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Accrual Accounting and Valuation: Pricing Book Values

Chapter 5. Accrual Accounting and Valuation: Pricing Book Values. Accrual Accounting and Valuation: Pricing Book Values. Chapter 4 showed how accrual accounting modifies cash accounting to produce a balance sheet that reports shareholders’ equity.

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Accrual Accounting and Valuation: Pricing Book Values

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  1. Chapter 5 Accrual Accounting and Valuation: Pricing Book Values

  2. Accrual Accounting and Valuation: Pricing Book Values Chapter 4 showed how accrual accounting modifies cash accounting to produce a balance sheet that reports shareholders’ equity. However, Chapter 2 also explained that the book value in the balance sheet does not measure the value of shareholders’ equity, so firms typically trade at price-to-book ratios different from 1.0. Link to previous chapter This chapter shows how to estimate the value omitted from the balance sheet and thus how to estimate intrinsic price-to-book ratios. This Chapter How are premiums over book value determined? How is the firm valued by forecasting income statements and balance sheets? How are strategies evaluated? How does the analysts infer the market’s assessment of fundamentals? Chapter 6 compliments this chapter. While Chapter 5 shows how to price the book value of equity, the “bottom line” of the balance sheet, Chapter 6 shows how to price earnings, the “bottom line” of the income statement Link to next chapter Go to the web page for more applications of the techniques in this chapter Link to web page

  3. What you will Learn from this Chapter • What “residual earnings” is • How forecasting residual earnings gives the premium over book value and the P/B ratio • What is meant by a “normal price-to-book 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 residual earnings valuation • How the residual earnings model applies to valuing bonds, projects, strategies as well as equities • 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 dividends, share issues and share repurchases affect residual earnings • 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 • How the residual earnings model is used in reverse engineering

  4. Valuing a One-Period Project (1) Investment $400 Required return 10% Revenue forecast $440 Expense forecast $400 Earnings forecast $ 40 This is a zero NPV project: DCF Valuation: This is a zero-residual earnings project

  5. Valuing a One-Period Project (2) Investment $400 Required return 10% Revenue forecast $448 Expense Forecast $400 Earnings forecast $ 48 The project adds value

  6. Valuing a Savings Account Value = Book Value + Present Value of Residual Earnings = 100 + 0 = 100

  7. 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

  8. Lessons from the Savings Account • An asset is worth a premium or discount to its book value only if the book value is expected to earn non-zero residual earnings. • Residual earnings techniques recognize that earnings growth does not add value if that growth comes from investment earning at the required return. • Even though an asset does not pay dividends, it can be valued from its book value and earnings forecasts. • The valuation of the savings account does not depend on dividend payout. The two scenarios have different expected dividends, but the same value. • The valuation of a savings account is unrelated to free cash flows: The two accounts have the same value, but different free cash flow.

  9. A Model for Anchoring Value on Book Value

  10. Derivation of the Equity Valuation Model: One Period Valuing a one-period payoff equation: Substitute for the expected dividend to get or The amount, is called Residual Earnings

  11. Derivation of the Equity Valuation Model: Multiperiod Substituting comprehensive earnings and book value for dividends in each period, If we set ,

  12. The Equity Valuation Model: Infinite Horizon The model can be extended for infinite horizons or 1 2 T

  13. Relation Between P/B Ratios and Subsequent RE

  14. 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

  15. Return or Common Shareholders’ Equity (ROCE)

  16. 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:

  17. Drivers of Residual Earnings Two Drivers: • 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

  18. P/B, ROCE and Growth in Book Value P/B in 2003 ROCE in 2004 Growth Rate for Book Value in 2004 The Gap Inc. 4.23 28.1% 30.7% General Electric Co. 4.16 22.3% 39.3% Verizon Comm. Inc. 3.32 23.4% 12.2% Citigroup Inc. 2.79 17.4% 11.5% Home Depot Inc. 2.62 19.2% 13.2% General Motors Corp. 1.19 11.1% 9.7% Federated Dept. Stores 0.92 12.0% 3.1%

  19. Current Data Residual earnings1 Residual earnings2 Residual earnings3 Forecasts Current year Year 1 ahead Year 2 ahead Year 3 ahead Current book value Book value1 Book value2 ROCE1 ROCE2 ROCE3 Current book value Current book value PV of RE1 Discount by  PV of RE2 Discount by 2 PV of RE3 Discount by 3 How the Residual Earnings Model Works

  20. ROCE and P/B Ratios: S&P 500

  21. Growth in Book Values (Net Assets) and P/B Ratios

  22. ROCE Over the Years

  23. Growth in Book Value (Net Assets) Over the Years

  24. A Simple Demonstration In millions of dollars. Required return is 10% per year. Forecast Year 0 1 2 3 4 5 Earnings 12.00 12.36 12.73 13.11 13.51 13.91 Dividends 9.09 9.36 9.64 9.93 10.23 10.53 Book value 100.00 103.00 106.09 109.27 112.55 115.93 RE (10% charge) 2.36 2.43 2.50 2.58 2.66 RE growth rate 3% 3% 3% 3% . With g = 1.03 and ρ = 1.10, the valuation is: $133.71 million The intrinsic price-to-book ratio (P/B) is $133.71 / $100 = 1.34.

  25. Buying Residual Earnings: Flanigan’s Enterprises Inc. Case 1: Zero RE after T Required rate of return is 9 percent. Forecast Year 1999 2000 2001 2002 2003 Eps 0.73 0.80 0.71 0.47 Dps 0.11 0.24 0.25 0.27 Bps 3.58 4.20 4.76 5.22 5.41 ROCE 20.4% 19.0% 14.9% 9.0% RE (9% charge) 0.408 0.422 0.282 0.000 Discount rate (1.09)t 1.09 1.188 1.295 1.412 Present value of RE 0.374 0.355 0.217 0.000 Total present value of RE to 2003 0.95 Value per share 4.53 Assuming zero RE after period T (zero premium at T):

  26. Continuing Value Case 1: Zero RE after T RE is forecasted to be zero in perpetuity at the horizon So The forecasted premium at the horizon is

  27. Buying Residual Earnings: General Electric (GE)Case 2: Constant RE after T Required rate of return is 10 percent. Forecast Year 1999 2000 2001 2002 2003 2004 Eps 1.29 1.38 1.42 1.50 1.60 Dps 0.57 0.66 0.73 0.77 0.82 Bps 4.32 5.04 5.76 6.45 7.18 7.96 ROCE 29.9% 27.4% 24.7% 23.3% 22.3% RE (10% charge) 0.858 0.876 0.844 0.855 0.882 Discount rate (1.10)t 1.100 1.210 1.331 1.464 1.611 Present value of RE 0.780 0.724 0.634 0.584 0.548 Total present value of RE to 2004 3.27 Continuing value (CV) 8.82 Present value of CV 5.48 Value per share 13.07 The continuing value: CV = = 8.82 Present value of continuing value = = 5.48 Assuming constant RE after period T:

  28. Continuing ValueCase 2: Constant RE after T RE is forecasted to be constant in perpetuity at the horizon So The forecasted premium at the horizon is For GE, CVT =

  29. Buying Residual Earnings: Dell Inc. Case 3: Growing RE after T Required rate of return is 11 percent. Forecast Year 2000 2001 2002 2003 2004 2005 Eps 0.84 0.48 0.82 1.03 1.18 Dps 0.0 0.0 0.0 0.0 0.0 Bps 2.06 2.90 3.38 4.20 5.23 6.41 ROCE 40.8% 16.6% 2 4.3% 24.5% 22.6% RE (11% charge) 0.613 0.161 0.448 0.568 0.605 Discount rate 1.110 1.232 1.368 1.518 1.685 PV of RE 0.553 0.131 0.328 0.374 0.359 Total PV of RE to 2005 1.75 CV 14.32 PV of CV 8.50 Value 12.31 The continuing value (growth at 6.5%): CV = = 14.32 Present value of continuing value = = 8.50 Assuming growing RE after period T :

  30. Continuing ValueCase 3: Growing RE after T RE is forecasted to grow at constant rate in perpetuity at the horizon So The forecasted premium at the horizon

  31. Forecasting Target Prices Case 1 (Flanigan’s) Case 2 (GE) Case 3 (Dell)

  32. Converting an Analyst’s Forecast to a Valuation: Nike Inc. Forecasts: 2005$4.45 2006 $5.04 Five-year eps growth rate: 14% 2004A 2005E 2006E 2007E 2008E 2009E Eps 3.59 4.45 5.04 5.75 6.55 7.47 Dps 0.74 0.92 1.04 1.18 1.35 1.54 Bps 18.17 21.70 25.71 30.27 35.47 41.40 ROCE 24.49% 23.23% 22.36% 21.64% 21.06% RE (10%) 2.633 2.870 3.175 3.523 3.920 Discount rate 1.110 1.210 1.331 1.464 1.611 PV of RE 2.394 2.372 2.386 2.406 2.434 Total PV to 2009 11.99 CV 67.95 PV of CV 42.19 Value 72.35 The continuing value (4% growth = GDP growth rate): CV = = 67.95

  33. Project Evaluation: Residual Earnings Approach Value added: PV of RE = 330 (same as NPV)

  34. Forecast Year , t 0 1 2 3 4 5 6… Residual Earnings Approach Revenues $430 $890 $1,350 $1,730 $1,980 $1,980 … Depreciation 216 432 648 864 1,080 1,080 … Strategy income 214 458 702 866 900 900 … Book value $1,200 2,184 2,956 3,504 3,840 3,840 3,840 … Book rate of return 17.8% 21.0% 23.8% 24.7% 23.4% 23.4% Residual Income (0.12) 70 195.9 347.8 445.5 439.2 439.2 … PV of RE 62.5 156.2 247.5 283.0 249.3 Total PV of RE 999 1 Continuing value 3,660 PV of CV 2,077 Value of strategy $4,276 Value add: $3,076 Discounted Cash Flow Approach Cash inflow $430 $890 $1,350 $1,730 $2,100 $2,100 … Investment $(1,200) (1,200) (1,200) (1,200) (1,200) (1,200) (1,200) Free cash flow (FCF) (1,200) (770) (310) 150 53 0 900 900… PV of FCF (687.5) (247.2) 106.8 336.7 510.7 Total PV of FCF 20 2 Continuing value 7,500 PV of CV 4,256 Value of Strategy $4,276 Net present value: $3,076 1 CV= 439.2/0.12=$3,660. 2 CV=900/0.12=$7,500. Strategy Evaluation: Residual Earnings Approach and DCF Approach Hurdle rate: 12%

  35. Advantages and Disadvantages of the Residual Earnings Model

  36. 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 Book value 100.00 153.00 161.09 169.77 179.10 189.14 RE (10% charge) 2.36 2.43 2.50 2.58 2.66 RE growth rate 3% 3% 3% 3% $133.71 million. Beware!

  37. Project (1): Write down book value to $360 Book Value $360 Required Return 10% Revenue $440 Earnings 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. Protection from Paying Too Much for Earnings Created by the Accounting: the Project Beware!

  38. 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 4 5 Earnings 4.00 20.36 12.73 13.11 13.51 13.91 Dividends 9.09 9.36 9.64 9.93 10.23 10.53 Book value 92.00 103.00 106.09 109.27 112.55 115.93 RE (10% charge) 1.16 2.43 2.50 2.58 2.66 RE growth rate 3% 3% 3% = $133.71 million. Beware!

  39. Tracking V/P Ratios: All U.S. Stocks, 1975 - 2002 Inputs: Analysts’ consensus forecasts Required return = Risk-free rate + 5% g = 4%

  40. Reverse Engineering the Growth Rate: A Simple Demonstration = g = 1.03 The market is forecasting a growth rate for residual earnings of 3% per year

  41. Reverse Engineering the Expected Return: A Simple Demonstration = 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:

  42. 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%

  43. Reverse Engineering for Nike Inc. P2004 = $75 Consensus forecast for 2005 = $4.45 Consensus forecast for 2006 = $5.04

  44. Implied Earnings Forecasts and Earnings Growth Rates Convert residual earnings forecasts to earnings forecasts as follows: This formula reverse-engineers the residual earnings calculation

  45. Plotting Implied Eps Growth Rates: Nike Inc. BUY SELL

  46. Building Blocks of a Residual Earnings Valuation: Nike Inc. (1) Book value, known for sure (2) Value from near-term forecasts (for two years’ ahead), usually are made with some confidence (3) Value from long-term growth forecasts, the most speculative part of the valuation

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