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YTM > Yield to Maturity on Bonds > Definition > Example > Calculation > Calculator

On this web page we look at the definition of yield till maturity on bonds, formula for YTM, and an example with YTM calculation using Linear interpolation, and a neat Yield to Maturity Calculator.
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How do you define YTM ?

he 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.

What is the YTM Equation or YTM Formula

ytm forumla

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 yield 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.

Illustration with YTM Example

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.

YTM Calculation

Suppose we start with a 10% discount rate and calculate the present value of the bond's expected future cash flows.
PV at 10%
INTEREST PVIFA @ 10% PRESENT VALUE
80 6.814 $545.12
Market Value PVIF @ 10% PRESENT VALUE
$1,000 0.31863 $318.63
Bond Price $863.75
 

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 further and drive their present value down to $761. Let's try a 15% discount rate

PV at 15%
INTEREST PVIFA @ 15% PRESENT VALUE
80 5.421 $433.68
Market Value PVIF @ 15% PRESENT VALUE
$1,000 0.186907 $186.91
Bond Price $620.59
 

A 15% discount rate produces a resulting present value for the bond that is lesser than the current market price of $761. 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

ytm linear interpolation

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



Bond Valutaion | YTC