Finance

Estimating the cost of equity for any firm is a task which requires a lot judgment and estimation. Different methodologies and theories exits on the best way to calculate the cost of equity which is basically the rate of return investors require on their investors. After careful consideration we are to present to the esteemed Board the findings on the subject. The dividend growth model provides the best estimate of the cost of equity. While it has its limitations, it uses dividends, the only cash flow other than capital gain associated with investments in stock, to derive at a cost of equity. It also uses the current market price which lends the method more credence as investors have the option to sell off their shares at the market price if they deem the return too low. A more detailed review of the dividend discount model, the capital asset pricing model and arbitrate pricing theory is given below.

Dividend Discount Model
There are two types of cash flow associated with a stock the dividends and the expected share price at the end of the holding period. And because the expected price is based on future dividends, the value of a stock is the present value of the dividends that will be relieved for an infinite period of time. The same concept can be used to calculate the cost of equity. With todays share price and the expected dividends, we can use the dividend growth model to come to a conclusion about the rate of return required by the investors.

One of the basic variants of the dividend discount model is the Gordon growth model. The main assumption underlying the Gordon growth model is that firms will continue to pay dividends which will grow at a sustainable and stable rate through infinity.  (Forbes, 2010)

While the major advantage of the Gordon growth model is its ease of use, its major limitation is the very assumption that makes it so easy to implement. The assumption that dividends will continue to grow at a stable rate till infinity is quite unrealistic. Since it is being assumed that dividends will continue to grow at a stable rate, it can also be said it is being assumed that earnings will also continue to grow at a stable rate. This is because if dividends continue to grow at a certain rate while earnings increase at a slower or deteriorating rate, there will come a time when dividends will equal earnings and there will be no more room for the dividends to continue to grow at the stable rate  (Damodaran Online, 2009).

The second limitation is also related to the stable growth rate. What criterion should be used to derive this stable growth rate How high or low should it The uncertainty regarding inflation, economic cycles, whether the firm is operating in a mature or growing industry, all make it more difficult to ascertain a growth rate for dividends which can be assumed to last till infinity. The assumption regarding the stable growth rate makes the Gordon growth model most appropriate for companies operating in mature industries where it is more reasonable to assume that dividends and earnings can both grow at a stable rate.  (Damodaran Online, 2009)

Now that we understand the basics of the dividend growth model, we look at some of its other variations. The two stage dividend growth model, as its name suggests, uses two stages of growth. There is an initial phase with a growth rate that is expected to last for a limited time horizon, followed by the growth phase with the stable rate of growth through infinity. The limitations of the Gordon growth model regarding the stable growth rate also apply to the two stage dividend growth model.  (Forbes, 2010)

Added limitations include specifying the length of the initial phase of extraordinary growth. Since the growth rate is usually higher during the initial phase, the value of the investment will increase at a higher rate during this period. When the growth rate declines and stabilizes, the rate of increase in the value of the investment will slow down. Consequently, the longer the initial phase, the higher the value of the investment. The second limitation specifically associated with the two stage growth model is that we assume that the growth decline overnight as the firm enters the stable phase. This is unrealistic as the growth will slow down gradually before stabilizing.  (Damodaran Online, 2009)
Another variation of the dividend discount model is the H Model which allows for a gradual linear decline in the growth rate during the initial phase. While this model overcomes the limitation of the low stage dividend model in that it allows for a gradual decline in the growth rate, the assumption that it decreases at a linear stage is a limitation of this model. Another variant, an extension of the two stages and H Model dividend growth model, allows for an initial phase of high growth, a second stage where growth declines and a final stage of infinite stable growth.  (Damodaran Online, 2009)

Capital Asset Pricing Model
The capital asset price model (CAPM) attempts to explain the relationship between risk and return. CAPM states that the expected return on scrip is equal to the rate of return on a risk free asset plus a risk premium. The required rate of return is also the cost of equity, i.e. the return at which investors are willing to invest in the company. CAPM is calculated using the following formula

Required rate of return  Risk free rate of return   (Market Return   Risk free rate)
Beta () is a measure of risk which is considered relative to the risk of the market. Each company has its own beta which tells us how risky the company is compared to the market. A company with a beta of 2 is considered to be twice as risky as the market. The CAPM differentiates between systematic risk and unsystematic risk. Systematic risk is the market risk which cannot be diversified away. Unsystematic risk is firm specific risk and can be eliminated through diversification. It also states that for a given level of risk, investors have a required rate of return and as risk increases so do their required rates of return.  (Forbes , 2010)

CAPM is based on a set of assumptions which are stated below
Investors are risk averse
Investors have homogenous expectations
There exists a risk free asset and investors can borrow and lend at the risk free rate
All assets are perfectly divisible and priced in a perfectly competitive market
All investors are equally informed about the market
No markets imperfections such as transaction costs or taxes exists
These assumptions are quite unrealistic and while the whole concept of CAPM is based on these assumptions, they are also its limitations. However, each of these assumptions can be relaxed one at a time to see the effect it has on the required rate of return. CAPM requires the calculation of beta which involves significant judgment. Another limitation of the CAPM is the risk free rate and the risk free asset. Generally, government securities are considered to be risk free but give the superfluity of such securities, an appropriate one needs to be chosen.  (Forbes , 2010)

Arbitrage Pricing Theory
Arbitrage pricing theory (APT) states that there are many sources of risk and a lot of uncertainty in the economic climate. It tries to explain the underlying reasons for assets returns and use them to derive an appropriate rate of return for a security. APT can be used to conduct a sensitivity analysis on the various economic factors and how they affect the risk and return of a particular security or portfolio. While this is advantageous in the sense that it allows us to incorporate specific factors and does away with the restrictive assumptions of the CAPM, it also makes the APT difficult to implement because of the large number of economic variables and the uncertainty regarding their impact on a security.  (Goetzmann, 1996) (Pietersz, 2006-2009)

APT is also based on a number of assumptions which are stated below
Security returns move in a linear manner because of the existence of some systematic risk
Inventors are able to distinguish these risks and estimate how they will impact security returns
Some investors will be risk takers who will try to exploit differences in returns through arbitrage

A major advantage of ATP is that it allows for a number of risk sources and that they are the drivers for security returns. However, it is required that investors are able to identify these risk sources and gauge their impact on security returns is a mammoth undertaking which is not always possible to a reliable degree of accuracy.  (Goetzmann, 1996)