# Decision 425-R-2011 - Additional Information

## Decision

### Exhibit 1

Exhibit 1 graphs two series between 2001 and 2009. The series are the forecasted weighted average cost of debt and the actual weighted average cost of debt. Between 2001 and 2007, the forecasted cost of debt is above the actual cost of debt. The two series begin to converge in 2006 and in 2008, the actual weighted cost of debt rises above the forecasted weighted cost of debt, however, the two series are very close in 2008 and 2009. **↑**

### Exhibit 3

Exhibit 3 graphs the volume of CN and CP common shares traded on the Toronto Stock Exchange (TSE) compared to the volume of shares traded on the New York Stock Exchange (NYSE) from 2002 to 2011. It shows that up to 2008 a greater proportion of CN and CP shares were traded on the TSE, but since 2008, the volume of CN and CP shares traded on the NYSE has overtaken the volume of CN and CP shares traded on the TSE. In 2002 60% of the volume of CN and CP shares traded on the TSE , and 40% on the NYSE. The volume of shares traded on the TSE increased to a peak of about 67% in 2005, then consistently declined year over year down to only 40% in 2009. During the same period, the volume of shares traded on NYSE, declined from 40% in 2002 to 33% in 2005, then increased consistently year over year to 60% in 2009. For 2010 and 2011, the proportion of CN and CP shares traded in each market has remained fairly constant at approximately 52% on the NYSE and 48% on the TSE. **↑**

### Exhibit 4

Exhibit 4 graphs the year over year percentage changes from the S&P/TSX Total Return Index and the S&P500 Total Return Index for the years 1956 to 2010. For the most part the indices follow each other fairly closely and fluctuate significantly from year to year. **↑**

### Exhibit 5 (Paragraph 297)

Exhibit 5 consists of two separate figures. The first relates to CN and the second relates to CP. Each figure graphs five separate series between crop years 2002/2003 and 2010/2011. Each series is an annual cost of equity estimate for the respective railway calculated using a different risk-free rate. The risk-free rates are the yields on bonds of different maturities. The maturity periods used in the cost of equity series are: 3 months, 1 to 3 years, 3 to 5 years, 10+ years, and the Agency's current practice, an average of short and long-term maturities. In the figure relating to CN, the cost of equity estimates calculated using a 3 to 5 year maturity period for the risk-free rate follows the Agency's current practice more closely than any other estimate. The 3- month t-bill consistently produces the lowest cost of equity estimates. For the most part, the 10+ year risk-free rate produces the highest cost of equity estimates and the 1 to 3 year risk-free rate produces cost of equity estimates somewhere between the Agency's current practice and the cost of equity estimates produced using 3 month t-bills. In the figure relating to CP, the cost of equity estimates calculated using a 3 to 5 year maturity period for the risk-free rate follows the Agency's current practice more closely than any other estimate. The 3- month t-bill produces the lowest cost of equity estimates for most years. For the most part, the 10+ year risk-free rate produces the highest cost of equity estimates and the 1 to 3 year risk-free rate produces cost of equity estimates somewhere between the Agency's current practice and the estimates produced using 3-month t-bills. **↑**

### Exhibit 8a

Exhibit 8a graphs the annual total percentage returns from the S&P/TSX Composite Total Return Index from 1924 to 2010. The returns are extremely volatile from year to year. There is no clear evidence of a structural break in the graph. **↑**

### Exhibit 8b

Exhibit 8b graphs the annual total returns from the S&P 500 Total Return Index from 1936 to 2010. The returns are extremely volatile from year to year. There is no clear evidence of a structural break in the graph. **↑**

### Exhibit 9

Exhibit 9 graphs two series between 1936 and 2009. The series are the historical annual income returns and historical annual total returns for 10+ year Government of Canada bonds. The figure illustrates the relative volatility of the total return estimate. The income return series is positive over the entire period and does not fluctuate much from year to year. The total return series fluctuates, sometimes wildly, from year to year between the band of 43% and negative 11%. **↑**

### Exhibit 10

Exhibit 10 graphs two series between 1980 and 2009. The series are the cumulative moving averages of total returns and income returns on 10+ year marketable bonds. The income return series is very smooth over the period. The total return series is somewhat volatile relative to the income return series. **↑**

### Exhibit 11

Exhibit 11 graphs three series between 2001 and 2010. The series are beta estimates for CN's US common shares, CP's US common shares and the US Market (represented by the S&P 500). Both CN and CP beta values are between 0.6 and 0.7 in 2001. After declining slightly between 2001 and 2004, both betas begin to increase towards one. CP's beta crosses over 1.0 in 2007 and steadily rises to just over 1.2 in 2010, while CN's beta remains close to one between 2007 and 2010. The US market beta has a constant value of 1.0. **↑**

### Formula (Paragraph 277)

Extended Description:

R sub e equals R sub f,DC plus Beta sub NA times open bracket R sub m,NA minus R sub f, DC close bracket

where:

*R sub e*_{ } is the expected return on equity;

*R sub f comma DC*_{ } is the risk-free rate in the domestic market;

*R sub m comma NA*_{ } is the return provided by the combined North American market; and

*Beta sub NA* is the systemic risk in the company relative to the North American market **↑**

### Formula (Paragraph 372)

Beta sub one equals 0.371 plus 0.635 times Beta sub zero

where:

Beta sub one is the prospective beta

Beta sub zero is the historical beta **↑**

### Formula (Paragraph 374)

Beta sub s1 equals sigma squared sub Beta s 0 times Beta sub zero divided by open bracket sigma squared sub Beta 0 plus sigma squared sub Beta s 0 close bracket plus sigma squared sub Beta 0 times Beta sub s 0 divided by open bracket sigma squared sub Beta 0 plus sigma squared sub Beta s 0 close bracket

where:

Beta sub s 1 is the Vasicek adjusted beta for security *s*

Beta sub s 0 is the historical beta for security *s*

Beta sub 0 is the beta of the market, industry, or peer-group

Sigma squared sub Beta 0 is the variance of betas for the market, industry or peer-group

Sigma squared sub Beta s 0 is the variance of the historical beta for security *s* **↑**

## Appendix A

### Paragraph 9

R sub e equals R sub f plus Beta times MRP

where:

R sub e is the cost rate of common equity;

R sub f is the risk-free rate;*MRP* is the historical market risk premium or excess stock market return over the risk-free rate; and*ß* is the measure of undiversifiable risk associated with the railway company’s stock returns. **↑**

### Paragraph 14

MRP equals open bracket one divided by T close bracket times the sum from t equals one to T of open bracket R sub m comma t minus R sub f comma t close bracket

where:*R sub m comma t* is the market return in year *t;* ...market index in year *t minus*1. ... same market index in year t minus 1.

R sub m comma t equals open bracket I sub m comma t divided by I sub m comma t minus one close bracket minus one.

where:*I sub m comma t* is the closing stock market index value in year *t*; and*I sub m comma t minus 1*is the closing stock market index value in year *t* minus 1

*R sub f comma t* is the risk-free return in year *t*; **↑**

### Paragraph 15

R sub c comma w minus R sub f comma w equals alpha sub c plus Beta sub c times open bracket R sub m comma w minus R sub f comma w close bracket plus Epsilon

where:*R sub c comma w* for ... is estimated as:

R sub c comma w equals open bracket P sub c comma w divided by P sub c comma w minus one close bracket minus one

where:*P sub c comma w* is the closing price of company *c* in week *w*;*P sub c comma w minus one* is the closing price of company *c* in week *w* minus one.

*R sub f comma w* for the ...;*R sub m comma w*... in week *w* minus one... in week *w minus one*. Each market return observation will be estimated using the equation:

R sub m comma w equals open bracket I sub m comma w divided by I sub m comma w minus one close bracket minus one.

where:*I sub m comma w* is the closing stock market index value in week *w*; and*I sub m comma w minus one* is the closing stock market index value in week *w minus one*.

*Alpha sub c* is a regression parameter using Ordinary Least Squares (OLS) regression;*Beta sub c* is the company beta and is a regression parameter in the (OLS) regression; and*Epsilon* is a stochastic error term. **↑**

### Paragraph 16

Beta sub adjusted equals open bracket two divided by three close bracket times Beta sub raw plus open bracket one divided by three close bracket.

where:*Beta sub adjusted* is the adjusted company beta to be used in the cost of capital estimate; and*Beta sub raw* is the company beta obtained from the regression analysis **↑**

### Paragraph 17

Canada/U.S. Cost of Equity equals w sub 1 times C sub 1 plus w sub 2 times C sub 2

where:

*C sub one* is the Canadian cost of equity;

*C sub two* is the U.S. cost of equity; and

W sub one equals the sum from d equals one to n of open bracket V sub T comma d close bracket divided by the sum from d equals one to n of open bracket V sub T comma d plus V sub N comma d close bracket

And

W sub two equals the sum from d equals one to n of open bracket V sub N comma d close bracket divided by the sum from d equals one to n of open bracket V sub T comma d plus V sub N comma d close bracket*V sub T comma d* is the volume traded on the Toronto Stock Exchange on day *d*, for each of the most recently ended calendar year ;*V sub N comma d* is the volume traded on the New York Stock Exchange on day *d*, for each day of the most recently ended calendar year; and*n* is the number of trading days in the most recently ended calendar year; **↑**

### Paragraph 19

Tax adjusted cost of equity equals Canada/U.S. Cost of Equity divided by open bracket one minus Corporate Income Tax Rate close bracket **↑**

### Paragraph 20

WACC equals W sub E times CoE plus W sub D times CoD plus W sub DT times CoDT **↑**

## Appendix B

### Paragraph 22

Weighted Average Cost of Capital equals W sub D times C sub D plus W sub E times C sub E plus W sub T times C sub T

Where: W sub D times C sub D is the weight of debt multiplied by the cost rate of debt; W sub E times C sub E is the weight of equity multiplied by the cost rate of equity; and W sub T times C sub T is the weight of deferred taxes multiplied by the cost rate of deferred taxes. **↑**

### Figure 1 Paragraph 26

Figure 1 shows the effect of the debt to equity ratio on the rate of return. It graphs the rate of return (on the vertical or y-axis) against the debt to equity ratio (on the horizontal or x-axis) from three series: Cost of Equity, WACC and Cost of Debt The cost of equity at first increases as the debt to equity ratio increases, then hits a maximum at an arbitrary point and starts to decrease. The WACC decreases at first and then hits a minimum value at an arbitrary point and begins to increase. The cost of debt remains steady at first and then begins to increase at higher levels of the debt to equity ratio. **↑**

### Paragraph 125

Where:

R sub e is the expected or required cost of equity;

R sub f is the risk-free rate;

MRP is the average returns from the market minus the average returns from the risk-free asset over a specified period of time; and

Beta is the systemic or non-diversifiable risk in the equity relative to the market. **↑**

### Paragraph 128

R sub E equals R sub f plus MRP

Where

R sub E is the cost of equity;

R sub f is the risk-free rate; and

MRP is the market risk premium **↑**

### Paragraph 131

R sub E equals open bracket D sub 0 times open bracket one plus g close bracket divided by P close bracket plus g

Where:

R sub E is the return on equity;

D sub 0 is the current dividend;

P is the current price of the stock;

D sub 0 divided by P is the current dividend yield; and

G is the dividend growth rate. **↑**

### Paragraph 132:

P equals D sub 1 divided by open bracket one plus R sub e close bracket plus D sub 2 divided by open bracket one plus R sub e close bracket squared plus D sub 3 divided by open bracket one plus R sub e close bracket cubed plus ellipsis plus open bracket D sub T plus D sub T times Open Bracket one plus g close bracket divided by open bracket R sub e minus g close bracket close bracket divided by open bracket one plus R sub e close bracket exponent T

Where:

D sub 1 ellipsis D sub T represents the divided cash flows in the various periods;

T represents the long run period when growth levels off; and

G represents the equilibrium growth rate in the long term. **↑**

### Paragraph 189

R sub e equals R sub f plus Beta times open bracket MRP close bracket

Where:

R sub e is the required return on the equity;

R sub f is the risk-free rate of return in the economy;

R sub m is the average return of the market as a whole; and

ß is a measure of the risk in the equity relative to the market as a whole. **↑**

### Paragraph 191

R sub e equals R sub F plus beta times open bracket MRP close bracket plus the sum from i equals one to n of gamma sub i times open bracket R sub i minus R sub f close bracket

Gamme sub i for i = 1, 2, dot dot dot n, referred to as risk loadings, measure the sensitivity of the asset to each of the risks that individuals care about and vary across assets; and

Open bracket R sub i minus R sub f close bracket are risk premia which measure the expected return compensation an individual must receive to bear one unit of the relevant risk. **↑**

### Paragraph 192

R sub e equals R sub f comma DC plus Beta sub WM times WMRP plus gamma sub DC times FCRP

Where:

R sub f comma DC is the domestic risk-free rate of return;

Beta sub WM is a measure of the risk in the equity relative to the world market (or a larger market than the domestic market);

Gamma sub DC is the sensitivity of domestic currency return to a change in the foreign currency;

WMRP is the world (larger than domestic) market risk premium; and

FCRP is the foreign currency risk premium. **↑**

### Paragraph 193

R sub e equals R sub f comma DC plus Beta sub WM times open bracket R sub m comma WM minus R sub f comma DC close bracket plus Gamma sub DC times open bracket R sub f comma DC minus R sub f comma FC close bracket **↑**

### Paragraph 196

R sub e equals R sub f plus Beta sub FF times MRP plus b sub s times SMB plus b sub v times HML

Where:

*SMB* (or Small Minus Big) is a factor representing the historical excess returns of two categories of stocks, as measured in terms of market capitalization;

*HML* (or High Minus Low) is a factor representing the historical excess returns of two categories of stocks, as measured in terms of high and low book to market ratio;

B sub FF is analogous but not equal to the traditional beta due to the presence of the two other factors;

R sub e and R sub f retain the same meanings as for the traditional CAPM; and

b sub s and b sub v are determined through multiple regression analysis. **↑**

### Paragraph 199

R sub s equals r plus Term Premium plus Beta times the expected value of open bracket r sub m minus r sub f close bracket. **↑**

### Paragraph 227

R hat sub t equals R sub ft plus beta hat sub t open bracket open bracket one divided by T close bracket times the sum from j equals one to T of open bracket R sub m comma j minus R sub f comma j close bracket close bracket

Where:

R hat sub t is the estimated rate of return on equity for the current year t;

Beta hat sub t is the estimated beta factor obtained through a regression model;

R sub m comma j is the composite rate of return on the market in historical year j;

R sub f comma t is the risk-free rate of return for the current year t;

R sub f comma j is the risk-free rate of return in historical year j; and

T is the number of years over which the market risk premium is estimated. **↑**

### Paragraph 231

Figure 2 graphs daily bond yields for Canadian and US Government Bonds for the month of August 2011. At the beginning of the month, the yields are very low for both bonds. US bond yields are close to zero and Canadian bond yields are close to one percent. The yields on both bonds rise throughout the month. Canadian bond yields rise steeply to a little over three percent around the tenth day of the month and then only moderately thereafter, ending the month slightly above three and half percent. US bond yields also rise steeply to a little over 3 percent around the tenth day of the month and more slowly after, ending the month slightly above four percent. **↑**

### Paragraph 235

R sub e equals R sub f1 plus Beta times the Expected Value of open bracket R sub m minus R sub f2 close bracket.

CN points out that R sub f one in the CAPM equation provides the forward-looking risk-free return to apply to a zero beta asset, while R sub f two is required to calculate risk premium to an asset with non-zero beta. CN disagrees with the Brattle Report recommendation that the same debt instrument should be used to provide the two risk-free rates R sub f one and R sub f two. **↑**

### Paragraph 236

R sub e equals R sub f1 plus Beta times the expected value of open bracket R sub m minus R sub f2 close bracket plus Term Premium **↑**

### Paragraph 237:

...by replacing open bracket R sub f1 plus Term Premium close bracket) in the above equation... **↑**

### Paragraph 252

R sub e equals R sub f plus Beta times open bracket 1 divided by T close bracket times the sum from J equals one to T of open bracket R sub m comma j minus R sub f comma j close bracket.

Where: open bracket 1 divided by T close bracket times the sum from J equals one to T of open bracket R sub m comma j minus R sub f comma j close bracket is the Market Risk Premium.

The first risk-free rate, R sub f, is a forward-looking risk-free rate in the economy, while the second, R sub f comma j, describes the historical risk-free rate in year *j* during the time period *T*, and is used in estimating the market risk premium. **↑**

### Paragraph 257

R hat sub t equals R sub f comma t plus Beta hat sub t times open bracket open bracket one divided by T close bracket times the sum from j equals one to T of open bracket R sub m comma j minus R sub f comma j close bracket close bracket

Where: open bracket open bracket one divided by T close bracket times the sum from j equals one to T of open bracket R sub m comma j minus R sub f comma j close bracket close bracket is defined as the estimated MRP

R hat sub t is the estimated rate of return on equity for the current year *t*;

Beta hat sub t is the estimated beta factor obtained through a regression model;

R sub m comma j is the composite rate of return on the market in historical year *j*;

R sub f comma t is the risk-free rate of return for the current year *t*;

R sub f comma j is the risk-free rate of return in historical year *j*; and

T is the number of years over which the market risk premium is estimated. **↑**

### Paragraph 282

Arithmetic Average equals open bracket one divided by T close bracket times the sum from t equals one to T of R sub m comma t.

where *R sub m comma t* is the observed market return in year *t* and *T* is the total number of years. **↑**

### Paragraph 283

Geometric Average equals open bracket the product from t equals 1 to T open bracket one plus R sub m comma t close bracket close bracket exponent open bracket one divided by T close bracket minus one **↑**

### Paragraph 287

Open bracket one minus open bracket H minus 1 close bracket divided by open bracket T minus one close bracket close bracket times arithmetic average plus open bracket open bracket H minus one close bracket divided by open bracket T minus one close bracket close bracket times geometric average. **↑**

### Paragraph 297

R sub e minus R sub f equals alpha plus Beta times open bracket R sub m minus R sub f close bracket

Where:

R sub e represents observations of historical returns associated with the investment;

R sub f represents the risk-free rate;

R sub m represents observations of historical returns associated with the market; and

a and ß are regression parameters. **↑**

### Paragraph 303

Beta sub BA equals one divided by three plus open bracket two divided by three close bracket times Beta sub UA

Where:

Beta sub BA is the Blume Adjusted Beta; and

Beta sub UA is the unadjusted Beta. **↑**

### Paragraph 316

R sub E equals open bracket D sub zero divided by P close bracket times open bracket one plus g close bracket plus g

Where:

R sub E is the return on equity;

D sub zero is the current dividend;

P is the current price of the stock;

D sub zero divided by P is the current dividend yield; and

g is the dividend growth rate **↑**

### Paragraph 318

P equals Stage one plus Stage two

Where:

Stage one equals the sum from i equals one to n of open bracket D sub zero times open bracket one plus g sub one close bracket exponent i divided by open bracket one plus R sub E close bracket exponent i close bracket;

Stage two equals D sub n times open bracket one plus g sub 2 close bracket divided by open bracket R sub E minus g sub 2 close bracket divided by open bracket one plus R sub E close bracket exponent n

Where g sub 1 is the dividend growth rate that is assumed to apply for the first n years;

G sub 2 is the terminal dividend growth rate;

D sub n is the dividend in year n;

N is the number of years in the first stage; and

All other variables are defined as before. **↑**

### Paragraph 320

P equals Stage one plus Stage two plus Stage three

Where:

Stage one equals the sum from i equals one to n1 of open bracket D sub zero times open bracket one plus g sub one close bracket exponent i divided by open bracket one plus R sub E close bracket exponent i close bracket;

Stage two equals the sum from i equals n1 plus one to n2 of open bracket D sub n1 times open bracket open bracket one plus g sub two close bracket exponent i divided by open bracket one plus R sub E close bracket exponent i close bracket;

Stage three equals D sub n2 times open bracket one plus g sub three close bracket divided by open bracket R sub E minus g sub 3 close bracket divided by open bracket one plus R sub E close bracket exponent n2 close bracket;

D sub n1 is the dividend in year n1;

D sub n2 is the dividend in year n2;

g sub 2 is the dividend growth rate that is assumed to apply for the second stage of the model;

g sub 3 is the terminal dividend growth rate;

n1 is the number of years in the first stage;

n2 is the total number of years in the first two stages of growth; and

all other variables are defined as before **↑**

### Paragraph 331

CF equals IBEI minus CAPEX plus DEP plus DT. **↑**

### Paragraph 333

CF equals IBEI minus CAPEX plus DEP plus DT. **↑**

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