 ### What is Zero Coupon Bond Valuation?

A zero coupon bond is a bond that makes no periodic interest payments, or coupons, while it grows to maturity, and is sold at a deep discount from face value. The buyer of the bond receives a return by the gradual appreciation of the security, which is redeemed at face value on a specified maturity date.

Zero-coupon bonds are usually long-term investments; they often mature in ten or more years. Although the lack of current income provided by zero-coupons bond discourages some investors, others find the securities ideal for meeting long-range financial goals like college tuition. The deep discount helps the investor grow a small amount of money into a sizeable sum over several years

### Zero Coupon Bond Valuation Variables

Not all bonds have coupon payments. Those that do not are referred to as zero coupon bonds. These bonds are issued at a deep discount and repay the par value, at maturity. The difference between the purchase price and the par value represents the investor's return.

#### Face Value of the Bond (F)

The face value, or par value, of a bond is the value investors expect to receive back from the bond issuer for the bond at the time of maturity.

#### Yield to Maturity or Rate to Yield (r)

The Yield to Maturity is the discount rate of return on a bond that is purchased by an investor. It takes into consideration economic effects such as interest, inflation, and other important factors that an investor may consider during their evaluation.

#### Time to Maturity (t)

The time to maturity is the number of periods during which a zero coupon bond will grow with interest until maturity. It is the life of a zero coupon bond, generally expressed in years.

#### Zero Coupon Bond Present Value (V)

The present value of a zero coupon bond is the value that a bond holds today to an investor, inclusive of rates of return, maturity, and face value. The final value of a zero coupon bond calculated by an investor is an indication of whether the market value of the bond is over or under valued in comparison to the calculated present value.

### How to Calculate the Zero Coupon Bond Valuation

A zero-coupon bond is a bond that pays no interest and trades at a discount to its face value. It is also called a pure discount bond or deep discount bond. U.S. Treasury bills are an example of a zero-coupon bond. Assume you are considering purchasing a zero coupon bond with a yield to maturity of 10%, a face value of \$1,000 and a time to maturity of 10 years. Using the calculation depicted above, you calculate the present value of the bond to you as follows:

V = F / (1 + r)t

V = 1,000 / (1 + 0.1)10

V = \$385.54

The zero coupon bond you are considering purchasing has a present value of \$385.54 to you. If you were to purchase it, you would make a profit of \$614.46 at the time of maturity. If the bond is selling today at a value lower than \$385.54 you would consider this bond undervalued and consider investing in order to make a greater profit. If the bond is overvalued and selling on the market at a price greater than the calculated present value, you would reconsider investment in this financial instrument. ### Advantages of Zero Coupon Bond Valuation

Because zero-coupon bonds essentially lock the investor into a guaranteed reinvestment rate, purchasing zero-coupon bonds can be most advantageous when interest rates are high. They are also more advantageous when placed in retirement accounts where they remain tax-sheltered. 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.

The lack of coupon payments on zero-coupon bonds means their worth is based solely on their current price compared to their face value. Thus, prices tend to rise faster than the prices of traditional bonds when interest rates are falling, and vice versa. The locked-in reinvestment rate also makes them more attractive when interest rates fall.

### Zero Coupon Bond Valuation Summary

A zero-coupon bond is a debt security instrument that does not pay interest. Zero-coupon bonds trade at deep discounts, offering full face value (par) profits at maturity. The difference between the purchase price of a zero-coupon bond and the par value, indicates the investor's return. ### Zero Coupon Bond Valuation with On Equation Finance Calculator

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