Bond Calculations Doc Essay Example
BONDS
COMPUTING THE COUPON RATE, PRICE, YIELD AND YTM OF A BOND
Compute the coupon rate of a bond:
Divide the coupon by the face value of the bond.
Example: A bond has a $1,000 face value, a market price of $1,115, and pays interest payments of $90 every year. What is the coupon rate?
Coupon Rate = Coupon/Face Value
Coupon Rate = $90/$1,000=9%
Compute the current price of a bond (annual coupon payments):
The price of a bond equals the present value of the coupon payments (calculated as an annuity) plus the present value of the par value (computed as the present value of a single amount).
Example: A $1,000 face value bond currently has a yield to maturity of 8.89 percent. The bond matures in 7 years and pays interest annually. The coupon rate is 9 percent. What is the current price of this bond?
Bond value = present value of coupons + present value of par
Bond value = C[1 – 1/(1+r)t] / r + FV / (1+r)t
Example #2: Suppose ABC Co. issues $1,000 par bonds with 20 years to maturity. The annual coupon is $110. Similar bonds have a yield to maturity of 11%.
Bond value = PV of coupons + PV of face value
Bond value = 110[1 – 1/(1.11)20] / .11 + 1000 / (1.11)20
Bond value = 875.97 + 124.03 = $1000
Since the coupon rate and the yield are the same, the price should equal face value.
Compute the current price of a bond (semi-annual coupon payments):
The general expression for the value of a bond is the same:
Bond value = present value of coupons + present value of par
Bond value = C[1 – 1/(1+r)t] / r + FV / (1+r)t
Semiannual coupons – coupons are paid twice a year. Everything is quoted on an annual basis so you divide the annual coupon and the yield by two and multiply the number of years by 2.
Example: A $1,000 bond with an 8% coupon rate, with coupons paid every 6 months, is maturing in 10 years. If the quoted YTM is 10%, what is the bond price?
C = .08(1,000)/2 = 40; r = .1/2 = .05; t = 10*2 = 20 Bond value = 40[1 –
COMPUTING THE COUPON RATE, PRICE, YIELD AND YTM OF A BOND
Compute the coupon rate of a bond:
Divide the coupon by the face value of the bond.
Example: A bond has a $1,000 face value, a market price of $1,115, and pays interest payments of $90 every year. What is the coupon rate?
Coupon Rate = Coupon/Face Value
Coupon Rate = $90/$1,000=9%
Compute the current price of a bond (annual coupon payments):
The price of a bond equals the present value of the coupon payments (calculated as an annuity) plus the present value of the par value (computed as the present value of a single amount).
Example: A $1,000 face value bond currently has a yield to maturity of 8.89 percent. The bond matures in 7 years and pays interest annually. The coupon rate is 9 percent. What is the current price of this bond?
Bond value = present value of coupons + present value of par
Bond value = C[1 – 1/(1+r)t] / r + FV / (1+r)t
Example #2: Suppose ABC Co. issues $1,000 par bonds with 20 years to maturity. The annual coupon is $110. Similar bonds have a yield to maturity of 11%.
Bond value = PV of coupons + PV of face value
Bond value = 110[1 – 1/(1.11)20] / .11 + 1000 / (1.11)20
Bond value = 875.97 + 124.03 = $1000
Since the coupon rate and the yield are the same, the price should equal face value.
Compute the current price of a bond (semi-annual coupon payments):
The general expression for the value of a bond is the same:
Bond value = present value of coupons + present value of par
Bond value = C[1 – 1/(1+r)t] / r + FV / (1+r)t
Semiannual coupons – coupons are paid twice a year. Everything is quoted on an annual basis so you divide the annual coupon and the yield by two and multiply the number of years by 2.
Example: A $1,000 bond with an 8% coupon rate, with coupons paid every 6 months, is maturing in 10 years. If the quoted YTM is 10%, what is the bond price?
C = .08(1,000)/2 = 40; r = .1/2 = .05; t = 10*2 = 20 Bond value = 40[1 –