Question

On 1 April 2020, the Government issued seven-year Government fixed-interest bonds with a face value of $25 million, paying half-yearly coupons at 6.50 per cent per annum. Coupons are payable on 31 March and 30 September each year until maturity.

On 15 September 2022, the holder of the bonds sells at a current yield of 6.75 per cent per annum. You are required to calculate:

1. n (number of periods)
2. i (current yield)
3. C (coupon payment)
4. k (fraction of elapsed interest period since the last coupon payment)
5. P (price at which the bonds will be sold)

Answer 1

a. The bond's life of 7 years is multiplied by 2 to arrive at 14 semiannual periods. The number of semiannual periods is symbolized by n. therefore n=14

b) the market interest rate is 3.375% per semiannual period. The 3.375% market interest rate per semiannual period is symbolized by i. (The market rate of 6.75 % per year was divided by 2 semiannual periods per year to arrive at the market interest rate of 3.375 % per semiannual period.)

c)  coupon payment is the amount of interest which a bond issuer pays to a bondholder at each payment date.

in year  20-21 :  $25million* 6.75% =1.6875million

in year 21-22 : $ 25million * 6.75% = 1.6875 million

interest as on  1.4.22 to 15.9.22 = $25* 6.75* (167days/365days ) = $ 0.7720890477

d) fraction of elapsed interest period since last coupon payment

If the number of days of interest accrual exceeds 365/f, or 182.5 days for a semi-annual pay bond:

Fraction of Coupon Period= 1 - [ { DaysRemainingInPeriod } / 365 ]

therefore Fraction of a Coupon Period = 1- [September 30, 2022- september 15, 2022] • 2/365

  = 1- 15• 2/365 = 1-0.021917808 = 0.9178082192