## Calculating the price of an instrument in the secondary market – Part Two

##### Published: Jul 2001

In last month’s issue, we started a two part process to calculate the price of an instrument on the secondary market. 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. Last month we showed how to calculate the maturity proceeds of the instrument. This month, we use that figure to calculate the present value, the price, of the instrument.

$$Price = \frac{Maturity \: proceeds }{1 \: + \: yield \: * \: time \: to \: maturity}$$

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%. We found that the maturity proceeds of this instrument would be £10,320,547.95.

Using that figure, we can now calculate the price of the bond in the secondary market, assuming that there are 32 days until maturity when the current interest rate is 7%.

$$The \: price =\frac {maturity \: proceeds }{1\: + \: yield \: * \: \frac{number \: of \: days \: to \: maturity}{number \: of \: days \: in \: the \: year}}$$

In this case:

$$Price = \frac{10,320,547.95}{1\: + \: 0.07 \: * \: \frac{32}{365}} = 10,257,597.22$$
##### Conventional calculator

Using a conventional calculator, press the following buttons:

10320547.95  M + (this puts the maturity proceeds figure in the memory)

C (this clears the display, but not the memory)

• 32 ÷ 365 =
• x 0.07 =
• + 1 =
• 1 / x
##### Scientific calculator

Using the scientific calculator on a Windows computer (Start, Programs, Accessories, Calculator, View, Scientific), you would need to press the following buttons:

• 10320547.95 / 1 + 0.07 * 32 / 365 = this will give the result  10257597.22
##### HP12C

Using an HP12C:

• .07  ENTER
• 32 x 365 ÷ 1 + 1 / x 10320547.95 this will give the result  10257597.22