Question

Problem 3 (Required, 25 marks) We consider a 5-year straight term bond issued today. The bond pays coupon quarterly and the current annual effective yield rate is i = 7.1859%. You are also given that • The current bond price is 2167.529. • The book value at the end of 15th month is 2130.929. Assuming that the yield rate remains unchanged over these 5 years, (a) find the book value of the bond at the end of 22nd month. (b) Find the market price of the bond at the end of 32nd month.

Answer 1

i = [1 + (r/n)]ⁿ – 1

where i = effective yield

r = nominal rate

n = number of payments per year

given data i = 7.1859%, n= 4 payments per year(quarterly)

so effectively r, nominal rate = n * [ (i+1)^1/n - 1)]

= 4 * [ (7.1859% + 1)^1/4 - 1]

= 6.99 %

Given bond price = 2167.529 , 5 year straight term bond.

bond at the end of 15th month = 2130.929

coupon rate = 6.99% Annually i.e. 1.7475% quarterly, Let x = face value

Book value initially = 2167.529 as no issuance fees given here.

Book value at the end of 15th month = 2167.529 - (premium/20) *1.25 = 2130.929

premium = 585.6, Face value = 1581.929

(a)hence book value at the end of 22nd month = 2130.929 - (premium/20)*0.583 = 2113.86

(b) n = 10.67 periods and interest rate of 1.7475%

hence market price of the bond at the end of 32nd month = 2167.529 * (1+ 1.7475%)^10.667

^{= 2607.48}