5. Valuation and Value Creation

The notion of efficient market has been studied extensively. Three forms of efficiency have been defined: Weak, semi-strong, and strong (see Malkiel 1962; Fama 1965, 1970; Shiller 1981; Malkiel 2003 on this topic). A discussion of this concept is beyond the scope of this book.

In practice, in a short sale, the investor borrows the security from someone who owns it and sells it in the market. The short position is later closed off (i.e., the debt is repaid) by buying back the security and giving it back to the lender (as well as paying out any interim cash flows to the lender) (see Broverman 2008; Kellison 2009 for details).

We recall that shorting is financially equivalent to borrowing.

As anticipated in the previous section, it is precisely the rational behavior of the individuals seeking disequilibrium that guarantees that the market as a whole tends to equilibrium.

We will remove this assumption in Chap. 6, showing that the same result holds for levered projects.

Notice that the market income rate, \(r_t\), is always defined, and then it is applied to some capital, whereas the project income rate may not be defined, since it derives from capital, which may well be zero.

Equation (5.16) uses the equality \(\sum _{t=1}^N f^e_t/(1+r)^t= n_0 p_0\) which holds because, before undertaking the project, the equity of firm f is an equilibrium asset.

Curiously, Luca Pacioli might have been taught mathematics by the Italian Renaissance painter Piero della Francesca and, in turn, taught mathematics to Leonardo da Vinci (Gleeson-White 2012, p. 8).

The term counterfactual was coined by Goodman (1947).

Or, equivalently, letting the capital providers invest themselves in the normal market. If the market is efficient, transactions costs are negligible and it is irrelevant whether the firm or the firm’s shareholders invest in the market.

This project has been introduced in Example 1.​10.

The risk is higher in the sense that B’s cash flow has a higher variance than A’s cash flow. However, variance is not the only measure of risk. The notion of risk itself is not a simple one and no agreed upon model of risk exists in academia or in practice. Hurdle rates are often used which are aimed to account for various sources of risk (see Sect. 5.6).

The same asset cannot be traded at different prices in a competitive, normal market, otherwise arbitrage opportunities would arise that would immediately sweep away the state of disequilibrium (see Sect. 5.1). See also below.

See Robichek and Myers (1965) and Haley and Schall (1979, Chap. 9) for a detailed treatment of the two approaches.

This implies risk premiums are equal to \(\pi ^B=4\%\) and \(\pi ^C=1\%\), respectively.

Among the various models developed in the financial literature, the Capital Asset Pricing Model (CAPM) (Sharpe 1964; Mossin 1966) is by far and large the most widely used. In essence, the risk premium should be computed as the product of the systematic risk of the project (so-called beta) and the market premium (difference between expected market return and risk-free rate). The rationality of the use of the CAPM for investment decisions has been shown by many scholars since 1960s (e.g. Tuttle and Litzenberger 1968; Hamada 1969; Bierman and Hass 1973; Bogue and Roll 1974; Mossin 1969; Rubinstein 1973. See also Senbet and Thompson 1978 and Magni 2007a, b). However, some problems of inconsistency with no-arbitrage pricing exist for CAPM-based decision-making; albeit unearthed long since (Dybvig and Ingersoll 1982), they are hardly ever mentioned (see Magni 2002, 2008a, b, 2009a).

The satisficing concept is particularly relevant in the engineering practice, to such an extent that engineering textbooks make a distinction between COC and MARR, where COC is a normative, market-determined rate of return, while MARR is a hurdle rate subjectively determined, which may well differ from the former (see also Rogers and Duffy 2012, pp. 10–11). More generally, small-sized, family-owned, companies often set MARRs subjectively when valuing projects. The use of a rigorous decision-making procedure alongside the use of a subjective hurdle rate was practiced since 13th century in the evaluations of properties, trees, lands, collieries, coppices, buildings, leases, shops etc. made by the legal, banking, business communities (see, for example, Wing 1965; Edwards and Warman 1981; Miller and Napier 1993; Scorgie 1965; Brackenborough et al. 2001).

Real options are investments that allow for some kind of flexibility; for example, investment may be deferred to next year or may be expanded in following years or abandoned.

Essentially, these three reasons fit the premises on which Gigerenzer (2001) bases the notion of adaptive toolbox: psychological plausibility (i.e., regard for constraints in time, knowledge, and computational abilities), domain specificity (a rule may be appropriate in one domain but not in another one, so the rule is changed or combined with other rules), ecological rationality (imitation and social learning may be ecologically rational due to success over time). See Magni (2009d) for details.

Bankruptcy costs include direct costs (legal and administrative expenses) and indirect cots (decrease in sales due to customers’s perception of the increased default risk).

For example, consider the cash-flow sequence \((-100, 40, 30, 20, 25, 40, 10)\). The payback period is 4, because time 4 is the first date where the cumulative cash flow is positive: \(-100+40+30+20+25=15>0\). A variant of the payback period is the discounted payback period, where present value of cash flows is considered. For example, if the discount rate is 10%, the discounted payback period is 5, for time 5 is the first date where the cumulative discounted cash flow is positive: \(-100+40/1.1+30/1.1^2+20/1.1^3+25/1.1^4+40/1.1^5=18.1>0\).

This implies that the notion of residual income becomes compelling, as it triggers the idea that value is created gradually over time (see Sect. 6.​6.​1 for details on this notion).

“Unfortunately, given the data, there is no completely satisfactory way to specify exactly how much higher or lower we should go in setting risk-adjusted costs of capital.” (Ehrhardt and Brigham 2016, p. 401)