Accounting Rate of Return vs. Economic Rate of Return

The accounting rate of return (ARR) has traditionally been used as a surrogate for the economic rate of return (IRR) in evaluating the effectiveness of managements' capital investment decisions. Over the years, some question has been raised as to the validity of using the ARR as an approximation of the IRR. Several papers have recently come to grips with this question with varying degrees of success. This paper is intended to expose the conceptual differences between these rates of return, with the goal of clearly pointing out just how useful the ARR can be to management.     

A Simulation-Based Investigation of Errors in Accounting-Based Surrogates for Internal Rate of Return

Accounting-based measures of a firm's ex post performance represent accessible, albeit imperfect, surrogates for its internal rate of return (IRR). Using a cross-sectional data set obtained via computer simulation, this study calculated the error with which the accounting rate of return (ARR) and conditional estimate of internal rate of return (CIRR) estimate IRR. The study compared the error with which both surrogates measure IRR, as well as the ability of growth in unit demand (gD), inventory cost flow assumption (INV) and depreciation method (DEP) to explain the measurement error in both surrogates.     

Accounting Returns Revisited: Evidence of their Usefulness in Estimating Economic Returns

Accounting information is used for measuring firm performance in various financial applications—a practice supported by empirical studies demonstrating the value relevance of accounting numbers, but disputed by theoretical papers arguing that a firm's accounting rate of return (ARR) serves poorly as a proxy for its internal rate of return (IRR). We derive a new model of the ARR–IRR relation, and describe how the conservatism of GAAP constrains a firm's IRR to fall in a range bounded by its historical growth rate and ARR. Using cross-sectional data, we demonstrate that economic returns can be estimated from accounting numbers for many firms. We link empirical results to underlying economic theory, and thus contribute to understanding why accounting information is value relevant.     

On the validity of accounting rates of return in cross-sectional analysis: Theory, evidence, and implications

This paper reports the results of an empirical examination of the relationship between firm accounting rate of return (ARR) and firm internal rate of return (IRR). The evidence presented shows that some of the analytically derived properties of the ARR-IRR relationship hold in a sample of U.S. manufacturing firms. This evidence can be interpreted as documenting the existence of a potentially important degree of measurement error in the ARR for a sample of actual firms and increases the credibility of those who have questioned the use of accounting rates of return as the dependent variable in cross-sectional studies of firm profitability.     

The evolution of the application of capital budgeting techniques in enterprises

This study examines the evolution of the application of capital budgeting techniques. Previous studies mostly used cross-sectional inquiries to understand the capital budgeting practices of firms. Only a few researchers have undertaken longitudinal studies to generalise the findings of the individual cross-sectional studies to the wider population and to identify the emerging trends in the use of capital budgeting techniques (CBTs). This longitudinal study surveys 83 studies of capital budgeting practices across firms in India, South Africa, the United Kingdom (UK) and the United States of America (USA) for the period from 1966 to 2016. The findings show that six capital budgeting techniques, namely, the net present value (NPV), the internal rate of return (IRR), the payback period (PBP), the accounting rate of return (ARR), the return on investment (ROI) and the real option valuation (ROV), are the most popular methods for evaluating capital investments. Of these techniques, the ROV is the least used, and a general lack of familiarity with this technique and its complexity are the most commonly cited reasons for not using it. Another method that is used less than the first four techniques is the ROI. However, this technique is of growing significance and is mainly used in the UK, followed by the USA, South Africa, and India. Firms in the USA and UK have increased their use of the IRR as a primary method for evaluating capital projects and have retained the PBP as an ancillary technique to strengthen the available information when evaluating capital projects. Firms in India and South Africa are increasingly excluding both the PBP and ARR methods and are increasingly using the NPV when evaluating capital investments. Although this development is in line with the theory, it limits the scope of the available information when evaluating capital projects.     

What is an Investment Project's Implied Rate of Return?

How to measure a project's implied rate of return has long been an unresolved problem, except for some special cases. This paper derives return on present cost (ROPC) as the correct measure of an investment project's implied rate of return. The IRR is a biased measure except for projects classified as simple projects, and this bias is likely to be substantial in many real‐world applications. Thus while net present values should be used to determine whether to accept/reject projects, I recommend that analysts use ROPC in place of the IRR as a measure of a project's true rate of return.     

万能寿险内在收益率测算与影响因素分析

保单实际收益率的衡量指标,指出结算利率不能如实反映保单收益率。通过构造定期寿险和投资组合的方式,提出以万能寿险保单资金账户内在收益率IRR来反映实际收益率较为合适,文章以目前中国市场上正在销售的B款万能终身寿险产品为样本对保单IRR进行了测算,结果表明保单IRR低于结算利率,用结算利率来反映保单收益会对投保人产生误导,文章还进一步对万能寿险保单IRR的影响因素做了分析,结果表明保单持有时间长度、费用的比例和结构等因素显著影响保单收益。最后,文章根据测算和分析的结果给出了相应的建议。     

The optimal trade-off between interest rate risk and annual return of bond ladders

Bond laddering is a popular fixed-income investment strategy. The main purpose of this paper is to develop a methodology for determining private investors’ most interest rate risk (IRR)-return-efficient investment horizon for bond ladders (BLs), which are virtually free of credit risk. Two IRR measures of a continuously rolling and homogenous BL (CRHBL) are analytically derived under the assumption that interest rates are martingales. The first measure is the modified duration, which assumes a flat term structure of interest rates. However, this assumption is not fully supported by the empirical data and, thus, an additional IRR measure is proposed. Under each of these two measures, the ratios between the annual return in excess of the demand deposit rate and IRR of CRHBLs with different investment horizons are calculated. As expected, CRHBLs with rather low IRR are most risk-return-efficient. The results for the theoretical CRHBLs also apply to “real-world” discrete BLs. Thus, the proposed methodology can help private investors construct IRR-return-efficient discrete BLs.     

Estimation of Internal Rate of Return Under Nonsteady Conditions

This study presents a method to estimate the IRR (internal rate of return) from published financial statement data under nonsteady conditions. The IRR is allowed to systematically change over time. The method provides an estimate for the current profitability of periodic total expenditure, its rate of change, and the firm-level profitability. Four competing steady and nonsteady statistical models are evaluated by simulation showing that a restricted nonsteady model may give the most reliable estimates. The model is applied to Finnish firms to illustrate how to use the model in practice. Three samples of publicly traded and nontraded firms are considered.     

ESTIMATING THE INTERNAL RATE OF RETURN FROM PUBLISHED FINANCIAL STATEMENTS

This paper presents a new approach to estimating the longrun internal rate of return (IRR) for the firm from the accountant's rate of profit based on published financial statements. The model developed for estimating the IRR includes both capital and net working asset investments. Modelling and estimating the growth of the firm is an integral part of the approach. Furthermore, estimating the parameters describing the long-run financing behavior of the firm is presented based on discounted average funds flow statements. Finally, the approach is applied on the financial data of a large Finnish business enterprise.     

Economic and Accounting Rates of Return A Statistical Model

This paper develops a number of statistical procedures than can be used to determine whether a firm's ex post accounting rate of return (ARR) is likely to provide guidance as to the economic return the firm will earn over its remaining life. The paper argues that if a corporation's future process cash flows are generated by some form of stochastic process, then the probability density function induced by this can be used to assess whether the ARR provides a reasonable reflection of the economic return the corporation is likely to earn over its remaining life. Five large listed companies are used as case studies to illustrate the model's application.     

ON DERIVING THE INTERNAL RATE OF RETURN FROM THE ACCOUNTANT'S RATE OF RETURN

L.A. Gordon (J.B.F.A. Vol. 1 No, 3) claims to have derived a method for approximating the IRR using the ARR. This paper demonstrates that the key relationship in Gordon's paper is only valid if the IRR is already known and used to calculate economic depreciation. It is suggested that Gordon has merely derived a means for refining ARR, but not for deriving IRR.
Dans son article paru dam Vol. 1 No 3 de ce journal, L.A. Gordon prétend avoir introduit une méthode qui permet d'évaluer "Internal Rate of Return" au moyen de "Accountant's Rate of Return". Ce papier démontre que le rapport-clé dont Gordon nous fait part n'est vérifiable que si "Internal Rate of Return" est préablement connu et sert a calculer l'amortissement économique. On insinue ainsi que Gordon a simplement présenté un moyen de perfectionner "Accountant's Rate of Return" mais n'en a pas démontré pour autant l'évaluation de "Internal Rate of Return".
L.A. Gordon (J.B.F.A. Band 1, Nr. 3) behauptet, er habe eine Annäherungsmethode abgeleitet, womit der interne Zinsfuss von dem RO1 Kriterium berechnet werden kann. Dieser Beitrag zeright, dass das Schlüsselverhältnis in Gordons Abhandlung nur dann gültig ist wenn der interne Zinsfull schon bekannt ist und als kalkulatorischer Zinssatz für ökonomische Abschreibungsbetrage verwendet wird. Es wird behauptet, dass Gordon keine Methode für die Ableitung des internen Zinsfusses entwickelt hat, sondern nur eine für die Verbesserung des R01 Kriteriums.     

SOME ANALYTICS OF WHY CONDITIONAL IRRs CAN CONTAIN GROWTH RATE RELATED MEASUREMENT ERROR

This paper investigates the consequences of incorrectly modelling the investment outflow/benefit inflow relationship on estimates of the internal rate of return (IRR) prepared by using cash recovery rates (CRRs). The main result of this paper is that CRR-based estimates of the IRR will contain such bias if and only if either the duration of the assumed shape of the investment outflow/benefit inflow relationship is less than the duration of the true investment outflow/benefit inflow relationship for all rates of interest or the duration of the assumed shape of the investment outflowlbenefit inflow relationship is greater than the duration of the true investment outflowlbenefit inflow relationship for all rates of interest. This result is then applied to the case where both the true and the assumed shape of the investment outflow/benefit inflow relationships have benefit inflows that change exponentially over time. It is shown that if the exponential rate of change is mis-specified the resulting CRR-based estimate of the IRR will contain systematic bias monotonically related to the rate of growth.     

Subjective Economic Risk to Beneficiaries in Notional Defined Contribution Accounts

This article aims to quantify the aggregate subjective economic risk to which beneficiaries would be exposed if a retirement pension system based on notional account philosophy were introduced. We use scenario generation techniques to make projections of the factors that determine the real expected internal rate of return (IRR) and the expected replacement rate (RR) for the beneficiary according to six retirement formulae based on the most widely accepted rates or indices. We then apply the model to the case of Spain. Our projections are based on Herce and Alonso's macroeconomic scenario 2000–2050 (2000) and include information about the past performance of the indices and the time period the forecast is to cover. The results of the IRR calculation—average value, standard deviation, and value‐at‐risk (VaR)—are analyzed both in objective terms and for different degrees of participants' risk aversion.     

Conservatism, growth, and return on investment

Return on Investment (ROI) is widely regarded as a key measure of firm profitability. The accounting literature has long recognized that ROI will generally not reflect economic profitability, as determined by the internal rate of return (IRR) of a firm’s investment projects. In particular, it has been noted that accounting conservatism may result in an upward bias of ROI, relative to the underlying IRR. We examine both theoretically and empirically the behavior of ROI as a function of two variables: past growth in new investments and accounting conservatism. Higher growth is shown to result in lower levels of ROI provided the accounting is conservative, while the opposite is generally true for liberal accounting policies. Conversely, more conservative accounting will increase ROI provided growth in new investments has been “moderate” over the relevant horizon, while the opposite is true if new investments grew at sufficiently high rates. Taken together, we find that conservatism and growth are “substitutes” in their joint impact on ROI.     

ESTIMATING THE INTERNAL RATE OF RETURN FROM PUBLISHED FINANCIAL STATEMENTS: A COMMENT

In a recent issue of this journal T. Salmi attempted to estimate the internal rate of return from published financial statements. Two reasons lead to the conclu- sions that his approach is partly in error. The first is a technical one. Also it has been proved that his objective, estimating the IRR in the case that it is approximately equal to the growth rate, can be reached in a much simpler way.     

The Implied Longevity Yield: A Note on Developing an Index for Life Annuities

I develop an index for tracking the dynamic behavior of life (pension) annuity payouts over time, based on the concept of self‐annuitization. Our implied longevity yield (ILY) value is defined equal to the internal rate of return (IRR) over a fixed deferral period that an individual would have to earn on their investable wealth if they decided to self‐annuitize using a systematic withdrawal plan. A larger ILY number indicates a greater relative benefit from immediate annuitization. I use age 65—with a 10‐year period certain—compared against the same annuity at age 75 as the standard benchmark for the index, and calibrate to a comprehensive time series of weekly (Canadian) life annuity quotes from 2000 through 2004. I find that during this period the ILY varied from 5.45 percent to 6.90 percent for males and from 5.00 percent to 6.42 percent for females and was highly correlated with a duration‐weighted average yield of 10‐year and long‐term Government of Canada bonds. I believe our ILY metric can help promote and explain the benefits of acquiring lifetime payout annuities by translating the abstract‐sounding longevity insurance into more concrete and measurable financial rates of return.     

On Testing the Assumptions of the Cash Recovery Rate Approach to the Estimation of Economic Performance

The first purpose of this paper is to investigate the necessary (as opposed to sufficient) assumptions underlying the CRR approach to the estimation of corporate economic performance. By so doing, the general circumstances in which an estimate of corporate economic performance based on CRRs will exactly equal a firm's IRR are identified. It is pointed out that these necessary assumptions are related to the concept of corporate economic performance being invoked (within the general idea that we are trying to estimate a firm's internal rate of return). Second, there is a drawing out of the empirical implications, as to the behaviour of corporate cash flows and CRRs, of the necessary assumptions for the CRR approach to produce an estimate of economic performance equal to a firm's IRR for each of these definitions of corporate economic performance. In particular, it is argued that these empirical implications depend upon the specific manner in which the CRR approach is applied in practice. A third purpose of the paper is to provide some empirical evidence as to whether an example of the practice of using the CRR approach employs data consistent with the necessary assumptions for this particular approach to be valid outlined in the paper. In fact, it turns out that this might not be the case. The evidence casts light on the extent to which CRR-based estimates of corporate economic performance are likely to be reasonable proxies of firms' IRRs.     

Higher risk,lower returns: What hedge fund investors really earn

The returns of hedge fund investors depend not only on the returns of the funds they hold but also on the timing and magnitude of their capital flows in and out of these funds. We use dollar-weighted returns (a form of Internal Rate of Return (IRR)) to assess the properties of actual investor returns on hedge funds and compare them to buy-and-hold fund returns. Our main finding is that annualized dollar-weighted returns are on the magnitude of 3% to 7% lower than corresponding buy-and-hold fund returns. Using factor models of risk and the estimated dollar-weighted performance gap, we find that the real alpha of hedge fund investors is close to zero. In absolute terms, dollar-weighted returns are reliably lower than the return on the Standard & Poor's (S&P) 500 index, and are only marginally higher than the risk-free rate as of the end of 2008. The combined impression from these results is that the return experience of hedge fund investors is much worse than previously thought.     

我国利率市场化进程中商业银行的利率风险管理分析

本文旨在通过对利率风险管理方法演变历程的概览,还原我国利率市场化下真实的利率风险环境和我国银行业的风险管理水平,揭示利率风险管控重点——利差的合理性,并探寻其忽视内含期权所致的真实利差偏差的重要隐患。实证分析我国存贷利差合理性的基础上,得出存在偏离真实合理水平的结论。由此,提出期权调整利差（OAS）模型,结合金融工程产品分解和期权定价思想,展示其操作流程与方法对比。所得调整后利差,运用于有效久期-凸度管理模型,形成完整的利率风险管理体系,从而提出了有关风险管理方法工具、银行业务拓展和市场数据系统建立的建议。