How to Calculate Yield to Maturity of a Zero-Coupon Bond

Zero-coupon bonds do not have re-occurring interest payments, which distinguishes yield to maturity calculations from bonds with a coupon rate.

Zero-coupon bonds trade on the major exchanges. They are commonly issued by corporations, state and local governments, and the U.S. Treasury. Corporate zero-coupon bonds are usually riskier than similar coupon-paying bonds because if the issuer defaults on a zero-coupon bond, the investor has not even received coupon payments, so the potential losses are greater.

The IRS mandates a zero-coupon bondholder owes income tax that has accrued each year, even though the bondholder does not actually receive the cash until maturity. The IRS calls this imputed interest.

Zero-coupon bonds are often regarded as long-term investments; they often mature in 10 or more years. The lack of current income provided by zero-coupon bonds discourages some investors. Others find the securities well suited for achieving long-term financial goals, such as college tuition. With the discounts, the investor is able to grow a small amount of money into a sizeable sum over several years.

Zero-coupon bonds essentially lock the investor into a guaranteed reinvestment rate. This arrangement can be most advantageous when interest rates are high and when placed in tax-sheltered retirement accounts. Some investors also avoid paying taxes on imputed interest by buying municipal zero-coupon bonds, which are usually tax-exempt if the investor lives in the state where the bond was issued.

With no coupon payments on zero-coupon bonds, their value is only based on current price compared to face value. As such, when interest rates are falling, prices are positioned to rise faster than traditional bonds, and vice versa.

Most time value of money formulas require some interest rate figures for each point in time. This consequently renders the yield to maturity easier to calculate for zero-coupon bonds because there are no coupon payments to reinvest, making it equivalent to the normal rate of return on the bond.

The formula for calculating the yield to maturity on a zero-coupon bond is:

$\text{Yield To Maturity} = \left (\frac{\text{Face Value}}{\text{Current Bond Price}} \right ) \left ( \frac{1}{\text{Years To Maturity}} \right ) -1$Yield To Maturity=(Current Bond PriceFace Value​)(Years To Maturity1​)−1

Consider a $1,000 zero-coupon bond that has two years until maturity. The bond is currently valued at $925 (the price at which it could be purchased today). The formula would look as follows: (1000 / 925) ^ (1 / 2) - 1. When solved, this equation produces a value of 0.03975, which would be rounded and listed as a yield of 3.98%.

The yield to maturity may change from one year to the next, depending on changes in the overall demand for bonds in the market. Case in point: if investors become more willing to hold bonds, due to economic uncertainty, bond prices would likely rise, which would spike the denominator in the yield to maturity formula, thereby reducing the yield.

Yield to maturity is an essential investing concept used to compare bonds of different coupons and times until maturity. Without accounting for any interest payments, zero-coupon bonds always demonstrate yields to maturity equal to their normal rates of return. The yield to maturity for zero-coupon bonds is sometimes referred to as the "spot rate."