Question

A 6 percent coupon bond with 12 years left to maturity is priced to offer a 6.5 percent yield to maturity. If the yield to maturity falls to 6.25 percent. What is the change about the bond if coupon is paid annually?

	A.	Coupon payment decreases $25.00
	B.	Bond price decrease $19.67
	C.	Bond price increase $20.11
	D.	Coupon payment increases $41.22

Answer 1

Method 1: Using Formula:

Suppose Face value of the bond = FV = $1000

Time to maturity = n = 12 years

Annual coupon rate = 6%

The bond pays coupons annually

Annual coupon payment = C = Annual coupon rate*Face Value = 6%*1000 = 60

Bond's Price is calculated using the Formula:

$Bond's.Price = \frac{C}{YTM}*[1-(1+YTM)^{-n}] + \frac{FV}{(1+YTM)^{n}}$

Case I: Yield to maturity = YTM = 6.5%

C = 60, YTM = 6.5%, n = 12 years, FV = 1000

$Bond's.Price = \frac{60}{0.065}*[1-(1.065)^{-12}] + \frac{1000}{(1.065)^{12}}$

Bond's price when YTM is 6.5% = 489.52351902459 + 469.682854390027 = 959.206373414618 ~ $959.21

Case II: Yield to maturity = YTM = 6.25%

$Bond's.Price = \frac{60}{0.0625}*[1-(1.0625)^{-12}] + \frac{1000}{(1.0625)^{12}}$

Bond's Price when YTM is 6.25% = 496.207236223858 + 483.117462266814 = 979.324698490673 ~ $979.32

Change in the Bond's Price = Price when YTM is 6.25% - Price when YTM is 6.5% = 979.32 - 959.21 = 20.118325076055 ~ 20.11

Hence the Bond price increase $20.11. Note that there will not be any change in the coupon payment as the coupon rate is the same.

Answer -> Bond price increase $20.11 (Option C)

Method 2: We know that the Yield to maturity of the bond and the Bond's price are inversely related. A decrease in Yield to maturity will result in an increase in Bond's price. In options, Only C is true because when the YTM is decreased from 6.5% to 6.25%, the bond price will increase.

Answer -> Bond Price increase $20.11 (Option C)