Question

A 6.5% bond makes coupon payments on March 10th, June 10th, September 10th, and December 10th and is trading with a YTM of 4.25%. The bond is purchased and will settle on August 21st when there will be 8 semesters coupons remaining until maturity. Calculate the flat price of the bond using actual days?

Answer 1

Flat Price = Full price ( Dirty Price ) - Accrued Interest

Where Accrued interest =(coupon Payment for the period)X(TIme held for the last coupon payment or coupon period)

Thus, Applicable discount rate is = 6.5%/4 = 1.625%

Assume Face value of bond is $1000

Interest for 3 months = $1000 * 6.5% * 3/12

Coupon payment for period of 3 months = $16.25

Using PV factors,

Price of Bond = (16.25 * 7.445) + (1000 * 0.879)

Price of Bond = $999.98

Now , Number of days left from Aug 21st to Dec 31st = 132 days

therefore, Interest for 132 days = $1000*6.5%*132/365 = $23.50

Flat price of Bond = $999.98 - $23.50

Flat price of Bond = $976.48

(Instead of 365 days, we can also assume 360 days)

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