Principles of Managerial Finance

CHAPTER 6 Interest Rates and Bond Valuation 291

9%. Because the $1,063.80 is closer to $1,080, the YTM to the nearest whole

percent is 9%. (By using interpolation,we could eventually find the more precise

YTM value to be 8.77%.)^15

Calculator Use [Note:Most calculators require eitherthe present value (B 0 in

this case) or the future values (Iand Min this case) to be input as negative num-

bers 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%.

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 Iby 2.


2. Converting the number of years to maturity, n, to the number of 6-month
   periods to maturity by multiplying nby 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 kdby 2.

Substituting these three changes into Equation 6.7 yields

B 0 





2 n

i (^1) 
M

(6.8)^17
1

1

I

2

15. For information on how to interpolate to get a more precise answer, see the book’s home page at http://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 (m2), can be found by using Equation 4.23:
    EAR 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  
    2
     1 (1.06)^2  1 1.1236  1 0.1236 1
    
    2
    
    .
    
    3
    
    6
    
    %
    Because most bonds pay semiannual interest at semiannual rates equal to 50% of the stated annual rate, their effec-
    tive 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 rate are equal; for
    B 0 to equal M,as would be expected in such a case, the maturity value must be discounted on a semiannual basis.

0.12

2

i

2

8.766

10 N

PV

FV

CPT

I

PMT

 1080
100
1000

Solution

Input Function

^1  

kd t

 2  1  

kd^2 n

 2

WWW