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risk-free rate of interest

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The bond rate can be found at http://www.bloomberg.com/markets/index.html

PROBLEM:

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).

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Hi, Please see the attached file. The latest US treasury bond rate was used.

1. 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%.

Go to the website and collect the information about U.S. 10-Year Treasury. Thus, the risk free rate is 3.59%. Market risk premium is 7.5%.

2. 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.

1. IBM's beta (ß): 1.64
2. IBM's current annual dividend: $0.80 per share (from supplied pdf file)
3. IBM's 3-year dividend growth rate (g): 8.2% (from supplied pdf file)
4. Industry P/E - 23.2 (from supplied pdf file)
5. IBM's EPS: $4.87

3. With the information you now have, use the CAPM to ...

Solution Summary

The risk-free rate of interest is examined.

$2.19
See Also This Related BrainMass Solution

Interest rates, risk-free rate, expectation, liquidity, 1 year treasury bond,

1. The interest rate on 1-year Treasury securities is 5 percent. The interest rate on 2-year Treasury securities is 6 percent. The expectations theory is assumed to be correct. If the real risk-free rate is assumed to be 3% every year, what is the inflation expected in year-2?

2. The real risk-free rate of interest is 3 percent. Inflation is expected to be 4 percent this coming year, jump to 5 percent next year, and increase to 6 percent the year 3. According to the expectations theory, what should be the interest rate on 3-year, risk-free securities today?

3. Assume that the expectations theory holds, and that liquidity and maturity risk premiums are zero. If the annual rate of interest on a 2-year Treasury bond is 10.5 percent and the rate on a 1-year Treasury bond is 12 percent, what rate of interest should you expect on a 1-year Treasury bond one year from now?

4. The real risk-free rate is expected to remain constant at 3 percent. Inflation is expected to be 2 percent a year for the next 3 years, and then 4 percent a year thereafter. The maturity risk premium is 0.1%(t - 1), where t equals the maturity of the bond. (The maturity risk premium on a 5-year bond is 0.4 percent.) A 5-year corporate bond has a yield of 8.4 percent. What is the yield on a 7-year corporate bond that has the same default risk and liquidity premiums as the 5-year corporate bond?

5. Two years back a firm had issued $1,000 par value bonds carrying the coupon rate of 12% payable annually. These bonds' maturity was 10 years at the time of issue, and the firm would pay 5% premium on maturity. Calculate,
(a) The cost of these bonds to the firm, if the firm's marginal tax rate is 38%? (Use Excel spreadsheet)
(b) An investor bought these bonds recently at $990 and intends to hold for the rest of the maturity period. If the investor is in 15% marginal tax rate, what is the after-tax return of the investor? (Use Excel spreadsheet)

6. If these bonds are currently traded at $975, and if the firm wants to issue the new bonds to day what coupon rate should the firm offer on the new bonds? Assume that the new bonds will be issued and paid on maturity at par. (Don't ignore maturity value effect.)

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