this dividend at the 9 percent rate, expected abnormal earnings growth for 2005 is $1.909, as follows: Earnings $53.00 $58.20 Dividends (31% payout) Reinvested dividends at 9% Cum-dividend earnings $ Normal earnings ($ ) AEG $ With these ingredients, we are ready to reverse engineer: 1 P =, = g