CAPITAL STOCK BOND VALUATION THEORY
Bill Adongo
Fellow of Society of Actuaries
Google Authorship (USA)
From Ghana, West Africa
In actuarial, banking, and corporation applications, we
often work stock bond and valuation for yield rates, prices, redemption values,
accumulative values, par values and net gains of investors at the end of time.
Although, others authors had introduced formulas for bonds
evaluation, I think their method of analysis is limited. As a fellow
of society of actuaries (FSA) and fellow of institute of actuaries (FIA),
I have invented a theory that is used to solve long standing problems that
proves worthy and sensitive than the rest.
It is obvious that when an investor buys the highest price
that guarantees, he will receive at least his desired yield rate regardless of
when the bond is called. If the investor holds the bond for i-years, after
annual yield rate, the principal amount of bond that is repaid at the end of
the term is calculated as;
Π=s/2(1+j)-N
S=2A(N/j)*Fr
N=i*n
Where,
Π=par values (or principal amount)
Fr=annual coupon
A(N/j)=annually
N=number of period that is annual.
i=years of bond
n=convertible period
Considered30-years bond with a par value of 1000 and 12%
coupons payable quarterly. Calculate the
i) selling price
ii) effective quarterly rate
iii) nominal yield rate
Solution
A(120/2.31%)=14.87675
i) selling price is 1190.14
ii) effective quarterly rate is 2.31%
iii) nominal yield rate is 9.24%
The risk that arises for bond owner from fluctuation interest
called interest rate risk. The sensitivity of the effective interest rate and
nominal interest rate of a coupon has depends on how sensitive its price is to
interest rate changes. The price of coupon is computed as;
P=2A(N/j)*Fr
Or
P=C/2(1+j)-N
Where,
P=price of coupon
C=redemption
Annual coupon divided by the par value convertible
periodically, called coupon rate is given as;
R=Fr/ Πn
Considered 100 par value bond 8% coupons semiannually with
effective semiannual interest rate 3% .Calculate the
i)price of the coupons
ii) nominal yield rate
iii)the redemption value
Solution
A(20/3%)=18.31194772
i) price of the coupons is146.50
ii) nominal yield rate is 12%
iii) redemption amount is132.30
Most insurance companies, banks, and corporation, stock the
deck against their bondholders, positioning. They involve benefiting from
interest rates. They do so by attaching them the right to reinvest the bonds
from investors under certain conditions. The amount repaid, accumulative
reinvest coupons and net gains are computed as;
Amount repaid=P*(1+r)i
Accumulative reinvest coupons=Fr*S(N/τ)
Net gain= Π+Fr* S(N/τ)-
P*(1+r)i
Where;
Π=par value
P=price of coupon
S(N/τ)=semiannually
