Non-Monotonic NPV Function Leads to Spurious NPV and Multiple IRR Problems: A Critical analysis using a modified capital amortization method that Resolves These Problems
This analysis is conducted using some popular non-normal net cash flow (NNCF) investment data available in public domain and other hypothetical NNCF data. The methodology is mainly based on capital amortization schedule (CAS) and modified CAS (MCAS) methods along with a comparison of the results with the common DCF method. The findings are summarised here:
a. The problem of multiple IRR is caused by reinvestment income and the resultant non-monotonic NPV function. The CAS methods clearly indicate whether there is any reinvestment. Non-monotonic NPV function of NNCF investment leads to multiple IRRs or spurious IRRs, NPVs and MIRRs. With non-monotonic NPV functions the DCF estimated criteria are all spurious.
b. The MCAS method eliminates the reinvestment thereby leads to monotonic NPV function and resolves the problem of reinvestment, spurious NPVs, MIRRs, IRRs and or multiple IRR.
c. Neither the NPV nor the MIRR could resolve the problem of multiple IRR. With normal NCFs and some of the NNCFs also, there are no reinvestment at IRR or at hurdle rate as wrongly asserted in many published works.
d. It is normal for the estimated IRR to be either ‘nil or zero or negative’ when the sum of net benefits or NCF is zero or negative. Such IRRs are consistent with NCF or net benefit. IRR of ‘zero or negative or no’ is not a weakness or problem but it reveals the real or consistent return.
e. MCAS is an appropriate method to estimate the rate of return (IRR and NPV) for both normal NCF and NNCF and resolves the multiple IRR problem and eliminates spurious NPVs and MIRRS. The estimated IRR and NPV by MCAS method are consistent with NCF.
f. Ultimately, IRR and NPV, estimated by MCAS, are the best criteria available to investment, project and cost-benefit analysis.
In summary, NPV and IRR estimated by MCAS method are equally appropriate and therefore one cannot be the best substitute for the other. The multilateral and bilateral organizations and corporate managements may wish to revisit their recommendation to use the NPV only and not the IRR while dealing with multiple IRRs associated with NNCF investments.
Safeguards against the Introduction of a Dual-Class Shares Structure
As revealed in a survey conducted in Asia Pacific by CFA Institute in March, a majority (60%) of the 450-plus respondents have not had any experience investing in firms with a DCS structure, which signalled the urgency for and need to educate investors and the general public on the implications of DCS structures.
The survey, “Dual-Class Shares and the Demand for Safeguards,” revealed that respondents in the region were divided when asked whether DCS structures should be introduced to the market, with 53% opposing the introduction and 47% in favour. Regardless of their position on DCS, almost all (97%) respondents considered it necessary to enact additional safeguards if DCS structures are permitted.
Among different possible safeguards, more than 90% of respondents considered it appropriate to implement enhanced mandatory corporate governance measures as well as time- and event-based sunset provisions, such as automatic conversion of shares with super voting rights to ordinary voting rights. Specifically, 94% of respondents considered it appropriate to introduce a time-based sunset provision; among which, 91% of such respondents considered it appropriate to convert shares with super voting rights to ordinary shares within 10 years. Separately, 93% of respondents considered introducing a maximum voting differential appropriate; 63% of these respondents found a 2:1 maximum voting differential optimal.
|In the latest issue (Issue 13 – August 2017), it covers the stories of:|
|Financial Crime Risk : Anti-Money Laundering Practices in Banking
To understand anti-money laundering, we have to understand what money laundering is. Money Laundering is the process of converting illegal funds into seemingly legitimate assets with the purpose of concealing the ownership or original source of these funds. This makes it difficult for the authorities to trace the origins of the funds. To counter this, the banking sector has established a set of internal regulations and system known as anti-money laundering. These are legal controls taken by financial institutions to investigate suspicious transactions to help prevent money laundering activities within the banking sector.
|The Rise of Text Mining in Financial Markets
The world is awash in data. Financial markets are awash in data. We are generating around 2.5 quintillion (2.5×1018) bytes of information every day, and there is an average of 4,000 brokerage reports a day comprising around 36,000 pages in 53 languages. As market participants try to maximize their competitive edge from the growing mountain of information, the nancial world increasingly feels there is a need to harness the power of big data and it has been shaping the way they acquire, analyze and utilize data. The recent development is the rapid expansion of text mining. Hence, this article will focus on the development of Text Mining technology as well as Text Mining technique.
当前10年期国债收益率3.6%附近，2倍于10年期收益率，要求投资收益率等于7.2%。也即E/P=7.2%， P/E=13.89。按照13.89倍P/E，17-21年末的期望价格为，16元，34元，50元，53.2 元，55.2 元。考虑到当前的价格为19.82，当前买入持有该标的，到17-21年，每年末期对应的理论收益为：-17%，73%，152%，168%，179%。考虑到一定的交易策略，未来2-3年的时间，投资温氏股份，可以实现200%的收益率。再考虑到温氏集团作为大公司，市场系统性风险Beta低，而高市值对应的流动性很强。因此，投资温氏集团在接下来2-3年可以获得，低风险下的200%收益。
Title: A Resolution to the Problem of Multiple IRR: A Modified Capital Amortization Schedule (MCAS) Method for Non-Normal Cash flow (NNCF) to Obtain a Unique IRR
The problem of multiple IRR remained unresolved for almost a century. This problem is associated only with some of the non-normal net cash flow (NNCF) that wrongly includes reinvestment income as income or benefit stream. The reinvestment income, which is not a benefit from the investment or project under analysis, causes the multiple IRR problem. This is often misinterpreted as problem of IRR but its neither a problem with IRR nor NPV. It is a problem associated with some NNCF data and the failure to update the discounted cash flow (DCF) or capital amortization schedule (CAS) methods to handle such problem.
Using NNCF data, analyses are conducted with special emphasis on topics such as:
a. A modified CAS (MCAS) method that eliminates multiple IRR associated with NNCF data;
b. Multiple IRR problem and the Descartes rule of sign and Norstrom’s criteria;
c. A NNCF data with a unique IRR under DCF / CAS methods vs IRR by MCAS method;
d. Resolving the problem of multiple IRR by MCAS Method Versus MIRR; and
e. A critical review of the GIRR and AIRR Methods to Estimate NNCF.
The salient findings of the present analysis are:
a. The MCAS method, presented in this paper, identifies and eliminates the reinvestment income associated with NNCF investments (with positive opening balance in one or more years in the CAS) from the benefit stream;
b. This new method overcomes the multiple IRR problem and leads to a unique and real IRR; The effectiveness of MCAS to handle the NNCF data is illustrated with numerical analysis;
c. The assumption of reinvestment at IRR or at hurdle rate in NPV are false assertions in the cases of normal NCF and some of the NNCFs. However, such reinvestment is evident only with NNCFs with positive opening balance in one or more years under the CAS.
d. The reinvestment income under the benefit stream causes multiple IRRs and multiple NPVs too. As NPV is a static point estimate (at hurdle rate) the multiple NPVs are not exposed. Without eliminating the reinvestment income, none of the criterions viz. NPV, IRR or MIRR, is useful as a decision criterion. Neither NPV or MIRR is a preferred criterion, under such circumstances, as recommended in some published works.
e. The MCAS method is appropriate for both normal NCF and NNCF as illustrated in this paper. CAS or DCF method is appropriate only for normal NCF investments.
f. Even when there is no multiple IRRs with some NNCFs under DCF/CAS method, the MCAS method estimated IRR or NPV, without reinvestment income, are different from that of the DCF/CAS estimated IRR and NPV. For a consistent estimate of IRR and NPV, the MCAS method is most appropriate both for NCF and NNCF investments.
g. The generalized IRR (GIRR) and the Average IRR (AIRR) are also not appropriate estimates for NNCF and they are not NCF consistent as discussed in this paper. The problem of multiple IRR associated with the popular cases of NCF investments used in GIRR and AIRR, are also resolved now.
In conclusion, the MCAS method resolves the problem of multiple IRR and leads to a unique IRR that is real and NCF-consistent. Neither the NPV nor the MIRR could resolve the problem of multiple IRR.
Valuation Insights is a quarterly e-newsletter that provides you with the latest news from Duff & Phelps and the trends and changes in valuation and accounting that could affect your business transactions in Asia.
In this edition, our top stories cover the Financial Accounting Standards Board issuing an Accounting Standards Update, robust fair value measurement, the International Valuation Standards Council releasing the 2017 edition of its International Valuation Standards, and a recent Duff & Phelps study about fairness opinions.
We will also look at important Duff & Phelps reports and articles, including a recorded forum presentation by Professor Damodaran and the Duff & Phelps Global Regulatory Outlook 2017.