A zero-coupon bond is a type of bond that doesn’t make coupon payments. This type of bond is issued with a big discount to its face value.

At the time of maturity, the bondholder receives the face value of the bond, which means that the current price has to be lower than the face price. The investor’s earnings come entirely from the gain on redemption because there are no coupon payments.

Bonds can be held until maturity date or they can be sold on the secondary markets (markets where previously issued financial instruments (including bonds) are sold and bought). Because the only payment is made at the maturity, prices of zero-coupon bonds fluctuate more significantly that prices of coupon bonds.

The more an investor has to wait until the maturity date, the lower the price of the bond should be. This happens because of the time value of money, according to which, the same amount of money available at the present time is worth more than the same amount available in the future because money available at the present time can be used to create more money.

### How to calculate the price of a zero-coupon bond?

Price of the zero-coupon bond is calculated much easier than a coupon bond price since there are no coupon payments. It is calculated as:

$P = \frac{M}{(1 + r)^{n}}$

Where P is the current price of a bond, M is the face or nominal value, r is the required rate of interest, n is the number of years until maturity.

### Example of price of a zero-coupon bond calculation

Let’s assume an investor wants to make 10% of return on a bond. The face value of the bond is $10,000. The bond is redeemed in 5 years. What price the investor would pay for this bond? • M =$10,000
• r = 10%
• n = 5
$P = \frac{10,000}{(1 + 0.10)^{5}} = \6,211.18$

The price of the bond should be $6,211.18 if the investor wants to make 10% of return. ### How to calculate YTM of a zero-coupon bond? YTM (yield to maturity) is an annual income level or profitability, which investors gain by buying a bond or other fixed-interest security at the current market price and holding it in their portfolio until maturity. Yield to maturity for zero-coupon bonds is calculated as: $YTM = \sqrt[n]{ \frac{Face\;value}{Current\;price} } - 1$ ### Example of YTM of a zero-coupon bond calculation Let’s assume an investor wants to buy a zero-coupon bond and wants to evaluate what YTM of this bond would be. • The face value of the bond is$10,000.
• The price of the bond is \$9,100.
• There are 2 years until maturity.
$YTM = \sqrt{ \frac{10,000}{9,100} } - 1 = 4.83\%$

YTM of this bond is 4.83%. Which means the investor would receive 4.83% of the nominal value every year until maturity.