3 Risk And Capital

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The risk-free rate of return (Krf) is the rate of return that investors demand from a project that contains no risk (Gallagher & Andrew). In order to find this amount, we must go to Bloomberg.com and find the current rate for today, July 28, 2006, which happens to be 5.05% (Bloomberg.com). This means that 5.05% is the least that an investor will accept for a return on their investment.

The values for IBM stocks that are given in the stock information document that accompanied this assignment:

IBMs beta (Ð² average = 1) = 1.64

IBMs current annual dividend = $0.80 per share

IBMs 3-year dividend growth rate (g) = 8.20%

Industry P/E = $23.20

IBMs EPS (net income/shares) = $4.87

The CAPM formula and the interpretation of its components are as follows:

kp = kRF + (kM – kRF) x Ð²

In this formula, the capital asset pricing model, we calculate the required rate of return on an investment project given its degree of risk as measured by beta. So the meanings of each component of this formula are as follows:

kp = the measured rate of return suitable for the investment project

kRF = the risk-free rate of return

kM = the required rate of return on the overall market

Ð² = the projects beta

So by inserting our quantities that we have already found we can find the answer to our CAPM formula for this problem. We must as remember to use the 5.00 as our risk-free rate of return, which was the answer we found for question 1. We must also use the assumed market risk premium of 7.5%, which was provided in the text of this assignment. Since our Km-Krf is equal to the market risk premium, we can therefore find our value using the premium rate we were already given. Below is our calculation once the numbers are plugged into the problem to reach our intended amount:

Ks = 5.05% + (7.5% X 1.64)

Ks= 17.35%

Use the CGM to find the current stock price for IBM. We will call this the theoretical price or Po.

The formula to calculate Po = D1 / (ks-g)

Here Po stands for the current price of the common stock. D1 represents the dollar amount of the dividend expected one period from now. ks represents the required rate of return per period on the common stock investment. g is equal to the expected constant growth rate per period of the companys common stock dividends. Utilizing the numbers we have already accumulated we can then find our theoretical price as follows

D1 = 0.80 (1+0.0820) = $0.8656 (next years dividend)

Ks-g = 0.1735 – 0.0820 = .0915

Po = 0.8656/0.0915 = $9.46

As of NYSE closing on July 26, 2006 the price of IBM stock is $75.83. Since, my theoretical price using the CGM method was only $9.51; this means there was a large difference between the theoretical and actual amounts. This is most likely due to the assumed value being off. Most likely, because this calculation is dependent

on a stocks value growth is at a constant rate. The CGM method relies on the growth rate remaining constant indefinitely (Gallagher & Andrew) whereas, in actuality there is no definite or constant in the future of any stock. This is mainly because if the return is expected to be low, people will start selling their stocks, therefore driving the price lower. If the expected return is high, more people will be looking to invest in this stock and the price will therefore be driven higher. What this tells us is that the price of stocks is basically dependent on the level of risk that individuals and businesses feel comfortable with compared to the level of risk of a certain type of stock

With the increase in risk premium to 10%, new ks comes to 21.45% (Ks= 5.05 + (10) X 1.64=21.45%). Using the Dividend Discount Model, the new Po comes to $6.53 (P0=.8656/