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**Unformatted text preview: **e are equal; for
B0 to equal M, as would be expected in such a case, the maturity value must be discounted on a semiannual basis. 292 PART 2 Important Financial Concepts I
2
EXAMPLE (PVIFAkd/2,2n) M (PVIFkd/2,2n) (6.8a) Assuming that the Mills Company bond pays interest semiannually and that the
required stated annual return, kd, is 12% for similar-risk bonds that also pay
semiannual interest, substituting these values into Equation 6.8a yields
B0 $100
2 (PVIFA12%/2,2 10yrs) $1,000 (PVIF12%/2,2 10yrs) Table Use
B0
Input
20 Function
N 6 I 50 PMT 1000 FV
CPT
PV Solution
885.30 $50 (PVIFA6%,20periods) $1,000 (PVIF6%,20periods) $50 (11.470) (0.312) $885.50 $1,000 Calculator Use In using a calculator to find bond value when interest is paid
semiannually, we must double the number of periods and divide both the
required stated annual return and the annual interest by 2. For the Mills Company bond, we would use 20 periods (2
10 years), a required return of 6%
(12% 2), and an interest payment of $50 ($100 2). Using these inputs, you
should find the bond value with semiannual interest to be $885.30, as shown at
the left. Note that this value is more precise than the value calculated using the
rounded financial-table factors.
Comparing this result with the $887.00 value found earlier for annual compounding (see Table 6.6), we can see that the bond’s value is lower when semiannual interest is paid. This will always occur when the bond sells at a discount. For
bonds selling at a premium, the opposite will occur: The value with semiannual
interest will be greater than with annual interest. Review Questions
6–16 What basic procedure is used to value a bond that pays annual interest?
Semiannual interest?
6–17 What relationship between the required return and the coupon interest
rate will cause a bond to sell at a discount? At a premium? At its par
value?
6–18 If the required return on a bond differs from its coupon interest rate,
describe the behavior of the bond value over time as the bond moves
toward...

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