Question

1. Consider the following bond which pays coupon semiannually on October 15 and April 15. It is being sold for settlement on August 10, 2020.

Coupon rate	8%
Yield to maturity	6%
Maturity date	April 15, 2024
Settlement date	August 10, 2020
Day count convention	30/360
Par	$1000

Calculate its flat price, accrued interest, and full price.

Answer 1

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

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

Coupon per period = (8% / 2) * $1000

Coupon per period = $40

Let us compute the Bond price on 15^th April 2020

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

Bond Price = $40 / (1 + 6% / 2)¹ + $40 / (1 + 6% / 2)² + ...+ $40 / (1 + 6% / 2)⁸ + $1000 / (1 + 6% / 2)⁸

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

Bond Price = $40 * (1 - (1 + 6% / 2)^-8) / (6% / 2) + $1000 / (1 + 6% / 2)⁸

Bond Price = $280.79 + $789.41

Bond Price = $1070.20

Days between 15^th April to 10^th August = 15(April) + 30(May) + 30(June) + 30(July) + 10(August) = 115 days

Days between 15^th April to 15^th October = 15(April) + 30(May) + 30(June) + 30(July) + 30(August) + 30(September) + 15(October) = 180 days

Full Bond price = Bond price * (1 + YTM / 2)^{(Days between 15th April to 10th August / Days between 15th April to 15th October)}

Full Bond price =  $1070.20 * (1 + 6% / 2)^{(115 / 180)}

Full Bond price = $1090.60

Accrued Interest = Coupon per period * (Days between 15^th April to 10^th August / Days between 15^th April to 15^th October)

Accrued Interest = $40 * (115 / 180)

Accrued Interest = $25.56

Flat Bond Price = Full Bond price - Accrued Interest

Flat Bond Price = $1090.60 - $25.56

Flat Bond Price = $1065.04