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Chapter 5 Accrual Accounting and Valuation: Pricing Book Values GROUP MEMBERS 1.SHONHIWA ARMSTRONG 2.OTTILIA MATANHIRE 3.MAPA INNOCENT R133923R R186653H R1812767E • Previous presenters showed how accrual accounting modifies cash accounting to produce a balance sheet that reports shareholders' equity. However, they explained that book value is not the value of shareholders' equity, so firms typically trade at price-to-book ratios different from 1.0. 0. • This presentation shows how to estimate the value omitted from the balance sheet and thus how to estimate intrinsic price-to-book ratios. 9 • Firms typically trade at a price that differs from book value. Previous presentations explained why: While some assets and liabilities are marked to market in the balance sheet, others are recorded at historical cost, and yet others are excluded from the balance sheet. • Consequently, the analyst is left with the task of estimating the value that is omitted from the balance sheet. The analyst asks: What is the premium over book value at which a share should trade? This presentation lays out a valuation model for calculating the premium and intrinsic value. It also models strategy analysis, and provides directions for analyzing firms to discover the sources of value creation • After reading this chapter you should understand: • • What "residual earnings" is. • • How forecasting residual earnings gives the premium over book value and the P/B ratio. • • How residual earnings are driven by return on common equity (ROCE) and growth in book value. • • The difference between a Case 1, 2, and 3 valuation. • • How the residual earnings model captures value added in a strategy. • • The advantages and disadvantages of using the residual earnings model and how it contrasts to dividend discounting and discounted cash flow analysis. • How residual earnings valuation protects the investor from paying too much for earnings added by investment. • How residual earnings valuation protects the investor from paying for earnings that are created by accounting methods. • After reading this chapter you should be able to: • Calculate residual earnings. • •Calculate the value of equities and strategies from forecasts of earnings and book value. • Calculate an intrinsic price-to-book ratio. • Calculate value added in a strategy. • THE CONCEPT BEHIND THE PRICE-TO-BOOK RATIO • Book value represents shareholders' investment in the firm. • Book value is also assets minus liabilities, that is, net assets. However, book value typically does not measure the value of the shareholders' investment. The value of the shareholders' investment- and the value of the net assets- is based on how much the investment (net assets) is expected to earn in the future. Therein lies the concept of the P/B ratio: Book value is worth more or less, depending upon the future earnings that the net assets are likely to generate. • Accordingly, the intrinsic P/B ratio is determined by the expected return on book value. This concept fits with our idea that shareholders buy earnings. Price, in the numerator of the P/B ratio, is based on the expected future earnings that investors are buying. So, the higher the expected earnings relative to book value, the higher the P/B ratio. • The rate of return on book value-sometimes referred to as the profitability-is thus a measure that features strongly in the determination of P/B ratios. This presentation supplies the formal valuation model to implement this concept of the P/B ratio, as well as the mechanics to apply the model faithfully. • The formality is important, for formality forces one to be careful. In evaluating P/B ratios, one must proceed formally because one can pay too much for earnings if one is not careful • Beware of Paying Too Much for Earnings • A basic precept of investing is that investments add value only if they earn above their required return. Firms may invest heavily- in an acquisition spree, for example- but that • investment, while producing more earnings, adds value only if it delivers earnings above the required return on the investment. This maxim refines the P/B concept: • The P/B ratio prices expected return on book value, but it does not price a return that just yields the required return on book value. The analysis in this presentation is designed to prevent you from making the mistake of paying for earnings that do not add value. • As you apply the model and methods in this presentation, you will see that P/B ratios should increase only if earnings from investments yield a return that is greater than the required return on book value. • Indeed, with the tools in this presentation, you can assess whether the market is overpaying (or underpaying) for earnings and so detect cases where the P/B ratio is too high or too low Anchoring valution • Fundamental analysis anchors valuation in the financial statements. Book value provides an anchor. The investor anchors his valuation with the value that is recognized in the balance sheet- the book value- and then proceeds to assess value that is not recognizedthe premium over book value: • Value = Book value + Premium • Valuing a Project Suppose a firm invested $400 in a project that is expected to generate revenue of $440 a year later. Think of it as buying inventory and selling it a year later. After subtracting the $400 cost of the inventory from the revenue, earnings are expected to be $40, yielding a rate of return of 10 percent on the investment. The required rate ofreturn for the project is 10 percent. Following historical cost accounting, the asset (inventory) would be recorded on the balance sheet at $400. How much value does this project add to the book value? The answer, of course, is zero because the asset is expected to earn a rate of return equal to its cost of capital. And the project would be worth its book value Valuing a One-Period Project (1) Investment Required return Revenue forecast Expense forecast Earnings forecast $400 10% $440 $400 $ 40 Residual earnings1 Earnings 1 (Required return x Investment) 40 - (0.10 x 400) 0 400 Value 0 1.10 400 This is a zero-residual earnings project This is a zero NPV project: DCF Valuation: V 440 400 1.10 Valuing a One-Period Project (2) Investment Required return Revenue forecast Expense Forecast Earnings forecast $400 10% $448 $400 $ 48 Residual earnings1 48 - (0.10 x 400) 8 Value Project 400 407.27 The project adds value 448 DCF value 407 . 27 1.10 8 1.10 Valuing a Savings Account Forecast Year ________________________________________ 2000 2001 2002 2003 2004 2005 5 5 100 5 5 100 5 5 100 5 5 100 5 5 100 Earnings withdrawn each year (full payout) Earnings Dividends Book value 100 Residual earnings 0 0 0 0 0 ______________________________________________________________________________________ No withdrawals (zero payout) Earnings Dividends Book value 100 Residual earnings 5 0 105 0 5.25 0 110.25 0 5.51 0 115.76 5.79 0 121.55 6.08 0 127.63 0 0 0 ______________________________________________________________________________________ Value = Book Value + Present Value of Residual Earnings = 100 + 0 = 100 The Normal Price-to-Book Ratio Normal P/B = 1.0 (Price = Book Value) The Normal P/B firm earns a rate of return on its book value equal to the required return Lessons from the Savings Account 1. An asset is worth a premium or discount to its book value only if the book value is expected to earn nonzero residual earnings. 2. Residual earnings techniques recognize that earnings growth does not add value if that growth comes from investment earning at the required return. 3. Even though an asset does not pay dividends, it can be valued from its book value and earnings forecasts. 4. The valuation of the savings account does not depend on dividend payout. The two scenarios have different expected dividends, but the same value. 5. The valuation of a savings account is unrelated to free cash flows: The two accounts have the same value, but different free cash flow. A Model for Anchoring Value on Book Value Value of common equity V0E B0 RE 1 RE 2 RE 2 3 ... ρE ρE ρE where RE is residual earnings for equity : Residual earnings comprehens ive earnings - (required return for equity x beginning -of-period book value ) RE t Earn t (ρ E 1)B t 1 Derivation of the Equity Valuation Model: One Period Valuing a one-period payoff equation: P0 P1 d1 ρE Substitute for the expected dividend d1 Earnings 1 (B1 B0 ) to get P0 Earnings 1 (B1 B0 ) P1 ρE or Earnings 1 (ρ E 1)B 0 P1 B1 P0 B0 ρE ρE The amount, Earnings 1 ρ E 1B0 is called Residual Earnings Derivation of the Equity Valuation Model: Multiperiod Substituting comprehensive earnings and book value for dividends in each period, P0 B0 Earnings 1 ρ E 1B0 Earnings 2 ρ E 1B1 ... 2 ρE ρE Earnings T ρ E 1BT 1 PT BT ... T ρE ρ TE If we set RE t Earnings t ρ E 1Bt 1 , RE 1 RE 2 RE T PT BT P0 B0 2 .... T ρE ρE ρE ρ TE The Equity Valuation Model: Infinite Horizon The model can be extended for infinite horizons P0 B 0 Earnings1 ρ E 1B 0 Earnings 2 ρ E 1B1 ... ρE ρ 2E ... EarningsT ρ E 1B T 1 ρ TE ... or P0 B0 RE 1 RE 2 RE 3 RE 4 RE 5 2 3 4 5 ..... ρE ρE ρE ρE ρE Relation Between P/B Ratios and Subsequent RE _____________________________________________________________________________________ Residual Earnings for Years After P/B Groups Are Formed (Year 0) P/B _____________________________________________________________ 0 1 2 3 4 5 6 _____________________________________________________________________________________ P/B Group 1 (High) 6.20 .173 .230 .218 .213 .211 .200 .204 2 3.66 .121 .144 .142 .140 .148 .149 .139 3 2.82 .101 .112 .108 .108 .101 .103 .116 4 2.33 .089 .100 .099 .096 .097 .108 .123 5 2.00 .076 .082 .080 .088 .085 .086 .094 6 1.76 .064 .066 .064 .058 .066 .071 .076 7 1.58 .057 .058 .058 .056 .061 .059 .073 8 1.43 .047 .052 .047 .049 .053 .060 .068 9 1.31 .040 .040 .041 .044 .046 .055 .056 10 1.22 .035 .036 .035 .040 .047 .054 .054 11 1.13 .032 .034 .035 .040 .045 .051 .055 12 1.05 .028 .027 .028 .032 .040 .043 .046 13 .98 .023 .023 .025 .031 .035 .037 .045 14 .94 .018 .019 .025 .029 .035 .037 .039 15 .85 .009 .008 .013 .020 .028 .033 .041 16 .79 -.001 -.001 .006 .015 .023 .024 .024 17 .72 -.011 -.015 -.005 .008 .011 .021 .022 18 .64 -.024 -.024 -.012 -.003 .008 .010 .017 19 .54 -.042 -.044 -.028 -.015 -.007 -.007 -.006 20 (Low) .39 -.068 -.070 -.041 -.028 -.020 -.017 -.014 _____________________________________________________________________________________ Residual income is deflated by book value at the beginning of year 0, the year the P/B groups are formed. Ingredients of the Model For finite horizon forecasts we need three ingredients, besides the cost of capital: 1. The current book value 2. Forecasts of residual earnings (earnings and book values) to horizon 3. Forecasted premium at the horizon Component 3 is called the continuing value As efficient prices equal intrinsic values, then E RE RE RE V B 1 V0E B0 2 2 ..... TT T T T ρE ρE ρE ρE Return or Common Shareholders’ Equity (ROCE) Comprehens ive earnings to common t ROCE t Book value t 1 Alternative Measure of Residual Earnings Residual earnings is the rate of return on equity, ROCE, expressed as a dollar excess return on equity rather than a ratio. But it can also be expressed in ratio form: Earnings t E 1Bt 1 ROCE t E 1Bt 1 Drivers of Residual Earnings Two Drivers: 1. ROCE • If forecasted ROCE equals the required return, then RE will be zero, and V = B • If forecasted ROCE is greater than the required return, then V > B • If forecasted ROCE is less than the required return, then V < B 2. Growth in book value (net assets) put in place to earn the ROCE RE will change with change with ROCE and growth in book value P/B, ROCE and Growth in Book Value P/B in 2003 The Gap Inc. General Electric Co. Verizon Comm. Inc. Citigroup Inc. Home Depot Inc. General Motors Corp. Federated Dept. Stores 4.23 4.16 3.32 2.79 2.62 1.19 0.92 ROCE in 2004 28.1% 22.3% 23.4% 17.4% 19.2% 11.1% 12.0% Growth Rate for Book Value in 2004 30.7% 39.3% 12.2% 11.5% 13.2% 9.7% 3.1% How the Residual Earnings Model Works Current Data Current year Forecasts Year 1 ahead ROCE1 Current book value Current book value PV of RE2 PV of RE3 Year 3 ahead Book value1 ROCE2 ROCE3 Book value2 Current book value Residual earnings1 PV of RE1 Year 2 ahead Discount by Discount by 2 Discount by 3 Residual earnings2 Residual earnings3 A Simple Demonstration In millions of dollars. Required return is 10% per year. Forecast Year 0 1 2 3 4 5 13.51 13.91 Earnings 12.00 12.36 12.73 13.11 Dividends 9.09 9.36 9.64 9.93 10.23 10.53 103.00 106.09 109.27 112.55 115.93 2.43 2.50 2.58 2.66 3% 3% 3% Book value 100.00 RE (10% charge) 2.36 RE growth rate RE1 . g V0E B0 With g = 1.03 and ρ = 1.10, the valuation is: V0E $100 $2.36 $133.71 million 1.10 1.03 The intrinsic price-to-book ratio (P/B) is $133.71 / $100 = 1.34. 3% Buying Residual Earnings: Flanigan’s Enterprises Inc. Case 1: Zero RE after T Required rate of return is 9 percent. Forecast Year Eps Dps Bps 1999 2000 2001 2002 2003 3.58 0.73 0.11 4.20 0.80 0.24 4.76 0.71 0.25 5.22 0.47 0.27 5.41 20.4% 0.408 1.09 0.374 19.0% 0.422 1.188 0.355 14.9% 0.282 1.295 0.217 9.0% 0.000 1.412 0.000 ROCE RE (9% charge) Discount rate (1.09)t Present value of RE Total present value of RE to 2003 0.95 Value per share 4.53 Assuming zero RE after period T (zero premium at T): V0E B0 PV of RE for T periods V0E 4.53 3.58 0.95 Continuing Value Case 1: Zero RE after T RE is forecasted to be zero in perpetuity at the horizon So CVT 0 The forecasted premium at the horizon is VTE BT 0 Buying Residual Earnings: General Electric (GE) Case 2: Constant RE after T Required rate of return is 10 percent. Forecast Year Eps Dps Bps 1999 2000 2001 2002 2003 2004 4.32 1.29 0.57 5.04 1.38 0.66 5.76 1.42 0.73 6.45 1.50 0.77 7.18 1.60 0.82 7.96 29.9% 0.858 1.100 0.780 27.4% 0.876 1.210 0.724 24.7% 0.844 1.331 0.634 23.3% 0.855 1.464 0.584 22.3% 0.882 1.611 0.548 ROCE RE (10% charge) Discount rate (1.10)t Present value of RE Total present value of RE to 2004 3.27 Continuing value (CV) Present value of CV 5.48 Value per share 13.07 8.82 The continuing value: CV = 0.882 = 8.82 0.10 Present value of continuing value = 8.82 = 5.48 1.6105 Assuming constant RE after period T: V0E 13.07 4.32 3.27 5.48 Continuing Value Case 2: Constant RE after T RE is forecasted to be constant in perpetuity at the horizon So CVT RE T +1 E 1 The forecasted premium at the horizon is VTE BT CVT For GE, CVT = 0.882 8.82 0.10 Buying Residual Earnings: Dell Inc. Case 3: Growing RE after T Required rate of return is 11 percent. Forecast Year Eps Dps Bps 2000 2001 2002 2003 2004 2005 2.06 0.84 0.0 2.90 0.48 0.0 3.38 0.82 0.0 4.20 1.03 0.0 5.23 1.18 0.0 6.41 40.8% 0.613 1.110 0.553 16.6% 0.161 1.232 0.131 24.5% 0.568 1.518 0.374 22.6% 0.605 1.685 0.359 ROCE RE (11% charge) Discount rate PV of RE Total PV of RE to 2005 1.75 CV PV of CV 8.50 Value 12.31 2 4.3% 0.448 1.368 0.328 14.32 The continuing value (growth at 6.5%): 0.605 1.065 CV = 1.11 1.065 = 14.32 14.32 Present value of continuing value = 1.685 = 8.50 1 RE T 1 V B PV of RE for T periods T E E g Assuming growing RE after period T : E 0 0 V0E 12.31 2.06 1.75 8.50 Continuing Value Case 3: Growing RE after T RE is forecasted to grow at constant rate in perpetuity at the horizon So RET +1 CVT ρE g The forecasted premium at the horizon CVT VTE BT 0.605 1.065 For Dell, CVT 1.11 1.065 14.32 Forecasting Target Prices Target Price T BT CVT Case 1 (Flanigan’s) E V2003 B2003 5.41 Case 2 (GE) E V2004 B2004 CV2004 7.96 8.82 16.78 Case 3 (Dell) E V2005 B2005 CV2005 6.41 14.32 20.73 Converting an Analyst’s Forecast to a Valuation: Nike Inc. Forecasts: $4.45 2006 $5.04 Five-year eps growth rate: 14% 2005 Eps Dps Bps ROCE RE (10%) Discount rate PV of RE Total PV to 2009 CV PV of CV Value 2004A 2005E 2006E 3.59 0.74 18.17 4.45 0.92 21.70 5.04 1.04 25.71 24.49% 2.633 1.110 2.394 23.23% 2.870 1.210 2.372 2007E 5.75 1.18 30.27 22.36% 3.175 1.331 2.386 2009E 6.55 1.35 35.47 7.47 1.54 41.40 21.64% 3.523 1.464 2.406 21.06% 3.920 1.611 2.434 11.99 67.95 42.19 72.35 The continuing value (4% growth = GDP growth rate): CV = 2008E 3.920 1.04 = 67.95 1.10 1.04 Project Evaluation: Residual Earnings Approach Project evaluation: residual earnings approach. Forecast year, t 0 Revenues 1 2 3 4 5 $430 $460 $460 $380 $250 Depreciation 216 216 216 216 216 Net Income 214 244 244 164 34 984 768 552 336 120 17.8% 24.8% 31.8% 29.7% 10.1% 70 126 152 98 (6) Discount rate (1.12t) 1.120 1.254 1.405 1.574 1.763 PV of RE 62.5 100.5 108.2 62.3 (3.4) Book value $1,200 ROCE RE (.12) Total PV of RE 330 Value of project $1,530 Value added: PV of RE = 330 (same as NPV) Strategy Evaluation: Residual Earnings Approach and DCF Approach Hurdle rate: 12% Forecast Year 1 2 0 Residual Earnings Approach Revenues Depreciation Strategy income Book value Book rate of return Residual Income (0.12) PV of RE Total PV of RE 1 Continuing value PV of CV Value of strategy $1,200 2 CV= 439.2/0.12=$3,660. CV=900/0.12=$7,500. $890 432 458 2,956 21.0% 195.9 156.2 3 4 5 6… $1,350 648 702 3,504 23.8% 347.8 247.5 $1,730 864 866 3,840 24.7% 445.5 283.0 $1,980 1,080 900 3,840 23.4% 439.2 249.3 $1,980 … 1,080 … 900 … 3,840 … 23.4% 439.2 … 999 3,660 2,077 $4,276 Discounted Cash Flow Approach Cash inflow Investment $(1,200) Free cash flow (FCF) (1,200) PV of FCF Total PV of FCF 20 2 Continuing value PV of CV 4,256 Value of Strategy $4,276 1 $430 216 214 2,184 17.8% 70 62.5 ,t Value add: $3,076 $430 (1,200) (770) (687.5) $890 (1,200) (310) (247.2) $1,350 (1,200) 150 106.8 $1,730 (1,200) 53 0 336.7 $2,100 (1,200) 900 510.7 7,500 Net present value: $3,076 $2,100 … (1,200) 900… Advantages and Disadvantages of the Residual Earnings Model Advantages Focus on value drivers: focuses on profitability of investment and growth in investment that drive value; directs strategic thinking to these drivers Incorporates the financial statements: incorporates the value already recognized in the balance sheet (the book value); forecasts the income statement and balance sheet rather than the cash flow statement Uses accrual accounting: uses the properties of accrual accounting that recognize value added ahead of cash flows, matches value added to value given up and treats investment as an asset rather than a loss of value Versatility: can be used with a wide variety of accounting principles (Chapter 16) Aligned with what people forecast: analysts forecast earnings (from which forecasted residual earnings can be calculated) Validation: forecasts of residual earnings can be validated in subsequent audited financial statements Disadvantages Accounting complexity: requires an understanding of how accrual accounting works Suspect accounting: relies on accounting numbers that can be suspect (Chapter 17) Forecast horizon: forecast horizons can be shorter than for DCF analysis and more value is typically recognized in the immediate future; also, forecasts up to the horizon give an indication of profitability and growth for a continuing value calculation; but the forecast horizon does depend on the quality of the accrual accounting (Chapter 16) Protection from Paying Too Much for Earnings Generated by Investment Invest $50 million in Year 1 with proceeds from a share issue: Forecast Year 0 1 2 3 4 5 Earnings 12.00 12.36 17.73 18.61 19.56 20.57 Net dividends 9.09 (40.64) 9.64 9.93 10.23 10.53 100.00 153.00 161.09 169.77 179.10 189.14 2.36 2.43 2.50 2.58 2.66 3% 3% 3% 3% Book value RE (10% charge) RE growth rate Beware! V0E $100 $2.36 1.10 1.03 $133.71 million. Protection from Paying Too Much for Earnings Created by the Accounting: the Project Project (1): Write down book value to $360 Book Value Required Return Revenue Earnings $360 10% $440 80 ($440 – 360) Earnings have been created Residual Earnings = 80 – (0.10 x 360) = 44 Value = 360 + 44 1.10 = 400 The valuation is unchanged. Beware! Protection from Paying Too Much for Earnings Created by the Accounting: the Simple Example Writing inventory down by $8 million in Year 0 creates lower cost-of-goods sold in Year 1: Forecast Year 0 1 2 3 13.11 13.51 13.91 9.93 10.23 10.53 112.55 115.93 Earnings 4.00 20.36 12.73 Dividends 9.09 9.36 9.64 Book value 92.00 RE (10% charge) RE growth rate 103.00 106.09 1.16 2.43 109.27 4 2.50 3% 2.43 11.16 1.10 1.03 = $133.71 million. V0E $92 1 . 10 1.10 2.58 3% 5 2.66 3% Beware! Reverse Engineering the Growth Rate: A Simple Demonstration P0 $133.71 = $100 $2.36 1.10 g g = 1.03 The market is forecasting a growth rate for residual earnings of 3% per year Reverse Engineering the Expected Return: A Simple Demonstration P0 $147.2 = $100 RE1 1.03 RE1 = $12.36 – [(ρ – 1) × 100.0] Solution: ρ = 1.0936 You expect a 9.36% return from buying the stock at the current market price. The formula for ρ is: P0 B0 Earn1 1 g 1 P0 P0 Reverse Engineering the S&P 500 S&P 500 Index, beginning of 2005 =1200 S&P 500 P/B ratio = 3.0 S&P 500 ROCE for 2004 = 16% Required return = Risk-free rate + risk premium = 4.6% + 5% = 9.6% P2004 B2004 RE 2004 x g g (0.16 0.096) x g $3.0 $1.0 1.096 g g 1.062 (6.2% growth rate)