## Translating future cash flows into a net present value

##### Published: Nov 2001

In order to present meaningful reports, it is often necessary to discount future cash flows into a net present value. Any future cash flow will have a present value, which is determined by the time until the cash flow and the relevant interest rate.

The present value of any future cash flow is the sum that would need to be invested today at the relevant interest rate to ensure that future cash flow on the date in question.

The net present value (NPV) of a series of future cash flows is the sum of the present value of all those cash flows, whether they are positive or negative.

To calculate the net present value of a series of cash flows

$$NPV = \Sigma^t\:\frac {CF_t}{1 \: + \: \frac{i}{n}d \: * \:n}$$
##### Where
• Σt= the sum of cash flows up to time period t
• CFt = Cash flow in period t
• i = yield to maturity
• n = number of interest payments per year
• d = number of days until cash flow t divided by number of days in the year (usually 360 or 365)

#### To give a worked example

For a bond with a face value of £1000, that matures in three years and pays annual coupons at an interest rate of 6%. This means that at the end of years one and two, there will be positive cash flows of £60 and at the end of year three there will be a positive cash flow of £1060.

$$NPV = \frac{60}{1.06}\: + \: \frac{60}{1.06^2} \: +\: \frac{1060}{1.06^3} \: =\:56.60\:+\: 53.40 \: + \: 890.00\: £1000$$

Note that to receive a cash flow of £1060 in three year’s time, one would have to invest £890 if the prevailing interest rate was 6%.

##### Conventional calculator

Using a conventional calculator, press the following buttons:

• 1.06 1/ x x 60 = M + C
• 1.06 x 1.06 = 1 / x  x 60 = M + C
• 1.06 x 1.06 x 1.06 = 1 / x x 1060 =
• + MR = this should give the result 1000
##### Scientific calculator

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

• 60 / 1.06 + 60 / 1.06 x ^ 2+ 1060 / 1.06 x ^ 3 = this should give the result  1000
##### HP12C

Using an HP12C (or a similar calculator using Reverse Polish Notation)

• 1.06 ENTER 1 / x 60 x
• 1.06  ENTER 2yx  1 / x 60 x +
• 1.06 ENTER  3yx  1 / x 1060 x + this should give the result  1000