PER, Value to Book Ratio & Growth

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Pablo Fernandez Ch27 PER, P to Book and growthIESE Business School, University of Navarra

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Price to Earnings ratio, Value to Book ratio and Growth

Pablo Fernandez, Professor of FinanceIESE Business School, University of Navarra

e-mail: [email protected] [email protected] Camino del Cerro del Aguila 3. 28023 Madrid, Spain

November 11, 2013

The PER is the most commonly used parameter in the stock market. The PER is the result of dividingthe equity market value by the company’s profit after tax.

The PER depends on a number of factors, some of which are out of the company’s control, such as

variations in interest rates, and others are intrinsic to the company, such as its risk, its growth and the return onits investments. The PER increases, ceteris paribus, if interest rates fall, if the company’s risk decreases, and ifthe company’s profit after tax increases. The PER increases with growth if the return on the company’sinvestments is greater than the required return to equity.

The relationship between share prices (their market value for listed companies) and their book value isthe subject of considerable study by financial analysts. We analyze the relationship between the two parametersin several companies and different countries. We also analyze the influence of the PER and on this relationship.

1. Evolution of the PER on the international stock markets2. Growth value and PER due to growth3. Market value and book value on the North American stock market4. Market-to-book ratio on the international stock markets5. Market-to-book ratio and interest rates on the North American stock market6. Relationship between the market-to-book ratio and the PER and the ROE7. Equity book value may be negative: the case of Sealed Air

Appendix 1. Splitting the PER: franchise factor, growth factor, interest factor and risk factor1. PER, franchise factor and Growth Factor2. PER*, franchise factor* and Growth Factor3. PER, Interest Factor and Risk Factor4. Value generation over time in companies with growth5. Influence of growth on the franchise factor and on the Growth Factor6. Influence of the ROE on the franchise factor7. Influence of the required return to equity on the Franchise Factor and on the PER8. Splitting the PER. Proof.

Tables and figures are available in excel format with all calculations in:

http ://web.iese.edu/PabloFernandez/Book_VaCS/valuation%20CaCS.html




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The PER is the most commonly used parameter in the stock market. The PER is the result of dividingthe equity market value by the company’s profit after tax.

PER = Equity market value / profit after tax = Price per share / earnings per share

Example. On 6 October 2000, General Electric had 9.901 billion shares outstanding. The price of oneshare was 59.4375 dollars. The price of all the shares (market capitalization) was therefore 588.52481 billiondollars. The profit after tax in 1999 was 10.396679 billion dollars and the earnings per share was 1.05 dollars.Therefore, General Electric’s PER on 6 October 2000 was 56.607 (59.4375/1.05 = 588.52481/10.396679). Theearnings per share forecast for 2000 was 1.24. Therefore, General Electric’s PER on 6 October 2000 on the basis of the expected earnings per share for 2000 was 47.93 (59.4375/1.24).

1. Evolution of the PER on the international stock marketsFigure 1 shows the evolution of the PER of two leading telecommunications companies in their

respective countries: Telefónica in Spain and British Telecom in the United Kingdom. In the case of Telefónica,it can be seen that the PER peaked in February 1994 and then fell until October 1995, when it started to riseagain. As we shall see in Figure 3, these variations were basically due to variations in the interest rates: wheninterest rates fall, the PER rises; and when interest rates rise, the PER falls.

Figure 1 also shows the “boom” experienced by the telecommunications companies during 1999 - particularly at the end- and the beginning of 2000. In this period, all stocks related with the telecommunicationsworld and the new Internet era were rewarded significantly on the stock market. The impressive rise in thesecompanies’ share price was due to the investors’ expectations which, as can be seen, shifted down to morereasonable levels after February 2000.

Figure 2 shows the evolution of the PER of three of the largest North American companies.Particularly noteworthy is the case of Cisco Systems, whose PER has been far above the rest. Cisco attained amaximum PER of 236.05. One can also see the fall of this company’s share price after February 2000.

Figure 1. Evolution of the PER of Telefónica and British Telecom. Source: Datastream

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PER

Figure 2. Evolution of the PER of GE, Microsoft and Cisco. Source: Datastream

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Figure 3, which shows the evolution of the average PER of the Spanish stock market and the interestrate paid on 10-year public debt, confirms that when interest rates fall significantly, the PER rises, and vice-versa. Figure 4 shows the evolution of the average PER of the Spanish, North American and English stockmarkets. Note that the Spanish stock market’s PER equaled that of the other two stock markets at the end of1993, then fell behind and subsequently surpassed the English stock market at the end of 1996 and equaled the North American stock market in 1997 and 1998.




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Figure 5 shows the ratio between the average PER of the United States stock market and the S&P 500.As PER= price/profit after tax, it is logical that the PER follows approximately the evolution of the S&P 500,which is an index that reflects the prices of the shares included in it. In this case, this ratio’s denominator breaksthis trend at certain times.

Figure 3. Evolution of interest rates and the average PER of the Spanish stock market. Source:Datastream

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Figure 4. Evolution of the average PER of the Spanish, English and United States stock markets. Source:Datastream

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Figure 5. S&P 500. Evolution and average PER. Source:Datastream

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2. Growth value and PER due to growthTo quantify the influence of expected growth (g) on the share price and the PER, we can calculate the

price that the share would have if the company did not grow, that is, if the previous year’s profit after tax wasconstant and the company distributed it entirely as dividends. The share’s price if the company did not grow isthe earnings per share (EPS) divided by the required return to equity:

P no growth= EPS / Ke

We can say that the share price is the price it would have if there was no growth (P no growth) plus thegrowth value1:

1 The value of the growth is also called the present value of the growth opportunities.




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P = P no growth + Growth value

Example. GE’s share price on 6 October 2000 was $59.4375. The earnings per share in 1999 was1.05. If the required return to equity was 11%, the no growth price of GE’s share would be $9.545 (1.05/0.11),and the growth value would be $49.89 (59.4375 - 9.545). Consequently, 16% (9.545/59.4375) of the value ofGE’s share was due to the profit after tax already attained by the company (P no growth) and 84%(49.89/59.4375) was due to the expected growth (growth value). By way of reference (see Appendix 2), on

average, 47.5% of the value of the companies included in the Euro Stoxx 50 in May 2001 was due to the profitafter tax already attained by the companies (P no growth) and 52,5% corresponded to the expected growth(growth value).

We can perform the same breakdown with the PER and consider it as the sum of the PER that thecompany would have if the incremental PER due to growth did not grow any further.

PER = PERno growth+ PERgrowth

As the PER is the price per share divided by the earnings per share, this gives:

PERno growth= 1/Ke PERgrowth = Growth value / EPS

Figure 6 shows that in the nineties the PER due to growth was almost 70% of the PER in early 1992and at the end of 1999.

Figure 6. US Stock Market. PER due to growth as a percentage of PER, and PER.Sources. PER USA MSDW. PER due to growth: author’s data

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Market Value and Book Value The relationship between share prices (their market value for listed companies) and their book value is

the subject of considerable study by financial analysts. We will analyze the relationship between the two parameters in several companies and different countries. We will also analyze the influence of the PER and onthis relationship.

3. Market value and book value on the North American stock market Figure 7 shows the evolution of the market-to-book ratio of the US stock market and the S&P 500 in

recent years. Obviously, both lines move in parallel: when stock prices rise, the shares’ market-to-book ratioalso rises and vice-versa. However, it is important to remember that the equity book value increases when thereare capital increases, when companies retain earnings and also when assets appreciate.

Figure 8 shows the evolution of the market-to-book ratio (E/Ebv) of Coca Cola and Pepsico. It isinteresting to see that although Coca Cola’s ratio has been markedly higher during the period 1991-2001, thetwo companies’ ratios have been converging since mid-1998 and had almost met by 2001.

Figure 9 shows the evolution of the ratio of three of the world’s largest companies: General Electric,Microsoft and Cisco. Note the enormous market-to-book ratio of Cisco in the second half of 1999 and 2000,coinciding with the Internet Speculative Bubble. In the first months of 2000, the market-to-book ratio (E/Ebv)for Cisco was higher than 40.




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Figure 7. Evolution of the average market-to-book ratio of the US stock market and evolution of the S&P500. Sources: Morgan Stanley and Datastream

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Figure 8. Evolution of the market-to-book ratio of Coca Cola and Pepsico. Source: Datastream

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Figure 9. Market-to-book ratio of General Electric, Microsoft and Cisco. Source: Datastream

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Figure 10. Evolution of the average market-to-book ratio of the US, UK and Spanish stock markets.Source: Datastream

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4. Market-to-book ratio on the international stock markets Figure 10 shows the evolution of the market-to-book ratio (E/Ebv) in the United States and compares it

with the evolution of the same ratio in the United Kingdom and Spain. As can be seen, during the period between 1991 and 1999, the North American market had the highest ratio and Spain the lowest ratio, although itwas above the British ratio in 2000 and 2001. The market-to-book ratio grew enormously in all three countriesuntil December 1999, and then fell in 2000 and 2001, following the general trend of the world stock markets.

5. Market-to-book ratio and interest rates on the North American stock marketShare prices and interest rate variations are closely linked. Consequently, it is to be assumed thatshares’ market-to-book ratio will also be related with interest rates. Figure 11 enables this ratio’s evolution to be compared with the evolution of the interest rates. It can be seen that, historically, when interest rates haverisen, the market-to-book ratio has fallen, and when interest rates have fallen, as happened after 1995, themarket-to-book ratio has increased.

Figure 11. Evolution of the average market-to-book ratio of the US stock market and the long-terminterest rates. Source: Morgan Stanley and Datastream

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6. Relationship between the market-to-book ratio and the PER and the ROEThe market-to-book ratio (E/Ebv) is closely related with the Price-to-Earnings Ratio (PER) and the

return on equity (ROE). It can be readily verified by means of a simple algebraic operation that the E/Ebv ratio

is equal to the PER multiplied by the ROE:

[1] E

Ebv

Market value

Book Value

Market value

Net income x

Net income

Book Value = PER x ROE

Table 1 shows the values of these three ratios for British Telecom, General Electric, Microsoft andCisco in recent years. The reader can see that the previous equation: E/Ebv = PER x ROE, is met in all cases.

Table 1. Evolution of the E/Ebv, PER and ROE of British Telecom, General Electric, Microsoft andCisco. Source: Datastream and own data.

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British Telecom.ROE (%) 16,4 19,7 17,4 10,0 13,6 14,4 15,7 18,7 15,8 20,0 13,0 3,1PER 10,6 10,5 12,5 12,3 11,5 10,1 12,1 16,7 27,3 29,4 26,5 NA

MV/BV 1,7 1,8 2,1 2,2 2,1 1,8 2,5 3,4 4,0 4,2 3,4 -36,8ROE (%) 19,9 12,2 20,1 16,7 17,9 22,2 23,4 23,8 23,9 25,2 25,2 25,0Gen. Electric PER 14,1 15,2 16,1 18,5 16,4 24,4 23,6 31,1 34,5 43,3 37,5 26,2

MV/BV 2,7 2,8 2,9 3,4 2,9 4,2 4,9 6,5 7,6 9,3 8,6 5,8ROE (%) 30,4 34,3 32,3 29,4 25,8 27,3 31,8 35,3 28,7 28,4 22,8 11,1

Microsoft PER 36,6 41,5 31,9 23,8 28,9 33,3 50,9 53,2 62,5 62,3 34,0 55,4MV/BV 9,1 10,5 7,7 5,3 6,7 8,3 11,9 12,2 14,9 13,6 7,1 6,2ROE (%) 20,1 33,9 34,4 36,2 37,1 30,5 32,4 24,5 19,0 18,0 10,1 -8,2

Cisco Systems PER 47,8 52,3 46,5 46,3 27,7 51,4 41,5 52,3 116,4 195,4 77,7 NAMV/BV 6,6 10,3 11,6 10,9 7,2 10,3 10,0 9,7 14,2 16,3 9,7 4,7




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2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

British Telecom.

ROE (%) -401,3 80,9 41,7 311,7 82,7 40,6 48,1 NA 234,0 588,5PER 7,6 10,7 12,6 10,8 14,0 10,9 4,3 6,8 8,8 9,4MV/BV 5,9 5,0 4,6 11,1 6,2 3,8 58,4 -3,8 7,5 12,8ROE (%) 22,2 19,0 15,1 15,0 18,6 19,2 16,6 9,4 9,8 12,1

Gen. Electric PER 15,2 21,4 22,8 21,3 18,2 15,5 6,2 14,5 17,6 15,5

MV/BV 2,9 3,2 3,5 3,0 3,1 3,4 1,0 1,4 1,9 1,7ROE (%) 17,1 12,8 21,2 29,5 32,5 49,3 50,0 36,7 42,4 36,6

Microsoft PER 27,3 33,0 28,6 22,6 25,0 16,2 10,6 15,4 11,8 10,9MV/BV 4,2 3,9 5,9 6,8 8,9 7,2 4,4 5,3 4,1 3,8ROE (%) 10,9 13,7 22,7 24,3 24,4 24,6 20,4 14,6 16,6 14,2

Cisco Systems PER 35,8 43,4 23,6 20,7 28,7 18,2 13,5 22,8 16,1 17,6MV/BV 3,3 6,5 4,9 4,5 5,3 4,0 2,6 3,0 2,5 2,1

Figure 12 shows the evolution of the average ROE of the US, UK and Spanish stock markets. Notethat the average ROE of the Spanish stock market has been less than the ROE of the American and British stockmarkets until 2000. However, in 2001 it was the highest of the three.

Figure 13 shows the evolution of the ROE of Coca Cola and Pepsico. As can be seen, Coca Cola’sROE has been markedly higher than Pepsico’s until the end of 1999. The fall in Coca Cola’s ROE in 1998,1999 and 2000 is surprising.

Figure 12. Evolution of the average ROE of the US, UK and Spanish stock markets. Source: Datastream

Figure 13. Evolution of the ROE of Coca Cola and Pepsico. Source. Datastream

Figure 14. Return on equity (ROE) of General Electric, Microsoft and Cisco. Source. Datastream




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Figure 14 shows the evolution of the ROE of three of the world’s largest companies. Cisco’s ROE wasnegative after the first quarter of 2001 as a consequence of the losses reported by the company. It is alsointeresting to see the cyclical evolution of Microsoft’s ROE and the growth of General Electric’s ROE.

The relationship between the equity market value (E) and book value (Ebv) depends on only threefactors: ROE, required return to equity (Ke), and expected growth of dividends (g).

[2] E

Ebv

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Ke-g

Return

on Equity

Return ROEon Equity

ROE Price/

Book Value

Growth

gPrice / earnigs E / Ebv Risk-free rate

ratio PER x ROE RF

PER Required returnto equity

KeRisk of

investment

Fama and French (1992) show that, on average, the companies with lower PER and E/Ebv have highershareholder returns than the companies with higher PER and E/Ebv. In the period 1963-1990, there was quite astrong relationship between the shareholder return and the market-to-book ratio. The authors divided the sharesinto portfolios and the portfolios with lower market-to-book ratios had higher shareholder returns. Table 2 shows this effect.

Table 2. Fama and French (1992). Relationship between market-to-book ratio and shareholder return.Market-to-book ratio Annual average shareholder return

Portfolio 1 (high) 5.9%Portfolio 2 10.4%Portfolio 3 11.6%Portfolio 4 12.5%Portfolio 5 14.0%Portfolio 6 15.6%Portfolio 7 17.3%Portfolio 8 18.0%Portfolio 9 19.1%

Portfolio 10 (low) 22.6%

7. Equity book value may be negative: the case of Sealed AirSealed Air Co. paid its shareholders a special dividend of 40 dollars per share in May 1989. In themonth prior to the special dividend, its share price had ranged between $44 and $46. The company had8,245,000 shares outstanding. The special dividend meant paying $329.8 million (87% of the shares’ marketvalue). As the company only had $54 million in cash, it borrowed most of the funds required to pay thedividend. After paying the dividend, the company had a negative equity book value of $160 million.

On the day after announcing the extraordinary dividend, there was a rush to buy the company’sshares2. The opening price was $53 per share, and it closed at $50.5 dollars, $4.38 above the previous day.

2 In the press release, the company’s president said: “the special dividend will enable the company’sshareholders to realize in cash a very significant portion of the company’s value, while at the same time




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Subsequently, the new shares increased value and ended 1989 at $20.4. Figure 15 shows how the share’s pricedropped after paying the dividend and its subsequent rise.

Figure 15. Share price of Sealed Air from 1987 to 1989, and from 1989 to 2000

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The company’s tremendous leverage was accompanied by a substantial increase in its efficiency ratios.

Sealed Air gave its shareholders a 290% return from April 1989 to December 1992, while the stock marketrose 36% during the same period. Before the special dividend, from December 1986 to April 1989, theshareholder return was 6%, while the market return was 48%.

Table 3 shows that the shareholder’s equity was negative in 1989 due to the dividend payment. It canalso be seen the debt increased during that year to cover the dividend payment. The shareholder’s equity

became positive again in 1994. Sales, operating profit, and net income also grew during this period.

Table 3. Sealed Air. 1987 to 1997

($ million) 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997

Sales 302.7 345.6 385.0 413.3 435.1 446.1 451.7 519.2 723.1 789.6 842.8Operating profit 38.2 43.6 53.7 67.4 69.5 72.2 74.1 83.9 108.9 130.1 138.1Net income 20.5 25.3 7.2 11.4 16.2 20.8 27.4 31.6 52.7 69.3 80.0Current assets 80.7 96.0 86.7 22.3 18.5 29.4 33.8 15.8 41.9 58.9 87.2Inventories 32.0 36.2 25.9 25.6 28.3 28.3 32.0 38.3 43.3 42.3 48.3

Shareholder's equit 141.1 162.3 -160.5 -131.6 -94.6 -66.3 -29.4 11.0 106.3 186.6 257.3

Long-term debt 34.4 33.5 311.1 259.0 253.7 225.3 190.1 155.3 149.8 99.9 48.5Investments 13.1 13.9 13.8 12.1 15.9 11.2 22.4 29.9 21.0 17.0 24.3

Founded in 1960, Sealed Air manufactured and sold a broad range of packaging products. One of itsmost famous products was the plastic wrapping with air bubbles. Other products were self-sealing envelops, paper for absorbing meat fluids for supermarkets, and plastic materials for packaging fragile goods.

When it announced the special dividend to the banks, the company found that many banks did notwant to lend money to a company with negative shareholder’s equity.

In spite of these problems, Sealed Air obtained a loan from Bankers Trust for $136.7 million (with the possibility of increasing it to $210 million) at an interest rate of 11.5%3. It also issued $170 million in 10-yearsubordinated bonds paying an interest rate of 12.625%. To finance the remaining $23.1 million, the companyrealized short-term investments. The agreement with the banks also required that any proceeds from the sale ofassets should be used to pay back loans. In addition, Sealed Air would not be able to take out any additionalloans.

Commissions and other expenses associated with the special dividend amounted to $20.9 million.After the special dividend, the company’s management shifted the emphasis in its policies to new

priorities: 1) putting the customer first; 2) cash flow; 3) working capital focus; 4) innovation; and 5) earnings per share.

maintaining their holding in it. Our strategy has always been to be market leader in packaging products. Withthe present investments, we believe that the company has sufficient production capacity to satisfy the growingdemand for its products for several years without any significant additional investments. We also believe that itis unlikely, in the present market circumstances, that we will find opportunities for major acquisitions at anacceptable price that are consistent with our strategy. The special dividend is not a response to any takeoveroffer”.3 The Bankers Trust prime rate plus 1.5%.




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The company implemented a new incentive plan for its managers. Before the recapitalization 4, theincentives were based on the earnings per share, then on the EBITDA (earnings before interest, tax,depreciation and amortization), inventory level, level of accounts receivable, and working capital. The aim ofthe new incentive plan was to focus the managers’ attention on the importance of generating cash flow. The president explained this change in incentives as follows: “In our company, our managers never had to worryabout the balance sheet and the company accepted the investments recommended by managers without demur.By changing from earnings per share to EBITDA, we have focused our managers more on the cash flow”. The

company also implemented a plan to enable employees to hold more shares in the company. In April 1989, theemployees had 7.9% of the company’s shares; by March 1992, their holding had increased to 24.6%.

Figure 16 shows that the company’s operating profit/sales ratios were higher than that of the industry.It also shows the reduction in net working capital and the inventories/sales ratio after paying the dividend 5.

Figure 16. Behavior of Sealed Air compared with the industry. Source: Wruck (1998)

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On 31 March 1998, the company merged with Cryovac, W.R. Grace & Co.’s packaging products

division. The merged company continues to be called Sealed Air.

Not all leveraged recapitalizations have been as profitable for shareholders as Sealed Air’s. Table 4 shows the shareholder return of 33 leveraged recapitalizations.

Table 4. Leveraged recapitalizations. Shareholder return in the year after the Leveraged Recap.Source: Wruck (1998)

Annual return Annual return

Company Company S&P 500 difference Company Company S&P 500 difference

Sealed Air Corp 62.8% 10.8% 52.1% Whittaker -1.8% 10.6% -12.3%

Holiday Corp 59.8% 5.5% 54.3% Phillips-Van Heusen -1.8% 5.2% -7.0%

Holly Corp 40.8% 12.0% 28.8% Triad Systems -3.7% 0.3% -3.9%

Shoney's 40.6% 11.8% 28.8% Service Merchandise -5.6% 8.4% -14.0%CUC International 39.5% 7.6% 31.9% Swank Inc -11.5% 6.1% -17.6%

Barry Wright 31.8% 22.5% 9.4% GenCorp -19.5% 6.9% -26.4%

Kroger 25.8% 13.0% 12.8% WNS Inc -28.0% 11.6% -39.5%

Colt Industries 24.1% 8.5% 15.6% Butler Manufacturing -30.0% -0.1% -29.9%

Cleveland-Cliffs 22.8% 13.8% 9.0% USG Corp -35.3% 12.8% -48.1%

Di Giorgio 18.8% 11.6% 7.2% Interlake Corp -36.2% 7.5% -43.7%

FMC Corp 17.6% 9.4% 8.2% Quantum Chemical -38.5% 13.5% -52.0%

Owens Corning 12.6% 10.5% 2.1% Standard Brands Paint -39.0% 13.2% -52.1%

Vista Chemical 12.0% 10.5% 1.6% Carter Hawley Hale -44.0% 5.8% -49.8%

Union Carbide 10.0% 12.1% -2.0% HBJ -49.2% 6.4% -55.6%

Optical Coating Lab 8.5% 5.7% 2.8% Interco -63.1% 13.9% -77.0%

Goodyear 5.8% 8.4% -2.6% Bank Bldg Equip -79.7% 3.7% -83.5%

General Signal 5.3% 13.6% -8.4% Average -1.5% 9.5% -10.9%The operations carried out as a defense measure against takeovers are in Italics

4 Recapitalization is the name given to the increase in the company’s indebtedness as a result of the payment ofthe special dividend.5 Those readers interested in finding out more about the company can see the Harvard Business School cases 9-294-122/3 “Sealed Air Corporation’s Leveraged Recapitalization”, written by Karen Wruck.




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Appendix 1. Sp li tt ing the PER: franchise factor, growth facto r, interest factor and risk facto r

The PER is the multiple of the profits at which the market values a company’s shares. This multiple basically depends on the market’s expectations regarding the company’s growth, profitability and risk. Growthalone is not enough to give a high PER, the company must invest in projects having a return greater than thecost of capital. In order to study in greater depth the factors that affect the PER, we shall split 6 the PER into two

addends: the first is the PER the company would have if it did not grow and the second is the contribution made by the company’s growth to the PER, which in turn splits into a product of two factors: the Franchise Factor,which measures the growth’s quality, and the Growth Factor. We shall see that for growth to contribute to thePER, the company must invest in projects having a return greater than the cost of capital.

Further on, the PER’s first addend is split into another two factors: the Interest Factor and the RiskFactor. The Interest Factor is -approximately- the PER of a long-term Treasury bond. The Risk Factor dependson the company’s risk, which is defined as the required return to equity.

1. PER, franchise factor and Growth Factor The PER can be split into two addends as follows (see the proof in 8):

PER 1

Ke+ FF x G FF =

ROE - Ke

ROE Ke G =

g

Ke - g

The first addend, 1/Ke = 1/10% = 10, is the company’s PER if it has no growth, regardless of thereturn on its investments.

The second addend (FF x G) is the contribution made by growth to the PER. It consists of twofactors:

- the Growth Factor G, which basically depends on the company’s growth.- the franchise factor FF, which mainly depends on the difference between the return on investment

and the cost of capital employed. The franchise factor measures what we could call the growth’s “quality”,understanding this to be the return above the cost of the capital employed.

This formula tells us that a company’s PER is the PER of the no-growth company plus an “extraPER” due to growth, which depends on the growth (G) and the “quality” of that growth ( franchise factor).

We shall now apply this split to six companies.

Table A1 shows all six companies’ Growth Factor G and franchise factor FF. Obviously, thecompanies that do not grow (company B and company C) have a Growth Factor of zero. The company thatgrows most (company D with 8%) has the highest Growth Factor: 4.

Table A1. PER, FF and G of six companies.

A B C D E F

PER 10.00 10.00 10.00 16.67 12.50 15.38

G 1.5 0 0 4 1.5 2.333

FF 0 0 1.667 1.667 1.667 2.308

G x FF 0 0 0 6.667 2.500 5.385

The companies investing in projects with a return equal to the cost of capital (company A and

company B) have a franchise factor of zero. The companies investing in projects with a return of 12%(companies C, D and E) have a franchise factor of 1.667 and the company investing in projects with a return of13% (company F) has a franchise factor of 2.308. The higher the return on investment, the higher the franchise

factor . We have seen with these simple examples that growth alone is not enough to have a high PER:growth is important, but only if the new investments have a return greater than the cost of capital (growth with“quality”).

A word of caution: in the above examples, the PER has been calculated by dividing the shares’ pricetoday by next year’s expected profit. Very often, the PER is calculated by dividing the shares’ price today bylast year’s profit. In this case (as we shall see in the following section), the PER’s breakdown is identical butthe expression of the franchise factor changes a little: all we have to do is add 1 and calculate the return oninvestment (ROE) also with this year’s profit, instead of with next year’s profit.

6 This splitting of the PER is discussed in the article of Leibowitz and Kogelman (1992).




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2. PER*, franchise factor* and Growth FactorWe use the asterisk (*) to identify the PER* calculated by dividing the shares’ price today by this year’s

profit.

As PER * =P0

EPS0

=E0

PAT0

and PER =P0

EPS1

=E0

PAT1

As PAT1=PAT0(1+g), the relationship between PER and PER* is: PER* = PER (1+g)

We use the asterisk (*) to identify the ROE* calculated by dividing this year’s profit by the equity’s book value this year.

Performing similar operations, we obtain: ROE* = PAT0 / Ebv0 = ROE / (1+g)

In 8, we show that PER* is split as follows:

PER* 1

Ke+ FF* x G FF* =

ROE * - Ke

ROE* Ke + 1 G =

g

K e - g

In 8, we also show that the difference between FF and FF* is:

FF *-FF= 1 -g

ROE = 1 -

g

ROE* (1+ g)

Table A2 shows PER* and FF* for all six companies in the previous example.

Table A2. PER* and FF* of six companies.

A B C D E F

PATo 9.434 10 12 11.111 11.321 12.150

DIVo = ECFo 3.774 10 12 3.704 5.660 5.607

PER* 10.60 10.00 10.00 18.00 13.25 16.46

ROE* 9.43% 10.00% 12.00% 11.11% 11.32% 12.15%

G 1.5 0 0 4 1.5 2.333

FF* 0.4 1 2.667 2 2.167 2.769

G x FF* 0.6 0 0 8.000 3.250 6.462

3. PER, Interest Factor and Risk Factor

We have already said that (1/Ke) is the PER the company would have if it did not grow. This term can be split into two terms:

1

Ke=

1

R F -

Ke - R F

Ke R F

The first term (1/R F) is the PER the company would have if it did not grow and had no risk. It is -approximately- the PER of a long-term Treasury bond. This term is called Interest Factor. The second termdepends primarily on the difference between the required return to equity (Ke) and the risk-free interest rate(R F). The value of this term increases as the required return to equity increases (which depends on the risk perceived by the market). This is why it is called Risk Factor.

Interest Factor =1

R F Risk Factor =

Ke - R F

Ke R F

1

R F

1

Ke

PER =1

RF -

Ke - RF

Ke RF+ FF x G

PER = Interest Factor - Risk Factor + Franchise Factor x Growth Factor

Likewise: PER * =1

RF -

Ke - RF

Ke RF+ FF * x G

PER* = Interest Factor - Risk Factor + Franchise Factor* x Growth Factor




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Franchise

Factor

PER FFdue to (ROE-Ke)/(ROE Ke)

growth

GrowthFF x G Factor

G

PER g/(Ke-g)

P / EPS Risk

Factor

PER

without (1/R F)-(1/Ke)

growth

Interest

1/Ke Factor

1/R F

4. Value generation over time in companies with growthFigure A1 shows the evolution over time of the profits and dividends of companies A (annual

growth = 6%) and B (without growth). Both companies have the same equity value (100 million). The expecteddividends of company B are 10 million every year. The expected dividends of company A are 4 million in year1, growing thereafter at an annual rate of 6% in the following years. The dividends of company A will not reach10 million (the dividends of company B) until 16 years from now.

Figure A1. Evolution of the profits and dividends of companies A and B.

0

5

10

15

20

0 5 10 15 20 25 30year

PAT A DIV A PAT B = DIV B

Figure A2. Evolution of the profits and dividends of companies A and C.

0

5

10

15

20

0 5 10 15 20 25 30year

PAT A DIV A PAT C = DIV C

Figure A2 shows the evolution over time of the profits and dividends of companies A (annualgrowth = 6%) and C (without growth). The equity value of company A is 100 million and the equity value of




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company C is 120 million. The expected dividends of company C are 12 million every year. The dividends ofcompany A will not reach 12 million (the dividends of company C) until 19 years from now.

Figure A3 shows the evolution over time of the profits and dividends of companies D (annual growth= 8%) and F (annual growth = 7%). Both companies have the same equity value (200 million). The expecteddividends of company D are 4 million in year 1, growing thereafter at an annual rate of 8%. The expecteddividends of company F are 6 million in year 1, growing thereafter at an annual rate of 7%. Although it seemsin Figure A3 that the dividends of company D are always less than those of company F, they will in fact catchup with the dividends of company F in 45 years’ time!!!!

Figure A3. Evolution of the profits and dividends of companies D and F.

0

10

20

30

40

0 5 10 15 20 25 30

year

PAT D

DIV D

PAT F

DIV F

Figure A4 and Table A3 show the equity value generation over time: the present value of the dividends

until a certain year. Thus, the present value of the dividends for the first 20 years is 52 million for company A,85 million for company B, 61 million for company D, and 85 million for company F. The present value ofcompanies B and F match in year 20 and that of companies B and D in year 36.

Figure A4. Equity value generation over time. Present value of the dividends until the year indicated.

0

25

50

75

100

125

150

175

200

0 20 40 60 80 100year

PV

Company A

Company B

Company D

Company F

Table A3. Equity value generation over time. Present value of the dividends until the year indicated. Year Company A Company B Company C Company D Company E Company F

5 17 38 45 18 25 26

10 31 61 74 34 46 48

15 43 76 91 48 64 68

20 52 85 102 61 78 85

30 67 94 113 85 101 113

40 77 98 117 104 116 134

50 84 99 119 120 126 150

75 94 100 120 149 141 175

100 98 100 120 168 146 187

125 99 100 120 180 149 194

150 100 100 120 187 149 197

175 100 100 120 192 150 198

200 100 100 120 195 150 199




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Figure A5 shows the equity value generation over time: the present value of the dividends until acertain year as a percentage of the equity’s value today. Thus, the present value of the first 20 years’ dividendsis 52% of its value (100 million) for company A, 85% of its value (100 million) for company B, 31% of itsvalue (200 million) for company D, and 42% of its value (200 million) for company F.

Figure A5. Equity value generation over time.Present value of the dividends until the year indicated as a percentage of the equity value.

0%

20%

40%

60%

80%

100%

0 20 40 60 80 100year

Company A

Company B

Company D

Company F

5. Influence of growth on the franchise factor and on the Growth Factor Figure A6 shows the relationship between the franchise factor multiplied by the Growth Factor and

the growth rate for four companies with different ROEs. Note that in the company with ROE = 9%, that is, lessthan the required return to equity, which is 10%, the higher the growth rate, the lower the product FFxG, which becomes negative. In the case of the company with ROE = 10% (equal to the required return to equity), the product FFxG is always 0. For companies with a ROE greater than the required return to equity, the higher thegrowth rate, the higher the product FFxG.

Figure A6. FF x G of a company with different growth rates (g). Ke = 10%

-10

-5

0

5

10

15

0% 1% 2% 3% 4% 5% 6% 7% 8% 9%g (growth)

FF x G

ROE = 9%

ROE = 10%

ROE = 11%

ROE = 12%

6. Influence of the ROE on the franchise factor

Figure A7. FF of a company with different values for ROE. Ke = 10%

-10

-8

-6-4

-2

0

2

4

6

5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20%ROE

FF

Figure A7 shows the franchise factor at different ROEs. Companies with different growth rates havean identical franchise factor , as the franchise factor does not depend on growth. Figure A7 also shows that ifthe ROE is equal to the required return to equity, i.e. 10%, the franchise factor is 0. For companies with a ROE






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Figure A11 shows how the franchise factor changes depending on the required return to equity. As islogical, the franchise factor decreases as the required return to equity increases.

Figure A11. FF of a company with different values for Ke. g=4%

-4

-2

0

2

4

6

8

6% 7% 8% 9% 10% 11% 12% 13% 14% 15%Ke

FF

ROE = 9%

ROE = 10%

ROE = 11%ROE = 12%

Figure A12 shows the evolution of the Spanish stock market’s franchise factor and the its averagePER. The franchise factor increased from 1994 to 1998, but was negative in 1992.

Figure A12. FF and PER of the US stock market.

-4

-2

0

2

4

6

8

12/90 12/91 12/92 12/93 12/94 12/95 12/96 12/97 12/98 12/99 12/00 12/01

10

14

18

22

26

30

34

FF USA

PER USA

Franchise factor PER

8. Splitting the PER. Proof.

It is easy to show that for a growing perpetuity, PER = p

Ke g

ROE - g

ROE (Ke g) (1)

In a company with constant growth and performing algebraic operations, it is readily deduced that7: E0

Ebv0

=ROE - g

Ke g

Substituting this expression into the previous one, we obtain:

PER = p

Ke g

ROE - g

ROE(Ke g)

1

ROE

E0

Ebv0

As g = ROE (1-p), substituting and performing algebraic operations, we obtain:

PER = p

K e - g

1

Ke

Ke p

Ke-g=

1

Ke Ke (ROE - g)

ROE (Ke - g)

1

Ke 1 +

Ke (ROE- g)- ROE (Ke- g)

ROE (Ke - g)

=

=1

Ke +

(ROE- Ke) g

ROE Ke (Ke - g)

1

Ke+ FF x G

7 Comparing ROE (which is an accounting number) with Ke (which is the required return) is always dangerous.As a general rule, it is not true (except for perpetuities, which is the case we are considering here) that thecondition for a company to “create value” is that ROE be greater than Ke.




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PER 1

Ke+ FF x G Where: FF =

ROE - Ke

ROE Ke G =

g

K e - g

Performing algebraic operations, the first addend can be expressed as: 1

Ke=

1

R F -

Ke - R F

Ke R F We call the first term Interest Factor and the second term Risk Factor:

Interest Factor =1

R F Risk Factor =

Ke - R F

Ke R F

PER =1

RF -

Ke - RF

Ke RF + FF x G

PER =1

R F -

Ke - R F

Ke R F +

ROE - Ke

ROE Ke x

g

K e - g

PER = Interest Factor - Risk Factor + Franchise Factor x Growth Factor

If PER * =P0

EPS0

=E0

PAT0

As PAT1=PAT0(1+g), the relationship between PER and PER* is: PER* = PER (1+g)

ROE* = PAT0 / Ebv0 = ROE / (1+g) g = ROE (1-p) = ROE* (1-p) (1+g)

p =ROE * (1+ g) - g

ROE * (1+ g)

Gx*FF+Ke

1

g)-(KeKe*ROE

gROE*)Ke+Ke-*(ROE +

Ke

1=

g)-(Ke *ROE

g)-(Ke*ROE-g]-g)+(1*[ROEKe +1

Ke

1

g)-(Ke *ROE

g]-g)+(1*[ROEKe

Ke

1=

g-Ke

g)+(1 pKe

Ke

1

g-Ke

g)+(1 p =*PER

FF*=ROE * - Ke

ROE* Ke + 1 G =

g

K e - g

PER* 1

Ke+ FF * x G Gx*FF+

R Ke

R -Ke -

R

1=*PER

F

F

F

FF* - FF = 1 – g/ROE = 1 – g/[ROE* (1+g)]

REFERENCESLeibowitz, M. L., and S. Kogelman (1992), “Franchise Value and the Growth Process”, Financial AnalystsJournal 48, pages 53-62.

QuestionsHow do you interpret figures 13 and 14?What did happen to Sealed Air Corp. for having negative book value of equity during 5 years?

Please define:Price to Earnings ratio Value to Book ratio Growth Leveraged recapitalization

Please define and differentiate:ROE (Return on Equity). Shareholder returnFranchise factor, growth factor, interest factor and risk factorEquity book value. Market capitalization

Documents

PER, Value to Book Ratio & Growth