### Capital investment decisions making

Capital investment decisions are long-term corporate finance decisions relating to fixed assets and capital structure. Decisions are based on several inter-related criteria. Corporate management seeks to maximize the value of the firm by investing in projects which yield a positive net present value when valued using an appropriate discount rate. These projects must also be financed appropriately. If no such opportunities exist, maximizing shareholder value dictates that management returns excess cash to shareholders. Capital investment decisions thus comprise an investment decision, a financing decision, and a dividend decision.

#### The investment decision

Management must allocate limited resources between competing opportunities (“projects”) in a process known as capital budgeting. Making this capital allocation decision requires estimating the value of each opportunity or project: a function of the size, timing and predictability of future cash flows.

#### Project valuation

In general, each project’s value will be estimated using a discounted cash flow (DCF) valuation, and the opportunity with the highest value, as measured by the resultant net present value (NPV) will be selected. This requires estimating the size and timing of all of the incremental cash flows resulting from the project. These future cash flows are then discounted to determine their *present value . *These present values are then summed, and this sum net of the initial investment outlay is the NPV.

The NPV is greatly influenced by the discount rate. Thus selecting the proper discount rate—the project “hurdle rate”—is critical to making the right decision. The hurdle rate is the minimum acceptable return on an investment—i.e. the project appropriate discount rate. The hurdle rate should reflect the riskiness of the investment, typically measured by volatility of cash flows, and must take into account the financing mix. Managers use models such as the CAPM or the APT to estimate a discount rate appropriate for a particular project, and use the weighted average cost of capital (*WACC*) to reflect the financing mix selected. (A common error in choosing a discount rate for a project is to apply a WACC that applies to the entire firm. Such an approach may not be appropriate where the risk of a particular project differs markedly from that of the firm’s existing portfolio of assets.)

In conjunction with NPV, there are several other measures used as (secondary) selection criteria in corporate finance. These are visible from the DCF and include payback period, IRR, Modified IRR, equivalent annuity, capital efficiency, and ROI; see list of valuation topics.

#### Valuing flexibility

In many cases, for example R&D projects, a project may open (or close) paths of action to the company, but this reality will not typically be captured in a strict NPV approach. Management will therefore (sometimes) employ tools which place an explicit value on these options. So, whereas in a DCF valuation the most likely or average or scenario specific cash flows are discounted, here the “flexible and staged nature” of the investment is modeled, and hence “all” potential payoffs are considered. The difference between the two valuations is the “value of flexibility” inherent in the project.

The two most common tools are Decision Tree Analysis (DTA) and Real options analysis (ROA):

- DTA values flexibility by incorporating
*possible events*(or states) and consequent*management decisions*. In the decision tree, each management decision in response to an “event” generates a “branch” or “path” which the company could follow; the probabilities of each event are determined or specified by management. Once the tree is constructed: (1) “all” possible events and their resultant paths are visible to management; (2) given this “knowledge” of the events that could follow, management chooses the actions corresponding to the highest value path probability weighted; (3) (assuming rational decision making) this path is then taken as representative of project value. See Decision theory: Choice under uncertainty. (For example, a company would build a factory given that demand for its product exceeded a certain level during the pilot-phase, and outsource production otherwise. In turn, given further demand, it would similarly expand the factory, and maintain it otherwise. In a DCF model, by contrast, there is no “branching” – each scenario must be modeled separately.)

- ROA is used when the value of a project is
*contingent*on the*value*of some other asset or underlying variable. Here, using financial option theory as a framework, the decision to be taken is identified as corresponding to either a call option or a put option – valuation is then via the Binomial model or, less often for this purpose, via Black Scholes; see Contingent claim valuation. The “true” value of the project is then the NPV of the “most likely” scenario plus the option value. (For example, the viability of a mining project is contingent on the price of gold; if the price is too low, management will abandon the mining rights, if sufficiently high, management will develop the ore body. Again, a DCF valuation would capture only one of these outcomes.)

#### Quantifying uncertainty

Given the uncertainty inherent in project forecasting and valuation, analysts will wish to assess the *sensitivity* of project NPV to the various inputs (i.e. assumptions) to the DCF model. In a typical sensitivity analysis the analyst will vary one key factor while holding all other inputs constant, *ceteris paribus*. The sensitivity of NPV to a change in that factor is then observed. For example, the analyst will set annual revenue growth rates at 5% for “Worst Case”, 10% for “Likely Case” and 25% for “Best Case” – and produce three corresponding NPVs.

Using a related technique, analysts may also run scenario based forecasts so as to observe the value of the project under various outcomes. Under this technique, a scenario comprises a particular outcome for economy-wide, “global” factors (exchange rates, commodity prices, etc…) *as well as* for company-specific factors (revenue growth rates, unit costs, etc…). Here, extending the example above, key inputs in addition to growth are also adjusted, and NPV is calculated for the various scenarios. Analysts then plot these results to produce a “value-surface” (or even a “value-space“), where NPV is a function of several variables.

Another application of this methodology is to determine an “unbiased NPV”, where management determines a (subjective) probability for each scenario – the NPV for the project is then the probability-weighted average of the various scenarios. Note that for scenario based analysis, the various combinations of inputs must be *internally consistent*, whereas for the sensitivity approach these need not be so.

A further advancement is to construct stochastic or probabilistic financial models – as opposed to the traditional static and deterministic models as above. For this purpose, the most common method is to use Monte Carlo simulation to analyze the project’s NPV. This method was introduced to finance by David B. Hertz in 1964, although has only recently become common; today analysts are even able to run simulations in spreadsheet based DCF models, typically using an add-in, such as Crystal Ball.

Using simulation, the cash flow components that are (heavily) impacted by uncertainty are simulated, mathematically reflecting their “random characteristics”. The simulation produces several *thousand* trials (in contrast to the scenario approach above) and outputs a histogram of project NPV. The average NPV of the potential investment – as well as its volatility and other sensitivities – is then observed. This histogram provides information not visible from the static DCF: for example, it allows for an estimate of the probability that a project has a net present value greater than zero (or any other value). See: Monte Carlo Simulation versus “What If” Scenarios.

Here, continuing the above example, instead of assigning three discrete values to revenue growth, the analyst would assign an appropriate probability distribution (commonly triangular or beta). This distribution – and that of the other sources of uncertainty – would then be “sampled” repeatedly so as to generate the several thousand realistic (but random) scenarios, and the output is a realistic, representative set of valuations. The resultant statistics (average NPV and standard deviation of NPV) will be a more accurate mirror of the project’s “randomness” than the variance observed under the traditional scenario based approach.

### The financing decision

Achieving the goals of corporate finance requires that any corporate investment be financed appropriately. As above, since both hurdle rate and cash flows (and hence the riskiness of the firm) will be affected, the financing mix can impact the valuation. Management must therefore identify the “optimal mix” of financing—the capitals structure that result in maximum value. (See Balance sheet, WACC, Fisher separation theorem; but, see also the Modigliani-Miller theorem.)

The sources of financing will, generically, comprise some combination of debt and equity. Financing a project through debt results in a liability that must be serviced—and hence there are cash flow implications regardless of the project’s success. Equity financing is less risky in the sense of cash flow commitments, but results in a dilution of ownership and earnings. The *cost of equity* is also typically higher than the *cost of debt* (see CAPM and WACC), and so equity financing may result in an increased hurdle rate which may offset any reduction in cash flow risk.

Management must also attempt to match the financing mix to the asset being financed as closely as possible, in terms of both timing and cash flows.

One of the main theories of how firms make their financing decisions is the Pecking Order Theory, which suggests that firms avoid external financing while they have internal financing available and avoid new equity financing while they can engage in new debt financing at reasonably low interest rates. Another major theory is the Trade-Off Theory in which firms are assumed to trade-off the tax benefits of debt with the bankruptcy costs of debt when making their decisions.

An emerging area in finance theory is right-financing whereby investment banks and corporations can enhance investment return and company value over time by determining the right investment objectives, policy framework, institutional structure, source of financing (debt or equity) and expenditure framework within a given economy and under given market conditions. One last theory about this decision is the Market timing hypothesis which states that firms look for the cheaper type of financing regardless of their current levels of internal resources, debt and equity.

### The dividend decision

The dividend is calculated mainly on the basis of the company’s inappropriate profit and its business prospects for the coming year. If there are no NPV positive opportunities, i.e. where returns exceed the hurdle rate, then management must return excess cash to investors. These *free cash flows* comprise cash remaining after all business expenses have been met.

All these decision are given here by financial analysis but the calculations are not shown here because of companies’ security. Generally this is the common way to take decision for starting a new business.