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Investment Analysis & Portfolio Management HW 6 Bond Pricing Assume a par value of $1000 on all bonds and annual interest payments unless otherwise stated. 1) 2) 3) What is the current value of of a $1000 par value 10 year bond with a 7% coupon rate with interest paid annually, if the current market interest rate is 7.75%? N I PV PMT FV What is the current value of of a $1000 par value 10 year zero coupon bond if the current market interest rate is 7.75%? N I PV PMT FV What is the current value of of a $1000 par value 12 year bond with a 8% coupon rate with interest paid semi- annually, if the current market interest rate is 6.9%? N 4) 5) I PMT FV What is the current value of of a $1000 par value 12 year bond with a 8% coupon rate with interest paid quarterly, if the current market interest rate is 6.9%? N I PV PMT FV What is the Yield to Maturity (YTM) and Yield to Call (YTC) for a bond which is currently priced at 1030 if the bond has a coupon of 6%, matures in 8 years but could be called at a price of 1010 in 4 years. Interest is paid semi- annually. Use the Bond Equivalent Method. a) Yield to Maturity (YT) N I PV PMT FV b) Yield to Call (YTC) N I 6 PV PV PMT FV Calculate the current value of the bonds under each of the following circumstances for period 1 and period 2 and the percentage change in the value between the two periods. Interest is paid annually. Market Interest Rate = Period 1 8% Maturity (Years) 3 15 4% 12% Coupon Rate Market Interest Rate = Period 2 7% Maturity (Years) 3 15 4% 12% Coupon Rate % Change in Bond Value from Period 1 to 2 3 Yr 15 yr 4% coupon 12% coupon b) What do you conclude about the relative sensitivity of bond prices to changes in interest rate? 1) Longer maturities relative to shorter maturities? 2) High coupon bonds relative to lower coupon bonds? 7a Calculate the Macaulay Duration for a 6% bond with 5 years to maturity if the market interest rate is 8% if interest is paid annually. You may choose to use the table below to help structure the calculation. Principal 1000 Period Market Discount Rate 6% 8% Total PV of Total (PVi/PVTotal)* Payment Payment Time Coupon 1 2 3 4 5 Total Macaulay Duration = 7b What do you think will happen to the Macaulay Duration of the bond in 7a if the market discount rate is higher? [ Note: you may want to recalculate the duration using a higher market rate of interest] Principal 1000 Period Market Discount Rate 6% Total PV of Total (PVi/PVTotal)* Payment Payment Time Coupon 1 2 3 4 5 Total Macaulay Duration = 7c) 7d) Calculate the Modified Duration of the bond in 7a. D* = Assume that market interest rates rose from 8% to 8.1%. What would be the percentage change in the bond price? 1) Using the Modified Duration estimate? %= 2) Directly calculating the new price and comparing it with the original price N i PV PMT FV 8.00% N i 8.10% PV PMT FV %= What are your conclusions regarding the Modified Macaulay 3) Duration to estimate changes in value
