The price of a bond, or similar instrument, in the secondary market is equal to its present value. The present value is determined by the proceeds of the instrument at its maturity, the yield (interest rate) at the time that the instrument is sold in the secondary market and the time to maturity.
\(Price = \frac{Maturity \: proceeds}{ 1 + Yield \: * \: time \: to \: maturity }\)
This month we calculate the maturity proceeds of the instrument.
To give a worked example – assume a bond issued with a face value of £10m for 180 days with a final coupon payable at a rate of 6.5%. To find the maturity proceeds of the bond, we need to perform the following calculation:
\(Maturity \: proceeds = Face \: value \: \times \: 1 \: + \: coupon \: rate *\frac{number \: of \: days \: for \: which \: instrument \: issued} {number \: of \: days \: in \: the \: year}\)
In this case:
\(Maturity \: proceeds = 10,000,000 \: \times \: 1 \: + \: 0.065 * \frac{180}{365} = £ 10,320,547.95\)
Conventional calculator
When using a conventional calculator, to perform the calculation above, you would need to press the following buttons:
- 180 ÷ 365 =
- x 0.065 =
- +1 =
- x 10,000,000 = this will give the result 10320547.95</mrow</mfenced
Scientific calculator
Using the scientific calculator in Windows (select Start, Programs, Accessories, Calculator, View, Scientific), you would need to press the following buttons:
- \( 10000000 \: \times \: 1 \: + \: 0.065 \: \times \: 180\: / \:365 = this \: will \: give \: the \: result \: 10320547.95 \)
HP12C
Using an HP12C
- .065 ENTER
- 180 x 365 ÷ 1 + 10000000 x this will give the result 10320547.95
Next month we will show how the maturity proceeds are discounted at current interest rates to provide a present value.
