Duration and YTM are inversely related. Solutions to Problem Set 2 CorporateFinance,Sections001and002 1. 2-4: Use the correct formula but forget to semi-annualize the annual rate before using Second, the yield is higher for riskier bonds. bond. We have to calculate the yield to maturity as if we were calculating the bond’s IRR. The yield rises from 5.06% to 5.20% when the rating drops from AAA to A. Compute the duration of an 8%, 5-year corporate bond with a par value of $1,000 and yield to (b) The yield-to-maturity is below the current yield, because the bond is selling above par. The yield to maturity is the required rate of return on a bond expressed as a nominal annual interest rate. Basic. A 30-year bond with a 10% coupon B. 1. Solutions to Questions and Problems 1. 1. Suppose you purchase the bond at a price of $1000, what is the yield to maturity? 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. There will be a loss of capital which causes the yield to be below the current yield. All other things equal (YTM = 10%), which of the following has the longest duration? Problem Set #13 Solutions 1. First, the longer maturity bonds of the same quality rating have a higher yield. 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. Rem ember that we defined yield to maturity as the IRR of the bond. Solutions to Questions and Problems 2. The current yield is based on the price while the coupon rate is based on par. (b) Bond prices. Price and yield move in opposite directions; if interest rates rise, the price of the bond will fall. 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. IRR stipulates the following relationship between price and yield. Yield to maturity is a complicated average of the separate spot rates of interest. Exercise 4. YIELD TO MATURITY OF THIS BOND (YOU DON’T HAVE TO COMPUTE THE EXACT FIGURE). For instance, for bonds with A rating, the yield for 2-year maturity is 5.13%; and for 20 years, it is 5.82%. (b) Bond prices or yields to maturity? (3.6) Which comes first in the market for U.S. Treasury bonds: (a) Spot interest rates or yields to maturity? (a) The 5-year spot rate (= yield) is 0.0362. 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. A. Problem 2. 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. The following R code computes the The yield to maturity is the interest ra te of the bond. The price of a pure discount (zero coupon) bond is the present value of the par value. For noncallable bonds, the yield to maturity and … Since the coupon payments are annual, this is the yield to maturity. However, the final answer for each problem is found without rounding during any step in the problem. Consider 5-year bonds. 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 ... 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