Net present value

The net present value (english net present value, NPV, Net Present Value ',' net present value ' [rather NGW ] or net present value ) is a business management code of the dynamic investment calculation. Discounting at the beginning of the investment payments are made comparable incurred at arbitrary times.

The principal value of an investment is the sum of the present values ​​of all caused by this investment payments ( deposits and withdrawals ). The sum of the discounted payments thus corresponds to the integral of the cash flow that is measured with a falling exponential function according to discount rate.

For a better understanding of the arithmetic operation of the capital value can also be considered as the calculated amount of money that would have to be used to arrive at a balance of 0 taking into account the interest rate and the cash inflows and outflows at the end of observation. The prerequisite for this is the reinvestment assumption, that is, the time between the investment of surplus discount rate.

The net present value or net present value method ( NPV less common method, or net-present - value method or NPV method) allows the assessment of an expansion of investment and determine the optimal replacement timing. The net present value method is used, inter alia, in company valuations under the name of discounted cash flow.

Calculation

The capital value is dependent on the discount rate and is based on the assumption of perfect capital market.

The net present value is calculated as follows:

  • : Capital Value at the time
  • : Discount rate
  • : Cash flow ( cash flow) in period, where ( Revenue - Expenditure in period ), or more generally represents a payment vector represents.
  • : Investment spending at the time (can also be construed as )
  • : Liquidation proceeds / proceeds remaining at the time (can also be construed as )
  • : Viewing time ( in periods)

Traps during the life of each period always equal payments, the equivalent capital value can also be easily determined using the present value of annuity formula:

  • : Payment per period

For different interest factors in different periods is calculated as the net present value, as follows:

  • : Cash flow in period
  • : Interest factor of the period with

Interpretation

An investment is absolutely advantageous if its net value is greater than zero.

NPV = 0: the investor gets back the capital invested and interest on the outstanding amount equivalent to the interest rate calculation. The investment has no advantage over the investment on the capital market at the same ( equivalent risk ) interest rate. Is the internal rate of return at this point.

NPV > 0: the investor gets back the capital invested and interest on the outstanding amount in excess of the discount rate.

NPV <0: The investment can not assure a return on capital employed for the discount rate.

If several mutually exclusive investment alternatives are compared, it is the one with the largest net present value, the relatively favorable. Furthermore, it is possible that capital values ​​across are not mutually exclusive investments sum up with different interest rates calculation, since it is an additive process.

The discrete-time formula of the capital value

Can also be represented in a continuous form.

The capital value can be viewed from the real number space as Laplace and Z - transform of the payment stream with the integral operator including the complex number s (= ln ( 1 i) approximately corresponds to the interest rate i or, more precisely s ). This results in well-known simplifications of cybernetics, system theory and control engineering. Imaginary parts of the complex number s describe here the tendency to oscillate (see the pig cycle and the phase shift of price and supply as well as the explanatory Spinnwebtheorem ), real to the compounding effect (see the damping).

Criticism

Benefits

It is a computationally simple method which allows easy interpretation, as the net present value is expressed in monetary units ( absolute income). It is also possible to carry out interest rate structure compliant calculations because of the discount rate can be adjusted in each period. In addition come in the net present value method, the advantages of the dynamic calculation ( attention the timing of the payments) over the static statement to fruition.

Disadvantages

Problem with the use of the net present value method, as well as all other discounted cash flow method, the assumption of perfect capital markets, in particular the assumption of equality of debit and credit interest rate based on subjective assumptions discount rate and the amount of future cash flows. Due to the simple calculation and interpretability of the risk of using the results without comment. It is therefore important that the assumptions made, especially on the level of the risk premium in the pricing interest rate and the future cash flows, called and justified.

If the option to make an investment several times, overlooked, this can lead to wrong decisions. Remedy the annuity here. This assumes the reinvestment of income to capital market rate.

Discounted Cash-Flow Z-transform
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