Chapter 5 Principles Of Finance Questions And Problems

Chapter 5 principles of Finance questions and problems involving yield calculations

6 Assignment Chapter 5principles Of Finance Ichapter 5questions 5 4

6 Assignment Chapter 5principles Of Finance Ichapter 5questions 5 4

6 Assignment "Chapter 5" Principles of Finance I Chapter 5 QUESTIONS: 5-4, The risk-free of interest is 4% Inflation is expected to 2% this year and 4% during the next 2 years Assume that maturity risk premium is zero. What is the yield on 2–years Treasury securities? What is the yield on 3–years Treasury securities? Question 5-5 A treasury bond that matures in 10 years has a yield of 6%. A 10-year corporate bond has a yield of 9%. Assume that the liquidity premium on the corporate bond is 0.5. What is the default risk premium on the corporate bond? PROBLEMS: 5-6, The real risk free rate is 3% and inflation is expected to be 3% for the next 2 years A 2-year. Treasury Security Yield 6.3%. What is the maturity risk premium for the 2 years security? Problem 5-12, A 10-year, 12% semiannual coupon bond with a par value of $1,000 may be called in 4 years at call price of $1060. The bond sells for $1,100. (Assume that the bond has just been issued.) a. What is the bond’s yield to maturity? b. What is the bond’s current yield? c. What is the bond capital gain or loss yield? d. What is the bond’s yield to call? Problem 5-20 Because of recession, the inflation rate expected for the coming year is only 3%. However the inflation rate in the year 2 and thereafter is expected to be constant at some level above 3%. Assume that the real risk free rate is r*=2% for all maturities and that there are no maturity premiums. If 3-year Treasury notes yield 2 percentage points more than 1-year notes. What inflation rate is expected after Year 1?

Paper For Above instruction

The principles of finance often involve understanding the relationship between risk, return, and interest rates, especially as they pertain to government and corporate securities. This paper examines various topics outlined in Chapter 5, including the calculation of yields on treasury securities, the determination of risk premiums, bond valuation and yield calculations, and inflation expectations. The understanding of these concepts is essential for investors, financial analysts, and policymakers to make informed investment decisions and anticipate future economic conditions.

Yield on Treasury Securities and Inflation Expectations

One fundamental concept in finance is the yield on Treasury securities, which reflects market expectations of interest rates, inflation, and risk premiums. For example, if the risk-free rate is 4% with an expected inflation of 2% this year and 4% over the next two years, the expected yields on 2-year and 3-year Treasury securities can be calculated using the expectations hypothesis of the term structure of interest rates. Since maturity risk premiums are assumed to be zero, the yields are primarily driven by expected inflation plus the real risk-free rate.

The yield on a 2-year Treasury security can be approximated as the average of the expected inflation rates over the next two years, added to the real risk-free rate. So, with inflation expectations of 2% this year and 4% next year, the 2-year yield is approximately:

Y_2-year ≈ r* + [(inflation₁ + inflation₂) / 2] = 4% + [(2% + 4%) / 2] = 4% + 3% = 7%

Similarly, the 3-year yield would incorporate inflation expectations over three years, which involves calculating the geometric average or extending the expectation. Given the same inflation expectations, the 3-year yield would roughly be:

Y_3-year ≈ r* + [(inflation₁ + inflation₂ + inflation₃)] / 3 = 4% + [(2% + 4% + 4%) / 3] ≈ 4% + 3.33% ≈ 7.33%

Risk Premiums in Corporate Bonds

The yield spreads between Treasury bonds and corporate bonds reflect additional risk premiums, such as default risk and liquidity risk. For example, if a 10-year Treasury bond yields 6%, and a 10-year corporate bond yields 9%, with a liquidity premium of 0.5%, the default risk premium can be deduced as:

Default risk premium = (Corporate yield − Treasury yield) − Liquidity premium = (9% − 6%) − 0.5% = 2.5%

This premium compensates investors for the higher risk of default inherent in corporate bonds compared to government securities.

Bond Yield Calculations

Bond valuation and yield calculations involve assessing the bond’s cash flows, maturity, coupon rate, and market price. The yield to maturity (YTM) is the interest rate that equates the present value of the bond’s cash flows to its current price. For a 10-year, 12% semiannual coupon bond with a par value of $1,000, priced at $1,100, the YTM can be estimated through iterative calculation or financial calculator methods. In this case, the YTM is approximately 10.5%, which balances the present value of coupons and principal repayment with the current market price.

Current yield is calculated as the annual coupon payment divided by the current price:

Current yield = (Coupon payment / Market price) = ($120 / $1,100) ≈ 10.91%

The capital gain or loss yield considers the difference between the purchase price and the face value at maturity or call, impacting total returns. The yield to call (YTC) involves calculating the yield assuming the bond is called at 4 years at a premium of $60, which generally results in a higher yield than YTM if the bond is called early.

Inflation Expectations and Future Rates

Inflation expectations are crucial for predicting future interest rates. Suppose the real risk-free rate is estimated at 2%, with no maturity premiums, and 3-year Treasury notes yield 2 percentage points more than 1-year notes. This spread indicates that investors expect higher inflation or increased risk over longer horizons.

The expected inflation after Year 1 can be inferred by examining the yield spread, adjusting for the real rate, and using the Fisher effect. If the 1-year rate is 2%, and the 3-year rate exceeds it by 2%, then inflation expectations in Year 2 and beyond are likely to be above 3%, reflecting anticipated economic conditions and monetary policy influences.

Conclusion

Understanding the intricacies of bond yields, risk premiums, and inflation expectations is vital for effective financial decision-making. Through these calculations, investors can better assess risk-adjusted returns and adjust their portfolios accordingly. These principles also inform policymakers about market perceptions of economic stability and expectations of future inflation, guiding monetary policy and economic forecasts.

References

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