Net Present Value and Internal Interest Rate

Use

The functions for the calculation of net present value and internal interest rate are used for the analysis of planned future payment flows. These functions let you answer the following questions:

- What is the net present value of the capital involved in a planned investment, taking into account the planned income that is achieved by the investment, and a calculated rate of interest which you specify?
- What internal interest rate would result in a net present value of 0?

The second question can also be phrased differently:

- At which interest rate would the available capital have to be invested in order to achieve just as much income as with the planned investment?

Net Present Value Formula

The calculation of net present value and internal interest rate are both based on the following net present value formula:

*K _{0}*: Net present value

The calculation is executed so that the start period is initialized with the value 0 (and not 1). This way the calculated net present value is lower than with an initialized value of 1, as any income is discounted in the start period at 0%. This method of calculation corresponds with the situation that the investment is made at the end of the start period, and thus only earns interest in the subsequent periods.

Additionally, you can set up the function so that at the end of the analysis period the remaining residual value (perpetual bond) is added to the calculated net present value. In this way, it is taken into account that the investment at the end of the analysis period does not instantly become worthless in reality, instead it can still be of benefit.

The formula displayed above changes in accordance with the following formula:

The formula shows the perpetual bond as an additional summand of the net present value formula: The perpetual bond corresponds to the balance from income and expenditure from the last period of the analysis period, divided by the rate of interest. From a business view, the perpetual bond portrays itself for example as possible sales revenue of the investment at the time *n*.

Scenario

The following planning layout shows a (very simple) sample scenario for the use of both functions:

An investment with the value of € 1 million is to be transacted. As the consequence of this investment, you plan additional income of € 1.54 million over a period of 10 years. With an assumed interest rate of 8%, the calculation results in a net present value of € 52,085.48 as the sum of the discounted difference between expenditure and income. This means: The gain from the planned investment is greater than the gain which would have been achieved from investing the same amount in an investment type at an interest rate of 8%. The excess gain is the net present value.

The internal interest rate is calculated at 9.18%. This means: The yield of the planned investment corresponds to the value of the internal interest rate. You can easily verify this by inserting the value of the internal interest rate as the calculation rate of interest in the net present value function, and then executing the function again. Net present value then amounts to 0.

In practice, when the internal interest rate is used as the calculation interest rate, the net present value calculation often results in a value that barely differs from 0. The reason for this is in the mathematical approach that is used for determining the internal interest rate: Because the underlying equation (that is, the NPV formula) cannot be resolved for the interest rate in a linear fashion, the system instead performs an iterative approximation (zero position search). The approximation finishes when it is close enough to 0, even if the exact value of 0 is not yet arrived at.

Integration

The functions described here are included in the role concept for characteristics and key figures, which provides suggestions for the occupying of equivalent characteristics and key figures within a planning area. See also the section Functions for Balance Sheet Planning.

The net present value functions are used within the planning application Investment Planning in Dynamic Preinvestment Analysis.

Prerequisites

The use of this function assumes that your data is prepared in the form of a chart of accounts – that is, the underlying planning area must therefore contain a characteristic, the values of which correspond to planning items. SAP delivers such a characteristic as Business Content ( 0SEM_POSIT).

Features

When creating a planning function for the calculation of net present value or internal interest rate, you assign certain roles to selected characteristics and key figures of the planning area. The following roles are involved:

*Planning item*: A field is to be selected, which assumes the role of a balance sheet item or an account.*Key figure for income and expenditures*: The values of the planned payment flows are read from this key figure.*Key figure for net present value or internal interest rate*: This key figure contains the calculated value as result of the function.*Characteristic for time reference*: This characteristic defines the period type used as a basis. You can choose between a calculation on fiscal year basis or a periodic view.- The last set of characteristics determines the details for storing time-related data.

The result after executing both functions is posted to a statistic item in the chart of accounts. You specify this item in the parameter group in the first period of the analysis time frame. The values for the remaining periods remain unchanged.

In the parameter groups for both functions you enter – corresponding to the field types – the desired characteristics and key figures. In the case of net present value functions, you also enter the interest rate to be used in the calculation. In addition, you can choose whether the net present value should be reported with or without consideration of the perpetual bond (see the section "Net Present Value Formula" above).