A 5%, $1,000 bond makes coupon payments on June 15 and December 15 and is trading with a YTM of 4% (APR). The bond is purchased and will settle on August 21 when there will be four coupons remaining until maturity. Calculate the full price of the bond using actual days.
The bond may have accrued interest at the time of sale from the last coupon payment therefore the actual price or full price is the dirty price which includes the interest for the period
Therefore,
Full Price = Price of the bond * (1+4%/2) ^ (Days since last payment of coupon/183)
Where,
Days since last payment of coupon =15th June – 21 Aug = 67 (assuming 365 days in a year & 183 days in a half year)
The Bond’s price can be calculated the help of following formula
Bond price P = C* [1- 1/ (1+i) ^n] /i + M / (1+i) ^n
Where,
The par value or face value of the Bond = $1000
Current price of the bond P =?
C = coupon payment or annual interest payment = 5% per annum, but it makes coupon payments on a semi-annual basis therefore coupon payment = 5%/2 of $1000 = $25
n = number of payments = 4
i = yield to maturity or priced to yield (YTM) = 4% per annum or 4%/2 = 2% semiannual
Therefore,
P = $25 * [1 – 1 / (1+2%) ^4] /2% + $1000 / (1+2%) ^4
= $95.19 + $923.85
= $1,019.039
The current bond price is $1,019.039
Therefore,
Full Price = $1,019.039* (1+2%) ^ (67/183) = $1,026.45
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