2. The price of any bond is the PV of the interest payment, plus the PV of the par value. Notice this problem assumes a semiannual coupon. The price of the bond at each YTM will be: a. P = $35({1 – [1/(1 + .035)]30 } / .035) + $1,000[1 / (1 + .035)30] P = $1,000.00 When the YTM and the coupon rate are equal, the bond will sell at par. b. P = $35({1 – [1/(1 + .045)]30 } / .045) + $1,000[1 / (1 + .045)30] P = $837.11 When the YTM is greater than the coupon rate, the bond will sell at a discount. c. P = $35({1 – [1/(1 + .025)]30 } / .025) + $1,000[1 / (1 + .025)30] P = $1,209.30 When the YTM is less than the coupon rate, the bond will sell at a premium. 3. Here we are finding the YTM of a semiannual coupon bond. The bond price equation is: P = $1,050 = $32(PVIFAR%,26) + $1,000(PVIFR%,26) Since we cannot solve the equation directly for R, using a spreadsheet, a financial calculator, or trial and error, we find: R = 2.923% Since the coupon payments are semiannual, this is the semiannual interest rate. The YTM is the APR of the bond, so: YTM = 2 2.923% = 5.85% 4. Here we need to find the coupon rate of the bond. All we need to do is to set up the bond pricing equation and solve for the coupon payment as follows: P = $1,060 = C(PVIFA3.8%,23) + $1,000(PVIF3.8%,23) Solving for the coupon payment, we get: C = $41.96 Since this is the semiannual payment, the annual coupon payment is: 2 × $41.96 = $83.92 And the coupon rate is the annual coupon payment divided by par value, so: Coupon rate = $83.92 / $1,000 = .0839 or 8.39% 6. Here we are finding the YTM of an annual coupon bond. The fact that the bond is denominated in yen is irrelevant. The bond price equation is: P = ¥92,000 = ¥2,800(PVIFAR%,21) + ¥100,000(PVIFR%,21) Since we cannot solve the equation directly for R, using a spreadsheet, a financial calculator, or trial and error, we find: R = 3.34% Since the coupon payments are annual, this is the yield to maturity. 14. Here we are finding the YTM of semiannual coupon bonds for various maturity lengths. The bond price equation is: P = C(PVIFAR%,t) + $1,000(PVIFR%,t)

Miller Corporation bond: P0 = $40(PVIFA3%,26) + $1,000(PVIF3%,26) = $1,178.77 P1 = $40(PVIFA3%,24) + $1,000(PVIF3%,24) = $1,169.36 P3 = $40(PVIFA3%,20) + $1,000(PVIF3%,20) = $1,148.77 P8 = $40(PVIFA3%,10) + $1,000(PVIF3%,10) = $1,085.30 P12 = $40(PVIFA3%,2) + $1,000(PVIF3%,2) = $1,019.13 P13 = $1,000 Modigliani Company bond: P0 = $30(PVIFA4%,26) + $1,000(PVIF4%,26) = $840.17 P1 = $30(PVIFA4%,24) + $1,000(PVIF4%,24) = $847.53 P3 = $30(PVIFA4%,20) + $1,000(PVIF4%,20) = $864.10 P8 = $30(PVIFA4%,10) + $1,000(PVIF4%,10) = $918.89 P12 = $30(PVIFA4%,2) + $1,000(PVIF4%,2) = $981.14 P13 = $1,000 All else held equal, the premium over par value for a premium bond declines as maturity approaches, and the discount from par value for a discount bond declines as maturity approaches. This is called “pull to par.” In both cases, the largest percentage price changes occur at the shortest maturity lengths. Also, notice that the price of each bond when no time is left to maturity is the par value, even though the purchaser would receive the par value plus the coupon payment immediately. This is because we calculate the clean price of the bond. 15. Any bond that sells at par has a YTM equal to the coupon rate. Both bonds sell at par, so the initial YTM on both bonds is the coupon rate, 7 percent. If the YTM suddenly rises to 9 percent: PLaurel = $35(PVIFA4.5%,4) + $1,000(PVIF4.5%,4) = $964.12 PHardy = $35(PVIFA4.5%,30) + $1,000(PVIF4.5%,30) = $837.11 The percentage change in price is calculated as: Percentage change in price = (New price – Original price) /