Question 1
The risk free rate from Bloomberg.com is 2.625%
Question 2
Beta = 1.64
Current annual dividend = $0.8
3-year dividend growth rate = 8.2%
Industry P/E = 15.65
Earnings per share = $4.87
Question 3
Ks = KRF + (Risk Premium) Bs
Where KRF is the risk free rate as determined by the central bank,
Risk premium is the difference between market risk and the risk free rate.
Bs is the security beta and is a volatility measure of the degree to which the securities returns moves in the same direction as market risk.
The required rate of return is then calculated as;
Ks =2.625 + (9) 1.64= 17.39%
Question 4
Current stock price using Constant Growth Model
(D0) = $0.8,
G=8.2%,
(D1) = $0.8*1.082 = $0.8656
Po= D1/ (Ks-g)
Where Po is the price of a share
D1 is the value of the expected dividends
Ks. is the expected rate of returns. It is the minimum rate of return investors will accept from their investment.
G is the rate at which dividends are expected to grow.
Price of the stock is then calculated as;
Po= 0.8656/ (0.1739-0.082) = $9.42
Difference =$76.28 - $9.42 =$66.86
The difference of $66.86 could have resulted from:
First is the assumption that the market risk premium is 9%. This premium is volatile and changes results in alteration of the required rate of return and consequently the stock price calculated.
Secondly, the demand for XYZ shares had been rising during the preceding month causing an increase in stock price. This is not reflected in the calculation of share price
Thirdly, the growth rate of 8.2% is an arbitrary estimation and might be different from the real growth rate. This will result to errors in the calculation of the price per share.
Question 5
Assuming that the risk premium increase from 9% to 12%
Ks = 2.625 + (12)1.64
Ks= 22.31%
P0 = D1/ (Ks-g)
Where Po is the price of a share
D1 is the value of the expected dividends
Ks. is the expected rate of returns. It is the minimum rate of return investors will accept from their investment.
G is the rate at which dividends are expected to grow.
Price of the stock is then calculated as;
Po = 0.8656/ (0.2231-0.082) = $6.13
There is a decrease in stock price because of the increase in market risk. This is because investors will demand a high return due to increased risk. The high returns will force prices down.
Question 6
Using the P/E ratio model, stock price can be calculated as follows
EPS = $4.87
P/E Ratio = 23.2
Po = EPS X P/E = $4.87 X 15.65 = $76.22.
The two models, constant growth model and price earnings ratio are different because CGM is based on historical data while the latter is based on investors future expectations. Price earnings ratio reflects future dividend expectation as well as the growth potential. This conceptual difference explains the disparity in the calculated prices per share.
References
Altman, E. (1968). The Journal of Finance. Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy, 589-609.
Bloomberg. (2013, January). Markets Overview. Retrieved March 3, 2013, from Bloomberg: http://www.bloomberg.com/markets/
Roberts, H. (1959). Stock-Market "Patterns" and Financial Analysis: Methodological. Suggestions. Journal of Finance, 1-10.
Zhu, Y., & Zhou, G. (2009). Technical Analysis: An Asset Allocation Perspective on the Issue of Moving Averages. Journal of Financial Economics, 519-594.
