Yield to maturity of a zero coupon bond

This yield to maturity calculator allows you to find yield to maturity of a zero coupon bond based on bond price, face value, compounding frequency, and years to maturity. By default the calculator assumes that the interest is compounded annually. You can change it to semi-annual compounding through the radio buttons.

As you enter or change values, the calculator automatically updates and displays the yield to maturity.

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What is Yield to Maturity of a zero-coupon bond?

The Yield to Maturity (YTM) of a zero-coupon bond is the rate of return an investor can expect to earn if the bond is held until maturity. Since a zero-coupon bond does not pay periodic interest (coupons) and is sold at a discount to its face value, the YTM is essentially the compounded annual return based on the difference between the purchase price and the bond’s face value.

Formula for YTM of a zero-coupon bond:

\text{YTM} = \left( \frac{F}{P} \right)^{\frac{1}{T}} - 1

where:

• F = Face value (or par value) of the bond.
• P = Purchase price (current price) of the bond.
• T = Time to maturity in years.

Example:

If a zero-coupon bond has a face value of $1,000, is purchased for $800, and matures in 5 years, the YTM would be calculated as follows:

\text{YTM} = \left( \frac{\$1,000}{\$800} \right)^{\frac{1}{5}} - 1 \approx 4.56\%

This means the bond would yield an annual return of about 4.56% if held to maturity.

Factors influencing YTM

Several factors influence the Yield to Maturity (YTM) of zero-coupon bonds. Since zero-coupon bonds are sold at a discount and do not make periodic interest payments, their YTM is derived from the difference between their purchase price and their face value. The key factors that influence YTM in this context include:

1. Purchase price of the bond

• The price at which the bond is purchased has a direct impact on its YTM. The lower the price relative to the bond’s face value, the higher the yield, and vice versa.
• If a bond is purchased at a deeper discount (lower price), the investor stands to make a higher return when the bond matures at face value.

2. Time to maturity

• The longer the time to maturity, the lower the YTM, assuming all else is equal. This is because the bondholder has to wait longer to receive the face value at maturity.
• Conversely, a shorter time to maturity means the bondholder will realize the return sooner, increasing the YTM for the same price.

3. Face value (par value)

• The bond’s face value is what will be paid to the investor upon maturity. It is fixed, but it directly impacts the YTM calculation. The larger the face value in relation to the purchase price, the higher the yield.

4. Interest rates in the market

• Interest rate environment: In a rising interest rate environment, the prices of bonds, including zero-coupon bonds, typically fall, which leads to a higher YTM for new buyers.
• Conversely, if interest rates fall, bond prices increase, leading to a lower YTM for new purchases.

5. Credit risk of the issuer

• Zero-coupon bonds issued by entities with higher credit risk will generally have to offer a higher yield to attract investors. This compensates for the greater risk of default.
• Conversely, bonds issued by high-credit entities (like government bonds) tend to offer lower yields, as they are considered safer investments.

6. Inflation expectations

• If inflation is expected to rise, investors will demand a higher YTM to compensate for the reduction in purchasing power over time. Conversely, lower inflation expectations may lead to lower yields.

7. Tax considerations

• Since zero-coupon bonds accumulate interest in the form of the price difference, some countries tax this imputed interest annually even though no actual cash payments are made to the investor until maturity. This can affect the after-tax YTM.

8. Liquidity

• The liquidity of the bond (how easily it can be bought or sold) can affect its price and thus its YTM. Less liquid bonds might trade at a discount, resulting in a higher yield.

9. Call or put features (if applicable)

• Although most zero-coupon bonds don’t have embedded options, if the bond can be called (redeemed early by the issuer) or put (sold back to the issuer by the bondholder), these options can affect the bond’s price and thus the YTM.