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Topic5DebtCapitalMarketAddendum-1.pptxThe Debt-Capital Market Fixed Income Securities Addendum
FINANCIAL MARKETS
Topic 5
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2
Bond pricing
From the lecture slides, one way to calculate the price of a bond is as follows:
When the summation term is expanded, it becomes:
9/17/2018
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Bond pricing
However, if we treat the first term in the formula as annuity, we get the following formula:
This is the same formula used in the calculation of slide 31 in the topic 5 lecture slides.
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3
Aside*: how do we get the second formula?
To get from (1) to (2), we need to treat the summation term as an annuity. An annuity is defined as a sum of constant finite payments, which strictly speaking, is the cae.
In mathematics, we call this sum a finite geometric series because 1) the ratio of each successive term is constant (hence geometric) and 2) it is a sum that terminates at some value n (hence finite) and takes the following form:
*aside = content that is non-examinable.
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Aside*: how do we get the second formula? (cont.)
The sum of the first n terms of a finite geometric series is:
Applying this to the summation term in (1), we get the following result:
We can substitute this back into (1), and then we get (2).
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5
Two formulas for calculating bond prices
Formula 1
Advantages:
Less prone to calculator error
Intuitive
Disadvantages:
Requires each cash flow to be discounted seperately takes longer
Formula 2
Advantages:
Significantly faster to calculate
Disadvantages:
More prone to calculator error; be careful about brackets!
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6
Theoretically, a bond that pays daily coupons with a maturity of 10 years will require 3,651 terms to discount using formula 1
With formula 2, it only requires 2 terms to discount!
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7
Bond pricing – example from slide 32
Face value = $1000, 3 years to maturity,
Semi annual coupon distribution
Coupon rate = 8% pa, market yield = 6%.
What is the present value/price of this bond?
Using formula 1…
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Bond pricing – example from slide 33 (2)
Using formula 2, we can get exactly the same answer!
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