Describle the observed differences in your answer to part (b) and (c)

(a) Coupon payment ($) = 1000*0.8 800 (1) Time unit payment (2) Cash flow ($) 3) PV of CF (Discount rate = 7%) ($) (4) Weight (5) = (1)*(4) BO 74.766 0.072 0.0723 80 69.8751 .0676 0.1352 65.3038 0.0632 .1895 4 1080 823.9268 0.7969 .1877 Column Sums 033.8721 1.0000 3.5847 Macaulay duration = 3.5847 Modified duration = Mac D/(1+r) Modified duration = 3.5847/(1+0.07) 3.3502 Modified duration = 3.3502 1) Time unit payment (2) Cash flow ($) (3) PV of CF (Discount rate = 7%) ($) (4) t+t^2 (5) = (3) *(4) 30 74.7664 2.0000 149.5327 80 69.8751 5.0000 419.2506 AWNG $5.3038 12.0000 783.6460 1080 323.9268 20.0000 16478.5366 Column Sum 1033.8721 17830.9658 Convexity = 17830.9658/[(1033.8721)*(1+0.07)^2] Convexity = 15.0640 (b) When yield changes to 5% (1) Time unit payment (2) Cash flow ($) (3) PV of CF (Discount rate = 5%) ($) 80 76.1905 80 72.5624 w 80 69.1070 1080 888.5187 Column Sums 106.3785 New bond price = $1106.3785 % change in the bond's price = (1106.3785-1033.8721)/1033.8721 % change in the bond's price = 7.01% (c) % change in price using the modified duration formula = (-modified duration)*(1+r) % change in price using the modified duration formula = (-3.3502)*(5%-7%) % change in price using the modified duration formula = 6.7% % change in price using the convexity and duration adjustment formula = (-modified duration)*(change in yield)+(1/2)(convexity)(change in yield)^2 % change in price using the convexity and duration adjustment formula = (-3.3502)(5%-7%)+(1/2)(15.0640)(5%-7%)^2 % change in price using the convexity and duration adjustment formula = 7%