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Return on invested capital. The amount, expressed as a percentage, earned on a company’s total
                       capital for a given period. (Practitioner — Appendix B)


                   Return on investment. See return on invested capital and return on equity. (Practitioner —
                       Appendix B)

                   Risk-free discount rates. See risk-free rate.


                   Risk-free rate. The rate of return available in the market on an investment free of default risk.
                       (Practitioner — Appendix B)


                   Risk-neutral probabilities. The actual cash flows may differ significantly from expected cash
                       flows. In contrast, risk-neutral probabilities are the result of a mathematical adjustment to the
                       probabilities of the expected cash flows, which allows them to be discounted at the risk-free rate.
                       Risk-neutral probabilities are a mathematical convenience evaluating binomial trees and stem
                       from no arbitrage assumptions. Risk-neutral probabilities are not the same as risk-adjusted or ob-
                       jective probabilities, that is, the actual risk of expected cash flows. Forecasted cash flows should
                       never be discounted at the risk-free rate, unless the cash flows are risk free. Risk-neutral proba-
                       bilities reflect the assumption that, as a risk-neutral investor they can always hedge the individual
                       outcomes of an investment at little or no cost, the investor is indifferent between an investment
                       that pays $10 and an investment that has an equal chance of paying nothing or $20. The investor
                       considers only the expected payoffs of an investment, not its risk. For general discussions of the
                       comparison of risk-adjusted and risk-free probabilities and discount notes see Chapter 4 of Real
                       Options: A Practitioner’s Guide, by Tom Copland and Vladimar Antikarow, Texere LLC
                       (2001).  fn 14

                   Risk premium. A rate of return added to a risk-free rate to reflect risk. (Practitioner — Appendix
                       B)

                   Rule of thumb. A mathematical formula developed from the relationship between certain variables
                       based on experience or observation.

                   Special interest purchasers. Acquirers who believe they can enjoy postacquisition economies of
                       scale, synergies, or strategic advantages by combining the acquired business interest with their
                       own. (Practitioner — Appendix B)

                   Standard of value. The identification of the type of value being utilized in a specific engagement;
                       for example, fair market value, fair value, investment value. (Practitioner — Appendix B)

                   Subject interest. A business, business ownership interest, security, or intangible asset that is the
                       subject of a valuation engagement. (Practitioner — Appendix C)

                   Subsequent event. An event that occurs subsequent to the valuation date. (Practitioner — Appen-
                       dix C)








        fn 14   See footnote 4.


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