Question

An 8% 15 year bond has a yield to maturity of 7%. If the YTM falls by 1%,

- what will the new price be?

- What will it be approximately?

- is duration adequate to describe this bond?

Answer 1

since bond face value is not given, i will assume it 100 dollar

A 100 dollar at 8% will yiels 8 dollar every year as interest for 15 years

If YTM Falls by 1% i.e 6% then value of bond will be

8 * PVAF( 6%, 15 YEAR) + 100*PVF(6%, 15TH YEAR)

=8*9.7122+ 100 *0.417( PVAF AND PVF value you can look through tables)

=77.70+41.7

=119.4 is the bond value

Hint:- Bond value will be higher than face value if interest rate is greater than yield to maturity

In this case Face value is 100, interest rate 8% is higher than yield to maturity 6% and therefore nd fair value is higher than face vaue