When the required return is more than coupon rate of interest the bond market value is less than par value or bond will sell at discount. On the contrary if required return is less than coupon rate the market value of the bond would be more than its par value or bond will sell at premium. This phenomenon can be more easily understood by the use of examples.
Example
A firm issued a 10% coupon interest bonds for a period of 10 years with a face value of $1000. The required rate of interest is 12% and interest is paid annually. Find out the value of the bond.
Solution
Annual Interest (I) = $1000 x 10% = $100
(PVIFA) 12%, 10 = 5.650 (from the annuity table)
(PVIF) 12%, 10 = 0.322
B = ($100 x 5.650) + 1000 x 0.322 = $887
Because the required return is greater than coupon rate in the above example the bond value is less than its par value.
Example
A firm issued a 10% coupon interest bonds for a period of 10 years with a face value of $1000. The required rate of interest is 8% and interest is paid annually. Find out the value of the bond.[sky]
Solution
Annual Interest (I) = $1000 x 10% = $100
(PVIFA) 8%, 10 = 6.710 (from the annuity table)
(PVIF) 8%, 10 = 0.463
B = ($100 x 6.710) + 1000 x 0.463 = $1134
Because the required return is less than coupon rate in the above example the bond value is greater than its par value.
The above two examples clearly show that required rate of return is the major determinant of market value of the firm’s bonds.
If the required rate of return remain constant over the life of the bond the bonds market price approaches its par value. On the other hand under the changing circumstances of required returns the shorter the time to maturity, the smaller the impact on bond value caused by given changes in the required return.
Semiannual Interest and Bond Value
The procedure towards the calculation of bond’s value paying interest semiannually is similar. As interest is two times in a year therefore half yearly interest should be calculated to find the present value. The required return over that the interest payments are discounted is also needed to be divided by two. Number of years in the maturity period is converted to discounting period by multiplying by two. Symbolically:
B = I / 2 x (PVIFA)kd/2 , 2n + M x (PVIF) kd/2 , 2n
Example
A firm issued a 10% coupon interest bonds for a period of 10 years with a face value of $1000. The required rate of interest is 14% and interest is paid semiannually. Find out the value of the bond.
Solution
Semiannual Interest (I / 2) = $1000 x 10% x 6 / 12 = $50
(PVIFA) 14% / 2, 10 x 2 = 10.594 (from the annuity table)
(PVIF) 14% / 2, 10 x 2 = 0.258
B = ($50 x 10.594) + 1000 x 0.258 = $787.7