Question

Consider a bond with a 10% coupon and with yield to maturity = 8%. If the bond’s YTM remains constant, then in one year, will the bond price be higher, lower, or unchanged? Please explain your answer and give examples to help demonstrate your explanation.

Answer 1

If the YTM of bond remains 8% for one year then the price of the bond will be higher than the face value or par value. The YTM < Coupon i.e. 8%<10%, the coupons are cash flows of the bond which get discounted over the life of the bond and at end the bond holder receives face value plus last coupon which is also discounted with YTM.

Let assume 2-Year bond. Face value = 1000 ; Coupon = 100; YTM = 8%

Bond value = Coupon of 1^st year / (1+YTM)^1 + (Coupon for 2^nd year + Face value )/(1+YTM)^2

Bond Value = 100/(1+8%)^1 + (100 + 1000)/(1+8%)^2

Bond value = $1,035.67

$1,035.67 is higher than the face value of the bond. Hence, we have demonstrated that if YTM < Coupon rate then the bond value will be higher than the face value.