In estimating the required rate of return three models can be applied. They include dividend growth, CAPM, and APT. APT immerges to be the most accurate and reliable model, suitable for estimating the required return rates.

## Dividend growth

According to the dividend discount model, the stock value is seen in the present value of the stocks expected divided. Despite this model being viewed as outmoded by some analysts, it is clear that a significant amount of intuition that drives discounted cash flow valuation is realized in this model, and as a result, many companies have maintained this model for estimating values. The model can be analyzed in two ways, which are general models and specific versions. In the general model, when one buys a stock, it is expected that two types of cash flows should be issued, that is, the dividends on the period of holding the stocks and the expected prices at the end of the holding period. In addition, the expected price is determined by the future dividends, which makes the stock value to be the present value of dividends through infinity. This implies that the “present value rule” is the determinant of the model’s rationale, and therefore the future value of any asset is based on its current value of expected future cash flow discounted at a rate that is appropriate to the risk that the cash flows hold. The expected dividends and the cost on equity are the basic inputs to the dividend discount model. In obtaining the expected dividends, the assumption on the future growth rates in earnings and payout ratios is made. In addition, determining the required return is based on the riskiness, measured in different ways using different models, for instance, the market beta in the CAPM model, and the factor-beta in the arbitrage and multi-factor models. Moreover, this model is known for its flexibility which is significant in allowing time-varying discount rates with the variation of time caused by the expected changes in interest rates or risk across time. On the other hand, the specific versions of the model are based on the fact that some entities, such as dollar dividends projection, cannot be made through infinity. Hence, a number of versions have been developed for these models, which are based on different assumptions concerning future growth (Michel, 1989).

One of these models is the Gordon Growth Model. This model is used to value a firm in a ‘steady state’ and whose dividends growth rate is sustainable forever. This is done by relating the stock’s value to the expected dividends in the next time period, the cost of equity, and the expected growth rate in dividends. As a result of a stable growth rate, other performance measures of the firm can be expected to grow at the same rate and this growth rate has to be equal or less than the economic growth on which the firm operates. Despite this, other factors such as inflation and the real growth of the economy will likely affect the expected results. The other version used is the two-stage Dividend Discount Model. Here, two phases are considered, which are an initial phase where the growth rate is not fixed, and a fixed phase where the growth rate is constant and expected to hold for a long time.

On the other hand, in defining the growth period, the assumptions that the growth rate is high at the first phase and lower at the end period and also the focus in this method which can lead to skewed firm estimation are major problems. The third model is The H Model for evaluating growth. This model argues that the growth rate in the initial growth is unstable, rather it decreases proportionately over a period to a steady growth rate in the end phase. Furthermore, the model assumes that the growth rate of earning inclines initially and decreases proportionately over the abnormal growth duration to a steadily growing rate. It is also based on the assumption that the dividends pay-out and cost of capital are not impacted by this unstable growth, but rather they are steady. The last model is the Three-stage Dividend Discount Model. Richard (2007), argues that the three-state dividend discount model combines the two-stage and H- models by allowing substantial growth in the initial period, and alteration stage of growth reduction, and the last steady growth stage. It does not impose any restriction on the payout ratio.

These models as based on assumption do not guarantee that the expected results will be obtained. This is because the economic growth and other factors such as inflation, market demand change as well as the currency exchange rate can alter the whole estimated outcome. Hence this model can be said to be environment-dependent. In addition, the assumptions ignore the very same factors of economic change and inflation since they are made on the current growth rate in determining future growth rate. Though they have considered flexibility in some models they still ignore the time factor which is crucial in determining future growth (Fabozzi, 1998).

## CAPM model

The Capital asset pricing model seeks to explain the connection between risk and the returns expected. Thus, it is useful in pricing risky securities. It argues that the returns expected of security comprises of the rate of the securities that are riskless and a risk premium, and any expected return which does not meet this standard is not undertaken. For example, if the risk-free rate is 5% and S&P 500 is expected to return to 12% next year, with the beta value being 1.9 then the expected return will be computed as 5%+(12%-5%)*1.9 which will be 18.3%. this means that if you have to invest in this job, you should expect a return of 18.3% and anything less than that should result in a consideration of investing in another company. In addition, if the beta share is higher, the expected returns are also higher, however, the higher the beta, the worse they perform when it comes to a marked decline. On the other hand, receiving higher returns from beta share does not guarantee that the returns in this CAPM method are realized.

This model gives an expected return that has a high probability of realization. This is because the already known risk-less security and risk premium determine the returns and they can be computed numerically to test their efficiency. On the other hand, although the assumptions are practically reliable, any effect on the market that can bring a decline in growth rate will lead to poor performance which will alter the expected returns. Otherwise, it’s only in a stable market, the assumptions are realistic and realizable. (Robert, 1990).

## The APT model

The Arbitrage Pricing Theory agrees with the CAPM theory in that the discount rate is determined by the exposed risk to the security but in addition, this model does not require all the investors to conduct their activities alike and that the “capital-weighted market portfolio” is not the only held risky asset. For example in a diversified market, multiple sources of risk are available. Hence, the investor does not just focus on market portfolio risk, but rather on what affects them individually, such as a shift in stock, inflation, GDP change, interest rate, or other macro-economic factors. Therefore, this model considers the actions that different securities will incur different risks and in return realize different returns. In addition, the model considers another factor such as short selling, which allows the investor to still earn profit even if the security prices are declining.

This model, therefore, considers several factors that affect the market as a whole. As a result, information on the necessary field in determining the return assists in avoiding limitations to the simple world of market portfolio risk and exercising the real-world risks experienced. Unlike CAPM, this model allows the selection of diversified portfolios that will allow low exposure to factors like inflation and change in the economy hence providing more accurate returns expected (Marcel, 1992).

The assumptions in this model are based on diversified world arguments concerning the risks which are experienced by a different investors in different fields. As a result, the APT model allows all factors which can alter the results expected to be analyzed, and basing the result expected on them, biases that can result in adjustments of the already set expectations are avoided. Thus the model becomes more reliable in estimating the rate of returns than the other models (Ho, Lee, & Yi, 2005).

Simply put, of the three methods estimation of the rate of return required, the APT immerges to be the best model. This model unlike the dividend growth and CAPM models whose assumptions are based on the simple world, and on limited approaches which ignore other major factors which determine the rates of returns, this model considers all the possible determinants in estimating the required rate of returns. It goes beyond simple assumption which affects the market as a whole and gets into the investor themselves dealing with the risks that they can encounter as a whole and as an individual, hence analyzing many major factors that can lead to alteration of the estimated results. Therefore, the APT comes out as being the most accurate and practical model that can be used in rate of returns estimation.

## Reference list

Ho, T., Lee, S. & Yi, S. (2005). *Securities valuation: applications of financial modeling*. London: Oxford University Press.

Fabozzi, F. (1998). *Valuation of fixed income securities and derivatives*. Hoboken: John Wiley and Sons.

Marcel, S. (1992). *New issues in the theory of investment: modernization and persistence effects*. Springer-verlag.

Michel, P. (1989) *Keynes, investment theory and the economic slowdown: the role of replacement and q-ratios*. University of California, Michigan.

Richard, A. (2007). *Principals of corporate finance*. Tata McGraw-hill, New Delhi.

Robert, A. (1990). *Modern investment theory*. Prentice hall, New York.