Solutions to Selected End-Of-Chapter Questions Chapters 1 Through 7(1)

SOLUTIONS TO EXERCISES AND CASES For FINANCIAL STATEMENT ANALYSIS AND SECURITY VALUATION

Stephen H. Penman

Fifth Edition

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CHAPTER ONE Introduction to Investing and Valuation Concept Questions

C1.1. Fundamental risk arises from the inherent risk in the business – from sales revenue falling or expenses rising unexpectedly, for example. Price risk is the risk of prices deviating from fundamental value. Prices are subject to fundamental risk, but can move away from fundamental value, irrespective of outcomes in the fundamentals. When an investor buys a stock, she takes on fundamental risk – the stock price could drop because the firm’s operations don’t meet expectations – but she also runs the (price) risk of buying a stock that is overpriced or selling a stock that is underpriced. Chapter 19 elaborates and Figure 19.5 (in Chapter 19) gives a display.

C1.3. This statement is based on a statistical average from the historical data: The return on stocks in the U.S. and many other countries during the twentieth century was higher than that for bonds, even though there were periods when bonds performed better than stocks. So, the argument goes, if one holds stocks long enough, one earns the higher return. However, it is dangerous making predictions from historical averages when risky investment is involved. Averages from the past are not guaranteed in the future. After all, the equity premium is a reward for risk, and risk means that the investor can get hit (with no guarantee of always getting a higher return). The investor who holds stocks (for retirement, for example) may well find that her stocks have fallen when she comes to liquidate them. Indeed, for the past 5-year period, the past 10year period, and the past 25-year period up to 2010, bonds outperformed stocks—not very

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pleasant for the post war baby-boomer at retirement age at that point who had held “stocks for the long run.” Waiting for the “long-run” may take a lot of time (and “in the long run we are all dead”). The historical average return for equities is based on buying stocks at different times, and averages out “buying high” and “buying low” (and selling high and selling low). An investor who buys when prices are high (or is forced to sell when prices are low) may not receive the typical average return. Consider investors who purchased shares during the stock market bubble in the 1990s: They lost considerable amount of their retirement “nest egg” over the next few years. See Box 1.1.

C1.5. This is not an easy question at this stage. It will be answered in full as the book proceeds. But one way to think about it is as follows: If an investor expects to earn 10% on her investment in a stock, then earnings/price should be 10% and price/earnings should be 10. Any return above this would be considered “high” and any return below it “low.” So a P/E of 33 (an E/P yield of 3.03%) would be considered high and a P/E of 8 (an E/P yield of 12.5%) would be considered low. But we would have to also consider how accounting rules measure earnings: If accounting measures result in lower earnings (through high depreciation charges or the expensing of research and development expenditure, for example) then a normal P/E ratio might be higher than 10. And one also has to consider growth: If earnings are expected to be higher in the future than current earnings, the E/P ratio should be lower than this 10% benchmark (and the corresponding P/E higher). In early 2012, the S&P 500 P/E ratio stood at 14.4.

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C1.7. Yes. Stocks would be efficiently priced at the agreed fundamental value and the market price would impound all the information that investors are using. Stock prices would change as new information arrived that revised the fundamental value. But that new information would be unpredictable beforehand. So changes in prices would also be unpredictable: stock prices would follow a “random walk.”

C1.9. a. If the market price, P, is efficient (in pricing intrinsic value) and V is a good measure of intrinsic value, the P/V ratio should be 1.0. The graph does show than the P/V ratio oscillates around 1.0 (at least up to the bubble years). However, there are deviations from 1.0. These deviations must either be mispricing (in P) that ultimately gets corrected so the ratio returns to 1.0, or a poor measure of V. b. Yes, you would have done well up to 1995 if P/V is an indication of mispricing. When the P/V ratio drops below 1.0, prices increase (as the market returns to fundamental value), and when the P/V ratio rises above 1.0, prices decrease (as the market returns to fundamental value). A long position in the first case and a short position in the latter case would earned positive returns. Of course, this strategy is only as good as the V measure used to estimate intrinsic value. c. Clearly, shorting Dow stocks during this period would have been very painful, even though the P/V ratio rose to well above 1.0. Up to 1999, the P/V ratio failed to revert back to 1.0 even though it deviated significantly from 1.0. This illustrates price risk in investing (see question C1.1 and Box 1.1). Clearly, buying stocks when the P/V ratio was at 1.2 would clearly involved a lot of price risk: The P/V ratio says stocks are too expensive and you’d be paying too much. But selling short at a P/V ratio of 1.2 in 1997 would also have borne considerable price risk, for the P/V ratio increase even further subsequently. In bubbles or periods of momentum investing, overpriced stocks get more overpriced, so taking a position in the hope that prices will

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return to fundamental value is risky. Only after the year 2000 did prices finally turn down, and the P/V ratio fell back towards 1.0. Chapter 5 covers the calculation of P/V ratios here.

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Exercises Drill Exercises E1.1. Calculating Enterprise Value This exercise tests the understanding of the basic value relation: Enterprise Value = Value of Debt + Value of Equity Enterprise Value = $600 + $1,200 million = $1,800 million (Enterprise value is also referred to as the value of the firm, and sometimes as the value of the operations.) E1.3

Buy or Sell? Value = $850 + $675 = $1,525 million Value per share = $1,525/25 = $61 Market price

= $45

Therefore, BUY!

Applications E1.5. Enterprise Market Value: General Mills and Hewlett-Packard (a)

General Mills Market value of the equity = $36.50  644.8 million shares = Book value of total (short-term and long-term) debt =

$23,535,2 million

Enterprise value

$30,420.3 million

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6,885.1

Note three points: (i)

Total market value of equity = Price per share  Shares outstanding.

(ii)

The book value of debt is typically assumed to equal its market value, but financial statement footnotes give market value of debt to confirm this.

(iii)

The book value of equity is not a good indicator of its market value. The price-tobook ratio for the equity can be calculated from the numbers given: $23,535.2/$6,616.2 = 3.56.

(b)

This question provokes the issue of whether debt held as assets is part of enterprise value

(a part of operations) or effectively a reduction of the net debt claim on the firm. The issue arises in the financial statement analysis in Part II of the book: Are debt assets part of operations or part of financing activities? Debt is part of financing activities if it is held to absorb excess cash rather than used as a business asset. The excess cash could be applied to buying back the firm’s debt rather than buying the debt of others, so the net debt claim on enterprise value is what is important. Put another way, HP is not in the business of trading debt, so the debt asset is not part of enterprise operations. The calculation of enterprise value is as follows: Market value of equity = $41  2,126 million shares = $

87,166 million

Book value of net debt claims: Short-term borrowing

$ 8,406 million

Long-term debt Total debt

14,512 $22,918 million

Debt assets

12,700

Enterprise value

10,218 97,384 million

The $10,218 million is referred to as net debt.

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Minicases M1.1 Critique of an Equity Analysis: America Online, Inc. Introduction This case can be used to outline how the analyst goes about a valuation and, specifically, to introduce pro forma analysis. It can also be used to stress the importance of strategy in valuation. The case involves suspect analysis, so is pertinent to the question (that will be answered as the book proceeds): What does a credible equity research report look like? The case can be introduced with the Apple example is Box 1.6. The case anticipates some of the material in Chapter 3 that lays out how to approach fundamental analsis You may wish to introduce that material with this case – by putting Figures 3.1 and 3.2 in front of the students, for example. You may wish to recover the original Wall Street Journal (April 26, 1999) piece on which this case is based and hand it out to students. It is available from Dow Jones News Retrieval. With the piece in front of them, students can see that it has three elements that are important to valuation – scenarios about the future (including the future for the internet, as seen at the time), a pro forma analysis that translates the scenario into numbers, and a valuation that follows from the pro forma analysis. So the idea – emphasized in Chapter 3 -- that pro forma analysis is at the heart of the analysis is introduced, but also the idea that pro forma analysis must be done with an appreciation for strategy and scenarios that can develop under the strategy.

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To value a stock, an analyst forecasts (based on a scenario), and then converts the forecast to a valuation. An analysis can thus be criticized on the basis of the forecasts that are made or on the way that value is inferred from the forecast. Students will question Alger's forecasts, but the point of the case is to question the way he inferred the value of AOL from his forecasts.

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Working the Case A.

Calculation of price of AOL with a P/E of 24 in 2004 Earnings in 2004 for a profit margin of 26% of sales: $16.000  0.26

$4.160 billion

Market value in 2004 with a P/E ratio of 24

$99.840

Present value in 1999 (at a discount rate of 10%, say)

$61.993

Shares outstanding in 1999

1.100

Value per share, 1999

$56.36

(Students might quibble about the discount rate; the sensitivity of the value to different discount rates can be looked at.) B.

Market value of equity in 1999: 105  1.10 billion shares

$115.50 billion

Future value in 2004 (at 10%)

$186.014

Forecasted earnings, 2004

$4.160 billion

Forecasted P/E ratio

44.7

So, if AOL is expected to have a P/E of 50 in 2004, it is a BUY.

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C. Use Box 1.6 as background for this part. There are two problems with the analysis: 1. The valuation is circular: the current price is based on an assumption about what the future price will be. That future price is justified by an almost arbitrary forecast of a P/E ratio. The valuation cannot be made without a calculation of what the P/E ratio should be. Fundamental analysis is needed to break the circularity. Alger justified a P/E ratio of 50, based on -

Continuing earnings growth of 30% per year after 2000

-

“Consistency” of earnings growth

-

An "excitement factor" for the stock.

Is his a good theory of the P/E ratio? Discussion might ask how the P/E ratio is related to earnings growth (Chapter 6) and whether 30% perpetual earnings growth is really possible. What is "consistency" of earnings growth? What is an "excitement factor"? How does one determine an intrinsic P/E ratio?

2. The valuation is done under one business strategy--that of AOL as a stand-alone, internet portal firm. The analysis did not anticipate the Time Warner merger or any other alternative paths for the business. (See box 1.4 in the text). To value an internet stock in 1999, one needed a well-articulated story of how the "Internet revolution" would resolve itself, and what sort of company AOL would look like in the end.

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Further Discussion Points 

Circular valuations are not uncommon in the press and in equity research reports: the analyst specifies a future P/E ratio without much justification, and this drives the valuation. Tenet 11 in Box 1.6 is violated.



The ability of AOL to make acquisitions like its recent takeover of Netscape (at the time) will contribute to growth -- and Alger argued this. But, if AOL pays a “fair price” for these acquisitions, it will just earn a normal return. What if it pays too much for an overvalued internet firm? What if it can buy assets (like those of Time Warner) cheaply because its stock is overpriced? This might justify buying AOL at a seemingly high price. Introduce the discussion on creating value by issuing shares in Chapter 3.



The value of AOL’s brand and its ability to attract and retain subscribers are crucial.



The competitive landscape must be evaluated. Some argue that entry into internet commerce is easy and that competition will drive prices down. Consumers will benefit tremendously from the internet revolution, but producers will earn just a normal return. A 26% profit margin has to be questioned. The 1999 net profit margin was 16%.



A thorough analysis would identify the main drivers of profitability and the growth. -

analysis of the firm’s strategy

-

analysis of brand name attraction

-

analysis of churn rates in subscriptions

-

analysis of potential competition

-

analysis of prospective mergers and takeovers and “synergies” that might be available

-

analysis of margins.

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Postscript David Alger, president of Fred Alger Management Inc., perished in the September 11, 2001 attack on the World Trade Center in New York, along with many of his staff. The Alger Spectra fund was one of the top performing diversified stock funds of the 1990s.

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CHAPTER TWO Introduction to the Financial Statements

Concept Questions C2.2. False. Cash can also be paid out through share repurchases. C2.4. For one of two reasons: 1.

The firm is mispriced in the market.

2.

The firm is carrying assets on its balance sheet at less than market value, or is omitting other assets like brand assets and knowledge assets. Historical cost accounting and the immediate expensing of R&D and expenditures on brand creation produce balance sheets that are likely to be below market value.

C2.6. Some examples: 

Expensing research and development expenditures.



Using short estimated lives for depreciable assets – resulting is high depreciation charges.



Expensing store opening costs before revenue is received.



Not recognizing the cost of stock options.



Expensing advertising and brand creation costs.



Underestimating bad debts



Not recognizing contingent warranty liabilities from sales of products.

See Box 2.4.

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C2.8. Dividends are distributions of the value created in a firm; they are not a loss in generating value. So accountants calculate the value added (earnings), add it to equity, and then treat dividends as a distribution of the value added (by charging dividends against equity in the balance sheet).

C2.10. Like depreciation of plant, amortization of intangibles recognizes a loss of value. Patents expire, and so the value of the original investment is lost. So, just as the cost of plant is expensed against the revenue the plant produces, the cost of patents is expensed against the revenue that the patent produces.

C2.12. The fundamental analyst wants to anchor on “what we know” so not to mix “what we know” with speculation. So he tells the accountants: Tell me what you know, don’t speculate; leave the speculation to me, the analyst. The reliability criterion enforces this request.

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Exercises Drill Exercises E2.2. Applying Accounting Relations: Cash Flow Statement Change in cash = CFO – Cash investment – Cash paid out in financing activities $130 = $400 ? $75 ? = $195 million E2.4. Preparing an Income Statement and Statement of Shareholders’ Equity Income statement: Sales $4,458 Cost of good sold 3,348 Gross margin 1,110 Selling expenses (1,230) Research and development (450) Operating income (570) Income taxes 200 Net loss (370) Note that research and developments expenses are expensed as incurred. Equity statement: Beginning equity, 2012

$3,270

Net loss $(370) Other comprehensive income 76 Share issues Common dividends

(294) 680 (140)

Ending equity, 2012

($76 is unrealized gain on securities)

$3,516

Comprehensive income (a loss of $294 million) is given in the equity statement. Unrealized gains and losses on securities on securities available for sale are treated as other comprehensive income under GAAP. Net payout = Dividends + share repurchases – share issues = 140 + 0 – 680 = - 540

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That is, there was a net cash flow from shareholders into the firm of $540 million. Taxes are negative (that is, the effect on income is positive) because income is negative (a loss). A loss yields a tax benefit that he firm can carry forward to reduce future taxes.

E2.5. Classifying Accounting Items

a. Current asset b. Net revenue in the income statement: a deduction from revenue c. Net accounts receivable, a current asset: a deduction from gross receivables d. An expense in the income statement. But R&D is usually not a loss to shareholders; it is an investment in an asset. e. An expense in the income statement, part of operating income (and rarely an extraordinary item). If the restructuring charge is estimated, a liability is also recorded, usually lumped with “other liabilities.” f. Part of property, plan and equipment. As the lease is for the entire life of the asset, it is a “capital lease.” Corresponding to the lease asset, a lease liability is recorded to indicate the obligations under the lease. g. In the income statement h. Part of dirty-surplus income in other comprehensive income. The accounting would be cleaner if these items were in the income statement. i. A liability j. Under GAAP, in the statement of owners equity. However from the shareholders’ point of view, preferred stock is a liability

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k. Under GAAP, an expense. However from the shareholders’ point of view, preferred dividends are an expense. Preferred dividends are deducted in calculating “net income available to common” and for earnings in earnings per share. l. As an expense in the income statement.

E2.7. Using Accounting Relations to Check Errors Ending shareholders’ equity can be derived in two ways: 1. Shareholders’ equity = assets – liabilities 2. Shareholders’ equity = Beginning equity + comprehensive income – net dividends So, if the two calculations do not agree, there is an error somewhere. First make the calculations for comprehensive income and net dividends: Comprehensive income = net income + other comprehensive income = revenues – expenses + other comprehensive income = 2,300 –1,750 – 90 = 460 Net dividend

= dividends + share repurchases – share issues = 400 +150 –900 = - 350

Now back to the two calculations: 1. Shareholders’ equity = 4,340 – 1,380 = 2,960 2, Shareholders’ equity = 19,140 + 460 – (-350) = 19,950 The two numbers do not agree. There is an error somewhere.

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Applications E2.9. Testing Accounting Relations: General Mills Inc. This exercise tests some basic accounting relations. (a)

(b)

Total liabilities = Total assets – stockholders’ equity =

17,679 – 5,648

=

12,031

Total Equity (end) = Total Equity (beginning) + Comprehensive Income – Net Payout to Common Shareholders 5,648 = 5,417 + ? – 737 ? = 968

Net payout to common = cash dividends + stock purchases – share issues = 648 + 692 - 603 = 737

E2.10. Testing Accounting Relations: Genetech Inc. (a) Revenue

= Net income + Net expenses (including taxes) = $784.8 + 3,836.4 = $4,621.2 million

(b)

ebit

= Net income + Interest + Taxes = $784.8 - 82.6 + 434.6 = $1,136.8 million

(Note: net interest is interest income minus interest expense) (c)

ebitda

= Net income + interest + taxes + depreciation and amortization

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= Ebit + depreciation + amortization = $1,136.8 + 353.2 = $1,490.0 million Depreciation and amortization is reported as an add-back to net income to get cash flow from operations in the cash flow statement. (a) Long-term assets = Total assets – Current assets = $9,403.4 – 3,422.8 = $5,980.6 million Total Liabilities = Total assets – shareholders’ equity = $9,403.4 – 6,782.2 = $2,621.2 million Short-term Liabilities = Total liabilities – Long-term Liabilities = $2,621.2 - 1,377.9 = $1,243.3 million (b) Change in cash and cash equivalents = Cash flow from operations – Cash used in investing activities + Cash from financing activities Change in cash and cash equivalents is given by the changes in the amount is the balance sheet = $270.1 – 372.2 = -$102.1 So, -$102.1 = $1,195.8 - $451.6 + ? So

?

= -$846.3 million

That is, there was a cash outflow of $846.3 million for financing activities.

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E2.12. Find the Missing Numbers in Financial Statements: General Motors a. Total Equity (end) = Total Equity (beginning) + Comprehensive Income – Net Payout to Common Shareholders -56,990 = -37,094 + ? – 283 ? = -19,613

(a loss)

b. Comprehensive income = Net income + Other comprehensive income -19,613 = -18,722 + ? ? = - 891 c. Net income = Revenue – expenses and losses -18,722 = ? – 60,895 ? = 42,173 d. June 30, 2008 Assets 136,046 Liabilities ? = 193,036 Equity -56,990

December 31, 2007 148,883 ? = 185,977 -37,094

E2.14. Calculating Stock Returns: Nike, Inc. The stock return is the change in price plus the dividend received. So, Nike’s stock return for fiscal year 2010 is Stock return = $73.38 - $57.83 + $1.06 = $16.61 The rate-of-return is the return divided by the beginning-of-period price: $16.61/57.83 = 28.72%.

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CHAPTER THREE How Financial Statements are Used in Valuation Concept Questions C3.1. Investors are interested in profits from sales, not sales. So price-to-sales ratios vary according to the profitability of sales, that is, the profit margin on sales. Investors are also interested in future sales (and the profitability of future sales) not just current sales. So a firm will have a higher price-to-sales ratio, the higher the expected growth in sales and the higher the expected future profit margin on sales. See Box 3.4. Note that the price-to-sales ratio should be calculated on an unlevered basis. See Box 3.2 C3.3. Merits: The price-to-ebitda ratio has the same merits as the price-to-ebit ratio. But, by adding back depreciation and amortization to ebit, it rids the calculation of an accounting measurement that can vary over firms and, for a given firm, is sometimes seen as suspect. It thus can make firms more comparable. Problems: 

This multiple suffers from the same problems as the price-to-ebit ratio.



In addition it ignores the fact that depreciation and amortization are real costs. Factories depreciate (lose value) and this is a cost of operations, just as labor costs are. Copyrights and patents expire. And goodwill on a purchase of another firm is a cost of the purchase that has to be amortized against the benefits (income) from the purchase, just as depreciation amortizes the cost of physical assets acquired. The accounting measures of these economic

p. 22 Solutions Manual to accompany Financial Statement Analysis and Security Valuation

costs may be doubtful, but costs they are. Price-to-ebitda for a firm that is “capital intensive” (with a lot of plant and depreciation on plant) is different from that of a “labor intensive” firm where labor costs are substituted for plant depreciation costs. So adding back depreciation and amortization may reduce comparability. During the telecom bubble, analysts priced firms based on ebitda. The telecoms over-invested in networks, producing excess capacity. The cost of this excess capacity does not affect ebitda, so is not counted.

C3.5. P/S 

P E   12  0.06  0.72 E S

C3.7. Traders refer to firms with high P/E and/or high P/B ratios as growth stocks, for they see these firms as yielding a lot of earnings growth. They see prices increasing in the future as the growth materializes. The name, value stocks is reserved for firms with low multiples, for low multiples are seen as indicating that price is low relative to value. A glamour stock is one that is very popular due to high sales and earnings growth (and usually trades at high P/S and P/E ratios). A contrarian stock is once that is said to be out of favor and trades at a low multiple.

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C3.9. Yes. The value of a bond depends on the coupon rate because the value of the bond is the present value of the cash flows (including coupon payments) that the bond pays. But the yield is the rate at which the cash flows are discounted and this depends on the riskiness of the bond, not the coupon rate. Consider a zero coupon bond – it has no coupon payment, but a yield that depends on the risk of not receiving payment of principal. C3.11. No. Dividends reduce the price of a firm (and the per-share price). But shareholder wealth is not changed (at least before the taxes they might have to pay on the dividends) because they have the dividend in hand to compensate them for the drop in the share price. In a stock repurchase, total equity value drops by the amount of the share repurchase, as with the dividend. Shareholders who tender shares in the repurchase are just as well off (as with a dividend) because they get the cash value of their shares. The wealth of shareholders who did not participate in the repurchase is also not affected: share repurchases at market price do not affect the per-share price. So share repurchases do not create value for any shareholders. Subsequent eps are higher with a stock repurchase than with a dividend (as explained in the answer to question C3.10). Shareholders who tendered their shares in the repurchase earn from reinvesting the cash received, as they would had they received a dividend. Shareholders who did not tender have lower earnings (because assets are taken out of the firm) but higher earnings per share to compensate them from not getting the dividend to reinvest.


Exercises Drill Exercises E3.1. Calculating a Price from Comparables P/E for the comparable firm = 100/5 = 20 P/B for the comparable firm = 100/50 = 2 Price for target, from earnings = $2.50 × 20 = $50 per share Price for target, form book value = $30 × 2 = $60 per share Average of the two prices = $55 per share

E3.3 Unlevered (Enterprise) Multiples Market price of equity = 80 × $7 = $560 million Market value of debt 140 (assumes book value – market value) Market value of enterprise $700 million Book value of shareholders’ equity = $250 - 140 = $110million a. P/B = 560/110 = 5.09 b. Unlevered P/S = 700/560 = 1.25 c. Enterprise P/B = 700/250 = 2.8 E3.5. Valuing Bonds For this question, first calculate discount factors for each of five years ahead. You can also get them from present value tables where the discount factor is given as 1/1.05t. At a 5% required return, the discount factors are: Year Ahead (t) 1 2 3 4 5

Discount factor (1.05t) 1.05 1.1025 1.1576 1.2155 1.2763

a. The only cash flow is the $1,000 at maturity Present value (PV) of $1,000 five years hence = $1,000/1.2763 = $783.51

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b. This is easy. If the coupon rate is the required rate of return, the bond is worth its face value, $1,000. You can show this by working the problem as in part b, but with an annual coupon of $50.

c. The yearly cash flows and their present value are: Year Ahead (t) 1 2 3 4 5

Discount factor (1.05t) 1.05 1.1025 1.1576 1.2155 1.2763

Cash Flow 40 40 40 40 1, 040

Total Present Value

PV 38.10 36.28 34.55 32.91 814.86 $956.70

(Your answers might differ by a couple of cents if you use discount factors to 5 or 6 decimal places.)

Applications E3.7

The Method of Comparables: Dell, Inc.

First calculate the multiples for the comparable firms from the price and accounting numbers:

Hewlett-Packard Co. Lenovo Group Ltd.

Sales

Earnings

Book Value

$84,229 14,560

$ 7,264 161

$38,526 1,134

Market Value $115,700 6,381

HP: Price/Sales = 1.37 P/E = 15.93 P/B = 3.00 Lenovo: Price/Sales = 0.44 P/E = 39.63 P/B = 5.63


Now apply the multiples to Dell: Dell’s Number

Average Multiples for Comparable Sales Earnings Book value Average of valuations

0.91 27.78 4.32

x x x

61,133 2,947 3,735

Dell’s Valuation = = =

$55,631 million 81,868 16,135 51,211

With 2,060 million shares outstanding, the estimated value per share = $51,211/2,060 = $24.86 Difficulties: - The “comparables” are not exactly like Dell. They have different aspects in operations—HP has a big printer business, for example. One firm may be a dominant firm in an industry, and thus not a comparable for others. - The calculation assumes the market prices for the “comps” are efficient - Not sure how to weight the three valuation based on sales, earnings and book values; the valuations differ considerably, depending on the multiple used E3.9. Measuring Value Added (a) Buying a stock:

Value of a share =

$

2 = 0.12

16.67

Price of a share

19.00

Value lost per share

$

2.33

(b) Value of the investments: Present value of net cash flow of $ $1M per year for five years (at 9%) Initial costs

3.890 million 2.000

Value added

$

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1.890 million

E3.11. Share Issues and Market Prices: Is Value Generated or Lost By Share Issues? This exercise tests understanding of a conceptual issue: do share issues affect shareholder value per share? The understanding is that issuing shares at market price does not affect the wealth of the existing shareholders if the share market is efficient: New shareholders are paying the “fair” price for their share. However, if the shares are issued at less than market price, the old shareholders lose value. (a)

Total value of equity prior to issue

= 158 million × $55

Value of share issue

=

= $ 8.69B

30 million × $55 =

Total value of equity after share issue

1.65B 10.34B

Shares outstanding after share issue = 188 million

Price per share after issue

= $55

Like a share repurchase, a share issue does not affect per share value as long as the shares are issued at the market price. Old shareholders can’t be damaged or gain a benefit from the issue. Of course, if the market believes that the issue indicates how insiders view the value of the firm, the price may change. But this is an informational effect, not a result of the issue. Old shareholders would benefit if the market were inefficient, however. If shares are issued when they are overvalued in the market, the new shareholders pay too much and the old shareholders gain. The idea that share issues don't generate value (if at market prices) is the same idea that dividends don't generate value. Share issues are just dividends in reverse.


(b)

Total value of equity prior to exercise = 188 million × 62 = $11.66B Value of share issue through exercise =

12 million × 30 =

Total value of equity after exercise

0.36B 12.02B

Shares outstanding after exercise

200 million

Price per share

$60.10

The (old) shareholders lost $1.90 per share through the issue: issue of shares at less than market causes “dilution” of shareholder value. E3.13. Betas, the Market Risk Premium, and the Equity Cost of Capital: Oracle Corporation a) The CAPM equity cost of capital is given by Cost of capital = Risk-free rate + (Beta × Market risk premium) = 4.0% + (1.20 × ?) Market Risk

Cost of

Premium

Capital

4.5% 6.0% 7.5% 9.0%

9.4% 11.2% 13.0% 14.8%

b) Market Risk

Beta

Cost of Capital

Premium 4.5% 6.0%

0.9 1.4 0.9 1.4

8.05% 10.30% 9.40% 12.40%

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7.5% 9.0%

c)

0.9 1.4 0.9 1.4

10.75% 14.5% 12.10% 16.60%

Lowest cost of capital:

8.05%

Highest cost of capital:

16.60%

Forecasted price in May 2012 = $2.17 × 20 = $43.40 Forecasted price, cum-dividend (total payoff) = $43.40 + 0.24 = $43.64 Present value at 8.05 % = $43.64 = $40.389 1.0805 Present value at 16.60% discount rate = $43.64 = $37.427 1.1660

Note that the current value is the present value of the total payoff one year hence, that is, the cum-dividend price one year hence. Put is another way, $37.427 in vesting in May 2011 is expected to yield a payoff of $43.64 (including dividends) one year hence if the required return is 16.60%.


CHAPTER FOUR Cash Accounting, Accrual Accounting, and Discounted Cash Flow Valuation Concept Questions C4.1. The first sentence is true: dividends are the payoff to equity investing. The second sentence is true in theory but not in practice. Equity value is the present value of the infinite stream of expected dividends that a going concern generates. But, in practice, one can’t forecast to infinity. Dividends paid over practical, finite forecast horizons are not relevant to value: the dividends firm pay up to the liquidating dividend can be any amount but that amount does not affect its present value. Consider the case of a firm that pays no dividend (in the short run), for example. Apple Inc., is a case in point: Apple pays no dividends (as of 2012). Cisco paid no dividends for many years, nor did Microsoft. Dell pays no dividends. Yet these are companies that have considerable value. This is this dividend conundrum: Value is based on expected dividends, but forecasting dividends is not relevant to value as a practical matter.

C4.3. Not necessarily. A firm can generate higher free cash flow by liquidating its investments. A highly profitable (and highly valuable) firm can have low (or even negative) free cash flows because it is investing heavily to capitalize on its investment opportunities. Again, see the GE and Starbuck examples in Exhibit 4.2.

C4.5. The answer is (b). Matching cash received from sales with cash spent on inventory does not match value received with value given up to earn the cash, because it recognizes the cost of unsold goods against the receipts from goods sold. Accrual accounting accomplishes the matching because only the cost of goods sold is recognized against the revenue from goods sold.

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C4.7. Free cash flow is earnings (before after-tax interest) minus operating accruals minus cash investment in operations: C – I (free cash flow) = Earnings + net interest payments – accruals – cash investment Or, as in equation 4.11 and Box 4.7, Earnings = C – I - net interest payments + accruals + cash investment C4.9. Statement b is much more likely to be true. Indeed, very profitable companies (with significant investment opportunities) are likely to invest a lot and so generate negative free cash flow.

Exercises Drill Exercises E4.1. A Discounted Cash Flow Valuation 2012 Cash flow from operations Cash investment Free cash flow Discount rate (1.10)t PV of cash flows Total PV to 2015 Continuing value* PV of CV a. Enterprise value Net debt b. Value of equity

2013

2014

2015

$1,450 $1,020 $ 430

1,576 1,124 452

1,718 1,200 518

1.10 391

1.21 374

1.331 389

$1,154 8,979 6,746 $7,900 million 759 $7,141 million

518  1.04  8,989 1.10  1.04 E4.3. Valuation with Negative Free Cash Flows * Continuing value =

Calculate free cash flow from the forecasts of cash flow from operations and cash investments. Your will see that free cash flow is negative in all years except 2013:


2013 Cash flow from operations Cash investments Free cash flow

730 673 57

2014

2015

932 1,023 ( 91)

1,234 1,352 ( 118)

2016 1,592 1,745 ( 153)

If you calculate the present value of these free cash flows (with any discount rate), you’ll get a negative price. Prices can’t be negative (with limited liability). The continuing value must be greater than 100% of the price, but we have no way to calculate it. The free cash flows are increasingly negative because, while cash flow from operations are positive and increasing, the firm is investing more.

E4.5. Reconciling Accrual and Cash Flow Numbers a. Accruals = Earnings – Cash flow from operations = $735 - $1,623 = -$888 million (Accruals are negative, as they are often, because depreciation is a big number) b. As there is no net debt (and thus no net interest), the reported cash flow from operations is the correct number Free cash flow = Cash flow from operations – cash investment = $4,219 -$2,612 = $ 1,607 million

Earnings = Cash flow from operations + accruals = $4,219 – 1,389 = $2,830 As the firm added accruals to earnings to get to the cash flow the accruals are negative. c. Cash from revenues = Accrual revenues + beginning accounts receivable – ending accounts receivable = $623 +281 - 312 = $592 million d. Tax expense = Cash paid for taxes – taxes payable at the beginning of the year + taxes payable at the end of the year

33

= $128 – 67 + 23 = $84 million

Applications E4.7. Calculating Cash Flow from Operations and Cash Investment for Coca-Cola Cash flow from operations: Reported cash flow from operations Interest paid $405 Interest received 236 Net interest paid 169 Tax deduction (at 36%) 61 Cash from operations

$7,150

108 $7,258 million

Cash investment: Reported cash investment Sale of investments $ 448 Purchase of investments (99) Cash investment in operations

$6,719 349 $7,068

Coke’s free cash flow was $7,258 – 7,068 = $190. E4.9. Cash Flow and Earnings: Kimberly-Clark Corporation Part a. Adjust cash flow from operations for after-tax net interest payments and cash investment for net investments in interest-bearing assets: Cash flow from operations reported Interest paid Interest income Net interest Tax on net interest (at 35.6%) Cash flow from operations Cash flow from investing reported Net investment in debt securities (38) + 11.5 Net investment in time deposits

$2,969.6 $175.3 (17.9) 157.4 56.0

101.4 $3,071.0 $(495.4) ( 26.5) 22.9

(499.0)


Free cash flow

$2,572.0

Note: As cash interest receipts are not reported (as is usual), use interest income from the income statement. Part b. Accruals = Net income – Cash flow from operations = $1,800.2 – 2,969.6 = $(1,169.4) E4.10. A Discounted Cash Flow Valuation: General Mills, Inc.

a. The exercise involves calculating free cash flows, discounting them to present value, then adding the present value of a continuing value. For part (a) of the question, the continuing value has no growth: 2005 Cash flow from operations Cash investment in operations Free cash flow (FCF) Discount rate Present value of FCF Total of PV to 2009 5,419 Continuing value (CV) PV of CV 12,885 Enterprise value 18,304 Net debt 6,192 Equity value 12,112

2006 2,014 300 1,714 1.09 1,572

2007 2,057 380 1,677 1.1881 1,411

2008 2009 2,095 2,107 442 470 1,653 1,637 1.2950 1.4116 1,276 1,160 18,189

Value per share on 369 million shares = $32.82

1,637  18,189 0.09 18,189 PV of CV =  12,885 1.4116 CV (no growth) =

b. With growth of 3% after 2009, the continuing value is:

CV 

1,637  1.03  $28,102 1.09  1.03

The present value of the continuing value is $28,102/1.4116 = $19,908. 35

Do the valuation is as follows:

Total of PV to 2009 Continuing value (CV) PV of CV Enterprise value Net debt Equity value

5,419 28,102 19,908 25,327 6,192 19,135

Value per share on 369 million shares = $51.86. E4.11. Free Cash Flow for General Motors Appropriate free cash flow calculation:

Cash flow from operations reported Net interest $4,059 Tax at 36% 1,461

Cash investment reported Net investment in debt securities Free cash flow

$(179) (1,618)

2005 $3,676 2,589 $6,274

(1,797) $4,477

2004 $12,108 $3,010 1,084

(24,209) ( 592)

1,926 $14,034

(24,801) $(10,767)

Mistakes by analyst: 1.

Includes net sales of marketable (debt) securities as cash investment in operations rather than sales of these securities to satisfy a cash shortfall. In both years, there is more sales (liquidations) of these securities than purchases, reducing reported cash investment.

2.

Treats the liquidation of investments in companies (of $1,367 million in 2005) as good news because it increases free cash flow. Selling off investments increases current cash flow but reduces future free cash flows.

3.

Treats increased sales of finance receivables (of $27,802 million in 2005) as increasing free cash flow (and thus as good news). Sales of finance receivables merely speed the receipt of cash. Booking the receivables from customers is what adds value.

4.

Treats the decrease in bookings of finance receivables (from a $31,731 million increase in 2004 to a $15,843 million increase in 2005) as good news.


E4.12. Cash Flows for Wal-Mart Stores a. Wal-Mart is an expanding company with opportunities to invest in new stores throughout the world. While it generates considerable cash flow from operations, cash investments routinely exceed cash from operations. So free cash flow is negative. This is a firm like General Electric in Exhibit 4.2. DCF analysis will not work for this firm. b. The difference between earnings and cash from operations is due net interest (after-tax) and accruals. The difference between earnings and free cash flows is due to net interest (after tax), accruals and investments in operations. c. DCF will not work. Negative free cash flows yield negative values.

E4.14. An Examination of Revenues: Microsoft Corp. Cash revenue = Revenue reported – Change in Accounts Receivable + Change in Unearned Revenue = $62.484 – 1.822 + 0.546 = $61,208 billion

Minicase M4.1 Discounted Cash Flow Valuation: Coca Cola Company Price: $62 Trailing P/E: 23.9 P/B: 6.6 P/Sales: 5.0 Annual sales: $28.9 billion Market cap: $143.7 billion

37

A. Calculating free cash flow for 2008-2010 As GAAP confuses operating and financing cash flows, the cash flow statement numbers must be adjusted. Equations 4.9 and 4.10 show how the adjustment are made and Box 4.5 demonstrates with Nike, Inc. Here are the adjustments for Coke: 2010 Reported cash flow from ops Interest payments Interest receipts Net interest payments Taxes (35.6%) Cash flow from operations

2009

9,532 733 317 416 148

268 9,800

Reported cash investment 4,405 Purchase of S/T investments (4,579) Sale of S/T investments 4,032

3,858

Free cash flow

5,942

2008

8,186 355 249 106 38

4,149 (2,130) -

68 8,254

7,571 438 333 105 37

68 7,639

2,363 2,019 -

2,363

6,235

5,276

Note that interest receipts are usually not reported, so interest income (that may include some accrued interest) is taken as an approximation. B. Valuation using DCF Following the template in Exhibit 4.1, the valuation proceeds as follows:

2007 Fee cash flow Discount rate (1.09t) PV of FCF Total PV of FCF to 2010 Continuing value (CV) 5,942  1.04  123,594 1.09  1.04 PV of CV =

123,594 1.295

2008 5,276 1.09 4,840

2009

2010

6,235 1.1881 5,248

5,942 1.2950 4,588

14,676 123,594

95,439


Enterprise value Net debt Value of equity

110,115 12,235 (23,417 – 11,182) 97,880

Value per share on 2,318 shares outstanding: $42.23 The continuing value here is based on FCF growing at the GDP growth rate of 4%. As the market price is $62, it is clear that the market sees higher growth rate if it agrees with the FCF forecasts. One might expect a higher growth rate for Coke than the average GDP rate, given that Coke has competitive advantage due to its brand positioning. Setting the growth rate at 5% (as in Exhibit 4.1), yields a continuing value of $155,978 million and an equity value of $122,887 million or $53.01 per share. It is clear that, without some more analysis as to what the growth rate should be, we are a bit at sea here (and the long-term growth rate has a big effect on the valuation). The only information we have is the FCF growth from 2009-2010 and that is 18.18% in 2009 but -4.70% in 2010. Not much help. But therein lies the problem: FCF growth is not a good measure to base a continuing value on. Indeed, FCF in 2010 is not a good base on which to apply a growth rate. The reason is that investment (that is made to yield growth) reduces FCF and thus induces negative growth. For Coke, we see increasing cash flow from operations over the years, 2008-2010, but we see FCF in 2010 has declined from 2009. The reason is, of course, the increased investment in 2010 in acquisitions and PPE. Investment makes free cash flow look bad. All we could say here is that we should have a higher growth rate on the low 2010 base, but what that growth rate should be is largely speculation…..and we would be left with a very speculative valuation.

Can we value Coke in 2004? The problem is more severe in 2004:

________________________________________________________________________ 2004 2005 2006 2007 Cash flow from operations Cash investments Free cash flow

5,929 618 5,311

6,421 1,496 4,925

5,969 2,258 3,711

7,258 7,068 190

Here the free cash flows are declining over the four years. If cash flows from operations and cash investments were declining at about the same rate, we might conclude that the firm indeed was in a state of decline: declining cash flows from the business lead to declining investments. However, cash flows from operations are increasing and cash investment is increasing at a faster rate: Coke is investing heavily. While free cash flow is declining 39

over these years, one would thus expect it to increase in future years as cash from the rising investment here comes in. These cash flow are not a good indication of future free cash flows (and nor is the $190 million of free cash flow in 2007 a good base to calculate a continuing value.) If you put yourself in the position of valuing Coke in early 2004 on the basis of these cash flows, you would be in a stew, particularly in calculating a continuing value at the end of 2007 on the $190 million base. This is another example of why free cash flow does not work, in principle: Investment (which is made to generate cash flows actually decreases free cash flow. The cases of General Electric and Starbucks in Exhibit 4.2 are extremes where FCF is actually negative due to investment. Discussion The chief discussion point of the case is the concept behind free cash flows. See that section in the chapter. Free cash flow is a liquidation concept, so that a profitable firm, like Starbucks in Exhibit 4.2, that invests heavily to take advantage of its profit opportunities, has negative free cash flow. But a firm that liquidates its investments (possibly destroying value) increases free cash flow. The measure is perverse. It does not capture value added. Home Depot has negative free cash flow for many years, as did Wal-Mart, and free cash flows turned positive only as these firms slowed their investment. At this point, introduce accrual accounting and show how it deals with investment (as in the text) and, in addition, attempts to correct the mismatching of value added and value surrendered that is the problem with free cash flow. That will help set up the accrual accounting valuation of the next two chapters. Financial statements for presenting the case are below.


41

CHAPTER FIVE Accrual Accounting and Valuation: Pricing Book Values Concept Questions C5.2. To trade at book value, as Jetform does (approximately), we must expect ROCE in the future to be equal to the cost of capital, 10%. Thus we conclude that the market expects an ROCE of 10% in the future. The current ROCE is not really relevant here, but it is somewhat confirming: current ROCE is an indicator of future ROCE. C5.4. No. If the firm is expected to earn an ROCE in excess of the required return, it should sell at a premium over book value. Given the forecast, the firm is a BUY if it trades below book value. C5.6. Firms create residual earnings through ROCE and growth in net assets that earn at the ROCE. The ROCE for GE are approximately level over the forecast years, but the book values are increasing. With constant ROCE and growing book values, residual earnings increase.

C5.8. If the analyst does not forecast all sources of earnings (that is, comprehensive earnings) then she will ignore some part of the payoff to shareholders, and will lose some value in her calculation of a value from the forecast.


Exercises

Drill Exercises E5.1. Forecasting Return on Common Equity and Residual Earnings Set up the pro forma as follows: 2012 Eps Dps Bps 20.00 ROCE RE (10% charge)

2013

2014

2015

3.00 0.25 22.75 15.00% 1.00

3.60 0.25 26.10 15.83% 1.325

4.10 0.30 29.90 15.71% 1.49

a. The answer to the question is in the last two lines of the pro forma b. As forecasted residual earnings are positive, the shares of this firm are worth a premium over book value.

E5.3. A Residual Earnings Valuation This question asks you to convert a pro forma to a valuation using residual earnings methods. First complete the pro forma by forecasting book values from earnings and dividends. Then calculate residual earnings from the completed pro forma and value the firm.

2013E

2014E

2015E

2016E

Earnings Dividends Book value

388.0 115.0 4,583.0

570.0 160.0 4,993.0

599.0 349.0 5,243.0

629.0 367.0 5,505.0

ROCE Residual earnings (10%)

9.0% -43.0

12.4% 111.7

12.0% 99.7

12.0% 104.7

43

2017E 660.4 385.4 5,780.0 12.0% 109.9

Growth in RE Growth in Book value Discount factor 1.110 PV of RE -39.1

8.9% 1.210 92.3

-10.7% 5.0% 1.331 74.9

5.0% 5.0% 1.464

5.0% 5.0% 1.611

a. Forecasted book values, ROCE, and residual earnings are given in the completed pro forma above. Book value each year is the prior book value plus earnings and minus dividends for the year. So, for 2011 for example, Book value = 4583 +570 –160 = 4,993. The starting book value (in 2012) is 4,310. Residual earnings for each year is earnings charged with the required return in book value. So, for 2014 for example, RE is 570 – (0.10 × 4,583) = 111.7. b. Forecasted growth rates in book value and residual earnings are given above. c. The growth rate in residual earnings is 5% after 2014. Assuming this growth rate will continue into the future, the valuation is a Case 3 valuation with the continuing value calculated at the end of 2014. That continuing value is the RE for 2015 of $99.7 growing at 5% per year. Book value, 2006 Total present value of RE to 2014 (-39.1 + 92.3) 99.7 Continuing value (CV), 2012:  1,994.0 1.10  1.05 Present value of CV: 1,994/1.210 Value of the equity, 2009 Per share value (on 1,380 million shares)

4,310.0 53.20

1,647.93 6,011.3 4.36

d. The premium is 6,011.3 – 4,310 = 1,701.3, or 1.23 on a per-share basis. The P/B ratio is 6,011.3/4,310 = 1.39.


E5.5. Residual Earnings Valuation and Return on Common Equity (a)

Set the current year as Year 0. Earnings, Year 1 = 15.60 × 0.15 = 2.34 Residual earnings, Year 1 = 2.34 – (0.10 × 15.60) = 0.78 This RE is a perpetuity, so V0  B 0 

RE 0 0.10

 15.60 

0.78  23.40 0.10

P B  23.40 15.60  1.5 (a) No effect: future payout does not affect current price (unless you have a tax story) and future dividends don’t affect current book value: P/B is still 1.5. But the issue is a little subtle. The idea that dividend payout does not matter is premised on the assumption that dividends do not affect investment activity—that is the assumption behind the famous Miller & Modigliani dividend irrelevance notion. If the retained earnings were invested at the same ROE of 15% (and thus affecting investments), then the value and P/B will change. For the value to stay the same, it has to be that management (who make the dividend decision) concludes that retained earnings cannot be invested at the same ROE of 15%. If they did not, they should not be paying a dividend and destroying value! (Of course, they could pay a dividend and borrow to replace the funds for investment).

45

E5.7. Using Accounting-Based Techniques to Measure Value Added for a Going Concern (a) Time line:

0

1

2

3

4

5

6

7

150

150 30 270

150 60 360

150 90 420

150 120 450

150 150 450

150 150 450

150 150 450

52.5 30.0 22.5

100.5 60.0 40.5

144.0 90.0 54.0

183.0 120.0 63.0

217.5 150.0 67.5

217.5 150.0 67.5

217.5 150.0 67.5

RE (0.12)

4.5

8.1

10.8

12.6

13.5

13.5

13.5

PV of RE

4.0

6.5

7.7

8.0

Investment Depreciation

1

Book value2 Revenue Depreciation Earnings (15%)

Total of PV of RE

26.2

Continuing value3 PV of CV

112.5 71.5

Value Lost Value added

247.7 150 97.7

1. Depreciation is $30 million per year for each project in place 2. Book value (t) = Book value (t-1) + Investment (t) – Depreciation (t) 3. CV =

13.5 = 112.5 0.12

The value of the firm is $247.7 million. The continuing value is based on a forecast of residual earning of 13.5 in year 5 continuing perpetually with no growth. This is a Case 2 valuation. (b)

The value added is $97.7 million


(c) The value added is greater than 15% of the initial investment because there is growth in investment: value is driven by the rate of return of 15% (relative to a cost of capital of 12%) but also by growth.

Applications E5.9. Residual Earnings Valuation: Black Hills Corp The pro forma for the exercise is as follows:

Eps Dps Bps

1999

Forecast Year ____________________________________ 2000 2001 2002 2003 2004

9.96

2.39 1.06 11.29

ROCE RE (11% charge) Discount rate (1.11)t Present value of RE Total present value of RE to 2004 3.78 Continuing value (CV) Present value of CV 0.00 Value per share 13.74

24.0% 1.294 1.110 1.166

3.45 1.12 13.62

2.28 1.16 14.74

30.6% 16.7% 2.208 0.782 1.232 1.368 1.792 0.572

2.00 1.22 15.52 13.6% 0.379 1.518 0.250

1.71 1.24 15.99 11.0% 0.003 1.685 0.002 0.0

a. ROCE and residual earnings are in the pro forma b. If ROCE is to continue at 11% after 2004, then residual earnings are expected to be zero. The continuing value is zero. The value is $13.74 per share – a Case 1 valuation. c. As the CV = 0, the target price is equal to forecasted bps of $15.99 at 2004.

47

E5.10. Valuing Dell, Inc. a. The pro forma for 2009 and 2010 and the value it implies is as follows: 2008 EPS DPS BPS RE (10%) Discount rate PV of RE Total PV to 2010

2009 1.47 0.00 3.283 1.289 1.10 1.172

1.813

2010 1.77 0.00 5.053 1.442 1.21 1.192

2.364

1.442  1.04 1.10  1.04 PV of continuing value

20.66

Value per share

24.84

Continuing value

24.99

Note: BPS at the end of fiscal-year 2008 = $3,735/2,060 shares = $1.813.

E5.11. Valuing General Electric Co. a. Here is the pro forma using a required return of 10%. 2004 EPS DPS (dividend payout 50%) BPS 10.47 RE (10%)

2005 1.71 0.86 11.32 0.663

2006 1.96 0.98 12.30 0.828

The value is calculated as follows, with a 4% growth rate in the continuing value:

$28.38  $10.47 

0.663 1 0.828   1.10 1.10 1.10  1.04

= $23.62


E5.13. Converting Analysts’ Forecasts to a Valuation: Nike, Inc. Here is a layout of the solution similar to Table 5.2:

Nike appears to be reasonably priced at $60 per share. If you accept the analysts’ forecasts up to 2012 (and you may well be skeptical). The calculation (with a value of $62.56) suggest that the market is forecasting a 4% long-term growth rate.

E5.15. Impairment of Goodwill (a) As the asset is at fair value (the acquisition price) on the balance sheet, it is expected to earn at the required return on book value: Residual earnings is projected to be zero. (Fair value in an acquisition always prices the acquisition to earn at the required rate of return.) (b) The book value must be marked down to fair market value under FASB Statement No. 142. The book value at the end of 2011 before the write down, is 301 + 79 = 380 (the depreciated amount of the tangible assets plus the good will).

49

Forecasted earnings for 2012 on this book value (at the forecasted ROCE of 9%) is 380 × 0.09 = 34.2 For a 10% required return, the book value that yields residual earnings in 2012 equal to zero = 34.2 × 10 = 342: RE2012 = 34.2 – (0.10 × 342) = 0 A book value of 342 is thus “fair value.” Accordingly, the amount of impairment = 380 – 342 = 38.

Minicases M5.3. Kimberly-Clark: Buy Its Paper? Price Book value (2007) Shares outstanding Bps

63.20 $5,224 420.9 million $5,224 / 420.9 = $12.41

Parts A – D and F of the case can be addressed with material from this chapter. Part E introduces the reverse engineering of Chapter 7 which you may wish to delay until then, or use it to set up the ideas in that chapter.

The Pro Forma 2007 4.13

Eps Dps Bps RE (9%) RE (8%) RE (10%)

12.41

A. Forward P/E

P/B

2008 4.54 2.32 14.63 3.423 3.547 3.299

2009 4.96 2.53 17.06 3.643 3.790 3.497

= $63.20 / $4.54 = 13.92 = $63.20 / $12.41 =5.09


B.

C. Book value (2009) Continuing value Price (2009)

= 17.06 = 75.77 (from part B) 92.83

(The continuing value is the last term in Part B before discounting) D. For a beta of 0.6, the required return = 5% + (0.6 x 5%) = 8% Repeat exercise in Part B: V (with required return of 8%) = $103.42 V (with required return of 10%) = $68.39

E.

RE (2010)

= RE (2009) x 1.02 =3.643 x 1.02 = 3.716

EPS (2010)

= BV (2009) x .09 + RE2010 =(17.06 X 0.09) + 3.716 = 5.251

EPS growth rate, 2010 = Compare with 9.93% in 2008 and 8.95% in 2009. Either analysts’ forecasts for 2008 and 2009 are too high or the market sees lower growth after 2009. F. Three points point to underpricing:

1.

As the EPS growth forecast for 2010 by the market price is lower than the growth rate forecasted by analysts for 2008 and 2009, the market price does look low.

2.

Our valuation also indicates that the market price is below calculated value even when we set a “high” required return of 10%. These valuations assume a standard (average) 4% growth rate (the GDP growth rate).

3.

With a 9% required return, the market is forecasting a 2% growth rate which is low relative to the GDP growth rate. 51

Where does our uncertainty remain? (i)

Analysts’ forecasts may be biased.

(ii)

We are unsure about the required return, although we have checked this uncertainty by using different rates from 8% to 10%.

(iii)

Growth: is 4%, a correct benchmark against which to compare the market’s growth rate of 2%?

CHAPTER SIX

Accrual Accounting and Valuation: Pricing Earnings Concept Questions C6.2. The historical 8.5% growth rate that is often quoted is the ex-dividend growth rate. It ignores the fact that earnings were also earned by investors from reinvesting dividends (in the S&P 500 stocks, for example) that were typically 40% of earnings. The cum-dividend rate is about 13%. See Box 6.1.

C6.4. The trailing P/E is normal: 1.12/0.12 = 9.33. The forward P/E is also normal: 1/0.12 = 8.33. (The forecasted growth rate must be the cum-dividend growth rate.)

C6.6. Cum-dividend earnings growth incorporates earnings that are earned from the reinvestment of dividends, and investors value those earnings. Ex-dividend growth rates are affected by dividends: dividends reduce assets which then earn lower earnings. As cum-dividend growth rates reflect the earnings from dividends, they are not affected by dividends. Cumdividend growth rates are effectively the rates that firms would have if they did not pay dividends.


C6.8. Incorrect. As the normal (forward) P/E ratio is the inverse of the required return and the required return for a bond is (usually) lower than that for a stock, the normal P/E ratio for a bond is greater than that for a stock. But P/E also values abnormal earnings growth. A bond cannot deliver abnormal earnings growth, so the P/E ratio for a growth stock might well be greater than that for a bond. C6.10. A PEG ratio is the ratio of the P/E to one-year-ahead expected earnings growth in percentage terms. As the P/E anticipates earnings growth, the PEG ratio should be 1.0 if the market is anticipating growth appropriately. However, more than one year of growth is involved in assessing P/E ratios (and there are other clumsy aspects to it—see text), so the measure should only be used as a first-pass check on the P/E ratio.

C6.12. Earnings-to-price ratios -- the inverse of price/earnings ratios -- are driven by three things: (1)

The required equity return

(2)

Expected growth

(3)

Market inefficiency in pricing the required return and expected growth.

The argument assumes that factors (2) and (3) do not explain the change in the earningsto-price ratio. Were growth expectations higher in the 1990s than in the 1970s? Were S&P 500 stocks overpriced?

53

C6.14. Yes; eps growth can be increased with investment, but the investment may earn only the required return, and thus not add value. A firm can also increase its expected earnings growth through accounting methods, but not add value.

Exercises Drill Exercises E6.1 Forecasting Earnings Growth and Abnormal Earnings Growth The calculations are as follows:

Dps Eps Dps reinvested at 10% Cum-div earnings Normal earnings AEG

2011

2012

2013

0.25 3.00

0.25 3.60 0.025 3.625 3.300 0.325

0.30 4.10 (1) 0.025 4.125 (2) 3.960 0.165

20.0% 20.83%

13.89% 14.58%

(a) Ex-div growth rate (from line 1) Cum-div growth rate (from line 2) - 3.625/3.00 for 2010 - 4.125/3.60 for 2011

(b) AEG is in pro forma above (c) Normal forward P/E = 1/0.10 = 10. (d) As AEG is forecasted to be greater than zero, then one would expect the forward P/E to be greater than 10. Equivalently, as the cum-dividend earnings growth rate is expected to be greater than the required return of 10%, the P/E should be greater than the normal P/E

E6.3. Valuation from Forecasting Abnormal Earnings Growth This exercise complements Exercise 5.3 in Chapter 5, using the same forecasts. The question asks you to convert a pro forma to a valuation using abnormal earnings growth methods. First


complete the pro forma by forecasting cum-dividend earnings and normal earnings. Then calculate abnormal earnings growth and value the firm.

2013E

2014E

2015E

2016

2017

Earnings 388.0 Dividends 115.0 Reinvested dividends Cum-div earnings Normal earnings Abnormal earn growth

570.0 160.0 11.5 581.5 426.8 154.7

599.0 349.0 16.0 615.0 627.0 -12.0

629.0 367.0 34.9 663.9 658.9 5.0

660.45 385.40 36.70 697.15 691.90 5.25

Growth rates: Earnings growth Cum-div earn growth (AEG) Growth in AEG

46.91% 49.87%

5.09% 7.89%

5.00% 10.83%

Discount rate PV of AEG

1.100 140.64

1.210 -9.92

5.00% 10.83% 5.0%

Note that the AEG for 2014 and 2015 are discounted back to the end of 2013. a. Forecasted abnormal earnings growth (AEG) is given in the pro forma above. AEG is the difference between cum-dividend earnings and normal earnings. So, for 2014, AEG = 581.5 – 426.8 = 154.7. Cum-dividend earnings is earnings plus prior year’s dividend reinvested at the required rate of return. So, for 2014, Cum-dividend earnings = 570.0 + (115 × 10%) = 581.5 Normal earnings is prior year’s earnings growing at the required rate. So, for 2014, Normal earnings = 388 × 1.10 = 426.8 Abnormal earnings growth can also be calculated as AEG = (cum-div growth rate – required rate) × prior year’s earnings 55

So, for 2014, AEG = (0.4987 – 0.10) × 388 = 154.7

b. The growth rates are given in the pro forma. c. The growth rate of AEG after 2015 is 5%. Assuming this rate will continue into the future, the valuation runs as follows: Forward earnings, 2013 Total present value of AEG for 2014-2015 (140.64 – 9.92 = 130.72) 5 Continuing value (CV), 2015  = 100.00 1.10  1.05 Present value of CV 

100.0 1.210

388.00 130.72

82.64 601.36

Capitalization rate Value of the equity 

0.10

601.36 0.10

6,013.6

Value per share on 1,380 million shares

4.36

This is a Case 2 valuation. If you worked exercise E5.3 using residual earnings methods, compare you value calculation with the one here. d. The forward P/E = 6,013.6/388 =15.5. The normal P/E is 1/0.10 = 10.

E6.4. Abnormal Earnings Growth Valuation and Target Prices

This exercise complements Exercise 5.4 in Chapter 5, using the same forecasts. Develop the pro forma to forecast abnormal earnings growth (AEG) as follows:

2013

2014

2015

2016


2017

Eps Dps Reinvested dividends (12%) Cum-dividend earnings Normal earnings (12%)

3.90 1.00

Abnormal earnings growth

3.70 1.00 0.12 3.82 4.368

3.31 1.00 0.12 3.43 4.144

3.59 1.00 0.12 3.71 3.707

3.90 1.00 0.12 4.02 4.021

-0.548

-0.714

0.003

-0.001

(a) See bottom line of pro forma for answer. (b) As AEG is forecasted to be zero after 2015, the valuation is based on forecasted AEG up to 2015:

E V2012 

1   0.548  0.714 3.90    0.12  1.12 1.2544 

= $23.68 Note that this is the same value as obtained using residual earnings methods in Exercise 5.4. (c) The expected trailing P/E for 2017 must be normal if abnormal earnings growth is expected to continue to be zero after 2017. The normal trailing P/E for a required return of 12% is 1.12/0.12 = 9.33. (d) With a normal trailing P/E of 9.33, V2017  d 2017 = 9.33 Eps 2017

So, V + d = $3.90 x 9.33 = $36.387 As the dividend is expected to be $1.00, the 2017 value (ex-dividend) is $35.387. E6.6. Normal P/E Ratios The normal trailing P/E ratio is

1 required equity return required equity return

57

The normal forward P/E is the trailing P/E – 1.0 The schedule for the trailing P/E is as follows. Subtract 1.0 to get the forward P/E. 8%

13.50

9%

12.11

10%

11.00

11%

10.09

12%

9.33

13%

8.69

14%

8.14

15%

7.67

16%

7.25

Applications E6.8. Calculating Cum-dividend Earnings: General Mills

Earnings on prior year’s reinvested dividends EPS 2006 2007 2008 2009 2010

Cumdividend EPS

DPS

1.53 1.65 1.93 1.96 2.32

0.67 0.72 0.78 0.86 0.96

Cum-div EPS

Normal earnings

0.0536 0.0576 0.0624 0.0688


1.7036 1.9876 2.0224 2.3888

Abnormal Earnings Growth (AEG)

2007 2008 2009 2010

1.7036 1.9876 2.0224 2.3888

1.6524 1.7820 2.0844 2.1168

0.0512 0.2056 -0.0620 0.2720

Normal earnings is prior year’s earnings multiplied by 1.08.

E6.9. Residual Earnings and Abnormal Earnings Growth: IBM The pro forma for the forecast is as follows: 2010 2011 2012 2013 2014 2015 Eps 13.22 14.61 16.22 18.00 19.98 Dps 3.00 3.30 3.66 4.07 4.51 Bps 18.77 28.99 40.30 52.86 66.79 82.26 Reinvested dividends at 10% Cum-dividend earnings Normal earnings

0.300 0.330 0.366 0.407 14.910 16.550 18.366 20.387 14.542 16.071 17.842 19.800

Abnormal earnings growth

0.368 0.479 0.524 0.587

Residual earnings

11.343 11.711 12.190 12.714 13.301

Change in residual earnings

0.368 0.479 0.524 0.587

The answers to parts a, b and c of the question are in the last three lines of the pro forma. E6.12. Valuation of Microsoft Corporation The Pro Forma 2011 2.60 0.40

Eps forecasted Dps Dps reinvested at 9% Cum-dividend earnings Normal earnings: 2.60 × 1.09 AEG

2012 2.77 0.036 2.806 2.834 -0.028

a. Normal forward P/E = 1/0.09 = 11.11 Traded forward P/E = $24.30/$2.60 = 9.346

59

b. Valuation with no growth: V2010 

1  - 0.028 2.60   0.09  1.09 

 $28.60

Intrinsic P/E = $28.60/$2.60 =11.00 c. The value without growth is higher than the market price. So, if you saw some abnormal earnings growth ahead, the stock is definitely underpriced. E6.14. Abnormal Earnings Growth and Accounting Methods The revised pro forma is as follows: 2013E

2014E

2015E

2016E

2017E

Earnings 502.0 Dividends 115.0 Reinvested dividends Cum-div earnings Normal earnings Abnormal earn growth

570.0 160.0 11.5 581.5 552.2 29.3

599.0 349.0 16.0 615.0 627.0 -12.0

629.0 367.0 34.9 663.9 658.9 5.0

660.45 385.40 36.70 697.15 691.90 5.25

Growth rates: Earnings growth Cum-div earn growth (AEG) Growth in AEG

13.55% 15.84%

5.09% 7.89%

5.00% 10.83%

Discount rate PV of AEG

1.100 26.64

1.210 -9.92

5.0% 10.83% 5.0%

(a) Forecasted earnings for 2013 increase by $114 million, to $502 million, because of the lower cost of good sold. (This assumes that the write-down has no effect on forecasted revenues on which forecasts for other years are based: it is often the case the an inventory write-down means that the firm will have more trouble selling its inventory.) (b) The valuation based on the revised pro forma is:

Forward earnings, 2013

502.00


Total present value of AEG for 2014-2015 (26.64 – 9.92 = 16.72) 5 Continuing value (CV), 2015  = 100.00 1.10  1.05 Present value of CV 

100.0 1.210

16.72

82.64 601.36

Capitalization rate Value of the equity 

0.10

601.36 0.10

6,013.6

Value per share on 1,380 million shares

4.36

The valuation is the same at that in Exercise 6.3. (c) As the additional earnings of $114 million in 2013 will incur a tax of $39.9 million, they will be lower by that amount, that is $462.1 million. However, the lower earnings provide a lower base for calculating AEG for 2014, so AEG in 2014 is higher than that in the pro forma in (a). The net effect is to leave the valuation unchanged. (This assumes forecasts for other years are already after tax.)

61

CHAPTER SEVEN Valuation and Active Investing Concept Questions C7.1. The measure of the required return from the CAPM is imprecise. It involves an estimate of a beta and the market risk premium. Betas are estimated with standard errors of about 0.25, so if one estimated a beta of 1.2, say, it could actually be 0.95 or 1.45 with reasonable probability. And the market risk premium is a big guess. See the appendix to Chapter 3. Fundamental investors do not like to put speculation into a valuation, and the CAPM required return is speculative.

C7.3. “Investing is not a game against nature” means that there is not a true intrinsic value to be discovered (as if it existed in nature). So the onus is not on the investor to come up with an intrinsic value. All the investor has to do is assess if the current market price is a reasonable one. That price is set by other investors, based on their analysis, beliefs, fashions, and fads. The question is: Are the forecasts in the market price justified? The game is against other investors who set the price, not against nature.

C7.5. Growth refers to outcomes in the long-term, and the long-term is uncertain. Growth can be competed away so that, unless the firm has protection―has build a moat around its castle―it’s expected growth may not materialize. Buying growth is thus risky.


C7.7. See the answer to C7.6. Exceptional growth is usually maintained only in the short-term. Eventually growth gets competed away, so that all firms look like the average firm in the economy in the long-run.

C7.9. Yes, growth is risky, so a high P/E stock with a lot of growth built into its price is risky. And, yes, P/E ratios are positively correlated with beta. Here are the average betas for 10 portfolios formed from a ranking on E/P (the inverse of P/E) for U.S. stocks from 1963-2006. You can see that betas are higher for low E/P (high P/E) stocks. Note also that the returns from buying stocks are lower for the E/P (high P/E) stocks: Buying growth is risky.

E/P Portfolio 1 (Low) 2 3 4 5 6 7 8 9 10 (High)

E/P (%)

Beta

Annual Returns (%)

-32.5 -3.3 2.0 4.5 6.1 7.4 8.6 10.0 11.8

1.38 1.32 1.28 1.22 1.14 1.06 1.01 0.97 0.96

16.0 10.3 11.4 12.8 14.8 15.2 17.9 18.1 20.8

16.3

0.99

25.3

C7.11. The market sees negative growth in the future.

63

Exercises Drill Exercises E7.1. Reverse Engineering Growth Rates a. The pro forma: 2012 EPS BPS (for a P/B of 2.0) Residual earnings (10%)

2013 2.60

13.00 1.30

Set up the reverse engineering problem:

Price  $26  $13.00 

1.30 1.10 - g

The solution for g = 1.0 (a growth rate of 0%). The market is giving this firm a no-growth valuation. b. The proforma:

2012 EPS BPS Residual earnings (9%)

2013 4.11

27.40 1.644

Set up the reverse engineering problem:

Price  $54  $27.40 

1.644 1.09 - g

The solution for g = 1.0282 (a growth rate of 2.82%). E7.2. Reverse Engineering Expected Returns a. Use the weighted average expected return formula: Book value = $13.00 (for a P/B of 2.0) B/P = 0.5 Forwards ROCE = 2.60/13.00 = 20.0%


With no growth, the weighted average expected return is ER = B/P × ROCE1 = 0.5 × 20% = 10% (You can also see this from the answer in part (a) of E7.1: the market price with a 10% required return is a no-growth valuation, so a price with no growth yields 10%. b. The weighted-average return formula now includes growth: B/P = 27.40/54.00 = 0.507 ROCE1 = 4.11/27.40 = 15.0% ER = [B/P × ROCE1] + [(1 – B/P) × (g-1)] = [0.507 × 15.0%] + [0.493 × 4%] = 9.577% E7.3. Reverse Engineering Earnings Forecasts The pro forma: 2012 EPS DPS BPS Residual earnings (9%)

239.0

2013 33.46 0.0 272.46 11.95

a. Set up the reverse engineering problem: Price = 2.6 × $239.0 = $621.4 million

Price  $621.4  $239.0 

11.95 1.09 - g

The solution for g = 1.0588 (a growth rate of 5.88%).

65

b. Reverse engineer the residual earnings calculation: Earnings2014 = (Book value2013 × 0.09) + RE2014 RE2014 = RE2013 × RE growth rate = $11.95 × 1.0588 = $12.653 Earnings2014 = (Book value2013 × 0.09) + RE2014 = $(272.46 × 0.09) + 12.653 = $37.17

E7.4. Expected Returns for Different Growth Rates Apply the weighted-average expected return formula to elicit the expected return in the market price: ER = [B/P × ROCE1] + [(1 – B/P) × (g-1)] B/P =1/2.2 = 0.455 ROCE1 = 15.0% Thus, ER = [0.455 × 15.0%] + [0.545 × (g-1)] Here is the ER for different growth rates: Growth Rate 3% 4% 6%

ER 8.46% 9.01% 10.10%

Applications E7.6. Reverse Engineering Growth Rates: Dell, Inc. To answer this question, you have to specify your required return: a 10% rate is used here. The pro forma is as follows: 2008 EPS DPS BPS

1.813

2009 1.47 0.00 3.283

2010 1.77 0.00 5.053


RE (10%)

1.289

1.442

The growth rate is calculated by reverse engineering:

P2008  $20.50  1.813 

1.289 1.442 1.442  g   1.10 1.21 1.21(1.10  g )

The solution for g = 1.025 (or a 2.5% growth rate). The solution is the same with the following calculation:

P2008  $20.50  1.813 

1.289 1.442  1.10 1.10  (1.10  g )

E7.7. Building Blocks for a Valuation: General Electric To answer this question, you have to specify your required return: a 10% rate is used here. a. Here is the pro forma using a required return of 10%. 2004 EPS DPS (dividend payout 50%) BPS RE (10%)

2005 1.71 0.86 11.32 0.663

10.47

2006 1.96 0.98 12.30 0.828

The value is calculated as follows, with a 4% growth rate in the continuing value:

$28.38  $10.47 

0.663 1 0.828   1.10 1.10 1.10  1.04

= $23.62

b.

The first building block is the book value

=

$10.47

The second component is the addition to book value if there is no growth, and is calculated as:

$11.12 

0.663 1  0.828  1.10 1.10  0.10 

=

67

8.13

The third (growth) component plugs to the market price

17.40

Market price

36.00

The three components are diagramed as follows:

Book Value

Value from Short-term Forecasts

Value from Growth

c. Reverse engineer the model:

$36.00  $10.47 

0.663 1 0.828   1.10 1.10 1.10  g

The solution is g = 1.0698, or approximately a 7% growth rate. E7.9. The Market’s Forecast of Nike’s Growth Rate The pro forma: 2010

2011

2012


EPS DPS BPS RE (9%)

20.15

4.29 1.16 23.28 2.477

4.78 1.29 26.77 2.685

The dividend for 2012 is forecasted to be at the same payout ratio as in 2011: 0.270 × 4.78 = 1.29. a. The growth rate is calculated by reverse engineering:

P2010  $74  20.15 

2.477 2.685  1.09 1.09  (1.09  g )

The solution for g = 1.0422 (or a 4.22% growth rate). b. Reverse engineer the residual earnings calculation: RE2013 = RE2012 × Growth rate = 2.685 × 1.0422 = 2.798 Earnings2013 = (Book value2012 × 0.09) + RE2013 = $(26.77× 0.09) + 2.798 = $5.207 RE2014= RE2013 × Growth rate = 2.798 × 1.0422 = 2.916 BPS2013 = 26.77 + 5.201 – 1.406 = 30.571

(dividend is at the payout ratio of 27%)

Earnings2014 = (Book value2013 × 0.09) + RE2014 = $(30.571 × 0.09) + 2.916 = $5.667

E7.11. The Expected Return to Buying a Google Share a. Price = $535 Book value = $143.92 B/P = 143.92/535 = 0.269

69

ROCE1 = 33.94/143.92 = 23.58%

The weighted-average return formula:

Similarly, the ER for a growth rate of 5% = 10.00%, and ER for a 6% growth rate = 10.73%. b. This is somewhat difficult. For this question, one has to apply the B/P ratio at the end of 2011and the ROCE for 2012: Book value2011 = 177.86 Price2011 = Price2010 × 1.10 = 535 × 1.10 = 588.50 B/P (2011) = 0.302 ROCE2012 = 39.55/177.86 = 22.24%

(from Exhibit 7.1)

The price at the end of 2011 is the current price growing at the required return of 10% in the exhibit. Note that one can solve the problem only by putting in a required return (that was not necessary in part a), but the estimate (just for one year) will not affect the calculation much. ER = [B/P (2011) × ROCE2012] + [(1 – B/P) × (g-1)] = [0.302 × 22.24%] + [0.698 × 4%] = 9.51% Similarly, the ER for a growth rate of 5% = 10.21%, and ER for a 6% growth rate = 10.91%. E7.13. Sellers Wants to Buy a. The Pro forma: 2006 EPS DPS BPS Residual earnings (10%)

12.67

2007 2.98 0.60 15.05

2008 3.26 0.70 17.61

1.713

1.755

The current book value per share = Book value/Shares outstanding = $26,909/2,124


= $12.67 Reverse engineer Seller’s price: $50  12.67 

1.713 1.755  1.10 1.10 x (1.10 - g)

g  1.0555 (a 5.55 % growth rate)

A.

Getting to EPS growth rates for 2009 and 2010:

2009 1.852 17.61 1.761 3.613

RE growing at 5.55% Prior BPS Prior BPS x 0.10 EPS (1) + (2) EPSgrowth rate

(2)

2.045 4.00 10.71% %

Book value on January 1, 2008 = 1,468 / 2.6 = 564.62 B/P = 564.62/1468 = 1/2.6 = 0.385 Forward ROCE for 2008

= 72.56 / 564.62 = 12.85%

b. The reverse engineering problem:

1,468  564.62 

(1)

10.83% %

DPS (at 2008 payout ratio) 0.776 BPS 20.447 Prior BPS x 0.10 EPS (1) + (3) EPS growth rate E7.15. The Expected Return for the S&P 500

a.

2010 1.955

72.56  (?  564.62) ?  1.04

? = 1.07403, or a 7.403% expected return

The following formula solves for the expected return:

71

(3)

B   B ?    ROCE1   1  ( g  1) P   P  0.385  12.85%  (1  0.385)  4% = 7.41%

c. Required return = 4% + 5% = 9% Do not buy, for the expected return is less than the required return.

d. Although the level of the index is not given, one can still work the problem based on the price-to-book of 5.4. For every $1 of book, the price is 5.4, so the reverse engineering problem can be set up as:

5.4  1 

(0.23  ?)  1 ? 0.04

($1 of book value)

? = 7.52% The weighted average expected return formula solves for the expected return: Expected return 

B0 B ROCE 1  (1  0 )( g  1) P0 P0

= (0.185 × 0.23) + (0.815 × 4%) = 4.255% + 3.26% = 7.52% If the required return is 9%, this expected return indicates that the S&P 500 stocks are overvalued. All the more so when one appreciates that a 23% ROCE used as an input is quite a bit above the historical ROCE of 17-18%. A 23% ROCE means a high residual earnings base to apply a 4% growth rate to. If one entered a 17% ROCE, then the expected return would be lower, at 6.41%. (Correspondingly, the forward ROCE for 2008 in part (a) is lower


than the historical average, and a higher return that the 7.41% there would be expected with a higher forward ROCE.

73

Solutions to Selected End-Of-Chapter Questions Chapters 1 Through 7(1)

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