i) Calculating cost of equity using CAPM Model:
Capital Asset Pricing Model, often abbreviated as ‘CAPM’, is the most fundamental concept in the investment theory of present time. This is an equilibrium model that predicts the expected return on a stock, given the expected return on the market, the stock’s beta-coefficient and the risk free rate. Considered from the borrower point of view, this model is used to calculate the cost of equity for the company using the following formula:
Cost of Equity= RFR+ Beta(Equity Risk Premium)
Below is the detailed explanation of cost of equity calculated for Tim Hortons Inc:
Risk Free Rate: This refers to rates being offered by treasury securities in the United States. Referring to the March 2014 data, the rate on 10 year US treasury Bond is 2.75%. Thus, this will be the risk free rate in our calculation.
Beta: For CAPM Model, we will be using Beta obtained from Yahoo Finance, which amounts to 0.78.
Equity Risk Premium: It is the additional return which the investors expect to receive above Risk Free Rate from their investment in a common stock. Using the research of American Appraisal, the equity risk premium prevailing in US is 6.0%
Hence, cost of equity for Tim Hortons Inc using CAPM Model will be:
Cost of Equity= RFR+ Beta(Equity Risk Premium)
= 2.75+0.78(6)
=7.43%
Assumptions of CAPM Model:
1)Investors are risk averse and are only concerned with the expected returns, variance and co-variance while selecting optimal portfolio.
2)Investors can borrow or lend at the risk free rate.
3)There are no taxes, transaction cost or any other friction to the investment process.
Limitation of CAPM:
Although, the CAPM Model Is widely accepted but it still have many limitations:
Unstable Beta Value:
Beta is an integral part of CAPM Model but the beta multiple itself do not stay stable. Hence, the validity of CAPM model is questioned.
Unrealistic Assumption:
Another limitation relating to CAPM Model is that it is based on unrealistic assumption. For Instance, the model assumes equal lending and borrowing rates which is not possible in real life.
ii)Calculating cost of equity using Dividend Discount Model:
The dividend discount model is based on the rationale that the intrinsic value of stock is the present value of its future dividends. Considering the period of dividends given, we calculate the growth rate on dividends to be 23%.
Dividend Declared on 21/2/2013: $0.26
Dividend Declared on 20/2/2014: $0.32
Growth Rate: 23%(Approx)
Thus, using the formula for constant dividend growth rate
Value of the Stock= Dividend(1+growth rate)/[Cost of Equity(k)- Growth Rate]
54.70= .32(1+.23)[k-.23]
54.70[k-0.23]= .3936
54.70k-12.581= .3936
54.70K= 12.974
K= 23.71%
Thus, cost of Equity using Dividend Discount Model is 23.71%.
Following are the assumption of the dividend discount model used:
- Dividends are the appropriate measure of the shareholder wealth
- The constant dividend growth rate, g, and the cost of equity are never expected to change
- The rate of cost of equity must be greater than the growth rate of dividends
Limitation of the Dividend Discount Model:
Although, the model is easy and simple to use, but the significant limitation of this case it produces absurd results when the growth rate of the dividends converges closely to the cost of equity. Thus, as we can see that while the CAPM Model produced Cost of Equity of 7.43%, DDM provided us with the result of 23.71%. Thus, it is not always suitable to use the DDM as part of our analysis.
iii)Beta using CRSP:
In the above equation:
reti,t = log of ( 1 + return for security i on day t)
n = number of observations for the year
Thus, Beta for Tim Hortons Inc, using CRSP data will be:
Beta=[ (.027314855)-{(1/364)(.1999763)(.027314855}]/ [.027242668-{(1/364)(.1889664)(.027314855)}]
Beta= .02729984862/ .02722848781
Beta= 1.0026
Data:
Final Conclusion:
Considering the advantages of CAPM Model and its wide applicability, we will use the cost of equity of so generated using the CAPM Model.
Works Cited
CRSP Calculations. (2014, March 22). Retrieved from Crsp.com: http://www.crsp.com/products/documentation/crsp-calculations
(2011). Equity Valuaton: Concept and Basic Tools. In C. Institute, Equity Investments (pp. 298-304). Boston: Custom.
UNITED STATES GOVERNMENT BOND 10Y. (2014, March 22). Retrieved from Tradingeconomics.com: http://www.tradingeconomics.com/united-states/government-bond-yield
Yahoo Finance. (2014, March 22). Tim Hortons Inc. Retrieved from Yahoo Finance: http://finance.yahoo.com/q?s=THI
