Question

There is a 5.5 percent coupon bond that has eighteen years to maturity. This bond is priced to offer a 6.25 percent yield to maturity. CNBC analysts believe that a year from now, the yield to maturity will be 5.75 percent. What is the change in price the bond will experience in dollars? (Assume semi-annual interest payments and $1,000 face value.)

If someone could walk me through how to do this, that would be fantastic! Thanks so much!

Answer 1

Calculation of Today's price:

face value =	1000
Years remaining to Maturity =	18
Semiannual periods (n)= (18*2) =	36
Coupon rate =	5.5%
Semiannual Coupon = 1000*5.5%/2 =	27.5
YTM =	6.25%
Semiannual yield (i) = 6.25%/2=	0.03125
Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n
27.5*(1-(1/(1+0.03125)^36))/0.03125 + 1000/(1+0.03125)^36
919.6349788
Bonds price today is	$919.63

Calculation of price after One year

face value =	1000
Years remaining to Maturity = 18-1	17
Semiannual periods (n)= (17*2) =	34
Coupon rate =	5.5%
Semiannual Coupon = 1000*5.5%/2 =	27.5
YTM =	5.75%
Semiannual yield (i) = 5.75%/2=	0.02875
Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n
27.5*(1-(1/(1+0.02875)^34))/0.02875 + 1000/(1+0.02875)^34
$973.11
Bonds price today is	$973.11

Change in bond price = Price after one year - todays price

=973.11-919.63

=53.48

So bond price will experience increase of $53.48 in price