Question

A 9.17% semiannual-pay corporate bond matures 15 August 2028 and makes coupon payments on 15 February and 15 August. The bond uses the 30/360 day-count convention for accrued interest. The bond is priced for sale on June 5, 2020 (that is, 110 days since the Feb. 15 coupon). What is its flat price (or clean price) per $ 100 of par value on June 5, 2020 if its yield to maturity is 4.6%? Carry intermediate calcs. to four decimals. Answer to two decimals. Assume 1,000 par value and semi annual compounding

Answer 1

Dirty price of bond is calculated using PRICE function in Excel.

Settlement = pricing date = June 5, 2020

Maturity = maturity date =  15 August, 2028

rate = coupon rate = 9.17%

yld = yield to maturity = 4.6%

redemption = redemption value (% of par) = 100

frequency = coupons per year = 2 (as it is a semiannual coupon bond)

By inputting the values into this function, we get the bond price per $100 of par value.

The price of the bond is $130.8958 (per $100 of par value)

Clean price = dirty price - accrued interest

Accrued interest = par value * coupon rate * (number of days since last coupon / 360)

Here, we take par value as 100, since we are calculating the clean price per $ 100 of par value

Accrued interest = par value * coupon rate * (number of days since last coupon / 360)

Accrued interest = $100 * 9.17% * (110 / 360)

Accrued interest = $2.8019

Clean price = dirty price - accrued interest

Clean price = $130.8958 - $2.8019

Clean price = $128.09 (per $ 100 of par value)