Problem Set #13 Solutions 1. 2-4: Use the correct formula but forget to semi-annualize the annual rate before using 1. A. Second, the yield is higher for riskier bonds. (b) Bond prices. Price and yield move in opposite directions; if interest rates rise, the price of the bond will fall. Solutions to Problem Set 2 CorporateFinance,Sections001and002 1. IRR stipulates the following relationship between price and yield. Compute the duration of an 8%, 5-year corporate bond with a par value of \$1,000 and yield to (a) The 5-year spot rate (= yield) is 0.0362. First, the longer maturity bonds of the same quality rating have a higher yield. Rem ember that we defined yield to maturity as the IRR of the bond. The following R code computes the The price of a pure discount (zero coupon) bond is the present value of the par value. Solutions Manual 8. This is because the fixed coupon payments determined by the fixed coupon rate are not as valuable when interest rates rise—hence, the price of the bond decreases. First write down the formula for yield to maturity: 1000 = 1000 10% A 20-year bond with a 9% coupon C. A 20-year bond with a 7% coupon D. A 10-year zero-coupon bond 2. 7. Duration and YTM are inversely related. Solutions to Questions and Problems 2. bond. Solutions to Questions and Problems 1. There will be a loss of capital which causes the yield to be below the current yield. (b) Bond prices or yields to maturity? (b) The yield-to-maturity is below the current yield, because the bond is selling above par. Problem 2. Since the coupon payments are annual, this is the yield to maturity. The yield rises from 5.06% to 5.20% when the rating drops from AAA to A. For noncallable bonds, the yield to maturity and … Suppose you purchase the bond at a price of \$1000, what is the yield to maturity? A 30-year bond with a 10% coupon B. Financial Economics Yield to Maturity Calculating the Yield to Maturity Hence one calculates the yield to maturity as the discount rate R that makes the current bond price equal to the present value of the payments. YIELD TO MATURITY OF THIS BOND (YOU DON’T HAVE TO COMPUTE THE EXACT FIGURE). Exercise 4. The current yield is based on the price while the coupon rate is based on par. The yield to maturity is the required rate of return on a bond expressed as a nominal annual interest rate. Solution: (a) Spot interest rates. All other things equal (YTM = 10%), which of the following has the longest duration? Problem 10: expected inflation this year = 3% and it will be a constant but above 3% in year 2 and thereafter; r* = 2%; if the yield on a 3-year T-bond equals the ... Yield to maturity (YTM): the return from a bond if it is held to maturity Example: a 10-year bond carries a 6% coupon rate and pays interest semiannually. The yield to maturity is the interest ra te of the bond. 1. Basic. However, the final answer for each problem is found without rounding during any step in the problem. (3.6) Which comes first in the market for U.S. Treasury bonds: (a) Spot interest rates or yields to maturity? Yield to maturity is a complicated average of the separate spot rates of interest. We have to calculate the yield to maturity as if we were calculating the bond’s IRR. For instance, for bonds with A rating, the yield for 2-year maturity is 5.13%; and for 20 years, it is 5.82%. Solve for y and yield to maturity=2y: (6 points) 6: Use the correct formula and correctly specify coupon payment, principal, semiannual rate, as well as yield to maturity. Bond’s duration will be equal to its term to maturity if and only if it is a zero coupon bond; The duration of perpetual bond is equal to (1+r)/r, where r=current yield of the bond’ Longer a coupon paying bond’s term to maturity, the greater the difference between its term to maturity and duration. Consider 5-year bonds. 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