**Unformatted text preview: **quire either the present value (B0 in
this case) or the future values (I and M in this case) to be input as negative numbers to calculate yield to maturity. That approach is employed here.] Using the
inputs shown at the left, you should find the YTM to be 8.766%. FV
CPT
I Solution
8.766 Semiannual Interest and Bond Values
The procedure used to value bonds paying interest semiannually is similar to that
shown in Chapter 4 for compounding interest more frequently than annually,
except that here we need to find present value instead of future value. It involves
1. Converting annual interest, I, to semiannual interest by dividing I by 2.
2. Converting the number of years to maturity, n, to the number of 6-month
periods to maturity by multiplying n by 2.
3. Converting the required stated (rather than effective)16 annual return for
similar-risk bonds that also pay semiannual interest from an annual rate, kd,
to a semiannual rate by dividing kd by 2.
Substituting these three changes into Equation 6.7 yields
I
2 B0 WW
W 2n
i1 1
kd
1
2 M t 1 1
kd
2 2n (6.8)17 15. For information on how to interpolate to get a more precise answer, see the book’s home page at www.aw.com/
gitman
16. As we noted in Chapter 4, the effective annual rate of interest, EAR, for stated interest rate i, when interest is
paid semiannually (m 2), can be found by using Equation 4.23:
EAR i
2 1 2 1 For example, a bond with a 12% required stated return, kd , that pays semiannual interest would have an effective
annual rate of EAR 1 0.12 2
2 1 (1.06)2 1 1.1236 1 0.1236 12.36% Because most bonds pay semiannual interest at semiannual rates equal to 50% of the stated annual rate, their effective annual rates are generally higher than their stated annual rates.
17. Although it may appear inappropriate to use the semiannual discounting procedure on the maturity value, M,
this technique is necessary to find the correct bond value. One way to confirm the accuracy of this approach is to
calculate the bond value for the case where the required stated annual return and coupon interest rat...

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