Question

A 8.7% 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 8%?

Answer 1

Price of Bond on 15 Feb 2020 (P0) = Present Value of Coupon Payments + Present Value of Redemption Value

P0 = P*[1-(1+r)^-n]/r + RV*1/(1+r)^n

Where , P = Periodic Payment , r = rate per period , n = number of period , RV = Redemption Value of bond

P0 = $100*8.7%*180/360*[1-(1+(8%/2))^-8.5*2]/(8%/2) + $100*1/(1+8%)^8.5

P0 = $4.35*[1-(1.04)^-17]/.04 + $51.99

P0 = $52.92 + $51.99

P0 = $104.91

Now, we will calculate price of bond on 05 Jun 2020

Price of Bond on 05 Jun 2020 (P1) = Price of Bond on 15 Feb 2020 + Accrued Interest till 05 Jun 2020

P1 = $104.91 + $100*8.7%*110/360

P1 = $104.91 + $ 2.66

P1 = $107.57

Hence, flat price (or clean price) per $ 100 of par value on June 5, 2020 at YTM of 8% will be $ 107.57