# Ytm formula for zero coupon bond

If they are denominated in a foreign currency, they are known as eurobonds. Dollar-denominated bonds issued in the U.

### Valuing Bonds

This formula shows that the price of a bond is the present value of its promised cash flows. The bond makes annual coupon payments. These results also demonstrate that there is an inverse relationship between yields and bond prices:. For a bond that makes semi-annual coupon payments, the following adjustments must be made to the pricing formula:.

• Current Yield.
• Nominal Yield, Coupon Rate.
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As an alternative to this pricing formula, a bond may be priced by treating the coupons as an annuity; the price is therefore equal to the present value of an annuity the coupons plus the present value of a sum the face value. This method of valuing bonds will use the formula:. The bond in the previous example can be priced using this alternate bond valuation formula as follows:.

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A zero-coupon bond does not make any coupon payments; instead, it is sold to investors at a discount from face value. The difference between the price paid for the bond and the face value, known as a capital gain , is the return to the investor. The pricing formula for a zero coupon bond is:. What is the market price of this bond?

In order to be consistent with coupon-bearing bonds, where coupons are typically made on a semi-annual basis, the yield will be divided by 2, and the number of periods will be multiplied by There are different types of yield measures that may be used to represent the approximate return to a bond. These include:. This equals the rate of return earned by a bond holder known as the holding period return if:. It is impossible to solve for the yield to maturity algebraically; instead, this must be done using a financial calculator or Microsoft Excel.

## Current yield

The variables in brackets fv, type and guess are optional values; the value of type is set to zero if it is not specified. Guess can be used to provide an initial estimate of the rate, which could potentially speed up the calculation time.

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5. Yield to maturity;
6. Zero Coupon Bond!
7. Note that either pv or fv must be negative, and the other must be positive. The negative value is considered to be a cash outflow, and the positive value is considered to be a cash inflow. Also note that entering semi-annual periods and coupon payments will produce a semi-annual yield; in order to convert this into an annual yield on a bond-equivalent basis , the semi-annual yield is doubled.

For a bond that is callable, the yield to call may be used as a measure of return instead of the yield to maturity. The process is similar to computing yield to maturity, except that the maturity date of the bond is replaced with the next call date. This is because yield to call is based on the assumption that the bond will be called on the next call date. The face value is replaced with the call price since this is the amount that the investor will receive if the bond is called. What is the yield to call? In this case, the bond will mature in eight years, but it can be called in three years.

## Zero Coupon Bond Yield - Formula (with Calculator)

The yield to call is computed as follows:. The current yield is simpler measure of the rate of return to a bond than the yield to maturity. The current yield is computed as:. This measure has the benefit of simplicity. It suffers from the drawback that it does not account for the time value of money. Excel contains a set of specialized bond functions that can be used to account for several complications that arise in bond pricing, such as day-count conventions.

Money market instruments e. Note that the settlement date and maturity date are represented as numerical values in Excel. The date January 1, is represented as 1; all later dates represent the number of days that have passed since January 1, As an example, suppose that a bond is sold on June 15, with a maturity date of June 15, What is the price of the bond?

Note that the price of the bond is entered as Also note that represents June 15, and represents For example,. This article is one part of a series on fixed income portfolios. Zero-coupon bonds trade on the major exchanges. They are commonly issued by corporations, state and local governments, and the U.

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.

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• Bond Yield to Maturity (YTM) Calculator.
• What are Zero Coupon Bonds? Who Should Invest in Them?.

The IRS calls this 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.

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