# Calculating the market price of a stock

The risk-free rate of return is 3 percent, and the expected return on the market is 8.7 percent. Stock A has a beta coefficient of 1.4, an earnings and dividend growth rate of 5 percent, and a current dividend of $2.60 a share.

A) What should be the market price of the stock?

B) If the current market price of the stock is $27, what should you do?

C) If the expected return on the market rises to 10 percent and the other variables remain constant, what will be the value of the stock?

D) If the risk-free return rises to 4.5 percent and the return on the market rises to 10.2 percent, what will be the value of the stock?

E) If the beta coefficient falls to 1.1 and the other variables remain constant, what will be the value of the stock?

F) Explain why the stock's value changes in c through e?

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#### Solution Preview

Please refer attached file for better clarity.

a)

Risk Free Rate=rf=3%

Beta=b=1.4

Expected Market Return=rm=8.70%

Expected Return on stock=r=rf+b*(rm-rf)=10.98%

Growth Rate=g=5%

Current Dividend=Do=$2.60

Expected dividend next year=D1=Do*(1+g)=$2.73

Current Market price of stock=Po=D1/(r-g)=$45.65

b)

Current market price is lower than estimated price, ...

#### Solution Summary

Solution describes the steps to estimate the current value of a given stock. It also checks the effect of variations in expected return of market, risk free rate and beta on the price of a stock.

By walking you through a set of financial data for IBM, this assignment will help you better understand how theoretical stock prices are calculated

By walking you through a set of financial data for IBM, this assignment will help you better understand how theoretical stock prices are calculated; and how prices may react to market forces such as risk and interest rates. You will use both the CAPM (Capital Asset Pricing Model) and the Constant Growth Model (CGM) to arrive at IBM's stock price. To get started, complete the following steps.

Find an estimate of the risk-free rate of interest, krf. To obtain this value, go to Bloomberg.com: Market Data [http://www.bloomberg.com/markets/index.html] and use the "U.S. 10-year Treasury" bond rate as the risk-free rate. In addition, you also need a value for the market risk premium. Use an assumed market risk premium of 7.5%.

Download this IBM Stock Information document (.pdf file). Please note that the following information contained in this document must be used to complete the subsequent questions.

IBM's beta (ß)

IBM's current annual dividend

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

Industry P/E

IBM's EPS.

With the information you now have, use the CAPM to calculate IBM's required rate of return or ks.

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

Now use appropriate Web resources to find IBM's current stock quote, or P. Compare Po and P. Do you see any differences? Can you explain what factors may be at work for such a difference in the two prices? This section is especially important - with more weight in grading - so you may want to do some study before answering such a question. Explain your thoughts clearly.

Now assume the market risk premium has increased from 7.5% to 10%; and this increase is due only to the increased risk in the market. In other words, assume krf and stock's beta remains the same for this exercise. What will the new price be? Explain what happened.

Recalculate IBM's stock using the P/E ratio model and the needed info found in the IBM pdf file. Explain why the present stock price is different from the price arrived at using CGM (Constant Growth Model).

To receive full credit on this assignment, please show all work, including formulae and calculations used to arrive at financial values