Question

a) Explain the relationship between the yield to maturity of a premium bond and its coupon rate. b) ABC Ltd issues two different bonds with the same yield to maturity: a 20-year zero coupon bond a 15-year semi-annual coupon bond Explain which bond is subject to less interest rate risk. c) ABC Ltd is planning to issue 16-year semi-annual coupon bonds with a face value of $1,000 and a coupon rate of 6.5%. The nominal yield to maturity of potential investors is estimated to be 7.6% per annum. Calculate the required number (expressed as an integer) of semi-annual coupon bonds to be issued if the firm aims to raise $15 million. d) You purchase a bond issued by XYZ Ltd, which is a 9% semi-annual coupon bond with a term to maturity of 12 years, and currently trading at par. 3 years later, immediately after receiving the 6th coupon payment, you sell the bond to your best friend. You best friend’s nominal yield to maturity is 7% per annum. Write down an equation that can be solved to find your total realised return over the 3-year holding period.

Answer 1

PART A If an Investor puchase an bond at premium it means Coupon payment is more than YTM. Since Investor only get PAR amount of maturity there is a capital loss which is covered by excess coupon over and above YTM. Premium Bond : Coupon rate > YTM

PART B Assume YTM = 8% Zero Coupon Bond On Financial Calculator type N = 20 I/Y = 8 PMT = 0 FV = 1000 Then press CPT and then PV Answer = 214.55 Assume YTM = 7% Zero Coupon Bond On Financial Calculator type N = 20 I/Y = 7 PMT = 0 FV = 1000 Then press CPT and then PV Answer = 258.42 1% Increase in Interest Rate led to (258.42 - 214.55) / 214.55 = 20.45% change in price. Assume YTM = 8% 6% Semiannual Coupon Bond (6% is assumption) On Financial Calculator type N = 15 * 2 = 30 I/Y = 8 / 2 = 4 PMT = 1000 * 6 % / 2 = 30 FV = 1000 Then press CPT and then PV Answer = 827.08 Assume YTM = 7% 6% Semiannual Coupon Bond (6% is assumption) On Financial Calculator type N = 15 * 2 = 30 I/Y = 7 / 2 = 3.5 PMT = 30 FV = 1000 Then press CPT and then PV Answer = 908.04 1% Increase in Interest Rate led to (908.04 - 827.08) / 827.08 = 9.79% change in price. Solution Part B: Clearly visble that % Change in price for coupon paying bond is much less than Zero coupon bond. Underlying reason is that ZCB only pay once however other bond periodically paid some Part..

Part C First Step is to Calculate the price On Financial Calculator type N = 16 * 2 = 32 I/Y = 7.6 / 2 = 3.8 PMT = 1000 * 6.5% / 2 = 32.5 FV = 1000 Then press CPT and then PV Answer = 899.14 Number of Bond to be Issued = 15000000 / 899.14 = 16682.60 = 16683 Bond Approx.

PART D First Calculate Bond Value after 3 Year On Financial Calculator type N = 9 * 2 = 18 I/Y = 7 / 2 = 3.5 PMT = 1000 * 9% / 2 = 45 FV = 1000 Then press CPT and then PV Answer = 1131.90 Total Return Realised = [Income +(End Value – Initial Value)] / Initial Value = [45 * 6 +(1131.90 – 1000)] / 1000 = 40.19% Annualised Realised Return = (1+40.19%) ^ (1/3) = 11.91%

Please Provide a feedback.