A bond has the following data:
Shell
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- 5.5% annual, 05/09; £1000; price 99.5
- Issuer: Shell
- Principal: £1000
- Interest rate: 5.5% (annual)
- Coupon: 1000 x 5.5% = £55
- Maturity: May 2011 (05/11)
- Price: 99.5
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Sara poses you a question:
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If you want to buy this bond now you will have to pay 99.5% of £1000, which is £995.
Why would somebody be prepared to sell you this bond for less than they paid initially?
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The formula of bond pricing is:
| P = | C1 | + | C2 | + | C3 | + | Cn+ FC |
| (1+y) | (1+y)2 | (1+y)3 | (1+y)n |
where:
- n = number of periods of time until maturity.
- y = yield of the bond.
- P = price of the bond.
Ci = coupons of each period ( expressed as a percentage).
FC = face value (as a percentage of the real face value. Usually it will be 100%).
The price of a bond is found by discounting the coupon with the yield and the principal to the present date in compound interest.
Question: What does 'yield' mean?
You need to remember that holding money in the form of cash is but one way to use money. You can invest that cash in a variety of different ways. Our clients are looking to find ways of maximising the returns on their holdings. If they choose to hold money in the form of cash, they are effectively giving up the interest that could have been earned on that cash - in other words, there is an opportunity cost to holding money as cash.
We are going to calculate the yield of this Shell bond (assume that today is May 2007):
| P = | 5.5 | + | 5.5 | + | 5.5 | + | 5.5 | + | 5.5 + 100 |
| (1+y) | (1+y)2 | (1+y)3 | (1+y)4 | (1+y)5 |
If we solve the equation, we get the value: y ≈ 5.6% (this is approximate - the real solution is 5.641%).
The yield of this bond is 5.6% instead of 5.5% due to the fact that you have pay a bit less than 100 for the bond (99.5).
Why have we put 5.5 as the coupon instead of 55, and 100 in the face value, instead of 1000? Because it is a convention that the use of the bonds is in base 100 (as a percentage).
For example, we have a British Telecom bond with a 5.75% coupon and maturity in 12/28 (December 2028) that has a price of 94.4 and a £1000 principal. If we have to buy the bond, we have to pay £944 to buy it (94.4% of £1000).
In the Shell example, if we have £55 and £1000, the price we would have to pay is 995, instead of 99.5 (that is we would have to express the price in real terms, not as a percentage). The most important thing is that you must understand the meaning of price in this context and what it represents.
It all seems very complicated, but you have experienced this feeling before and overcome it, so you know that practice is going to be necessary to understand how it all works.
