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than its par value. EXAMPLE Whenever the required return on a bond differs from the bond’s coupon interest
rate, the bond’s value will differ from its par value. The required return is likely
to differ from the coupon interest rate because either (1) economic conditions
have changed, causing a shift in the basic cost of long-term funds, or (2) the
firm’s risk has changed. Increases in the basic cost of long-term funds or in risk
will raise the required return; decreases in the cost of funds or in risk will lower
the required return.
Regardless of the exact cause, what is important is the relationship between
the required return and the coupon interest rate: When the required return is
greater than the coupon interest rate, the bond value, B0, will be less than its par
value, M. In this case, the bond is said to sell at a discount, which will equal
M B0. When the required return falls below the coupon interest rate, the bond
value will be greater than par. In this situation, the bond is said to sell at a
premium, which will equal B0 M.
The preceding example showed that when the required return equaled the
coupon interest rate, the bond’s value equaled its $1,000 par value. If for the
same bond the required return were to rise or fall, its value would be found as follows (using Equation 6.7a):
B0 $100 12% (PVIFA12%,10yrs) $1,000
$887.00 Required Return
B0 8% $100 (PVIFA8%,10yrs) $1,000
$1,134.00 14. Note that because bonds pay interest in arrears, the prices at which they are quoted and traded reflect their value
plus any accrued interest. For example, a $1,000 par value, 10% coupon bond paying interest semiannually and
having a calculated value of $900 would pay interest of $50 at the end of each 6-month period. If it is now 3 months
since the beginning of the interest period, three-sixths of the $50 interest, or $25 (i.e., 3/6 $50), would be accrued.
The bond would therefore be quoted at $925—its $900 value plus the $25 in accrued interest. For convenie...
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