Question

so year government bond YTM = 2.40 Coupon rate 2.25% If yields drop to 2%, find new price

Answer 1

Bond Question

Given:

New YTM = 2%

Coupon rate = 2.25%

Time to maturity = 30 years

Face Value = $1000 (In the absence of information, face value is assumed to be $1000)

Maturity Value = $1000 (In the absence of information, maturity is assumed to be at par that is $1000)

Now, we will calculate the fair price of bond as follows as per new YTM

Fair B0 = [Interest/ (1 + Kd)1 + Interest/ (1 + Kd)2 .....................+ Interest/ (1 + Kd)30 + Maturity value/ (1 + Kd)30]

Fair B0 = [22.5/(1 + 0.02)1 + 22.5/(1 + 0.02)2..................................+ 22.5/(1 + 0.02)30 + 1000/(1 + 0.02)30]

Fair B0 = [(22.50 x 22.40) + (1000 x 0.552)]

Fair B0 = (504 + 552)

Fair B0 = $1056

Comment: If yields drops to 2%, the new price of the bond will be $1056.

Now let us calculate the fair price of the bond as per the old YTM and compare

OLD YTM = 2.4%

Coupon rate = 2.25%

Time to maturity = 30 years

Face Value = $1000 (In the absence of information, face value is assumed to be $1000)

Maturity Value = $1000 (In the absence of information, maturity is assumed to be at par that is $1000)

Now, we will calculate the fair price of bond as follows:

Fair B0 = [Interest/ (1 + Kd)1 + Interest/ (1 + Kd)2 .....................+ Interest/ (1 + Kd)30 + Maturity value/ (1 + Kd)30]

Fair B0 = [22.5/(1 + 0.024)1 + 22.5/(1 + 0.024)2.................................+ 22.5/(1 + 0.024)30+ 1000/(1 + 0.024)30]

Fair B0 = [(22.50 x 21.21) + (1000 x 0.491)]

Fair B0 = (477 + 491)

Fair B0 = $968

YTM	Price of the Bond
2.4%	968
2%	1056

Comment: Hence, we can see that as the YTM decreases, the fair price of bond will increase as there is an inverse relationship between YTM and price of the bond.