At a price of 102462 the bond yields 102 convertible

At a price of 1,024.62, the bond yields 10.2% convertible semi-annually.
Exercise (4.5)
What is the price of the bond in (4.4) if the required yield is 9.8%
convertible semi-annually?
Answer: 1050.98
In Example (4.4) , the redemption value (1,100) is different from the face value
(1,000). If an exam problem does not specify a separate redemption value, you
can assume that the bonds will be redeemed at par.
Note that raising the redemption value to 1,100 resulted in a price above 1,000.
It is natural to ask what redemption value would give a price of 1,000.
Example (4.6)
Suppose that the company issuing the bonds of Example (4.1) wants to
increase the redemption value to keep the price at 1,000 for a required
nominal yield of 10.2% We can find the required redemption value on
the BA II Plus.
Set N=20, I/Y=5.1, PMT=50, PV = − 1,000, and CPT FV= 1,033.42.
The required redemption value is 1,033.42.
Exercise (4.7)
What redemption value would assure a price of 1,000 for the above
bonds if the required nominal yield were 10.1%?
Answer: 1016.62
An investor who wishes to buy a bond is usually quoted a market price for the
bond. In that case, the investor would like to know the bond’s yield at that price.
Example (4.8)
A 1,000 par value bond with a term of 10 years and a coupon rate of 10%
payable semi-annually is offered at a price of 990. We can find the yield
per semi-annual period on the BA II Plus.
Set N=20, PV = − 990, PMT=50, FV=1,000, and CPT I/Y=5.08.
This gives a nominal yield convertible semi-annually of
5.08% 2 10.16%   .
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Page M4-4 Module 4 – Bonds
ACTEX Learning Exam FM – Financial Mathematics
Dinius, Hassett, Ratliff, Garcia, & Steeby
Exercise (4.9)
A 1,000 par value bond with a term of 10 years and a coupon rate of 10%
payable semi-annually is offered at a price of 1,020. Find the implied
yield (convertible semi-annually).
Answer: 9.68%
You may have observed by now that we have solved all the problems to this
point using the financial calculator and have not introduced any mathematical
notation or formulas. It is important to recognize when exam problems can be
solved easily and directly like this. As always, there are formulas and notation
to learn, and some problems will require their use. The key variables are:
F = par value (or face value)
r = coupon rate per coupon period (e.g., per semi-annual period)
Fr = coupon amount
C = redemption (maturity) value (= F in most cases)
n = number of coupon periods to redemption
P = price
i = yield per coupon period
i
v 

1
1 i
The most basic formula for the price P is:
(4.10)
If the bond is redeemed at par, then F C  , and we can write
 
n
i
n i
P Fr a Fv  
.
Since
1
n
i
n
i
n i
v
Fv F Fi F Fi a
i

     , we can derive the following formula for a
bond’s price in terms of its premium or discount:
(4.11)
We illustrate this with another example.
Example (4.12)
Consider again a 1,000 par value bond redeemable at par in 10 years with
a nominal coupon rate of 10% payable semi-annually. This bond has
F =1,000, r =0.05 and n =20. We have already shown in Example (4.2) that
the price of this bond at a yield of 10.2% is 987.64. We can check this
using the above formula with  0.051 i .