Question

Please write your answer clearly,especially the last question.

Consider two bonds, each pays semi-annual coupons and 5 years left until maturity. One has a coupon rate of 5% and the other has a coupon rate of 10%, but both currently have a yield to maturity of 8%. How much will the price of each bond change if its yield to maturity decreases from 8% to 7%?

Answer 1

Qi) lets and at assume Face value of Bond is to after 5 years It will be redeeman par F.V= $ 1000 redemption value $1000 Bond- maturity = 5 years or payments - Semi annually is site coupon = 51. proro sroled swara a face value = $1000 soni or Coupon payment = 1000 x 2.5% 39.83 = 25 - since the payments are made f semiannually (Twice a year) we take coupon rate Coupon rate 2.5% (5.1.) Gr Y.T.M = 86 r. for semiannually = 4% maturity 5 years = lo periods Apresent value & price of a bond is present value of all future Coupon payments discounted at YoToM that is 4% Present value interest factor of annuity CPVIFA) for (n=10 and r=4./.) = 8.11 p.v. factor at {m= 10 , r=4.1.] = 0.61556

e value of Bond = Coupon payments & PVIFA + redemption Price x p.v. Facter] - 25x8.11 + 1000 x 0-67556] = 20115 + 67556 Niroo in rete out = 6 878.31 when Y.T.M decreases from 8.1. To The Y.T.M = 1.1. Latate anterrs for semi annually = 14 = 3:51 PUITA for (n=10&r= 3.54.] = 8.32 op. v. factor {n o 8 = 3.51.] = 0.708918 value of Bond = 25x8.32 + 1000 x 0.708918] JO-1301 208+ 708.92 916.92 change in price of Bond = 916.92-818-3) when YTM changes by of the bond Increases by $38.61 to price of suloyo

Borid 2 roquel tro do F: V = $1000 redemption value $1000 Coupon payment 1000 x 10.% . 22.30 =$100 For semi annually = 100 - $50 YTM= 4% { & mot maturity = 5 years = 10 periods PVIFA[n 10 r= 41.] = 8.11 ) Be PVF at (n=76 7=41] = 0.6755.6 I value of Bond = 50 +8:11 + 1000 x 0.61556 resolo tusol t slog = 405.5 +675.56 sute - 1081.06 when y.Tim decreases to 7% y.T.M- 7.1 Zapaper period semi annually = 7.1. - 3.5% PVIFA [no r = 3.5 = 8.32 p.v. F at [no, v = 3.5] = 0. Tosaiq ue e value of Bond = (50 x 8.32 + 1000x 0.70898) - 416+ 7o8.92 . - 1124.92 a. In crease in value of Bond = ll24.92 - 1881.06 - 43.86

Q2) Yied to call (YTC) = Call price - Market value Coupon Interst payment t- number of years untill call calprice & Market value here in given Questions, Coupon payment = 10.1 per year . semi anual 10 = $1. Face value = $1000 (assume) Coupon payments = $1000 45% $50 number of years to call Buyears n = 8 periods call price = logo Market value = $1135.90 10550 - 11.35.90 eur Y.T. (= 50+ oo-1135.90 8 1050 + 1135.90 = 39.2625 1092.95 7:181

Time line – 99 12 12 12 and 141 N.p. v = -99 + 12x 1 [1- 20) 141 (1+r) 21 21+ here r= 12% de -99+ :. -99+ 12x 1 pr1 7 0.12 1 (1.12) ini (1.12) 3 1 -12 = -99 7:80 - 13.05 Nop ve 232-05 million 6) NO, IRR rule is not reliable, because the project has a negative cash flow that comes after the positive ones. c) Because the total cash flows are equal to zero [-99 + 12+20 -141] one IRR must be o% and also because

the cash once, we This IRR flows change sign more than can have a second IRR. should solve 12xl [ 1 - 1 1772 ) 14 in - 99=0 O Rя 0. trail and error method we can I find second IRR.