How to calculate the YTM of a bond
About this lesson
In this video, I will show how you can calculate a bond’s yield to maturity or YTM. I will also show what the bond’s price would be some years later, given a specific assumption of YTM or the required rate of return.
What yield to maturity means
The yield to maturity (YTM) is the single interest rate that makes the present value of a bond’s payments equal to its price. It’s the average annual return you’d earn if you buy the bond today, hold it to maturity, and reinvest the coupons at the same rate.
Price = Σ C ÷ (1 + YTM)t + F ÷ (1 + YTM)T
There’s no simple formula to solve for YTM, so it’s found by trial and error, or in Excel.
Example
A 10-year bond with an 8% annual coupon ($80) and a $1,000 face value sells for $950.
In Excel:
=RATE(10,80,-950,1000) → 8.77%
The price is entered as negative because it’s money you pay out.
Because the bond sells below face value (at a discount), its YTM (8.77%) is higher than its coupon rate (8%). The extra return comes from the bond rising to $1,000 at maturity.
The bond’s price years later
If the YTM stays at 8.77%, what will the bond be worth in 3 years, with 7 years left?
=PV(8.77%,7,80,1000) → about $961
A discount bond’s price rises toward face value as it nears maturity, if the yield doesn’t change. A premium bond’s price falls toward face value.
Related yields
- Current yield = annual coupon ÷ price = 80 ÷ 950 = 8.42%. It ignores the gain to face value.
- Yield to call: for bonds the issuer can repay early, the same calculation using the call date and call price.
Next: the invoice price of a bond.