# Bond Calculator

Governments and corporations issue bonds to raise cash (borrow money). When you purchase a bond, you are lending the bond's issuer money.

Bonds trade in established markets, usually in face amounts of $1,000. However, by convention, bond prices are quoted as if the face amount were $100. So if a bond broker quotes you a price of $93, you'll pay $930 plus perhaps accrued interest, fees, and commissions.

Calculate either a bond's price or its yield-to-maturity plus over a dozen other attributes with this full-featured bond calculator.

If you are considering investing in a bond, and the quoted price is $93.50 (sometimes referred to as the **bond valuation**), enter a "0" for yield-to-maturity. Also, enter the settlement date, maturity date, and coupon rate to calculate an accurate yield.

Or conversely, if you want to achieve a particular yield, enter the desired yield-to-maturity, and the calculator will calculate the amount you should pay for the bond.

See this Wikipedia page for an introduction to fixed income investing. More about the calculator below

## How to Use the Bond Calculator

#### Your inputs:

**Bond price** - while bonds are usually issued at par, they are available in the resale market at either a premium or a discount. If a bond is quoted at a discount of $86, enter $86 here. If you enter a '0' (zero) for Bond Price and a value other than 0 for the Yield-to-Maturity, the calculator will calculate the price.

The **settlement date** is the date that the buyer and seller exchange cash and securities. Generally, the settlement date is one business day after the trade date for bonds of all types. When the settlement date does not fall on a coupon date (very likely), the result is a **stub period**. This calculator supports accurate **accured interest** calculations for stub periods.

The **coupon rate** is the rate of interest a bond pays annually. (Coupon interest, however, is most frequently paid semiannually.) To determine the dollars of interest paid annually, multiply the par value by the coupon rate.

The **call date** (if a bond is callable) is essential information when evaluating a bond. The issuer of the bond may have the right to 'call' the bond prior to maturity. The date this can happen is the "call date". When the issuer calls the bond, the bondholder gets paid the **callable amount**. Coupon interest payments cease. The former bondholder now must find another investment.

NOTE: **Callable at this amount** should not be confused with the **price-to-call** input. price-to-call is what the purchaser will pay for the bond at a particular yield-to-call. This calculator will let you calculate either the price-to-call or the yield-to-call. If you want to guarantee yourself a particular yield and the bond has a call provision, enter your desired yield in the yield-to-call input and enter "0" (zero) for the price-to-call.

Caution: Be careful buying a bond with a call provision that is selling for a premium. If the issuer called such a bond, you might experience a capital loss. The loss results when they pay you the call price, and you had purchased it for a premium price.

The **issue date** is the date the bond starts trading in the resale market. **You only need to provide the issue date if the settlement date is before the first coupon date.** In such cases, check the checkbox and enter the date. The calculator will calculate the accrued interest from the issue date to the settlement date. If the first coupon date has passed, leave this option unchecked.

The **maturity date** is the date the issuer must repay the redemption (par) value. Any maturity date is legally permissible; however, bonds usually have a maturity of between 10 and 40 years from the issue date.

**Redemption value or par value** is the stated face value of the bond; it is often $1,000. Par is the amount of money that the bond issuer needs to repay on the maturity date. Bond traders usually quote prices per $100 of Par Value. That is, if a bond's par value is $1,000 and its current price is $860, the price quoted will be $86. This calculator follows this pricing convention by setting the default par value to $100.

Please note that you don't have to do the calculations per a single bond. If you want to purchase bonds worth $50,000 at par, you can enter 50 as the "Number of Bonds". The resulting calculations will show the "Total Trade Amount" the purchaser has to pay for the 50 bonds with a total face value of $50,000.

**Coupon frequency** is the frequency the bondholder will receive coupon interest payments. The most common payment frequency is semiannually (twice per year). However, other frequencies, such as monthly or annually, are also used.

**Day Count Method**

**30/360 NASD (National Association of Security Dealers)**: assumes a yea consists of 12 periods of 30 days. Therefore, a year consists of 360 days. The difference between this method and the European method is how the calculations handle the last day of a month.

**Actual/360 Days**: the number of days between two dates is actual, and the number of days in a year is 360. Interestingly, when the terms for calculating interest dictate this day count method, a year maybe longer than a year. January 1, 2021, to January 1, 2022, consists of 365. Applying this convention 365/360 equals 1.013889 (approximately).

**Actual/365 Days**: the number of days between two dates is actual, and the number of days in a year is 365. January 1, 2021, to January 1, 2022 consists of 365. Applying this convention 365/365 equals 1.0.

**Actual/Actual**: the number of days between two dates is actual, and the number of days in a year is actual. July 1, 2023, to July 1, 2024 (spans a leap year) consists of 366 days. Applying this convention, 366/366 equals 1.0. January 1, 2024, to July 1, 2024 (semiannual calculation) consists of 182 days. 182/366 = 0.497268 (approximately).

**European Method/360 Days**: assumes a year consists of 12 periods of 30 days. Therefore, a year consists of 360 days. The difference between this method and the NASD method is how the last day of a month is handled. If the second date is the last day of February or the 31st, the day is adjusted to the 30th.

## Bond Calculation Results

**Previous or first coupon date** is the coupon date immediately preceding the settlement date. This calculator follows the convention of calculating this date backwards from the maturity date. However, you can edit this value if the bond does not make coupon payments as anticipated. Confirm that this date is set accurately so that the "Dirty Price" and "Accrued Interest" calculations are accurate.

Bond prices change as interest rates change. It is possible to calculate the anticipated price change per a predetermined change in interest rate expressed in **basis points**. Bond prices move inversely to rates. If you wish to know how much a bond's price will decrease if interest rates increase by 2.0%, enter -200 basis points in the "For every 'X' basis point change" input.

If you want to buy or sell more than one bond, enter the number of bonds in the **number of bonds** input box. The total price for these bonds as well as the accrued interest will be calculated.

The calculator performs **five yield calculations**: current yield, yield-to-maturity (YTM), yield-to-call (YTC), after-tax yield, and taxable equivalent yield. Yield is the rate of return expressed as a percentage. Looking at potential yields allows you to evaluate a bond's attractiveness as an investment. Yield computations do not, however, take into account the risk involved with a particular issue.

The **current yield** is the dollars of interest paid in one year divided by the current price. (One year's interest is equal to the par value multiplied by the coupon rate.) The current yield assumes you will not reinvest the interest payments.

The **yield-to-maturity (YTM)** assumes that you will be able to reinvest the interest payments at a rate equal to the bond's original YTM. YTM calculations do not provide total return information on an absolute basis since this assumption is being made. The YTM calculation gives you a tool to compare different bonds to each other on a relative basis.

The **yield-to-call (YTC)** calculation is the same calculation as the YTM, except the yield-to-call date is used rather than the maturity date.

**After-tax yield** is the yield after the impact of taxes. The calculator only calculates a meaningful yield if you enter your marginal tax rates. Click for the latest U.S. marginal rates from the I.R.S. This link has the latest capital gains tax rates.

**Taxable equivalent yield** is the yield one would have to earn if the yield-to-maturity is tax-free.

**(Macaulay) Duration** is the weighted average of the time until the bond holder receives all the cash flows. Duration is always less than the time to maturity unless the bond is a zero coupon bond. For a more in depth discussion about duration, see the Oblivious Investor.

**Modified Duration** measures the price sensitivity to a change in yield.

## Finmargin says:

Nice explanation on bond calculation. Would be great if you could provide automated calculation templates. Below is my blog on finance

https://www.finmargin.com/

## Karl says:

Thanks. Not sure what you mean by "automated calculation templates" though.

## Finmargin says:

Hi karl its like an excel which has formulas to autocalculate

## Carl says:

Add capability for zero coupon munis (0 coupon frequency).

## Karl says:

Yes, not having a zero-coupon is a gap. I’ll try to add one before the end of the year. Currently, I’m working on other enhancements.