Question

3. A bond with a face value of $100,000 and coupon interest paid semi-annually at an annual rate of 7.50% per annum was issued on 8 May 2013 for 4 years. Similar bonds are now selling at a yield-to-maturity of 7.41% per annum. Based on the most recent and next coupon dates, work out the accrued interest on the settlement date (20-Jan-2015). Please use Actual/Actual as the interest rate basis and leave the Calc_method as its default.

Answer 1

No of periods = 4 years * 2 = 8 semi-annual periods

Coupon per period = (Coupon rate / No of coupon payments per year) * Face value

Coupon per period = (7.5% / 2) * $100,000

Coupon per period = $3750

Days between 8^th November to 20^th January = 22(Nov) + 31(Dec) + 20(Jan) = 73 days

Days between 8^th November 2014 to 8^th May 2015 = 23(Nov) + 31(Dec) + 31(Jan) + 28(Feb) + 31(Mar) + 31(Apr) + 8(May) = 181 days

Accrued Interest = Coupon per period * (Days between 8th November to 20th January / Days between 8th November to 8th May)

Accrued Interest = $3750 * (73 / 181)

Accrued Interest = $1512.43

The belowe part is for Illusatration purpose of usage of Accrued interest

Let us compute the Bond price on 8^th June 2015

Bond Price = Coupon / (1 + YTM / 2)^period + Face value / (1 + YTM / 2)^period

Bond Price = $3750 / (1 + 7.41% / 2)¹ + $3750 / (1 + 7.41% / 2)² + ...+ $3750 / (1 + 7.41% / 2)⁴ + $100,000 / (1 + 7.41% / 2)⁴

Using PVIFA = ((1 - (1 + Interest rate)^{- no of periods}) / interest rate) to value coupons

Bond Price = $3750 * (1 - (1 + 7.41% / 2)^-4) / (7.41% / 2) + $100,000 / (1 + 7.41% / 2)⁴

Bond Price = $13,707.28 + $86,457.21

Bond Price = $100,164.49

Full Bond price = Bond price * (1 + YTM / 2)^{(Days between 8th November to 20th January / Days between 8th November to 8th May)}

Full Bond price =  $100,164.49 * (1 + 7.41% / 2)^{(73 / 181)}

Full Bond price = $101,645.00

Flat Bond Price = Full Bond price - Accrued Interest

Flat Bond Price = $101,645.00 - $1512.43

Flat Bond Price = $100132.57