On this web page we look at the definition of yield to call on callable bonds, formula for YTC, and an example with YTC calculation using Linear interpolation, and a neat Yield to Call YTC Calculator.
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How do you define YTC ?
Yield to Call or YTC is the investor's expected rate of return at which Market Price of the callable bond equals the present value of sum of interest payments and the Par Value of the bond.
What is the YTM Equation or YTM Formula
If we now substitute actual values for INT, Call Price, and P0, we can solve for kd, which in this case would be the bond's yield to call. However exact calculation for yield to call is rather complex and requires bond value tables, or a sophisticated handheld calculator, or a computer. We can use a process called Linear interpolation with trial and error to approximate the yield to call.
Illustration with YTC Example
To illustrate this, say we have a $2,000 par-value callable bond with the following characteristics: 15 years until maturity, and an 10% coupon rate (with interest paid annually). Say at the beginning of Year 1 the interest rates rose thus driving down the Market Price of this bond to $1500. We want to determine the discount rate that sets the present value of the bond's expected interest payments and Par Value equal to the 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.
Bond Price @ 10%
| Interest | PVIFA @ 10% | Present Value | |
| 200 | 7.367 | $1,473.40 | |
| Call Price | PVIF @ 10% | Present Value | |
| $2,200 | 0.263 | $578.60 | |
| Bond Price | $2052 | ||
A 10% discount rate produces a resulting present value for the bond that is greater than the current market price of $1500. Therefore we need to try a higher discount rate to handicap the future cash flows further and drive their present value down to $1500. Let's try a 15% discount rate.
Bond Price @ 15%
| Interest | PVIFA @ 15% | Present Value | |
| 200 | 5.724 | $1,144.80 | |
| Market Value | PVIF @ 15% | Present Value | |
| $2,200 | 0.141 | $310.20 | |
| Bond Price | $1455 | ||
A 15% discount rate produces a resulting present value for the bond that is lesser than the current market price of $1500. The rate necessary to discount the bond's expected cash flows to $1500 must fall between 10% and 15%. To approximate the rate, we interpolate between 10% and 15% as follows Interpolated discount rate
This is an approximation , the use of a computer provides a precise yield to maturity of 14.62%. It is important to keep in mind that interpolation gives only an approximation of the exact percentage.