Hello,

I am looking for some guidance on 2 related questions (b & c) for a Corporate Finance course. Please see the questions in attachment with my attempt to answer them. However I don't feel confident that I'm on the correct path with these calculations. Can you please indicate the correct calculations so that I may learn in the process.

Thank you

b. Calculate the duration of a coupon bond with the following features. What general conclusion can we make about the duration of coupon bonds relative to their time to maturity? (3 marks) Face value of $1000 Five years to maturity Coupon rate of 11%, paid semi-annually Current price of $970 (Hint: The effective annual yield should be 12.1604%.) 1 PMT Period Cash Flow Present Value of Weight = wt Weight of each (Year) = t (CF) CF CF/1 +rt PV of CF/Sum of PV CF CF (t x wt) 0.5 55 53.40 0.043997693 0.021998847 55 51.85 0.042720606 0.042720606 1.5 55 50.34 0.041476477 0.062214715 2 55 48.88 0.040273544 0.080547087 2.5 55 47.45 0.039095328 0.097738321 3 55 46.07 0.037958309 0.113874928 3.5 55 44.73 0.036854247 0.128989866 4 55 43.43 0.035783142 0.14313257 4.5 55 42.17 0.034744995 0.156352476 5 1,055 785.38 0.647095658 3.23547829 1,213.70 4.083047705 The duration on this coupon bond is approximately 4.08 years. We can conclude that the duration of a coupon bond is relatively lower than its time to maturity. 1 Duration is a measure of interest rate risk. Specifically, it measures the approximate percentage change in bond price given a small percentage change in interest rate (% bond price change / % interest rate change). For example, for a bond with a duration of five years, a 0.1% change in interest rate would change the bond's price by 5 * 0.1% = 0.5%, approximately. Suppose that the interest rates on all bonds increase uniformly by 0.1% (this is what is commonly called a "parallel upward shift in yields of 10 basis points"). What is the percentage change in the price on the coupon bond in part (b)? What is the approximate coupon bond price? Note that bond yield and bond price are inversely related to each other (i.e., an increase in yield should lead to a decrease in bond price). (2 marks) Solution Calculation Bond duration x Interest rate change 4.08 x 0.10 = 0.408% Bond price x Percentage increase 970 x 0.408 = $395.76 Approximate coupon bond price = 970 + 395.76 = $1,365.76 Percentage change in price of coupon bond = 395.76/970 = 40.80%