Appendix 1

Bond Market Price Calculations

STRAIGHT BOND CALCULATIONS

Simple yield to maturity and gross redemption yield have been developed to value and price these instruments. These measures take into account the pattern of coupon payments, the remaining life to maturity and the capital gain or loss arising over the remaining life of the bond.

Simple yield to maturity

The formula for simple yield to maturity is:

For example, given a bond with a 5.5% coupon rate, a current clean price of 98.3% and seven years remaining until maturity, the equation is:

Gross redemption yield

Simple yield to maturity is a good rough and ready guide to bond valuation, but it does not take into account the affect of compound interest. To take this factor into account, the concept of gross redemption yield was developed, and this valuation methodology uses the following equation:

where:

Pd is the dirty price of the bond

rm is the yield to maturity

Ntc is the number of days from today to the next coupon dat

C is the coupon rate

M is the redemption payment of the bond at maturity (usually face value) S is the number of coupon payments before redemption.

The simple yield to maturity and gross redemption yield formulae may be applied to straight bonds. They cannot be applied to FRNs because the future values of coupons are not known, so alternative evaluation methods are used for these instruments. Therefore the concepts of simple margin and discounted margin have been developed.

FRN CALCULATIONS

Simple margin

Simple margin is the average return on an FRN for its life compared to the reference interest rate. It is composed of two elements, the margin (i.e. the difference between the actual coupon rate and the benchmark interest rate), and the capital gain or loss that will be made when the bond matures (i.e. the difference between the cost price and the maturity value of the bond). The formula may be expressed as:

This formula amortises the element of capital gain or loss in a straight line over the remaining period to maturity, rather than at a constantly compounding rate. To achieve this, the discounted margin concept may be used. However, this method relies on a forecast of the benchmark interest rate over the life of the bond.

Discounted margin

This method constantly amortises the capital gains element at a constantly compounding rate. However, it relies on an accurate forecast of the benchmark interest rate over the life of the bond, which can be hard to predict. The formula is:

where:

Pd is the dirty price of the bond

DM is the discounted margin

re is the current value of the benchmark interest rate

re* is the assumed (forecast) benchmark rate over the remaining life of the bond

Ntc is the number of days from today to the next coupon date

QM is the quoted margin

S is the number of coupon payments before redemption.

VALUATION METHODOLOGIES FOR OTHER TYPES OF DEBT INSTRUMENT

None of these methods can be used to value and compare convertible bonds and bonds with warrants attached, because it is necessary to take into account the values of the equities into which the bonds can be converted or the warrants may be used to purchase. Nor are they suitable for index linked securities, where the coupon and/or the redemption value depend upon the inflation rate. It is beyond the scope of this book to provide a comprehensive summary of all the analytical methods that are used for all types of debt instruments, but Appendix 3 suggests some other publications that may be used as reference works.