2.6.2 Dynamic methods

Major difference to the static methods of capital budgeting is that dynamic methods consider the time value of money. In consequence the project’s cash flows over the project life time are discounted to today’s of money.

Today’s value of money differs from the value in the future because if invested it would earn interest over time.

The present value of an amount of cash at some future date is calculated⁸

With FV= future value, PV = present value, i = discounting factor (interest rate or cost of capital), n = number of periods

The NPV method

The net present value (NPV) represents the sum of the present value of future cash flows discounted to today at a given intereset rate.

NPV compares the present value of money today to the present value of money in the future.

calculating the net present value

With FV= future value, PV = present value, i = the rate of return; the opportunity cost of capital, N = number of periods, I_{0 = initial investment}

The rate of return used to discount future cash flows is either the cost of capital⁹ or the rate of return of an investment with similar risk, also called opportunity cost¹⁰.

If the NPV is positive the investment is creating more value than alternative investments with the applied rate of return.

The IRR method

The internal rate of return (IRR) is defined as the rate of return (interest) that makes the net present value equal to zero.

With FV= future value, PV = present value, IRR = internal rate of return, N = number of periods, I_{0 = initial investment}

If the IRR is greater than the cost of capital, the project is creating value. The IRR method provides relative values for the return compared with the absolute results of the NPV method. The IRR is interpreted according to Volckart as a rate of return per period for the capital still tied-up during that period¹¹. Other interpretations assume reinvestment of interim cash flows in projects with equal rates of return (the reinvestment can be the same project or a different project). Therefore, IRR overstates the annual equivalent rate of return for a project whose interim cash flows are reinvested at a rate lower than the calculated IRR¹².

For this reason the IRR should not be used to rate mutually exclusive projects, but only to decide whether a single project is worth investing in.

NPV vs IRR

Applying the method of NPV or IRR for the same project gives usually the same answer to the question if the investment creates value or not.

In case different projects (different in initial investment, life time, pay back characteristics) are compared and rated, the question which investment adds more value is not answered equally, but depending on the applied method of calculation. The rating of the rate of return for different projects requires more detailed evaluation¹³ and is not discussed in this paper.

Choosing the appropriate method for capital budgeting

Given the character of an IP (long life time, dynamic income, and dynamic expenditure), dynamic methods are the preferred techniques to calculate the IP’s economic value even if they require more time and effort for data collection and calculation compared to static capital budgeting methods. The advantages of dynamic methods as the consideration of the time value of money and the effective cash flows instead of average values enable a more detailed analysis of the investment project and, given the investment volume and the project’s life-time, are therefore of advantage.

The required input data for the capital budgeting are based on the results of the studies prepared during the pre-investment phase¹⁴.

Table 4: Input data for capital budgeting

Calculating the project’s periodic cash flows

The cash flows of every period during the project’s lifetime are calculated according to common practise¹⁵ and discounted to the present value and evaluated with different methods of capital budgeting.

Table 5: Calculation of project cash flow

⁸ Volckart p 186, 187
⁹ Investitionsrechnung, WRW Verlag, 3. Auflage 2010, p 20
¹⁰ Wikipedia.org „Net present value”, Jan 3rd, 2013
¹¹ Volckart p 287, 293
¹² Investitionsrechnung, WRW Verlag, 3. Auflage 2010, p 27ff
¹³ Volckart p 285, Investitionsrechnung, WRW Verlag, 3. Auflage 2010, p 30ff
¹⁴ See chapter 4.2
¹⁵ according to Volckart page 591