A bond is a type of asset in which a government or a company issues these securities as a long – term debt to borrow money from institutional investors (Banks) or public sector. Each bond has a time to maturity which is usually 5, 10, and 20 or 30 years. Initial value of bond is named par value or face value equal to $1000 with a coupon interest rate on the bond which is the percentage of par value and it will be paid annually or semiannually (two times in one year). In fact, the government or the company is committed regularly and continuously to pay these payments and also repayment of initial value (par value) at maturity time.
The purpose of this article is to
present a model for analysis of bond value where there are seven independent variables
including current bond price (bond value), YTM, coupon rate, purchased year, purchased
month, purchased day and time period (n). This model simultaneously solves an
equation with three independent variables accompanied by generating maximum and
minimum of this function for given domain and range and also non simultaneously
analyzes seven independent variables. One of the most crucial applications of
this model is to obtain YTM (return rate) for current price equal to bond value
without using any trial and error.
A coupon interest rate always stay
the constant while the purchasers of bonds strongly look at and compare it with
premium risk of market which is named the return rate or required rate on the
capital or yield to maturity (YTM). This is why the price of bond varied with
bond value. Of course, there are two factors for this discrepancy: (1) the
difference between coupon interest rate and return rate (YTM) and (2) entering
time (the time of purchasing). Below diagrams as well as show us the impact of
these factors for time periods of 30, 20 and 10 years:
Above diagrams say to us, when YTM
(rd) is greater than the coupon rate,
the bond value will be less than its par value (Discount Bond), when YTM (rd) is less than the coupon rate, the
bond value will be greater than its par value and when YTM (rd) is equal to coupon rate, the bond
value will be equal to par value.
Generally the basic valuation model
for any asset can be made by using below equation:
Where:
V0 = value of the asset at time zero
CFt = cash flow expected at the end of year t
r = appropriate required return
(discount rate)
n = relevant time period
But for each specific asset such as
Bonds, Stocks, Real estate and so on, we have to change a little bit above
basic equation. For instance, the formula to evaluate the bond value can be as
follows:
B0 = value of the bond at time zero
I = annual interest paid in dollars
r = appropriate required return
(discount rate)
n = number of years to maturity
M = par value in dollars
rd = required return on a bond
I also used above equation to make
this model for analysis of the bonds. Below figure as well as shows the
features of this model:
As you can see in the figure above,
there are seven independent variables (Inputs) which have been highlighted by
red color. First, we enter the period of maturity which is “n”. Then, according
to the issue date and the maturity date, we enter Year, Month and Day as
current date. After that, we choose a range for Current price, YTM and Coupon
rate (Low and High) and next we consider a specific current bond price which is
into the range of current price. Finally, this model gives us the outputs which
are the minimum and maximum bond value with the appropriate YTM and Coupon rate.
In the meanwhile, you can see that specific bond price (input) is approximately
equal to specific bond value (output) that it says to us about the appropriate YTM and Coupon rate for the specific bond price where we do not need to use
any trial and error to obtain YTM for a specific bond price.
You can see below clips as the
examples for this model:
The model for n = 30
The model for n = 10
All researchers, investors and
individual people who are interested in having this model, don’t hesitate to
send their request to below addresses:
