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 6^th 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. Hence, Coupon Paing Bond is less subject to Interest Rate Risk.

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 Feedback