an investigation into the relationship between the peg ratio and the capitalization rate by gaylen...

An Investigation into the relationship between the PEG Ratio and

the Capitalization Rate

By

Gaylen Bunker

Peter Lynch quote

“The p/e ratio of any company that’s fairly priced will equal its growth rate”

“One Up On Wall Street,” Lynch & Rothchild, Simon and Schuster,

New York, 1989, page 198

“Earnings multiples or capitalization factors are simply the reciprocal of cap rates. A 20% cap rate is the same as an earnings multiple of five times. In the above example, capitalizing the $100,000 earnings at 20% is the same as valuing the business at five times earnings.”

The CPA Journal

http://www.nysscpa.org/cpajournal/old/16373958.htm

Typical Capitalization Rate Sources 1. Market (1÷ P/E ratio) = cap rate

This cap rate incorporates TOTAL market expectations regarding future growth, future value, holding period, etc.... In theory, it is the best available method of estimating market value since it relates value to earnings…using market derived data.

2. Discount Rate - estimated growth rate = cap rate

http://www.bus.ucf.edu/weaver/BV%20&%20Litigation%20Support%20Articles/articles/businessvaluationtechniques.htm

Lynch’s equality

• For PEG: P / e = g (Lynch equality)

• 1 / (P / e) = e / P = 1 / ge / P = Capitalization Rate

• (k - g) = Capitalization Rate

• k - g = e / P = 1 / g

Lynch’s equality

• For PEG: 24 / 2 = 12% (Lynch’s Equality)

• 1 / (24 / 2) = 2 / 24 or .0833 2 / 24 = Capitalization Rate

• (k – g) = .0833 = (.2033 - .12)

• (.2033 - .12) = 2 / 24 = 1 / 12

PEG CapRates/Growth

Growth 1 / g

.05 .2000

.10 .1000

.15 .0667

.20 .0500

.25 .0400

.30 .0333

.35 .0286

.40 .0250

PEG line and Market line (interest rate change)

Capitalization Rate to Growth

y = 0.01x-1

y = 0.0075x-0.75

0.00

0.05

0.10

0.15

0.20

0.25

0 0.1 0.2 0.3 0.4 0.5 0.6

Growth Rate

Cap

ital

izat

ion

Rat

e

2001 CapR per Growth

y = 0.0095x-0.7163

0.000

0.020

0.040

0.060

0.080

0.100

0.120

0.00% 10.00% 20.00% 30.00% 40.00%

Growth

Cap

R2002 CapR per Growth

y = 0.0061x-0.8723

0.000

0.020

0.040

0.060

0.080

0.100

0.120

0.140

0.160

0.00% 10.00% 20.00% 30.00% 40.00%

Growth

Cap

R


y = 0.0116x-0.4416

0.0000.0100.0200.0300.0400.0500.0600.0700.0800.0900.100

0.00% 10.00% 20.00% 30.00% 40.00%

Growth

Cap

R


y = 0.0067x-0.7037

0.000

0.010

0.020

0.030

0.040

0.050

0.060

0.070

0.00% 10.00% 20.00% 30.00% 40.00%

Growth

Cap

R

Historic Market AveragesBased on Damodaran Industry Averages

Year Variable Exponent

2001 .0095 .7163

2002 .0061 .8723

2003 .0116 .4416

2004 .0067 .7037

Average .0085 .6835

Estimate .0075 .7500

“The valuation of a privately owned company is both

science and art.”

http://www.vrbusinessbrokers.com/pages/mergers/valuation_services.jsp

“Of course, bullish market observers argue that times have changed. Specifically, they believe that some of these older valuation models are less relevant today because interest rates are

so low. According to an economic model of stock valuations known as the Fed Model, lower interest rates can help support higher valuation

levels in the market.” Paul Tracy

http://www.zacks.com/experts/featured/view_article.php?art_id=1587&newsletter_id=148

Problems with comparing PE ratios to expected growth

• In its simple form, there is no basis for believing that a firm is undervalued just because it has a PE ratio less than expected growth.

• This relationship may be consistent with a fairly valued or even an overvalued firm, if interest rates are high, or if a firm is high risk.

• As interest rate decrease (increase), fewer (more) stocks will emerge as undervalued using this approach.

http://pages.stern.nyu.edu/~adamodar/New_Home_Page/lectures/peg.htm

Variable Relationship

y = 0.0005x + 0.005

R2 = 1

0

0.002

0.004

0.006

0.008

0.01

0.012

0 2 4 6 8 10 12

Interest Rates

Var

iab

le

Exponent Relationship

y = -0.05x - 0.5

R2 = 1

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0 2 4 6 8 10 12

Interest Rates

Exp

on

ent

The Gaylen Curve

Cap Rate = (.0005r + .005)g-(.05r + .5)

Cap Rate = (ke – g)

r = interest rate (risk adjusted)

g = growth rate

Portfolio managers and analysts sometimes Portfolio managers and analysts sometimes compare PE ratios to the expected growth rate compare PE ratios to the expected growth rate to identify undervalued and overvalued stocks. to identify undervalued and overvalued stocks. In the simplest form of this approach, In the simplest form of this approach, firms with PE ratios less than their firms with PE ratios less than their expected growth rate are viewed as expected growth rate are viewed as undervalued. In its more general form, undervalued. In its more general form, the ratio of PE ratio to growth is used as the ratio of PE ratio to growth is used as a measure of relative value, with lower a measure of relative value, with lower values believed to indicate values believed to indicate undervaluation relative to other firms.undervaluation relative to other firms.

Peters, DJ. (1991) Valuing a growth stock. Peters, DJ. (1991) Valuing a growth stock.

Journal of Portfolio Management Journal of Portfolio Management 17:49-51. 17:49-51.

http://dignet.home.mindspring.com/limitsofpeg.htmhttp://dignet.home.mindspring.com/limitsofpeg.htm

Peters (1991) provides a simple test of this Peters (1991) provides a simple test of this proposition by classifying firms into deciles proposition by classifying firms into deciles based upon the ratio of PE ratio to expected based upon the ratio of PE ratio to expected long-term growth, for every quarter from January long-term growth, for every quarter from January 1982 to June 1989. The lowest PE/growth decile 1982 to June 1989. The lowest PE/growth decile outperformed the market in 26 out of the 30 outperformed the market in 26 out of the 30 quarters for which returns were measured and quarters for which returns were measured and earned significantly higher returns than the earned significantly higher returns than the Standard and Poors 500. The compounded Standard and Poors 500. The compounded return over the period was 1,536% for the lowest return over the period was 1,536% for the lowest PE/growth decile, while the return on the S&P PE/growth decile, while the return on the S&P 500 index over the same period was 356%.500 index over the same period was 356%.

Peters, DJ. (1991) Valuing a growth stock. Peters, DJ. (1991) Valuing a growth stock. Journal of Portfolio Management Journal of Portfolio Management 17:49-51. 17:49-51.


The PE ratio of a high-growth firm is a function The PE ratio of a high-growth firm is a function of the expected extraordinary growth rate; the of the expected extraordinary growth rate; the higher the expected growth, the higher the PE higher the expected growth, the higher the PE ratio for the firm. The PE ratio can be graphed ratio for the firm. The PE ratio can be graphed as a function of the extraordinary growth rate. as a function of the extraordinary growth rate. In Figure 14.1, as the firm's anticipated In Figure 14.1, as the firm's anticipated extraordinary growth rate in the first five years extraordinary growth rate in the first five years declines from 25% to 8%, the PE ratio for the declines from 25% to 8%, the PE ratio for the firm also decreases from 28.75 to 15.firm also decreases from 28.75 to 15.

Peters, DJ. (1991) Valuing a growth stock. Peters, DJ. (1991) Valuing a growth stock.

Journal of Portfolio Management Journal of Portfolio Management 17:49-51. 17:49-51.


PE Ratio versus growth: The effect PE Ratio versus growth: The effect of interest rates and riskof interest rates and risk

In Figure 14.1 the Treasury bond rate used was In Figure 14.1 the Treasury bond rate used was 6%. The effect of increasing the Treasury bond 6%. The effect of increasing the Treasury bond rate on PE ratios is examined in Figure 14.2. As rate on PE ratios is examined in Figure 14.2. As illustrated in the graph, the PE ratio for this illustrated in the graph, the PE ratio for this firm is lower than the expected growth rate firm is lower than the expected growth rate when the Treasury bond rate is greater than when the Treasury bond rate is greater than 7%, though it is not undervalued. For instance, 7%, though it is not undervalued. For instance, the PE ratio will drop to 11.96 if the Treasury the PE ratio will drop to 11.96 if the Treasury bond rate increases to 10%, well below the bond rate increases to 10%, well below the expected growth rate of 25% in the first five expected growth rate of 25% in the first five years but still correctly valued.years but still correctly valued.



The danger of concluding that a firm is The danger of concluding that a firm is undervalued just because its PE ratio is less than undervalued just because its PE ratio is less than its expected growth rate is that it may be the its expected growth rate is that it may be the wrong conclusion for high-risk (high-beta) firms wrong conclusion for high-risk (high-beta) firms or when interest rates are high.or when interest rates are high.

Consider two firms with the same expected Consider two firms with the same expected growth rates of 25% for the first five years and growth rates of 25% for the first five years and 8% after that, the same payout policies (payout 8% after that, the same payout policies (payout ratio in the first five years of 20% ; 50% ratio in the first five years of 20% ; 50% thereafter), but different levels of risk (beta of thereafter), but different levels of risk (beta of 1.0 for the first firm and 1.5 for the second). The 1.0 for the first firm and 1.5 for the second). The PE ratio of the safer firm will be higher than the PE ratio of the safer firm will be higher than the PE ratio of the riskier firm at every level of PE ratio of the riskier firm at every level of growth, as illustrated in Figure 14.4. growth, as illustrated in Figure 14.4.



an investigation into the relationship between the peg ratio and the capitalization rate by gaylen...

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