Title: Comparing the dividend growth and CAPM Approaches to evaluating the cost of equity capital; A report

Summary

The dividend growth model and the CAPM are comparatively explored as alternative approaches to calculating the required rate of returns on investments. The CAPM is found to be an advancement being free from the very restrictive drawbacks of the dividend growth model of requiring constant dividend payments to be satisfied. A way of evaluating the cost of equity of a company that does not have its stocks traded in the market is briefly mentioned.

(1) The Dividend growth model

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 The dividend growth approach to valuation of a stock is based upon the notion that its intrinsic value is essentially the present value of the future stream of income expected from the stock. This approach is based upon the following assumptions:

1. The stock under consideration is to be held over an infinite period of time

2. The stock yields a dividend (Di, i = 1, 2,..,?) payment annually over its infinite lifetime

3. In equilibrium the intrinsic value (V) of the stock equals its market price (P)

4. The growth rate of the dividends is constant[1] (g) and is lower than the discount rate (k)

To perceive the necessity of these assumptions we have to go through the mechanism of the derivation of the valuation formula. Based upon such assumptions, the intrinsic present value of the stock at period ‘0’ is given by the equation

Similarly,

Putting these relations in the expression for V0,

Similarly, we arrive at

This leads to

Now, for constantly growing dividends, we have

                                    (since k> g is assumed)

So,

This is the expression for the value of the stock in the dividend growth approach. Here, k is the required rate of return and the cost of equity for the company in question. Evidently with information about the dividend return in the next period, the market price of the stock and the growth rate of the dividend, the required rate of return can be calculated by solving for it from

                                                k = D1/P0 + g.

This approach has the great advantage of being extremely easy to compute as it involves a very easy formula. However, I do feel it to be inappropriate to apply for the valuation of our company primarily because it requires constant growth of dividends and moreover that rate has to be lower than the cost of equity capital for the formula to be applied. This perpetual constancy of dividend growth is very unlikely to be met. Moreover, this approach is applicable only if the company pays dividends and that too at a constant growth rate. Another large drawback is that the risk involved in investing is excluded although that does play a large role in determining the choice of the investor. (Gordon. 1962)

 (2) The CAPM

The Capital Asset Pricing Model (CAPM) determines the optimality of an investment through analyzing the expected returns and risk relationship. It is advancement over the dividend growth model in that it is not limited by the restrictive assumptions of requiring constant dividend growth rates that lie below the required rate of return and further in that the risk of investing is incorporated. The model is based upon the following assumptions

1. Expectations are assumed to be homogeneous. This implies that the beliefs regarding the returns distribution are the same. This assumption is required to allow analysis in terms of a single representative investor.

2. A single period time horizon is assumed for all investors. This is done to keep the computation simple. Although this simplifies the model, it by no means does so at the cost of losing generality.

3. Every investor is allowed to lend or borrow at a risk free rate. This risk free rate is generally the return on risk free investments like government securities. It is incorporated to exhibit the relative risk involved in investing in any given asset.

4. For simplicity any form of transaction costs are assumed away.

5. The investors are assumed to have preference for any type specific returns. In particular, they are assumed to be indifferent between choosing from dividends and capital gains of the same value.

6. Unanticipated price level rises are assumed away so that isolation of the systematic and unsystematic risk is facilitated.

7. The number of investors is assumed to be large enough so that no single investor can influence the prices through individual actions.

8. The markets are assumed to be in equilibrium so that the marginal optimization conditions can be applied.

9. The investors are assumed to be rational agents. This is to ensure that the model deals with agents that are attempting to optimize investment choices only.

Based upon these assumptions the cost of equity capital or the required rate of return is derived as

 Re = Rf + B ( MRP)

Where, Re = required rate of return, Rf = the risk free rate, B = coefficient measuring responsiveness of the returns of a particular asset to the market returns rate[2], and MRP = Market Risk Premium, measured as the difference between the market rate of returns and the rate of returns from the risk free asset. (Campbell, 1995)

(3) The relation between CAPM and modern Portfolio approach

 Modern portfolio theory in essence models the optimal diversification that is to be undertaken by rational investors. By choosing the right assets the investor aims to minimize risks and maximize returns. The portfolio is created by combining various assets and thus in the model it is taken as the weighted mix of the chosen assets. The expected returns of the portfolio thus are the weighted average of the expected or required returns of each asset calculated using the CAPM. So in the modern portfolio approach the optimal combination of assets are chosen by minimizing risk and maximizing the returns and the computation depends crucially on using CAPM values for individual asset required return values.

To calculate the cost of equity capital for a firm that does not has its stocks traded, the primary hindrance arises out of the fact that while to estimate the Beta for the firm, the past prices have to be known, these are not available for types of firms under question. So, the normal mechanism of computing the Beta fails. A way out is to apply the following formula that uses proxies from comparable firms. (Damodaran, 2007)

Betaprivate firm = Betaunlevered (1 + (1 – tax rate) (Optimal Debt/Equity))

    The unlevered Beta values for any business can be calculated by using the relation

                        bunlevered = blevered / (1 + (1 – tax rate) (Debt/Equity))

The levered Beta is an average of the Beta values of publicly traded comparable firms.

 Essentially, the Beta value is estimated using data from comparable firms after adjusting for the risk (Damodaran, 2007).

Using this cost of equity capital is estimated.

Campbell, H.(1995), The CAPM, WWWFinance, Retrieved February 2008 from: http://www.duke.edu/~charvey/Classes/ba350/riskman/riskman.htm

Damodaran, A., (2007), “Valuing Private Companies and Division, Process of Valuing Private Companies”. Retrieved February 19, 2008 at: http://pages.stern.nyu.edu/~adamodar/New_Home_Page/lectures/pvt.html , or here.

Gordon, Myron J. (1962). The Investment, Financing, and Valuation of the Corporation. Homewood, Ill.: R.D. Irwin. (Accessed through questia)

[1] This constancy of the growth rate essentially implies

[2] Measured as the ratio of covariance of the returns of the particular asset and the market returns to the variance of the market returns

x

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