There are different methods that can be used to value shares. For instance, the Gordon model is one of the most commonly used in stock valuation. The Gordon model assumes that a company pays constant growth dividends to its shareholders every year. The input in the model is the required rate of return, growth rate, and dividends per share. The required rate of return represents the minimum expected return by shareholders for investing their money in a risky business rather than in risk free T-bills. The growth rate represents the amount of increase in dividends per share from one year to the other. However, the model assumes that a company will exist forever and pay constant dividends that grow at a constant rate (Keenan, 2013, p.254). In order to estimate the value of a share, the model takes all the dividends and discounts them into the present using a predetermined required rate of return. The computation of the intrinsic value is calculated by a mathematical formula of an infinite series of numbers. This memorandum seeks to explain how the Gordon model is used to calculate the intrinsic value of a share. Moreover, it explain systematically how the Gordon model can be employed to calculate the value of shares of the company in order to identify whether they are under or overvalued.

The Gordon constant growth model is represented below.

Intrinsic value = D (1+g) / (r-g)

Where,

*g = dividend growth rate*

r = the required rate of return

*D = annual dividend*

For instance, in question 1, the intrinsic value of the share when the required rate of return is 8% is calculated as shown below:

3(1+0.06)/0.08-0.055 =126

In order to calculate the value of a share, the annual dividends must be established together with the estimated future growth rate. In this case, the dividend growth rate is 5.5% and annual dividends paid is $3 per share. Moreover, it is critical to establish the required rate of return, which can also be referred as the “hurdle rate.” However, calculating the required rate of return requires more information. In question one, the required rate of return is given as 6%, 8%, 10%, and 12% (computation in the excel).

Although the Gordon model is commonly used, it assumes a constant growth in dividends per share. However, in the real world, it is very difficult for a company to pay constant dividends because of changes in the business cycle and unexpected events in the market. The model also assumes that the required rate of return is greater than the growth rate. If the growth rate is greater than the required rate of return, the result will be negative, thus, the model will be worthless.

When applying these assumptions, the value of the stocks is undervalued which makes it a “buy” because the maximum price that investors should pay is above the share prices. Therefore, investors will gain if they buy the stocks today and anticipation for prices changes in future to reflect the intrinsic value. Although the intrinsic value of a share is important when determining a buy or a sell decision, it is imperative to consider the earning capability of a company. Since buying shares means acquiring part of a company, investors should only invest in profitable businesses. Any investors will want to know how much return they can obtain by investing in the company. Investors should also consider the price to earnings ratio. When investors buy shares, they expect a return from their investments. Therefore, the earnings per share become imperative when making a decision whether to buy shares or not. Investors want to earn high return on their investment. It becomes critical to analyze a company in order to ensure it has a high prospect of growth that will be reflected in the earnings per shares.

Before buying shares, an investor will consider the amount of dividends paid by the company and the pattern. It is essential to consider the amount of dividends paid because many companies have a particular pattern of dividends payment trend. Some companies make huge profits but do not pay high dividends. This can be affected by management decisions regarding future expansion plans. Ideally, executive might decide to pay low dividends irrespective of a company making high profits because they want to expand the operations of the business. An investor should evaluate financial statements because some companies that pay high dividends make losses. Today, many firms borrow long-term debts in order to be able to sustain constant dividends. However, this goal is not sustainable in the long term. Investors do not want to invest in such a company because they might risk losing their investments. Therefore, although it is critical to evaluate the intrinsic value of a share, many factors affect share prices. A comprehensive analysis of the statement of financial position will help an investor to know how a company funds its dividend policy. For instance, a company that acquires long-term debts at the end of each accounting period might be a signal that debt capital is used to pay dividends. Therefore, investors must be careful before investing their money in a company. In summary, the intrinsic value is one of the factors that can help an investor to make sound investment decisions.

## Calculating the market premium

The market premium represents the expected return from a market portfolio and the risk-free rate. It is also equal to the slope of the security market line. The market risk premium for all investors is equal because it shows the overall risk in the market (Heinrichs, Hess, Homburg, Lorenz, & Sievers, 2013). However, the market premium differs from one investor to the other based on their attitude toward risk tolerance and investment decisions. It can be calculated using the following formula:

*Market Risk Premium = Expected Return of the Market – Risk-Free Rate*

The expected return from the market is usually based on the S&P 500. It can be calculated by replacing the formula as shown below.

0.11-0.04 = 0.07 or 7%

### Calculating the required rate of return

The required rate of return is calculated in corporate finance and in equity valuation. It considers many factors affecting a firm including the risk associated with a particular investment and industry (Stowe, Mcleavey & Pinto, 2009, p.173). It sets the minimum rate of return an investor should accept before buying shares considering all the options available and the business cycle of the firm. Before calculating this rate of return, an investor must consider the performance of the market as a whole including the rate of return on the current T-bill in the market. The required rate of return can be calculated using the following formula;

k = risk free rate + [market risk premium x beta]

0.04 + (0.07*1.2) = 12.4%

The intrinsic value of the stock can be calculated using the Gordon formula as shown below.

D1 / (r-g)

1.65/0.124-0.1 = 68.75

## References

Arora, A., & Gruber, R. (2010). Valuation Project: A Practical Approach to Estimating the Intrinsic Value per Share. *Journal of the Academy Of Business Education*, *11*82-110.

Heinrichs, N., Hess, D., Homburg, C., Lorenz, M., & Sievers, S. (2013). Extended Dividend, Cash Flow, and Residual Income Valuation Models: Accounting for Deviations from Ideal Conditions* Extended Dividend, Cash Flow, and Residual Income Valuation Models: Accounting for Deviations from Ideal Conditions. *Contemporary Accounting Research*, *30*(1), 42-79.

Keenan, M. (2013). Models of equity valuation: the great serm bubble. *Journal of Finance*, *25*(2), 243-273.

Spiegel, M., & Tookes, H. (2013). Dynamic Competition, Valuation, and Merger Activity. *Journal of Finance*, *68*(1), 125-172.

Stowe, J. D., Mcleavey, D. W., & Pinto, J. E. (2009). Share Repurchases and Stock Valuation Models. *Journal of Portfolio Management*, *35*(4), 170-179.