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Chapter 6 Equity: Concepts and Techniques

1. The book value represents mostly the historical value of the firm. Most assets and liabilities are carried at their historical cost, allowing for possible depreciation. The stock market price reflects the future earning power of the firm. If rapid growth in earnings is expected, the stock price could be well above the book value.

2. General provisions (“hidden reserves”) appear as a liability, although they are in fact equity reserves. These provisions are “hidden” as a liability to allow the firm to use them in the future to smoothen earnings. Accordingly, the true book value is greater than the reported book value by the amount of these reserves. Thus, the practice of allowing corporations to build general provisions leads to an understatement of the reported book value, and an overstatement of the ratio of market price to book value.

3. Some of the reasons why German earnings are understated compared with U.S. earnings are as follows:

German firms take provisions quite generously, and they are deducted from the reported earnings when initially taken.

Reported earnings are tax earnings that are subject to many actions taken to reduce taxation.

Many German firms tend to publish separately the nonconsolidated financial statements of the various companies belonging to the same group.

4. a. Without expensing the options, the firm’s pretax earnings per share are $2,000,000/500,000 $4 per share.

b. The expense due to the options is 20,000 $4 $80,000. The pretax income per share would be ($2,000,000 $80,000)/500,000 $3.84 per share.

c. The expense due to the options based on the different valuation is 20,000 $5.25 $105,000. The pretax income per share would be ($2,000,000 $105,000)/500,000 $3.79 per share.

5. a. Consolidated earnings are as follows:

Company A: 10 million 10% of 30 million 13 million

Company B: 30 million 20% of 10 million 32 million

b. The P/E ratios are as follows: Company A Company B

Nonconsolidated 200/10 20 450/30 15 Consolidated 200/13 15.4 450/32 14.1

Due to nonconsolidation, the earnings are understated. Thus, the P/E ratios are overstated due to nonconsolidation. As seen here, the consolidation of earnings adjusts the P/E ratios downward.

Chapter 6 Equity: Concepts and Techniques 29

6. Under the assumption that the total worldwide revenue of all firms in this industry was $250 billion, the market shares of the top five corporations are the following:

AOL Time Warner: $38 billion/$250 billion 15.2% Walt Disney: 25/250 10.0%

Vivendi Universal: 25/250 10.0%

Viacom: 23/250 9.2%

News Corporation: 13/250 5.2%

a. The three-firm concentration ratio is the combined market share of the largest three firms in the industry 15.2 10 10 35.2%.

The five-firm concentration ratio is the combined market share of the largest five firms in the industry 15.2 10 10 9.2 5.2 49.6%.

b. The three-firm Herfindahl index is the sum of the squared market shares of the largest three firms in the industry 0.1522 0.102 0.102 0.043, or 430% squared. The five-firm Herfindahl index is the sum of the squared market shares of the largest five firms in the industry 0.1522 0.102 0.102 0.0922 0.0522 0.054.

c. The combined market share of the top five firms, as computed in part (a), is 49.6%. Therefore, the combined market share of the 40 other firms is 100 49.6 50.4%. Assuming that each of them has the same share, the share of each is 50.4/40 1.26%. So, the Herfindahl index for the industry, which is the sum of the squared market shares of all the firms in the industry, is 0.1522 0.102 0.102 0.0922 0.0522 0.01262 . . . 0.01262 0.054 40 0.01262 0.0603.

d. The combined market share of the 10 other firms is 100 49.6 50.4%. Assuming that each of them has the same share, the share of each is 50.4/10 5.04%. So, the Herfindahl index for the industry, which is the sum of the squared market shares of all the firms in the industry, is 0.1522 0.102 0.102 0.0922 0.0522 0.05042 . . . 0.05042 0.054 10 0.05042 0.0794.

e. There is greater competition in the scenario in Part (c) than in Part (d). The Herfindahl index in Part (c) is smaller than that in Part (d), reflecting a more competitive industry structure in Part (c). Also, the reciprocal of the Herfindahl index is 16.6 in Part (c) and 12.6 in Part (d). Thus, the market structure in Part (c) is equivalent to having 16.6 firms of the same size, and the market structure in Part (d) is equivalent to having 12.6 firms of the same size. This reflects that the market structure in Part (d) is relatively more oligopolistic, or less competitive, than in Part (c).

7. a. Though News Corporation is based in Australia, it is really a global conglomerate, and a majority of its businesses are outside of Australia. About 77 percent of its revenues are in the United States, 15 percent in Europe, and only 8 percent in Australia and Asia together. Its major competitors include firms headquartered in the United States and Vivendi Universal, a firm headquartered in France. In view of the global characteristics of News Corporation, its valuation should be done primarily relative to the global industry.

b. Due to differences in accounting standards and practices among countries, the analyst would be concerned if he were comparing ratios of News Corporation, computed as per Australian GAAP, with those of Vivendi Universal, computed as per French GAAP. However, both firms trade in the United States as registered ADRs and prepare statements as per U.S. GAAP. Therefore, the analyst could simply compare ratios computed based on these statements.

30 Solnik/McLeavey • Global Investments, Sixth Edition

8. a. ROE NI/Equity. So,

ROE for Walt Disney 1,300/20,975 0.062

ROE for News Corporation 719/16,374 0.044

Clearly, Walt Disney did better than News Corporation in terms of ROE.

b. One version of the DuPont model breaks down ROE into three contributing elements, as follows:

ROE Net profit margin Asset turnover Leverage

where Net profit margin NI/Sales

Asset turnover Sales/Assets

Leverage Assets/Equity

The three contributing elements for both the companies are computed based on the data given in the problem, and are given in the following table:

Walt Disney News Corp.

Net profit margin 0.056 0.050 Asset turnover 0.536 0.403 Leverage 2.082 2.179

The numbers in the table indicate that the main reason Walt Disney did better than News Corporation is that it had a better asset turnover. That is, it utilized its assets more efficiently than did News Corporation. Walt Disney also had a higher net profit margin than did News Corporation. The only contributing element that is higher for News Corporation is leverage, implying that News Corporation levered its operating results using more debt than did Walt Disney.

To analyze why the net profit margin for Walt Disney is a little higher than that for News Corporation, the net profit margin is broken down as follows:

Net profit margin NI/EBT EBT/EBIT EBIT/Sales.

The breakdown of net profit margin is given in the following table:

Walt Disney News Corp.

NI/EBT 0.562 0.593 EBT/EBIT 0.762 0.666 EBIT/Sales 0.130 0.126

The data in the table suggest that the net profit margin for Walt Disney was higher than that for News Corporation because of a higher EBT/EBIT ratio (i.e., a lower debt burden, because a higher value of EBT/EBIT implies a lower debt burden). This is not unexpected, because we saw in the breakdown earlier that Walt Disney had a lower leverage than did News Corporation.

9. In an efficient market, all available information is already incorporated in current stock prices. The fact that economic growth is currently higher in Country A than in Country B implies that current stock prices are already “higher” in A than in B. Only unanticipated news about future growth rates should affect future stock prices. Current growth rates can explain past performance of stock prices, but only differences in future growth rates from their current anticipated levels should guide your


country selection. Hence, you should decide whether your own economic growth forecasts differ from those implicit in current stock prices.

10. The intrinsic value is given by:

1 10

(1 )D E bP

r g r g

where E1 is next year’s earnings €4 per share 1 b is the earnings payout ratio 0.70 r is the required rate of return on the stock 0.12 g is the growth rate of earnings 1.25 2.8% 3.5% or 0.035

so, P0 4 0.70/(0.12 0.035) €32.94 per share

P0/E1 0.70/(0.12 0.035) 8.24

11. a. Intrinsic P/E ratio

0

1

P 1 (ROE )1 .

E ROE

b r

r r b

In this case, b 0, because the company pays out all its earnings. So, P0/E1 1/r 1/0.13 7.69. b. Again, P0/E1 1/r 1/0.13 7.69. c. It is clear from the expression in part (a) that if b 0, the intrinsic P/E value is independent of

ROE. To further explore this, realize that the intrinsic P/E value can also be expressed as P0/E1

(1/r) FF G, where the franchise factor is FF (ROE r)/(ROE r) or 1/r 1/ROE, and the growth factor is G g/(r – g). If b 0, then g 0, and therefore, the growth factor G 0. Thus, regardless of how big the ROE—and consequently the franchise factor FF—is, the franchise value, FF G, is zero, and the intrinsic P/E value is simply 1/r.

d. Again, P0/E1 1/r 1/0.13 7.69. e. In part (d), ROE r 13%. It is clear from the expression in part (a) that if ROE r, the intrinsic

P/E value is independent of the retention ratio, b. To further explore this, let us again look at the expression for intrinsic P/E value discussed in part (c). If ROE r, then the franchise factor FF 0. Thus, regardless of how large the retention ratio—and consequently the growth factor G—is, the franchise value, FF G, is zero, and the intrinsic P/E value is simply 1/r.

12. a. Franchise factor 1/r – 1/ROE 1/0.10 – 1/0.12 1.67.

b. Growth factor g/(r g) (b ROE)/(r – b ROE) (0.70 0.12)/(0.10 – 0.70 0.12) 5.25.

c. Franchise P/E value Franchise factor Growth factor 1.67 5.25 8.77. d. Tangible P/E value 1/r 1/0.10 10. e. Intrinsic P/E value Franchise P/E value Tangible P/E value 8.77 10 18.77. We can

also verify that intrinsic P/E value (1 – b)/(r – g) (1 – 0.70)/(0.10 – 0.70 0.12) 18.75 (the slight difference is due to rounding).

13. The P/E is equal to

0 1

1P / E

(1 )r l I


where I rate of inflation 3% real required rate of return 8% 3% 5%

a. 1: P0/E1 1/ 1/0.05 20. b. 0.4: P0/E1 1/(0.05 0.60 0.03) 1/0.068 14.71.

c. 0: P0/E1 l/( I) 1/0.08 12.50.

We observe that the higher the inflation flow-through rate, the higher the P/E ratio. In other words, the less a firm is able to pass inflation through its earnings, the more it is penalized.

14. For both Company B and Company U, 0.60, or 1 0.40. Also, 0.08 for both.

P0/E1 for Company B 1

(1 )I 1/(0.08 0.40 0.09) 8.62

P0/E1 for Company U 1

(1 )I 1/(0.08 0.40 0.025) 11.11

P/E for Company B, which is subject to a higher inflation rate, is smaller than that for Company U. Thus, if full inflation pass-through cannot be achieved, then the higher the inflation rate, the more negative the influence on the stock price.

15. a. If the company can completely pass inflation through its earnings, P/E 1/ 1/0.07 14.29 in each of the years. Inflation has no effect on the P/E ratio, because the firm can completely pass inflation through its earnings.

b. P/E

11/(0.07 0.50 )

(1 )I

I

Year Inflation (%) P/E

1995 22.0 5.561996 9.1 8.661997 4.3 10.931998 2.5 12.121999 8.4 8.93

c. As mentioned in Part (a), inflation has no effect on the P/E ratio if the firm can completely pass inflation through its earnings. However, if the firm cannot completely pass inflation through its earnings as in Part (b), then the higher the inflation rate (e.g., in the year 1995), the more severe the influence on the stock price.

16. Due to the appreciation of the euro relative to the dollar, the French goods will become more expensive in terms of the dollar. If the French company is able to completely pass through this increase to its U.S.-based customers, its P/E ratio will not suffer. Regardless of the extent of the appreciation of the euro, the company’s P/E ratio will be unaffected if it is able to completely pass the appreciation through to its customers. However, if the company is able to only partially pass the euro appreciation through to its U.S.-based customers, the P/E ratio will go down. The higher the euro appreciation, the more severe will be the decline in the P/E ratio.


17. a. Because the portfolio is equally invested in the two stocks, the factor exposures of the portfolio would be equally weighted averages of the factor exposures of the two stocks. So, the factor exposures of the portfolio would be as follows:

Portfolio

Confidence 0.4 Time horizon 0.7 Inflation 0.3 Business cycle 3.0 Market timing 0.85

b. The stocks have a positive exposure to business cycle and a negative exposure to inflation. Also, you expect strong economic growth and an increase in inflation. Therefore, you should overweigh the stock with a greater exposure to business cycle and a smaller exposure (in absolute terms) to inflation. Stock A satisfies both, and accordingly you should overweigh Stock A.

18. It is clear by looking at the table that in each of the three size categories, the low price-to-book value stock (P/BV) outperforms the high P/BV stock. Thus, there seems to be a value effect, as the value firms seem to outperform the growth firms. That is, the value factor seems to be significant.

To clearly see the size effect, we rearrange the stocks in the two P/BV categories, as follows:

Stock Size P/BV Return (%))

A Huge High 4 C Medium High 9 E Small High 13 B Huge Low 6 D Medium Low 12 F Small Low 15

In both P/BV categories, smaller firms outperform bigger firms. Thus, there seems to be a size effect, and the size factor seems to be significant.

19. We first compute the changes in the two factors and the returns on each stock. The following table has the numbers. Because we are computing the changes, we lose one observation.

Period Change in

Interest Rate Change in Approval

Return on Stock

A B C

2 2.1 5 0.12 0.49 0.453 0.3 1 0.22 0.39 0.394 1.7 –2 0.40 0.42 0.215 1.8 19 0.33 0.33 0.196 0.2 19 0.16 0.30 0.227 2.3 23 1.10 1.14 0.968 0.1 27 0.01 0.14 0.259 2.3 2 0.50 0.48 0.23

10 0.2 20 0.14 0.15 0.24


We now estimate the following factor model for each of the three stocks, using the respective nine observations from the preceding table.

1 1 2 2i i i i iR a b f b f

where Ri is the rate of return on stock i t is a constant f1 and f2 are the two factors common to the three stocks (f1 is the change in interest rate, and f2 is the change in approval rating) 1i and 2i are the risk exposures of stock i to each of the two factors ei is a random term specific to stock i

The results of the estimation are as follows:

Stock A Stock B Stock C

0.05 0.10 0.03

(t-statistic) (0.56) (1.31) (0.36)

0.25*** 0.31*** 0.22***

(t-statistic) (4.32) (6.20) (3.89)

2 0.01 0.01 0.01

(t-statistic) (1.27) (1.18) (1.66)

***Statistically significant at the 99% level.

The values of 1 are highly statistically significant, with a p-value of less than 0.01, for each of the three stocks. In contrast, none of the values of 2 are statistically significant (each of the p-values is greater than 0.10). The magnitudes of 1 are several times bigger than the magnitudes of 2. Clearly, the first factor (change in interest rate) influences stock returns in this country, while the second factor (change in approval) does not.

20. a. SFr4%, 5%, and 1%.f wR RP RP

1 2So ( ) 4% 5% 1%iE R

Accordingly,

( ) 4% 1 5% 1 1% 10%

( ) 4% 1 5% 0 1% 9%

( ) 4% 1.2 5% 0.5 1% 10.5%

( ) 4% 1.4 5% 0.5 1% 10.5%

A

B

C

D

E R

E R

E R

E R


b. Stocks that should be purchased are those with a forecasted return, higher than their theoretical expected return, given the stock’s risk exposures. Because the forecasted returns given in the problem are the returns in Swiss francs, we need to convert them to dollar returns first. We expect the Swiss franc to appreciate relative to the dollar by 2 percent. Therefore, using a linear approximation, the dollar return is the return in Swiss francs 2 percent. The following table summarizes the forecasted returns in francs and in dollars, and the theoretical expected returns in dollars [computed in Part (a)].

Stock A Stock B Stock C Stock A

Forecasted return (in francs) 8% 9% 11% 7% Forecasted return (in dollars) 10% 11% 13% 9% Theoretical expected return (in dollars) 10% 9% 10.5% 10.5%

Looking at this table, we find that the broker forecasts superior returns for Stocks B and C. Therefore, they should be bought. Conversely, Stock D should be sold.

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