1. Accrual Accounting and Valuation: Pricing Book Values
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
This chapter shows how to
estimate the value omitted from the balance sheet and thus how to estimate intrinsic price-to-book ratios.
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?
Link to next chapter
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 web page
Go to the web page for more applications of the techniques in this chapter

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 %
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 %
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

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 ROCE in Growth Rate for
Book Value in 2004
The Gap Inc % %
General Electric Co % %
Verizon Comm. Inc % %
Citigroup Inc % %
Home Depot Inc % %
General Motors Corp % %
Federated Dept. Stores % %

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

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
Earnings
Dividends
Book value
RE (10% charge)
RE growth rate % % % % .
With g = 1.03 and ρ = 1.10, the valuation is:
$ million
The intrinsic price-to-book ratio (P/B) is $ / $100 = 1.34.

25. Buying Residual Earnings: Flanigan’s Enterprises Inc
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
ROCE % % % %
RE (9% charge)
Discount rate (1.09)t
Present value of RE
Total present value
of RE to
Value per share
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 Eps Dps Bps ROCE 29.9% 27.4% 24.7% 23.3% 22.3% RE (10% charge) Discount rate (1.10)t Present value of RE Total present value of RE to Continuing value (CV) 8.82 Present value of CV 5.48 Value per share The continuing value: CV = = 8.82 Present value of continuing value = = 5.48 Assuming constant RE after period T:

28. Continuing Value Case 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
Eps
Dps
Bps
ROCE % % % % %
RE (11% charge)
Discount rate
PV of RE
Total PV
of RE to CV
PV of CV
Value
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 Value Case 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:
$4.45
$5.04
Five-year eps growth rate: 14%
2004A E E E E E
Eps
Dps
Bps
ROCE % % % % %
RE (10%)
Discount rate
PV of RE
Total PV to CV
PV of CV
Value
The continuing value (4% growth = GDP growth rate):
CV = = 67.95

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

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

35. Advantages and Disadvantages of the Residual Earnings Model
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)

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
Earnings
Net dividends (40.64)
Book value
RE (10% charge)
RE growth rate % 3% 3% 3%
$ million.
Beware!

37. Protection from Paying Too Much for Earnings Created by the Accounting: the Project
Project (1): Write down book value to $360
Book Value $360
Required Return 10%
Revenue $440
Earnings ($440 – 360)
Earnings have been created
Residual Earnings = 80 – (0.10 x 360)
= 44
Value =
1.10
= 400
The valuation is unchanged.
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
Earnings
Dividends
Book value
RE (10% charge)
RE growth rate % % 3%
= $ 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 =
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