Problem 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?
Problem 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?
Problem 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?
Problem 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?
Problem 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)
Problem 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.)