Today the standard discounted cash flow (DCF) model is the benchmark valuation model. The model is often praised for its simplicity – but it is built on some strong assumption. In line with Myers (1984a), we believe it is necessary to develop a better understanding of the model to facilitate an improved application. However, it will become clear that the model is not able to properly value wind farms under development due to its embedded assumptions.
3.3.1. Fundamentals
The origin of the discounted cash flow model is the valuation of bonds and stock.21 This is seen in the DCF model’s perception of investment projects as “mini-firms” with expected cash flows, which could be valued and sold on the stock market. The feature that the DCF model is based on an intrinsic value measure (i.e. expected cash flows), and not measures such as book values, is an often praised advantage of the model (Brealey et al. 2006: 88-89 and 318-20).22 The model calculates the net present value (NPV) of an investment, based on its ability to generate future income adjusted for the time-value-of-money and risk. Several models are based on DCF principles, however the most well-known and simple model is expressed in Formula 3.1 below, and will be referred to as the standard DCF model.
Formula 3.1 Standard DCF Model
𝐍𝐏𝐕= 𝐈𝟎+� 𝐅𝐂𝐅𝐭 (𝟏+𝐫)𝐭
∞ 𝐭=𝟏
𝑵𝑷𝑽: Net present value 𝑰𝟎: Initial investment 𝑭𝑪𝑭t: Free cash flow 𝒓: Discount rate 𝒕: Time
Source: Brealey et al. 2006: 36
Of the four input (time, initial investment, free cash flow and discount rate), the two initial ones are known, whereas the two last ones are estimates. The free cash flow is the profit after tax less capital expenditures and changes in working capital, but with depreciation added back (Brealey et al. 2006:
509). The discount rate is used to adjust the cash flows for market risk and time-value of money.
For any given point in time there can only be one discount rate and one cash flow although both estimates can change over time, so the modeling in time is linear with only one estimation point per
21 The originator of the theory of the discounted cash flow analysis was J. B. Williams (1938) in his work The Theory of Investment Value, who wanted to find a better way of valuing stock following the 1929 crisis. The work was “rediscovered” by Shapiro and Gordon in Capital Equipment Analysis: the Required Rate of Profit (1956).
22 It should be noted that cash flows are not totally free of accounting measures due the effect depreciation of assets has on tax (Myers 1984a: 129).
30 time period. This has led to critique from authors such as Copeland and Antikarov (2003: 73) because uncertainty is not explicitly modeled in cash flows. Based on this brief introduction, we will now discuss how the DCF model perceives and measures market uncertainty.
3.3.2. Market Uncertainty
The standard DCF model focuses the discussion of market uncertainty in relation to its adverse consequence, risk. Risk is divided into two categories: market/systematic/undiversifiable risks – which are the economy-wide perils that threaten all companies (macroeconomic states), and the private/unsystematic/diversifiable risks – which are the perils of a company or industry.23 The distinction makes it possible to assume that by holding a portfolio of diversified assets, an investor can diversify all the private risk away, thereby ending up with only the undiversifiable systematic risk (Brealey et al. 2006: 160-163). The distinction is particularly handy, as it allows investors to only care about the systematic risk when identifying an appropriate discount rate for the project. As we will see when discussing flexibility, the standard DCF model does recognize other types of uncertainty as well, but has large difficulties in handling them.
3.3.2.1. The Discount Rate
The discount rate in the DCF model addresses the value of money and a market risk. The time-value of money is the fact that a dollar today is worth more than a dollar tomorrow, so an investor should be rewarded for giving up a present cash flow for a later one. The market risk reflects that some investments are more risky than others and that an investor should be rewarded for undertaking risky cash flows. As the discount rate only address the downside risk and not the potential upside chance, an increase in the project’s market uncertainty will equal a higher discount rate and hence a lower value. Finally the debt-equity mix can also influence the discount rate. We will here focus on the discount rate without debt, i.e. the cost of equity, and treat debt separately in chapter 5.
The most common way to estimate the cost of equity within corporate finance is by use of the Capital Asset Pricing Model (CAPM) seen below. Other models exist, such as management estimates and arbitrage pricing theory. The latter links expected return to a set of specified macro economic factors influencing stock returns. While such a model can provide valuable insights to an investments exposure, it does not specify which exact factors to use or look for, and as such its
23 We will use these names of risk interchangeably, as each name highlight different nuances of the models risk definition.
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practical value can be questioned.24 In general, the different models agree that investors require a higher return for taking on more risk and are predominantly occupied with market risk (Brealey et al. 2006: 205). Seeing that the CAPM contains these two dimensions and that it is seen as the standard model, we recommend applying it as well.
The advantage of the CAPM (which can be seen in the formula below) is its simplicity and ease of use, however, it builds on strong assumptions, which is one of the main reasons that it is questioned.25 The implications of the assumptions are that investors have perfect information, and can easily hold a well-diversified market portfolio. Despite the realism being questioned CAPM does “…an amazingly good job of describing prices in the capital market.” (Elton et al. 2007: 284).
Formula 3.2 Capital Asset Pricing Model
𝐄(𝐑𝐢) =𝐫𝐟+𝛃𝐢(𝐄(𝐑𝐦)− 𝐫𝐟)
𝑬(𝑹𝒊): Expected return on asset 𝒓𝒇: Risk-free rate
𝜷𝒊: Beta on asset 𝑹𝒎: Market risk premium Source: Brealey et al. 2006: 189.
The CAPM states a linear relationship between the return on a stock and its beta, the market risk premium and the risk-free rate. Out of these, only one is individually defined for an investment:
beta. The two others, the market risk premium and the risk-free rate, should be the same for all stocks and will be treated thoroughly in chapter four. The beta measures the sensitivity of the movement in returns of a stock (dividend adjusted) relative to the movement in returns on some measure of the market (Pratt 2002: 87). The beta thus expresses the market risk which a company’s stock is subject to, i.e. the additional risk it adds to a diversified portfolio, and is not an expression of total risk of the stock. Therefore, the shareholders should only care about how the individual asset affects the portfolio. The idea that the cost of equity depends on the risk relative to the market, i.e. the use and not source of capital, is an essential point, since it makes it possible to estimate the cost of equity independently of the investors’ preferences (Myers 1984a: 128).
3.3.3. Flexibility
An investment in any project is not only subject to market risk, but is also subject to other project specific uncertainties, such as the events in the development stages in a wind farm under development. The standard DCF model suggests that these events should be accounted for by
24 The most famous arbitrage pricing theory model is the three factor model by Fama and French, which in addition to the market portfolio return also relates the expected return of a stock to the difference in returns between small-cap and large-cap stocks and the difference in returns between stocks with high-book-to-market and low book-to-market-ratios (Fama and French 1995: 131).
25 For an overview of CAPM’s assumption see Appendix 6.
32 adjusting the individual cash flows with the probability of success. This is because cash flows
“…are supposed to be unbiased forecasts, which give due weight to all possible outcomes, favorable or unfavorable.” (Brealey et al. 2006: 223). In the same way, events in the operational phase can also be included, for example by applying scenario analysis, discussed later. While it might be true that DCF recognizes these events, it is not able to capture the value of reacting to uncertainty through active decision making (Leslie and Michaels 1997: 11-12). When investing in financial securities, this is not a problem, since they are passively held. Therefore the DCF model, when originally developed, did not have to consider the value of active management. Investments in a real project are different. In such a case the management is able to take active decisions as information becomes available.
It is not possible to incorporate the value of decision making in the standard DCF model due to the model’s assumption of reversibility or irreversibility (Dixit and Pindyck 1994: 6). Reversible means that decisions can somehow be undone and all expenditures recovered, whereas irreversible means that the investment is a now or never type decision. In the case of wind farm development, where the majority of the development investment is made in research and negotiations with authorities, the investment will not be reversible. On the other hand, the irreversibility assumption could be stated to be at least partially fulfilled, as it is true that if we do not undertake the investment today, the landowner is likely to either try to lease the land to someone else, or perhaps the municipality will withdraw their permit, if other sites in the area have been developed. This assumption implies that all future investment decisions related to a project are taken today, and therefore management is perceived as being unable to make decision during the project life, which could have minimized losses or maximized returns based on changes in the market situation (Villiger and Bogdan 2005b:
116). The DCF model is therefore only recommended for situations where such decisions cannot significantly impact the project value.
3.3.4. Usability
The standard DCF model has for a long period been very popular and is today used in the majority of financial valuations, though it took many years for it to achieve this status.26 In general, the estimation of the input and the calculation of the present value are perceived as having a high
26 A study by Gitman and Vandenberg (2000: 58) found that 70% of a sample of 1997 Fortune 1000 corporations use cost of capital techniques (standard DCF combined with NPV) and of these 93% use CAPM. This compares to similar 1980 survey by Gitman and Mercurio (1982), which found only 36% of companies using cost of capital techniques indicating a lag in the adaptation of new valuation concepts in corporations.
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usability. This is to some extent due to experience with the model more than actual ease, because the estimation of the input is by no means an easy exercise, as we will see in the next chapter.
In addition the intuition of the result of the DCF calculation can be debated. It is clear that the calculation together with the value maximization principle, gives a consistent and easily understandable decision, which can be widely communicated and understood in an organization.
However the gain from easy communication might be offset by a loss of information. Due to using just a single cash flow estimate for each time period, the model does not explicitly show the uncertainty of the cash flows and they might thus be perceived as depicting a certain reality (Amram and Kulatilaka 1999: 13). Furthermore, the standard DCF model’s problematic assumption of handling flexibility makes it hard to use it for strategic decision making. Therefore the standard DCF model cannot bridge the gap between strategy and finance (Myers 1984a: 136), but it seems readily applicable to proverbial “cash cow businesses”. In search of alternative models, we turn towards two extensions of the standard DCF model that proposes ways for handling these short comings. A summary of the DCF models criteria can be seen in Table 3.2.
3.3.5. Discounted Cash Flow Model Overview
Table 3.2 Discounted Cash Flow Model Criteria
Fundamentals Flexibility
Object of Analysis Modeling Event Decision
Company or Project Linear CF stream Probability of project
success No
Market Uncertainty Usability
Perception Measure Implementation Interpretation
Risk Beta Seems easy due to
experience with model Relatively easy
Source: Own construction
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