Question

Problem 12-01 What would be the initial offering price for the following bonds (assume $1,000 par value and semiannual compounding)? Do not round intermediate calculations. Round your answers to the nearest cent. a. A 14-year zero-coupon bond with a yield to maturity (YTM) of 12%. $ b. A 22-year zero-coupon bond with a YTM of 10%. $

Answer 1

Computation of Price of Zero-coupon Bond: a) 14 year zero coupon bond: = Redemption amount * PVF(6%,28 semi annual years) = $1000 * 0.19563 = $195.63 a) 22 years zero coupon bond: = Redemption amount * PVF(5%,44 semi annual years) = $1000 * 0.11686 = $116.86 Computation of Mcaulay Duration: = ((1+y)/y) - (((1+y)+t(c-y))/(c*((1+y)^t-1)+y)) Volatility of Bond: = Duration/(1+y) Where, с t = Yield to maturity of bond = 7% semi annualy = Coupon rate of bond = 4% semi annualy = Maturity period = 6 Semi annual years Duration: = ((1+0.07)/0.07) - (((1+0.07)+6(0.04-0.07))/(0.04*((1+0.07)^6-1) +0.07)) = 5.4 semi annual years That is 2.7 years Volatility of Bond: = 2.7 years / (1+0.14) = 2.7 / 1.14 = 2.34% Means, for every 1% change in YTM, The price reversely change by 2.34% Here, YTM reduces to 12.50% that is reduces by 1.50% therefore, price increase by 3.51% (2.34*1.5)