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# Earning a return; price of bond; estimated per-share price

1) As an investment analyst, you are typing to determine the probability of different returns on Omega Corporation's common stock. As a first step you will determine Omega's required rate of return. The 10-year Treasury bond rate is 4%. The market risk premium is 5% and Omega's beta is 1.4. You have already completed calculations that indicate Omega's expected rate of return is 13% with a standard deviation of 8%.

a) Determine the probability of earning a return.
b) Determine the probability of earning a negative return.
c) Explain whether or not you would advise an investor to buy Omega's common stock.

2) Doisneau 20-year bonds have a 10% annual coupon interest, make interest payments on a semi-annual basis, and have \$1,000 par value. If the bonds are trading with a 12% market's required yield to maturity, is the bond a premium or discount bond? Explain your answer. What is the price of the bond?

3) Suppose the real risk-free rate is 3.50%, the average future inflation rate is 2.25%, a maturity premium of 0.08% per year to maturity applies, i.e., MRP=0.08% (t), where t is the years to maturity. Suppose also that a liquidity premium of 0.5% and a default risk premium of 0.85% apply to A-rated corporate bonds. Determine the rate required for the 5 year Treasury bond and the 5 year A-rated corporate bond.

4) Five years ago, XYZ International issued some 30-year zero coupon bonds that were priced with a market's required yield to maturity of 8%. What did these bonds sell for when they were issued? Now that five years have passed and the market's required yield to maturity on these bonds has climbed to 10%, what are they selling for? If the market's required yield to maturity had fallen to 6%? what would they have been selling for?

5) An analyst is estimating the intrinsic value of Harkleroad Technologies' stock.
Harkelroad's free cash flow is expected to be \$25 million this year, and grow at a rate of 20% for the next 3 years and thereafter at a constant growth rate of 7%. The company's cost of money is 10%. Harkleroad has \$200 million of long-term debt and preferred stock, and 30 million outstanding shares of common stock. What is the estimated per-share price of Harkleroad Technologie's common stock?

#### Solution Preview

1) As an investment analyst, you are typing to determine the probability of different returns on Omega Corporation's common stock. As a first step you will determine Omega's required rate of return. The 10-year Treasury bond rate is 4%. The market risk premium is 5% and Omega's beta is 1.4.

Using CAPM, the return is
Return = Rf + (Rm-Rf) beta
Rf = risk free rate = T bond rate = 4%
(Rm-Rf) = market risk premium = 5%
Return = 4% + 5% X 1.4 = 11%

You have already completed calculations that indicate Omega's expected rate of return is 13% with a standard deviation of 8%.

a) Determine the probability of earning a positive (the word positive should be here) return.

The probability can be seen from the normal distribution. The mean return is 13% and the standard deviation is 8%. We would have all positive return on the right side of the graph since they would be above 8%. On the left side, positive returns would be till 13%/8% = 1.625 times standard deviation since 8% X 1.625 = 13% and beyond this the return would turn negative. We find the probability of returns being 1.625 times the standard deviation (see the standard normal probability distribution for z=1.63) and this comes to 0.4484. The probability of right side is 0.5. Total probability of positive return is 0.5+0.45 = 0.95 or 95%

b) Determine the probability of earning a negative return.

The probability of earnings negative return = 1-0.95 = 0.05 or ...

#### Solution Summary

The probability of earning a return, price of a bond and the estimated per-share price are determined. The expert explains whether or not you would advise an investor to buy Omega's common stock is determined.

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