Question

A 9.81% 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 5.7%? Carry intermediate calcs. to four decimals. Answer to two decimals.

Answer 1

Coupon rate = 9.81%, Par value = 100, Yield to maturity = 5.7%

Since it is semi-annual pay coupon bond therefore

Semi-annual coupon = (Coupon rate x 100) / 2 = (9.81% x 100) / 2 = 4.9050

Semi annual yield = r = Yield to maturity / 2 = 5.7% / 2 = 2.8500%

Last coupon date = 15 February 2020, Next coupon date = 15 August 2020, Settlement date = 5 June 2020, Maturity date = 15 August 2028

30/360 Convention considers 30 days in a month and 360 days in a year

No of days between last coupon date and next coupon date = No of days between 15 February 2020 and 15 August 2020 = T = Days of February + Days of March + Days of April + Days of May + Days of June + Days of July + Days of August = 15 + 30 + 30 + 30 + 30 + 30 + 15 = 180

No of days between last coupon date and settlement date = No of days between 15 February 2020 and 5 June 2020 = t = Days of February + Days of March + Days of April + Days of May + Days of June = 15 + 30 + 30 + 30 + 5 = 110

No of half years from last coupon date to maturity date = no of half years from 15 Feb 2020 to 15 August 2028 = 17 half years

First we will calculate the full price of the bond

Full Price of bond = PV x ( 1 + r)^t/T

where PV = Present value at last coupon datae of cash flows of bond from next coupon date to maturity date = Present value at 15 February 2020 of cash flows of bond from 15 August 2020 to 15 August 2028

For finding PV we will use pv function in excel

Formula to be used in excel: =pv(rate,nper,-pmt,-fv)

Using pv function in excel, we get PV = 127.3860

Full Price = PV x ( 1 + r)^t/T

Full Price = 127.3860 x ( 1 + 2.85%)^110/180 = 127.3860 x x (1.0285)^110/180 = 127.3860 x 1.0173 = 129.5897

Accrued Interest = (t/T) x semi annual coupon = (110/180) x 4.9050 = 2.9975

Flat Price = Full price - Accrued Interest = 129.5897 - 2.9975 = 126.5922

Hence Flat Price of the bond = 126.5962 = 126.59 (two places off decimal)