Risk And Capital

Introduction

For this paper, I will discuss how theoretical stock prices are calculated and how prices may react to market forces such as risk and interest rates. By using financial data for IBM, I will show the formulas for Capital Asset Pricing Model (CAPM) and the Constant Growth Model (CGM) and how they determine IBM's stock price. Lastly, I will compare and discuss IBM's theoretical stock price (Po) and its actual market stock price (P) and discuss why there is such a difference between the two.

Risk Free Rate of Interest

The first thing we need to do for this assignment is to find an estimate of the risk-free rate of interest (krf). According to the Bloomberg.com website, the krf for U.S. Treasuries 10-year Notes and Bonds is 4.25%. Our assignment gives us an assumed market risk premium of 7.5%.

We then need to know the following information from the IBM Stock Information provided in the assignment:

1. IBM's beta (Ð"ÑŸ) = 1.64

2. IBM's current annual dividend = 0.80 or 80 cents

3. IBM's 3-year dividend growth rate (g) = 8.2%

4. Industry Price/Earnings = 23.2

5. IBM's EPS = $4.87

Capital Asset Pricing Model (CAPM)

With the information we now have, we need to use the Capital Asset Pricing Model (CAPM) to calculate IBM's required rate of return, or ks:

ks = krf + (km Ð'- krf) * beta

ks = risk free rate + (market risk premium * beta)

ks = 4.25% (or .0425) + (7.5% (or .075) * 1.64) = 0.16550 or 16.55%

Constant Growth Model (CGM)

Now we use the Constant Growth Model (CGM) to find the current stock price for IBM. This is called the theoretical price or P0. When you want to find the value of a share of common stock, the Constant Growth Model, or Gordon Growth Model, is an easy formula to use, as the dividends are growing at a constant rate:

Formula: P0 = D1/ks Ð'- g

D1 = IBM's current annual dividend = $0.80 or 80 cents

ks = 16.55% (from previous calculations)

g = IBM's 3-year dividend growth rate (g) = 8.2%

P0 = $0.80 / (.1655 - .082) = .90/.01125 = 80

P0 = $9.580838 = $9.58

According to the Bloomberg.com website, the current stock quote, or P, as of January 30, 2008 for IBM is $101.220. This is much higher than the theoretical price, or P0, of the stock, which is $80.

Summary of Calculations

Does this mean the price of the stock is over or under priced? Not necessarily. According to an article on AllExperts.com, "The market is forward looking and any model is based on past performance. To understand this, one must look at future situations and the future economic environment. Models do help to determine a starting point but everything else must be future looking. Implied volatility is just that, implied. Most if not all models use past volatility and project that same volatility forward." (2006, AllExperts.com)

Market risk, or volatility, is the day-to-day fluctuations in a stock's price. The higher the volatility, the more prone a stock is to large price swings. On the other hand, low volatility stocks tend to show a history of stable prices.

Increased Market Risk Premium

For the next part of this assignment, we are to assume that the market risk premium has increased from 6% to 10%; and this increase is due only to the increased risk in the market, so our krf and the beta will remain the same. Therefore, we will need to compute a new ks to reflect this increase.

The new ks would be:

ks