# Theoretical Stock Prices

**Topics:**Capital asset pricing model, Risk-free interest rate, Time value of money

**Pages:**3 (675 words)

**Published:**April 5, 2008

Running head: RISK AND CAPITAL: THEORETICAL STOCK PRICES

Risk and Capital: Theoretical Stock Prices

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FIN410, Unit 3, IP

Risk and Capital: Theoretical Stock Prices

Have you ever wondered how companies come up with stock prices? What makes one company’s stock prices so much different from another company and why do the prices go up and down? We will analyze at a set of financial data to calculate theoretical stock prices for IBM. We will use a systematic approach utilizing the Capital Asset Pricing Model (CAPM) and the Constant Growth Model (CGM) to determine IBM’s stock price. 1. An estimate of the risk-free rate of interest (krf) was obtained by going to Bloomberg.com and using the U.S. 30-year Treasury bond rate. Even though our assignment sheet asks us to use the 10-year rate, we have determined the 30-year rate is more accurate. krf = 4.375 and the market risk premium is 7.5%. 2. According to the IBM Stock Information Document:

IBM’s Beta (β) = 1.64

IBM’s Current Annual Dividend = .80

IBM’s 3-Year Dividend Growth Rate (g) = 8.2%

Industry P/E = 23.2

IBM’s EPS = 4.87

3. Using the CAPM to calculate IBM’s required rate of return (ks):

ks= β(market risk premium) + risk free rate

= 1.64(7.5) + 4.375

= 16.675% (required rate of return)

Theoretical Stock Prices 3

4. Using the CGM to calculate IBM’s current stock price (Po):

Po = D1 / (r – g)

D1 is next year’s dividend calculated as D0(1 + g)

= .80(1+.082) / (.1667 - .082)

= .8656 / .0847

= $10.21

5. As of 02/29/2008, IBM’s stock price (p) is $113.86 (Rogue Investor, 2008). P = $113.86 whereas Po = $10.21

There is quite a difference in the two prices. The reason for these differences is simply that CAPM and CGM use many assumptions in their models. IBM has been around a long time and many investors see the value of this company. Investors may also expect IBM’s growth rate to increase in...

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