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

Yield to maturity (YTM) is an important metric used in bond markets that describes the total rate of return that is expected from a bond once it has made all of its future interest payments and repays the original principal amount. Zero-coupon bonds (z-bonds), however, do not have reoccurring interest payments, which distinguishes YTM calculations from bonds with a coupon rate.

Since z-bonds are a common type of debt issuance by certain organizations, including some U.S. Treasury securities, yield to maturity is an important consideration. Instead of paying coupons, z-bonds are typically issued at a discount in the market and then mature to their face value. Here, we look at how to estimate the YTM of a bond that does not pay regular interest.

Key Takeaways

  • Yield to maturity (YTM) tells bonds investors what their total return would be if they held the bond until maturity.
  • YTM takes into account the regular coupon payments made plus the return of principal.
  • Zero-coupon bonds do not pay interest at regular intervals.
  • Instead, z-bonds are issued at a discount and mature to their face value.
  • As a result, YTM calculations for zero-coupon bonds differ from traditional bonds.

How Do I Calculate Yield To Maturity Of A Zero Coupon Bond?

Zero-Coupon Bond Formula

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

Yield To Maturity = ( Face Value Current Bond Price ) ( 1 Years to Maturity ) 1 begin{aligned}&text{Yield To Maturity}\&qquad=left(frac{text{Face Value}}{text{Current Bond Price}}right)^{left(frac{1}{text{Years to Maturity}}right)-1}end{aligned}
Yield To Maturity=(Current Bond PriceFace Value)(Years to Maturity1)1

Zero-Coupon Bond YTM Example

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 begin{aligned}=left(frac{1000}{925}right)^{left(frac12right)-1}end{aligned}

When solved, this equation produces a value of 0.03975, which would be rounded and listed as a yield of 3.98%.

Time value of money (TVM) formulas usually require interest rate figures for each point in time in order to discount future cash flows to their present value. This actually makes YTM easier to calculate for zero-coupon bonds. There are no coupon payments to reinvest, making it equivalent to the normal rate of return on the bond.

YTM Over Time

The yield to maturity may change from one year to the next. It depends on changes in the overall prices in the bond market. For example, suppose that investors become more willing to hold bonds due to economic uncertainty. Then 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 also known as the spot rate.

Special Considerations

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. If the issuer defaults on a zero-coupon bond, the investor has not even received coupon payments, so the potential losses are higher.

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. This is called imputed interest.

Zero-coupon bonds often mature in ten years or more, so they can be long-term investments. 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 saving for a child’s college expenses. With the discounts, the investor can grow a small amount of money into a substantial 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-advantaged retirement accounts. Some investors also avoid paying taxes on imputed interest by buying zero-coupon municipal bonds. They 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 entirely based on the 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. That can make zero-coupon bonds, especially zero-coupon Treasuries, an effective hedge for stock portfolios.

Why Do Zero-Coupon Bonds Have a Different YTM Than a Conventional Bond?

Conventional bonds pay regular interest payments, called coupons, often semi-annually or annually. These coupon payments are theoretically to be reinvested when they are paid, but because interest rates can change over the life of a bond, there is reinvestment risk. Since a zero-coupon bond does not have this risk, the YTM will differ accordingly.

What Is Yield to Maturity?

YTM is the total return a bond investor will expect if it is held to maturity. It is effectively a bond’s internal rate of return (IRR).

What Is the Formula for the Yield to Maturity of a Coupon Bond? 

YTM = C + FV PV t FV + PV 2 where: C = Interest/coupon payment FV = Face value of the security PV = Present value/price of the security t = How many years it takes the security to reach maturity begin{aligned}&text{YTM}=frac{text{C}+frac{text{FV}-text{PV}}{text{t}}}{frac{text{FV}+text{PV}}{2}}\&textbf{where:}\&text{C}=text{Interest/coupon payment}\&text{FV}=text{Face value of the security}\&text{PV}=text{Present value/price of the security}\&text{t}=text{How many years it takes the security to reach maturity}end{aligned}
YTM=2FV+PVC+tFVPVwhere:C=Interest/coupon paymentFV=Face value of the securityPV=Present value/price of the securityt=How many years it takes the security to reach maturity