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ll SurveyMonkey-onnaire tool Citation Mach..urnal article myBusinessCourse Capital One-Accounts Su- CourseSmart. Book Homework #5 McGraw-Hill Connect ebook Figure 8.4.jpg 663* B Homework #5 Question 7 (of 7 value: 10.00 points Laurel, Inc., and Hardy Corp. both have 8 percent coupon bonds outstanding, with semiannual interest payments, and both are priced at par value. The Laurel, Inc., bond has five years to maturity, whereas the If interest rates suddenly rise by 2 percent, what is the negative answer should be indicated by a minus sign. Do not round intermediate calculations a enter your answers as a percent rounded to 2 decimal places, e.g, 32.16) nd Percentage change in price of Laurel Percentage change in price of Hardy If interest rates were to suddenly fall by 2 percent instead, what would the percentage change in the these bonds be then? (Do price of not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g 32.16.) Percentage change in price of Laurel Percentage change in price of Hardy Hints References eBook & Resources Hint #1 Hint#2

Explanation / Answer

1) Percentage change in the price of Laurel -7.72% Percentage change in the price of Hardy -15.80% Working: When bonds are priced at Par.Coupon rate and market rate(Yield to maturity) is same. So, current market rate is 8% for both bonds. Further, price of bond is the present value of cash flows from bond. Now we calculate percentage change in the price after 2% rise in the market rate. Suppose Par Value of both bonds is $ 1000. Semi annual coupon Interest = $       1,000 x 4% = $             40 Laurel: Hardy: # 1 # 1 Present value of annuity of 1 = (1-(1+i)^-n)/i Where, Present value of annuity of 1 = (1-(1+i)^-n)/i Where, = (1-(1+0.05)^-10)/0.05 i 5% = (1-(1+0.05)^-32)/0.05 i 5% = 7.7217349 n 10 = 15.802677 n 32 # 2 # 2 Present value of 1 = (1+i)^-n Present value of 1 = (1+i)^-n = (1+0.05)^-10 = (1+0.05)^-32 = 0.6139133 = 0.2098662 # 3 # 3 Present Value of coupon interest $             40 x 7.721735 = $     308.87 Present Value of coupon interest $            40 x 15.80268 = $     632.11 Present Value of Par Value $       1,000 x 0.613913 = $     613.91 Present Value of Par Value $      1,000 x 0.209866 = $     209.87 Price of Bond $     922.78 Price of Bond $     841.97 # 4 # 4 Percentage change in price = (922.78-1000)/1000 Percentage change in price = (841.97-1000)/1000 = -7.72% = -15.80% 2) Percentage change in the price of Laurel 8.53% Percentage change in the price of Hardy 20.39% Working: Now we calculate percentage change in the price after 2% fall in the market rate. Suppose Par Value of both bonds is $ 1000. Semi annual coupon Interest = $       1,000 x 4% = $             40 Laurel: Hardy: # 1 # 1 Present value of annuity of 1 = (1-(1+i)^-n)/i Where, Present value of annuity of 1 = (1-(1+i)^-n)/i Where, = (1-(1+0.03)^-10)/0.03 i 3% = (1-(1+0.03)^-32)/0.03 i 3% = 8.5302028 n 10 = 20.388766 n 32 # 2 # 2 Present value of 1 = (1+i)^-n Present value of 1 = (1+i)^-n = (1+0.03)^-10 = (1+0.03)^-32 = 0.7440939 = 0.388337 # 3 # 3 Present Value of coupon interest $             40 x 8.530203 = $     341.21 Present Value of coupon interest $            40 x 20.38877 = $     815.55 Present Value of Par Value $       1,000 x 0.744094 = $     744.09 Present Value of Par Value $      1,000 x 0.388337 = $     388.34 Price of Bond $ 1,085.30 Price of Bond $ 1,203.89 # 4 # 4 Percentage change in price = (1085.30-1000)/1000 Percentage change in price = (1203.89-1000)/1000 = 8.53% = 20.39%

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