BILL ADONGO

                  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