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The market required rate of return on a bond (kd)
is more commonly referred to as the bond's yield to maturity. Yield to maturity
(YTM) is the expected rate of return on a bond if
bought at its current market price and held to maturity; it is also known as
the bond's internal rate of return (IRR) .
Mathematically, it is the discount rate that equates the present value of all
expected interest payments and the payment of the principal (face value) at
maturity with the bond's current market price. The following equation refects
this: P0
If we now substitute actual values for I, MV,
and P0, we can solve for kd, which in this case
would be the bond's yield to maturity. However precise calculation for yeild to
maturity is rather complex and requires bond value tables, or a sophisticated
handheld calculator, or a computer. Linear Interpolation: We can use a trial
and error procedure to approximate the yield to maturity.. EXAMPLE 1 SOLUTION Suppose we start with a 10% discount rate and calculate the
present value of the bond's expected future cash flows.
V = This time the chosen discount rate was too large.
The resulting present value is less than the current market price of $761.
A 10% discount rate produces a resulting present
value for the bond that is greater than the current market price of $761.
Therefore we need to try a higher discount rate to handicap the future cash
flows forther and drive their present value down to $761. Let's try a 15%
discount rate
To illustrate this, say we have a $1,000 par-value
bond with the following characteristics: a current market price of $761, 12
years until maturity, and an 8% coupon rate (with interest paid annually). We
want to determine the discount rate that sets the present value of the bond's
expected future cash flow stream equal to bond's current market price.
The rate necessary to discount the bond's expected cash flows to $761 must fall between 10% and 15%. To approximate the rate, we interpolate between 10% and 15% as follows Interpolated discount rate
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This is an approximation , the use of a computer provides a precise yield to maturity of 11.82 percent. It is important to keep in mind that interpolation gives only an approximation of the exact percentage
Behavior of Bond Prices
A number of observations can be made concerning bond prices.
1. When the market required rate of return is more than the stated coupon rate, the price of the bond will be less than its face value. Such a bond is said to be selling at a discount from face value.
2. When the market required rate of return is less tan the stated coupon rate, the price of the bond will be more than its face value. Such a bond is said to be selling at a premium over face value.
3. When the market required rate of return equals the stated coupon rate, the price of the bond will equal its face value.
Using MS Excel to compute Yield
Returns the yield on a security that pays periodic interest.
Use YIELD to calculate bond yield. If this function is not
available, and returns the #NAME? error, install and load the Analysis ToolPak
add-in.
How? On the Tools menu, click Add-Ins. In the Add-Ins available
list, select the Analysis ToolPak box, and then click OK. If necessary, follow
the instructions in the setup program. Syntax YIELD(settlement,maturity,rate,pr,redemption,frequency,basis)
Important Dates should be entered by using the DATE function, or as
results of other formulas or functions. For example, use DATE(2008,5,23) for
the 23rd day of May, 2008. Problems can occur if dates are entered as text.
Settlement is the security's settlement date. The security
settlement date is the date after the issue date when the security is traded to
the buyer.
Maturity is the security's maturity date. The maturity date is the
date when the security expires.
Rate is the security's annual coupon rate.
Pr is the security's price per $100 face value.
Redemption is the security's redemption value per $100 face value.
Frequency is the number of coupon payments per year. For annual
payments, frequency = 1; for semiannual, frequency = 2; for quarterly,
frequency = 4. Basis is the type of day count basis to use.
Basis
Day count basis
0 or omitted US (NASD) 30/360
1
Actual/actual
2
Actual/360
3
Actual/365
4 European
30/360