Cash Flows In Perpetuity Research Articles

Valuation of cyclical assets and exit value

PurposeOrdinary direct capitalization is normally considered procyclical in its present form (De Lisle Grissom, 2011); for this reason, an alternative approach to direct capitalization may be useful in the determination of a robust opinion of value. The valuation standards propose an alternative determination of terminal value in the discounted cash flow analysis, recommending that for cyclical assets, the terminal value should consider … “the cyclical nature of the asset and should not be performed in a way that assumes “peak” or “trough” levels of cash flows in perpetuity” (IVS 105 Valuation Approaches and Methods para 50.21 lett e).Design/methodology/approachThe introduction in International Valuation Standards (IVS) of Cyclical Assets raises several questions for the community of real estate professionals and academicians (IVS, 2022, 105 Valuation Approaches and Methods para 50.09 lett d). Cyclical assets can be defined as property whose value is “influenced by upturn and downturn of the market in a significant way” (d’Amato et al., 2019).FindingsThe paper proposes different solutions to the problem. The determination of the exit value using cyclical capitalization allows for a prudent assessment of the value and may be used either as a valuation procedure or a risk analysis method.Research limitations/implicationsThe valuation comparison with the traditional valuation techniques will be based on an iteration of exit value in order to determine the effects of the valuation procedure on the opinion of value.Practical implicationsThe implication of the valuation procedure is the introduction of a countercyclical valuation method to determine the exit value in order to reach stable and reliable valuations for income-producing properties.Social implicationsThese models may have a social implication, providing valuation for income-producing properties that may deal with the property market cycle in a more efficient way, providing efficient valuation for banks and institutions.Originality/valueThe paper is the first application of such a valuation procedure to the determination of exit value.

Duration of a Perpetual Cash Flow

Duration of a Perpetual Cash Flow

Price Discounts for Unlisted Equity Securities with Random or Indefinite Liquidity Horizons

Illiquidity discounts for restricted stocks depend on the contractual length of the restriction period. The author provides a methodology for extending the application of restricted stock discount models to situations where trading restrictions are stochastic or perpetual. By viewing a private equity investment as a portfolio of restricted equity strips representing claims on the future cash flows in perpetuity, the author obtains a converging upper bound for the illiquidity discount of an unlisted equity security with a random or indefinite liquidity horizon. The model introduces a simple and robust approach for quantifying illiquidity discounts for private equity investments, which is of practical importance to valuation consultants, regulators, and risk managers. <b>TOPICS:</b>Security analysis and valuation, private equity, quantitative methods <b>Key Findings</b> ▪ Illiquidity discounts depend on the length of the trading restriction period. Existing theoretical restricted stock discount models are adapted to situations in which the trading restriction period has a well-defined fixed length. ▪ In many scenarios, the private equity investor faces a liquidity horizon that may be random or indefinite rather than of known fixed length. ▪ The investment’s equity duration provides the missing link that allows us to extend the use of restricted stock discount models to scenarios in which the trading restriction period is stochastically distributed or perpetual.

Cash Flows in Perpetuity with Different Growth Rates for the FCF and the Debt: A Numerical Illustration

In this note, we present a simple numerical example to illustrate the case where the growth rate for the Free Cash Flow (FCF) gU is greater than but different from the growth rate for the Cash Flow to Debt (CFD) gD. Here we assume that the value of the appropriate discount rate for the tax shield KTS equals the cost of debt KD.

New Properties of the Old Present Value Operator

Advances in computing technology have greatly enhanced methods for numerical calculations of present value and related measures such as duration and convexity. Nevertheless, closed form solutions continue to play an important role both in the classroom and in the real world. For example, it is well known that if r is the rate of discount and if C1 denotes the value in period 1 for a cash flow that grows at constant percentage rate, g, then the present value of the future cash flow can be represented as C1 / (r – g). Yet how many students or practitioners, and dare we ask how many finance professors, are aware that the duration of a perpetual cash flow that grows at a uniform geometric rate can be represented as (1 r) / (r –g) ? For that matter, how widely is it known that a simple closed form solution exists for the present value of a cash flow that exhibits cyclical variation over time or a cash flow that grows by a constant dollar amount each period rather than by a constant percentage amount? The objective of this paper is to demonstrate that these results, and countless others, can be derived from one simple but previously under developed property of the traditional present value operator.

The Weighted Average Cost of Capital (WACC) for Firm Valuation Calculations: A Reply

Llano-Ferro (2009) proposes a solution to avoid 'significant errors' when the Weighted Average Cost of Capital (WACC) obtained by the standard formula leads to significant errors in Net Present Value of the Firm calculations; particularly in those that apply to perpetual cash flow series. In this paper we show that there are not 'significant errors' but a wrong use of the formula and improper calculations of values.

Constant Leverage And Constant Cost Of Capital: A Common Knowledge Half-Truth

A typical approach for valuing finite cash flows is to assume that leverage is constant (usually as target leverage) and the cost of equity, Ke and the Weighted Average Cost of Capital, WACC are also assumed to be constant. For cash flows in perpetuity, and with the cost of debt, Kd as the discount rate for the tax shield, it is indeed the case that the Ke and WACC applied to the FCF are constant if the leverage is constant. However this does not hold true for finite cash flows.In this document we show that for finite cash flows, Ke and hence WACC depend on the discount rate that is used to value the tax shield, TS and as expected, Ke and WACC are not constant with Kd as the discount rate for the tax shield, even if the leverage is constant. We illustrate this situation with a simple example. We analyze five methods: DCF using APV, FCF and traditional and general formulation for WACC, present value of CFE plus debt and Capital Cash Flow, CCF.

A New Approach to WACC, Value of Tax Savings and Value for Growing and Non Growing Perpetuities: A Clarification

In this note we correct the findings reported by Velez-Pareja and Tham (2005). Although perpetuities are somewhat artificial in the sense that in practice they do not exist, they are relevant because no matter how detailed and complex a forecasted financial plan for a firm or project could be, terminal value usually is calculated as a perpetuity. This terminal value might be a growing or a non growing perpetuity. On the other hand, usually terminal value is a substantial part of the firm value. In this note we examine in detail the proper discount rate for cash flows in perpetuity, the present value of tax savings and the calculation of terminal value, which is the value of the perpetuity. We compare the typical textbook proposals for calculating the value of a perpetuity and we found that there are significant deviations. We compare with the Miller and Modigliani (1961) plowback proposal adopted by Copeland et al. (2000). The findings contradict what is generally accepted in the literature.

Wacc, Value of Tax Savings and Terminal Value for Growing and Non Growing Perpetuities

Although perpetuities are somewhat artificial in the sense that in practice they do not exist, they are relevant because no matter how detailed and complex a forecasted financial plan for a firm or project could be terminal value usually is calculated as perpetuity. This terminal value might be a growing or a non growing perpetuity. On the other hand, usually terminal value is a substantial part of the firm value. In this note we examine in detail the proper discount rate for cash flows in perpetuity, the present value of tax savings and the calculation of terminal value. The findings contradict what is generally accepted in the literature.

For Finite Cash Flows, what is the Correct Formula for the Return to Levered Equity?

For cash flows in perpetuity without growth, analysts typically use the following formula for the return to levered equity Ke. Ke = Ku + (Ku ­ Kd)(1 ­ T)D/E (1) where Ku is the return to unlevered equity, Kd is the cost of debt, T is the tax rate, D is the market value of debt and E is the market value of equity. What is the corresponding formula for finite cash flows? Is it the same as equation 1? In other words, is equation 1 appropriate for both finite and infinite cash flows? One may be tempted to believe that equation 1 is the general formulation for the return to levered equity and applies to both cash flows in perpetuity and finite cash flows. However, this conclusion is misleading. In this short note, using simple algebra, we derive the general formulation for the return to levered equity for finite cash flows, and show that equation 1 is not the general formulation for finite cash flows.

Corporate governance, capital theory, and corporate finance theory: An approach from property theory

An analysis of the corporate governance debate is developed using a descriptive theory about the system of private property and contract in a market economy. There are strong implications for capital theory and corporate finance theory. The structure of the main results is that what often appears as being an owned property right is upon analysis seen to be only a contractual position—and contractual positions only extend a few years into the future. An enterprise could be described concretely as specific people working with specific machines producing a certain product or it could be described more abstractly using the economists’ notion of a production function. But either way, it is not determined who is legally undertaking the enterprise until the contracts between the factor suppliers are given. Thus the determination of who undertakes an enterprise is contractually determined; it is not an owned property right. In this sense, there is no such thing as the "ownership of the firm" since the party undertaking an enterprise, the residual claimant, is determined by the direction of the hiring contracts. There is the ownership of a conventional joint stock corporation, but a corporation does not "own" the enterprise that it is currently undertaking by virtue of its contractual position. For another party to take over the enterprise, it is sufficient to redo the contracts, not "buy the firm." Since a corporation’s paid contracts at best extend only a few years into the future, there is no basis for the common assumption in capital theory or corporate finance theory that the corporation "owns" the future enterprise cash flows in perpetuity. This simple result thus has rather strong implications for considerations of enterprise governance as well as for capital theory and corporate finance theory. Many of the "ownership" assertions that fuel the debate about enterprise governance are groundless, and the discounting of future enterprise net returns beyond the horizon of current contracts does not represent the valuation of current property rights.

Comment on 'The Value of Tax Shields is NOT Equal to the Present Value of Tax Shields'

In a recent paper, Pablo Fernandez (2002) makes the unusual and paradoxical sounding claim that for cash flows in perpetuity with a constant growth rate g, the value of the tax shields VTS is NOT equal to the present value of the tax shields. To be specific, Fernandez purportedly shows that the formula for the present value of the tax shields is as follows. VTS = TDKu/(Ku - g) Where Ku is the return to unlevered equity, g is the constant growth rate, T is the tax rate and D is the market value of debt. Fernandez (2002) asserts that the value of the tax shield, as given in equation, should be properly interpreted as the difference in the taxes paid by the unlevered and levered firms, where the taxes have different risk profiles. Let VTxU be the present value of the taxes paid by the unlevered firm, discounted by KTxU, which is the appropriate risk-adjusted discount, and let VTxL be the present value of the taxes paid by the levered firm, discounted by KTxL, which is the appropriate risk-adjusted discount. In this note, we assess the validity of the proposed expression for the value of the tax shield. The note is organized is as follows. In Section One, we review and discuss the assumptions underlying the model that Fernandez uses to derive equation 1. In Section Two, we examine critically the derivation of equation 1 and its general relevance and applicability.

Multiperiod Financial Discount Rates in Project Appraisal: The No-Tax Case (Suat Chiet Khau Tai Chinh Nhieu Giai Doan trong Tham Dinh Du An: Truong hop Khong Co Thue)

The typical assumption about cashflows in perpetuity is not appropriate in practical project appraisal because the length of project life is always finite. In this paper, I discuss the calculation of multiperiod financial discount rates for a project with a finite life. For simplicity, I assume that there are no taxes. The analysis is conducted without and with inflation. There are two possibilities for calculating the discount rates. First, we may assume that a constant debt-equity ratio is maintained during the life of the project. In this case, the loan schedule is constructed to keep the debt-equity ratio constant for the life of the project. Since the debt-equity ratio is constant, the Weighted Average Cost of Capital (WACC) and the return to equity e will be constant. Second, the loan schedule may be fixed for the life of the project. In this case, as the loan is repaid, the debt-equity ratio changes because the principal is being repaid over the life of the project. In each period, the return to equity e will be a function of the debt-equity ratio for the period. The return to equity e varies with the change in the debt-equity ratios. The return to equity e will be adjusted to keep the WACC constant. By explicitly calculating the appropriate discount rate for each period of the project with a finite life, it is not necessary to assume that the debt-equity ratio is constant and the cashflows are in perpetuity.

Financial Discount Rates in Project Appraisal

In the financial appraisal of a project, the cashflow statements are constructed from two points of view: the Total Investment (TI) Point of View and the Equity Point of View. One of the most important issues is the estimation of the correct financial discount rates for the two points of view. In the presence of taxes, the benefit of the tax shield from the interest deduction may be excluded or included in the free cashflow (FCF) of the project. Depending on whether the tax shield is included or excluded, the formulas for the weighted average cost of capital (WACC) will be different. In this paper, using some basic ideas of valuation from corporate finance, the estimation of the financial discount rates for cashflows in perpetuity and single-period cashflows will be illustrated with simple numerical examples.

Multiperiod Financial Discount Rates in Project Appraisal

The typical assumption about cashflows in perpetuity is not appropriate in practical project appraisal because the length of project life is always finite. In this paper, I discuss the calculation of multiperiod financial discount rates for a project with a finite life. The impact of taxes and inflation will also be included in the analysis. First, we may assume that a constant debt-equity ratio is maintained during the life of the project. The loan schedule is constructed to keep the debt-equity ratio constant for the life of the project. Second, the loan schedule may be fixed. In this case, the debt-equity ratio changes over the life of the project. By explicitly calculating the appropriate discount rate for each period, it is not necessary to assume that the debt-equity ratio is constant and the cashflows are in perpetuity.

Cost of capital: estimation and applications

Cost of capital: estimation and applications

THE WEIGHTED AVERAGE COST OF CAPITAL: SOME QUESTIONS ON ITS DEFINITION, INTERPRETATION, AND USE: COMMENT*

maximization of the total market value of the firm. The primary purpose of this comment is to reconcile the generally accepted definition of the after-tax weighted average cost of capital (wacc) with the definition proposed by Arditti. In accomplishing this objective we will derive three definitions of the wacc, and will show that the capital structure that minimizes two of the three definitions (within Arditti's framework) is an optimal one. The traditional wacc is derived from the relationship between the market value of a levered firm, VL, and its unlevered counterpart, Vu, both of which are expected to earn the perpetual cash flow X before interest and taxes.' Specifically,

VALUATION, LEVERAGE, AND THE COST OF CAPITAL IN THE CASE OF DEPRECIABLE ASSETS

THE TWO COMMENTS on our paper by William Bradford and Ronda Paul allow us the opportunity to clarify and expand upon several points made in our paper. Nevertheless, the two comments mentioned above are basically different. While Bradford raises several problems and offers some fruitful extensions of our paper, unfortunately Paul did not understand the basic message of our paper. Modigliani and Miller (M&M) discount the expected perpetual cash flow (1-t)X, where t is the corporate tax rate and X denotes expected earnings before interest and taxes (EBIT). While this expression for expected cash flow is correct for a firm assumed to have non-depreciable assets, in the case of depreciable assets the cash flow is given by (1-t) (C-K) + K where C is the pre-tax cash flow (C is later used to symbolize its expected value) and K is the annual depreciation charge. (Note that like Paul we confine our reply to consideration of the unlevered firm's cash flow stream and valuation). We claim in our paper that even if one assumes that the annual depreciation K is exactly the investment needed to assure a perpetual expected pre-tax cash flow stream C, the M&M formulae are inapplicable, and some adjustments are called for. The cash flow stream is instead given by