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Problems:
Easy Problems 1-6
• 5-1 Bond Valuation with Annual payments
Jackson Corporation’s bonds have 12 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 8%. The bonds have a yield to maturity of 9%. What is the current market price of these bonds?
80*7.1607+1000*.3555 = $928
• 5-2 Yield to Maturity for Annual payments
Wilson Wonders’s bonds have 12 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 10%. The bonds sell at a price of $850. What is their yield to maturity?
100+1000-850/12/1000+850/2 = 112.5/925 = .1216 or 12.16%
• 5-6 Maturity Risk Premium
The real risk-free rate is 3%, and inflation is expected to be 3% for the next 2 years. A 2-year Treasury security yields 6.3%. What is the maturity risk premium for the 2-year security?
6.3-3-3 = 0.3%
Intermediate Problems 7-20
• 5-7 Bond Valuation with Semiannual payments
Renfro Rentals has issued bonds that have a 10% coupon rate, payable semiannually. The bonds mature in 8 years, have a face value of $1,000, and a yield to maturity of 8.5%. What is the price of the bonds?
50*11.44+1000*.5138 = 1086
• 5-13 Yield to Maturity and Current Yield
You just purchased a bond that matures in 5 years. The bond has a face value of $1,000 and has an 8% annual coupon. The bond has a current yield of 8.21%. What is the bond’s yield to maturity?
Current price = 80/.0821 = 974
YTM = 80+1000-974/5/1000+974/2 = 85.2/987 = .0863 or 8.63%
(Brigham, Eugene F. . Financial Management: Theory & Practice, 13th Edition. South Western Educational Publishing, 03/2010. pp. 210 - 211).
Questions
(6-6) If a company’s beta were to double, would its expected return double?
It is not necessary, for example if the risk free rate of return is 4% and market risk premium is 6% and this point with beta is 1, the rate of return will be 10%, but beta is 2 the rate of return is 16% ,which shows a double beta but expected return is just 1.6 times not doubled.
Brigham, Eugene F. . Financial Management: Theory & Practice, 13th Edition. South Western Educational Publishing.
Problems:
Easy Problems 1-3
(6-1) Portfolio Beta
An individual has $35,000 invested in a stock with a beta of 0.8 and another $40,000 invested in a stock with a beta of 1.4. If these are the only two investments in her portfolio, what is her portfolio’s beta?
.8*35000/75000+1.4*40000/75000 = .3733+.7467 = 1.12
(6-2) Required Rate of Return
Assume that the risk-free rate is 6% and that the expected return on the market is 13%. What is the required rate of return on a stock that has a beta of 0.7?
6+.7*13-6= 10.9%
(6-7) Required Rate of Return
Suppose rRF = 9%, rM = 14%, and bi = 1.3.
a. What is ri, the required rate of return on Stock i?
9+1.3*14-9=15.5%
b. Now suppose rRF (1) increases to 10% or (2) decreases to 8%. The slope of the SML remains constant. How would this affect rM and ri?
Ri will be at 10% = 10+1.3*14-10 = 15.2%
It has decreased by 0.3%
Ri will be at 8% = 8+1.3*14-8 = 15.8%
It has increased by 0.3%
It may be assumed that there will not be any impact on rM
c. Now assume rRF remains at 9% but rM (1) increases to 16% or (2) falls to 13%. The slope of the SML does not remain constant. How would these changes affect ri?
Ri will be at 16% = 9+1.3*16-9 = 18.1%
It has increased by 2.6%
Ri will be at 13% = 9+1.3*13-9 = 14.2%
It has decreased by 1.3%
Brigham, Eugene F. . Financial Management: Theory & Practice, 13th Edition. South Western Educational Publishing.
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