To compare different fixed-income securities, you’ll need to calculate the ‘yield to maturity’. This brings together the purchase price of the bond and the coupon rate, and reflects the true underlying interest rate of return for the investor. Bonds are sometimes quoted and traded on a yield to maturity basis, from which the purchase price can then be calculated. For bonds that trade on the ASX, they are quoted and trade on a price basis, and the yield to maturity can be back calculated.
There are two formulas used to calculate the yield to maturity. The first gives you an approximate figure, while the second gives the exact yield. However, the second formula requires you to guess the yield, ‘r‘, and work it into the formula by trial and error (although some financial calculators can do the calculation.)
Where: C = the coupon payment in dollars
F = the face value
P = the purchase price
n = number of years to maturity
c(1 + r)-1 + c(1 + r)-2 + . . . + c(1 + r)-Y + B(1 + r)-Y = P
c = the annual coupon payment in dollars
Y = the number of years to maturity
B = the par value
P = the purchase price
r = the yield (guessed through trial and error)
Calculating accrued interest
There is one further small addition to the pricing calculation and this is the concept of ‘accrued interest’. If a bond is partway through a coupon period, it will notionally have accrued some interest and this interest should be considered if you want to understand the full value of the bond you’re about to buy. The ‘market price’ can then be adjusted for the accrued interest to determine the ‘capital price’, which more accurately describes the true value of the bond.
- Market price: calculated using yield to maturity, actual purchase date, coupon and maturity date
- Accrued interest: calculated by measuring the number of days from the last coupon date to the purchase date, dividing that by the number of days in the whole coupon period, and then multiplying by the coupon for the period
- Capital price: the market price less accrued interest
For example, a government bond with a coupon of 8% pa (paid semi-annually) maturing on January 15, 2014 is purchased at a yield of 6% pa on June 15, 2011. Coupons of 4% are paid every six months on July 15 and January 15. The components of the price will be as follows:
Market price: $107.191
Accrued Interest: $3.337
Capital price: $103.854
Click here for a list of bonds available on the Australian stock market.
Important information: This content has been prepared without taking account of the objectives, financial situation or needs of any particular individual. It does not constitute formal advice. For this reason, any individual should, before acting, consider the appropriateness of the information, having regard to the individual’s objectives, financial situation and needs and, if necessary, seek appropriate professional advice.