How to Calculate Yield to Call of a Bond

This lesson is part 9 of 18 in the course Yield Measures, Spot Rates, and Forward Rates

For callable bonds that are likely to be called before their maturity, it is more useful to calculate yield to call instead of yield to maturity. The formula and steps to calculate yield to call are exactly the same as how we calculate yield to maturity, i.e., you calculate the discount rate that makes the present value of the future bond payments (coupons and par) equal to the market price of the bond plus any accrued interest. There are two deviations from the standard formula:

For calculating yield to call the bond price will be taken as the price at which the bond is called back.
The maturity will be the date with expected call date.

Bonds will have a call schedule which will specify how much the issuer will pay on the date the bond is called. Investors can calculate various types of yield to call such as yield to first call or yield to next call.

Let’s take an example:

Consider a $1,000 par 8% coupon, 5 years maturity bond selling at $800. The bond is callable and the first call date is 2 years from now at a call price of $1010.

The cash flows from the bond upto call date are the coupon payments every 6 months, and the call price after two years. So, the yield to call will be the interest rate that will make the present value of these cash flows equal to the bond price of $800.

Assuming semi-annual coupon payments, the yield to call will be calculated as follows:

$800 = 40/(1+y) + 40/(1+y)^2 + 40/(1+y)^2 + 1050/(1+y)^2

Solving for y, we get:

Y = 10.61%

As you can see, yield to call consider all sources of income such as coupon income, capital gains, and reinvestment income upto the call date. This measure assumes that investor is going to hold the bond till the call date and that the bond will be called on the scheduled date. These assumptions are not practical and it’s also not possible to directly compare the yield to call of a callable bond with the yield to maturity of a non-callable bond.

Just like yield to call we can also calculate yield to put, where the bond can be put (sold) back by the investor back to the issuer as a scheduled at and at a specified put price.