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Bond Calculations

Bond functions require the input of date values. For more information on the input of dates, refer to the Date Calculations section.

Bond Price (PRICE)

The [PRICE] key calculates a bond price, expressed as a percentage of par. It uses the following input values in the calculation, which are read from the TVM registers:

n - Number of payments per year*.
i - Yield to Maturity.
PMT - Coupon percentage rate.

PRICE accepts two date values, the settlement (purchase) date, followed by the maturity (redemption) date, and returns the calculated bond price. Additionally, it calculates the interest accrued since the last interest date. The latter result is stored in the K memory register, and if you are working in RPN mode, it is also placed in the Y stack register. If you are using an algebraic mode, you can recall the K register to retrieve the accrued interest result.

Given the differences between RPN and algebraic input modes, it is worthwhile to give the following example in both.

Example: What price should you pay on April 25th 2005 for a 6.75% U.S. Treasury bond that matures on June 1st 2015, if you want a yield of 8.25%. Assume that you normally express dates in the month-day-year format.

Reverse Polish Notation:

2 [n] (semi-annual)
8.25 [i] (enters YTM)
6.75 [PMT] (enters coupon rate)
4 [DATE] 25 [DATE] 2005 (settlement date)
[ENTER]
6 [DATE] 1 [DATE] 2015 (maturity date)
[PRICE]
Displays: 89.85 (price as percentage par)
[+]
Displays: 92.55 (total price inc. accrued interest)

Algebraic Modes:

2 [n] (semi-annual)
8.25 [i] (enters YTM)
6.75 [PMT] (enters coupon rate)
4 [DATE] 25 [DATE] 2005 (settlement date)
[PRICE]
6 [DATE] 1 [DATE] 2015 (maturity date)
[ENTER]
Displays: 89.85 (price as percentage par)
[+]
[RCL] [K] (recalls accrued interest)
Displays: 2.70
[ENTER]
Displays: 92.55 (total price inc. accrued interest)

The [PRICE] key does not update any values in the TVM registers.

* See Bond Conventions, below.

Yield to Maturity (YTM)

The [YTM] key calculates the Yield to Maturity of a bond, expressed as percentage of par. It uses the following values in the calculation, which are read from the TVM registers:

n - Number of payments per Year*.
PV - Quoted price (percentage par).
PMT - Coupon percentage rate.

YTM accepts two date values, the settlement (purchase) date, followed by the maturity (redemption) date, and returns the calculated Yield to Maturity.

In the following example, the same input values given in the previous demonstration of bond price calculations are used. In effect, YTM is demonstrated by reversing the calculation, so as to arrive at the original YTM value we used earlier. The example is shown in Reverse Polish Notation only.

Example: You buy a 6.75% US. Treasury bond on April 25th 2005, that matures on June 1st 2015. The quoted price is 89.85%. What yield will this provide? Assume that you normally express dates in the month-day-year format.

2 [n] (semi-annual)
89.85 [PV] (enters price as percentage par)
6.75 [PMT] (enters coupon rate)
4 [DATE] 25 [DATE] 2005 (settlement date)
[ENTER]
6 [DATE] 1 [DATE] 2015 (maturity date)
[YTM]
Displays: 8.25

The [YTM] key does not update any memory register values.

* See Bond Conventions, below.

Bond Conventions

DreamCalc Coupon & Day Count Basis

Bond calculations may be performed for coupon payments per year from 1 (annual) to 12. The number of payments register "n" is used to specify this, where a value of 2 is semi-annual. If the register contains a value of less than +1, semi-annual is assumed. If the value has a fractional component, it is rounded down to the nearest integer. A payments per year value of more than 12 will result in a Range Error.

DreamCalc assumes an ACT/ACT day count basis and divides by the Julian epoch (325.25 days) to calculate bond time periods. You may wish to treat the results of bond calculations as good estimates, rather than exact values.

Bond Market Conventions in Various Countries

Country	Coupon Payments
Australia (CGSs)	Semi-annual
Canada(Treasury)	Semi-annual
Eurobond	Annual
Eurozone (Gov)	Annual or semi-annual
Japan (JGBs)	Semi-annual
Sweden (Gov)	Annual
Switzerland (SGBs/SGNs)	Annual
United Kingdom	Semi-annual
United States	Semi-annual

Bond Market Conventions in Various Countries
Source: Walmsley (2000) Table 8.1. Bank of England, Practical Issues Arising from the Euro.