As described above, the initial investment outlay, the future cash inflows and outflows, the economic life, the liquidation value and the discount rate all go into determining net present values for investment appraisal. Issues related to the collection of these data are discussed here. Also, an approach to the special problem of dealing with inflation is analysed. Although the following hints in this section refer to NPV examples, they also apply to other methods described in this book.
It is important to remember that NPV calculations involve a comparison between undertaking and rejecting an investment project. Therefore, a project's cash flow profile should indicate changes in the cash inflows and outflows that are a direct result of undertaking the project, i.e. the difference between the additional cash flows created and eliminated by the project. The intended subsequent activities and their consequences should be included as relevant data as well, e.g. the net cash flows of a known subsequent investment project. Finally, the cash flow effects may be influenced by various company decisions such as scheduling, project, cost or cash management decisions. Where known, these impacts should also be incorporated into the project appraisal.
The initial investment outlay for an investment project is a cash outflow resulting from the acquisition of the project, and/or the company-wide activities necessary for its provision and establishment (i.e. any set-up costs). The purchase price should reflect any discounts received, but must also include any costs associated with procurement, for example freight and customs/import duties. Cash flows resulting from the in-company production of an investment project can be derived from the cost accounting system, as a calculation of production costs. However, any discrepancy between recorded costs and cash outflows should be scrutinised, as it might require adjustments to the data.
It is often difficult to work out the cash flows caused by additional in-company activities associated with the acquisition or production of an investment project, particularly where there are 'indirect cash flows' caused by the joint use of indivisible assets (staff, capital assets etc.) by several projects. This is comparable to the problem of indirect costs and revenues in cost accounting systems.
Investment projects can result in changes to current assets (e.g. increased inventories) or the initiation of projects needed to improve company-wide infrastructure, which themselves represent an investment by the company. Outflows caused by such 'subsequent investment projects' should also be included and considered as part of the investment analysis. The same applies to governmental or other institutional financial investment incentives, and to the cash inflows and/or outflows resulting from the directly associated release of other assets (particularly liquidation revenues from replaced projects, or outflows following their sale and disposal).
Current cash inflows and outflows, or current net cash flows, are the central components of the cash flow profile and must be explicitly forecasted for all periods of the project's economic life. Current cash inflows often result primarily from the sales of products produced as an outcome of the investment project. These cash inflows are calculated as the additional production volume multiplied by the unit sales price. Forecasting this data can be difficult. The forecasts need to be supported by detailed sales planning and control activities, differentiated by product types/markets served etc., and based on estimates of the additional production capacity that will be achieved as a result of undertaking the investment project.
Additionally, in contrast with the previously discussed assumption (c) (see Section 3.2), the cash inflows resulting from a particular investment project might not be determinable because they cannot be attributed to a single project (for example when several investment projects jointly increase the amount of saleable production by increasing the capacity of a production process). Such investment projects should be assessed using simultaneous investment and production decision models, as described in Section 7.3. The net cash flow effects resulting from investments in areas not directly related to the products and customers (e.g. investments in improving infrastructure or enhancing operational readiness), are even more difficult to estimate, making the identification of relevant net cash inflows very challenging for projects of this type.
The current cash outflows of a company can be either increased or reduced by investment projects. For example, a rationalisation investment can reduce current costs (cash outflows) and thus increase net cash flows. Such changes can impact on any production factors and in all company areas. Therefore, precise forecasts of relevant cash outflows may require a detailed analysis of effects across all of the company's areas and divisions and for all production factors. As with initial investment outlays and cash inflows, a frequent problem is the difficulty in isolating additional cash outflows caused by an investment project. Cost accounting data can provide some of the information needed, but usually not all of it. For planning consistency, estimated cash outflows should build on the same assumptions used for cash inflows, i.e. on factors like sales and production volumes, price levels, etc. If relevant, tax-related effects can also be included in the analysis of relevant cash inflows and outflows, as described in Section 5.1.
It is worth mentioning that, although cash inflows and outflows might appear to be equivalent to revenues and costs, the use of this (and other) data from the company's accounting system is not always appropriate for investment appraisal purposes. As mentioned above concerning the initial investment outlay, discrepancies between recorded costs and cash outflows (e.g. resulting from depreciation) should be identified and corresponding adjustments made to convert accounting data into cash flow information. The amount of adjustment work needed will depend on how divergent the accounting and cash flow measures are, and how aggregated the accounting data is. Theoretically, it can also be shown that investment appraisal decisions based on cash flow analysis are, under certain assumptions, identical to those based on traditional accounting measures (e.g. the Lücke and Preinreich theorem (Lücke, 1955, Lücke 1991, Preinreich, 1937). In practice, however, accounting data usually needs careful adjustments if it is to be used as a basis for capital investment decision-making.
Another part of an investment project's cash flows is the liquidation or residual value at the end of the project's economic life or planning period. Forecasts of liquidation value must include any cash inflows from the sale of the project or its components, together with any cash outflows resulting from its dismantling, sale or disposal. Therefore the liquidation value can be negative when there is an excess cash outflow. Forecasting liquidation cash flows is particularly difficult because they occur well into the future. The cash flows will depend on future prices that potential buyers will be willing to pay for the investment project and their planned utilisation of it. For some marketable projects, however, data or market prices exist that support the said forecast.
A simplified variation of the model can be constructed by setting the planning period shorter than the economic life of the investment project and summarising the remaining project cash flows as a residual value. That is, the cash flows expected after the designated planning period are discounted back to the end of the planning period and aggregated into a single 'residual value'. This approach simplifies the forecasting activity. For example, a constant cash flow surplus can be assumed for the period beyond the planning horizon. However, this approach is by no means uncomplicated since the data (cash flows generated after the planning period, the number of periods for which they will occur, and the relevant interest rate) are difficult to estimate beyond the designated planning period. Thus, both approaches are characterised by a high degree of uncertainty in regard to the liquidation or residual value. Moreover, defining the planning period also presents a decision problem for the model construction.
The choice of a relevant discount rate is an important consideration for every net present value calculation. Choosing this discount rate presents challenges in itself. The discount rate must fulfil two functions: on the one hand it should permit comparability between alternative investments, and on the other hand it should reflect both current and future investment opportunities.
To compare alternatives, the cost of financing an investment (i.e. the 'cost of capital') needs to be considered. This cost is not included within the project's cash flows - instead, it must be reflected in the discount rate used in the NPV calculation. One way to determine the relevant discount rate is to derive it directly from financing costs. Where internal funds are used to finance a project, the relevant 'cost of capital' is the rate of return that could have been earned on the next best alternative investment. For example, if it has to be decided whether to invest in project A, and the best alternative use for the funds is to invest them in project B, then the (internal) rate of return that project B would earn should be used as the cost of capital for analysing project A.
With debt financing, the rate of interest is readily known (from the interest paid on the borrowed capital). Or, if a project is to be funded from a mix of internal funds and debt financing, a 'weighted average cost of capital' can be calculated by taking a proportion of the financing cost for each source (debt and internal funds).
However, deriving the relevant discount rate from financing costs brings certain problems:
• The forms of capital by which separate investment projects are financed are often not known (the company may have a combined 'pool' of debt and internal funds, from which several projects might be funded).
• It is hard to determine alternative return(s) that could be earned on internal funding.
• Interest payments for future investment opportunities will not always correspond with current financing costs.
An alternative approach is to consider opportunity costs. Here, it is assumed that a project's financing cost (or discount rate) is the rate of return that have been given up by not investing this money in an alternative project. However, it is often not known which investment project is crowded out by the investment under consideration and, thus, which represents the relevant alternative. Simultaneous planning models can help here (see Sections 7.1 and 7.2 later in the book). From their optimum solution, a uniform discount rate can be derived, based on the interest of the best 'crowded out' investment project: the so-called 'endogenous uniform discount rate'. However, this can be known only after the relative profitability of alternative investment projects has been assessed.
The second function of the uniform discount rate lies in balancing capital tie-up and economic life differences. Here, again the interest rate of the 'best crowded out' investment opportunity can be applied to fictitious current or future projects that 'balance out' differences in projects that are being compared.
Until this point, it has been assumed that the uniform discount rate is independent of the time-span between the occurrence of a cash flow (time t) and the beginning of the planning period (t = 0), i.e. a 'flat' interest curve exists. However, in reality, interest from bonds depends on their length: typically rates rise with increasing lengths of the bond. So, if the capital market is to be viewed as an alternative investment possibility, it is useful to fix uniform discount rates relative to time spans. To do this, interest rates from zero bonds that start in the planning period can be used. A zero bond is a loan that leads to only one cash inflow (CIFt) at the end of its life span (a period lasting from t = 0 to point in time t). The rate of interest is derived from the difference between this cash inflow and the cash outflow (I0) at the beginning of the period. For a period of length t, the rate of interest iZBt can be described by:
The NPV of an investment can then be determined by discounting (to the beginning of the planning period) the cash flows of any given point in time by the interest rate payable for a current loan up to that point in time: T
Where zero bonds are traded only intermittently, i.e. interest rates are not available for all relevant periods, rates for other bonds or warrants can be used. Additionally, interest rates on zero bonds might in some cases correlate with the interest rates (ip^) for all annual financial investments that jointly cover the same time span, according to the following relationship: t
Using this approach, the result is identical to the one for the NPV calculation described above, if the annual interest rates are applied to the discount rates for each period up to t:
Whether time-span-specific interest rates are applied or not, a 'correct' uniform discount rate which fulfils the described functions (comparability as well as representing current and future investment opportunities) can be achieved only under the simplistic assumption of a perfect capital market. Therefore, practical applications of the NPV method must aim to find a uniform discount rate that leads to an approximate fulfilment of both functions.
Besides these considerations, the problem of determining a uniform discount rate can be reduced by finding an upper and a lower limit for the rate of interest and using both for NPV calculations. A minimum rate, for instance, could be the interest rate on risk-free securities, while an upper limit could be the maximum interest obtainable for the best alternative investment or the most expensive loan. It is then reasonable to assume that investment projects will show absolute profitability if they achieve a positive NPV using the upper limit discount rate. Conversely, if a negative NPV is obtained using the minimum discount rate, the project will normally be unprofitable.
In reality, interest rates are different for borrowing and investing. Methods have been developed to allow for these differential rates, thus accommodating an imperfect capital market. They are described in the next chapter. For instance, the 'compound value method' assumes different credit and debt interest rates. Moreover, the 'visualisation of financial implications method' (VoFI method) enables the utilisation of a large number of different credit and debt interest rates.
Further considerations are necessary if taxes, inflation, or risk need to be included in the derivation of a realistic uniform discount rate. The inclusion of taxes and risk is discussed in Chapters 5 and 8, and the case of inflation is taken up below.
Because of the typical long-term effects of investment projects, a question arises as to whether inflation (and the purchasing power losses it causes) should be included in the investment appraisal method, and in what form. Increases in price levels usually affect the various components of cash flows associated with an investment project, as well as the discount rate(s) to be used. In regard to cash flows either nominal values or real values may be used. In general, the forecast of nominal values is less problematic. When using nominal values for cash flows, either a nominal interest rate i (nominal NPV method) or a real uniform discount rate ir tied to the currency depreciation rate g (real NPV method) can be used as a uniform discount rate. Both approaches lead to the same discounting factors and, thus, to the same NPV result, provided interest rates and inflation rates remain constant throughout the planning period and the so-called Fisher condition applies (Fisher, 1930):
In this case, real interest rates are independent of inflation.
Finally, it should be noted that the ways in which a project's NPV is affected by incorporating inflationary effects, are governed by the specific inflationary outcomes for the cash flows as well as on the uniform discount rate. If both are affected in the same way, the NPV remains the same whether or not inflation is included in the calculation. However, if the project's net cash flows inflate more (or less) strongly than the uniform discount rate, the NPV will increase (decrease).
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