This has further been described in the provisions of the Statement of Financial Accounting Concepts No. The US GAAP FASB 142 outlines the fair value measurement of intangibles and goodwill impairment by using the discounted approach. Since few years, companies like Infosys have used this approach to value their brands and represent the same in their balance sheet. This method is most useful in judging the risk and uncertainty of a project. This has consequences for the applicability of the well-known present-value formula for annuities and for building consistent valuation models for both finite and perpetual cash flows.ĭiscounted cash flows (DCF) have been a traditional method in business valuation. Contrarily, in the M&M setup, all discount rates change across time, except for the constant discount rate of the tax shield. Furthermore, in M&E’s model, all discount rates are time-invariant, except for the discount rate applied to tax shields, which depends on the lifetime of the cash flows. We show that in the M&E model, all cash flows and values are path-dependent, while they are not in M&M’s world. For this purpose, we perform a numerical experiment that allows the determination of values and discount rates by means of the risk-neutral approach. Therefore, the main objective of this paper is to illustrate and accentuate the effect of these two mutually exclusive stochastic processes on the timely behavior of cash flows, discount rates, and values of the firm, equity, debt, and tax shield. However, this subtle difference has not been fully exposed, and previous literature has produced partly erroneous statements or inconsistent valuation models. While M&M assumes a strictly stationary process, M&E’s process is a martingale. The main difference between these two models concerns the stochasticity of the free cash flows. This paper addresses the differences between the Modigliani-Miller model (1958, 1963) and the Miles-Ezzell model (1980, 1985). We do this by applying a risk-neutral backward iteration process for showing the timely behavior of discount rates, cash flows, values and the correct relations between different discounted-cash-flow methods, namely the equity method, free-cash-flow method, the adjusted-present-value approach and the capital-cash-flow approach. The sole purpose of this paper is therefore to pinpoint the sole difference between M&M and M&E, and to show its implications for discounted-cash-flow methods. In our opinion, these effects have not been fully appreciated or have been confusingly described and applied in the previous literature. All other discount rate change over time. Contrary to this, in the Modigliani-Miller annuity the discount rate of debt and the tax shield remain constant and equal the risk-free rate. In the Miles-Ezzel framework all discount rates except for the discount rate for the tax shield remain constant. When it comes to annuities instead of perpetuities, the difference in the cash-flow stochasticity affects the timely behavior of discount rates. Furthermore, the required discount rate of the tax shield as well as the mathematical formulae for translating the required return on unlevered equity to either the required return on levered equity or the discount rate in the free-cash-flow will differ in these two environments. Contrary, in the M&E model the values are state-dependent. In the M&M model all values are time invariant (constant) and state-independent. First, this assumption affects the behavior of the values (firm, equity, debt, tax shield) over time and states of the world. While M&M assume a strictly stationary process, M&E depart from a process with the martingale property. The only assumption that is different but decisive in these two models concerns the stochasticity of the free cash flows. This paper addresses the differences between the Modigliani-Miller model (19, abbreviated by M&M) and the Miles-Ezzel model (1980, abbreviated by M&E).
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