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“Arithmetic vs. Geometric Means: Empirical
Evidence and Theoretical Issues” by Jay B. Abrams, ASA, CPA, MBA
Copyright 1996
There has been a flurry of articles about the relative merits of using the arithmetic mean
(AM) versus the geometric mean (GM). The Ibbotson SBBI Yearbook took the first position that the arithmetic mean is the correct mean to use in valuation. Allyn Joyce’s June 1995
BVR article initiated arguments for the GM as the correct mean.
The previous articles have centered around Professor Ibbotson’s famous example using a binomial distribution with 50%-50% probabilities of a +30% and -10% return. The debate has been very interesting, but it is off on a tangent, focused on the wrong issue.
There are theoretical
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Regression #1: Returns as a Function of Risk
The arithmetic mean outperforms3 the geometric mean in this regression, with Adjusted R2 of 97.78% versus 81.93% and t-statistic of 19.9 versus 6.5. Additionally, the constant of
2 “A Breakthrough in Calculating Reliable Discount Rates,” Valuation, August, 1994. Additionally, Grabowski and King subsequently published articles on the same topic in Business Valuation Review, June 1995, p. 69-74 and September 1996, p.
103-115.
3 In other words, AM does a better job of explaining risk than GM.
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5.24% for the arithmetic mean makes economic sense, i.e., it matches the 70-year average Treasury Bond rate—the best proxy for the risk-free rate—while the constant for the geometric mean matches nothing in particular; and how could it? The geometric mean is stripped of some of the information relating to volatility, so therefore it will obviously do an inferior job of forecasting returns based on volatility.
Let’s see how it does in explaining returns as a function of log size.
Regression #2: Returns as a Function of Log Size
Again, the arithmetic mean outperforms the geometric mean. Its adjusted R2 is 91.43% compared to 84.48% for the geometric mean. The absolute value of Its t-statistic is 9.2,
We conduct an independent sample t-test using Excel, and obtain the following output (see t-test-height)
Valuations depend on forecasts. The reliability of the forecasts will then depend heavily on complete analysis of the industry, in addition to the evolving changes in the economy. It also requires understanding of the business and financial characteristic of the industry.
Professor Thomas Piper prepared the original version of this note, “Assessing a Firm’s Future Financial Health,” HBS No. 201-077, which is being
The proposed LBO deal of Comark Building Systems is an attractive investment for Brazos because it fits into Brazos’ “sweet spot”- a reasonable priced company with solid cash flow and good management. We can project cash flow at $6.8 million in 2002 and $12.3 million in 2006. In terms of the purchase price at $40 million, it is very attractive because we can get very good Total Post Money Valuation at $194 million. We can also confirm that the Market Value/EBITDA (1.38) of CoMark is lower than its competitor’s (3.42) when we compare multiple ratios, which means CoMark is undervalued. However, there are two major concerns; gaining competitive advantage and determining comparable valuations.
Decision Making Area 3:Investment Decisions * Table of Articles * Summary of Articles * Observations * Conclusion
Star Appliance is looking to expand their product line and is considering three different projects: dishwashers, garbage disposals, and trash compactors. We want to determine which project would be worth doing by determining if they will add value to Star. Thus, the project(s) that will add the most value to Star Appliance will be worth pursuing. The current hurdle rate of 10% should be re-evaluated by finding the weighted average cost of capital (WACC). Then by forecasting the cash flows of each project and discounting them by the WACC to find the net present value, or by solving for the internal rate of return, we should be able to see which projects Star should undertake.
Correct valuation of real assets can present challenges to financial analysts. Different models can be used to arrive at the closest estimate of value and yet certain issues will always arise.
The productive assets of property, plant, and equipment changed dramatically in 1996 they were 5,581 to 2010 an increase to 21,706. In total current assets there was a increase in 1996 from 5,910 to in 2010 21,579. Another significant change is in long term debt in 1996 of 1,116 to in 2010 an increase to 14,041. Also an important figure to note is in the retained earning in 1996 they were 94% (15,127) to 2010 68%
Most rely on valuation heuristics involving P/E, PEG, and price-to-sales . The simplicity of using heuristic triggers dependence on valuation heuristics as an alternative for the fundamental valuation. P/E, PEG, and price-to-sales need few variables and use simple formulas. Therefore , the estimates are rather perceptive THUS subject to bias. The cause of these biases arise from weak assumption made towards P/E, PEG, and price-to-sales inputs.
Since the “estimates are common, and some inaccuracy is likely. As long as this estimate is represented faithfully. We could consider that the current market price ($6.1) is the reliable and realizable market price)
Since 3.27 the t statistic is in the rejection area to the right of =1.701, the level of
1. Introduction 2. Analysis of current position 3. Analysis of new project 3.1 Methodologies and processes of Valuation 3.2 processes of Valuation 4. Conclusion
The Following involves the analysis of the costing techniques followed by the company along with its Budgeting system. It also involves the Investment appraisal analysis for the given data.
Gad, S., (November 2013). The Market Value Versus The Book Value. Retrieved on May 28, 2014 from:
The five investment appraisal techniques used for this report are the Accounting Rate of Return (ARR), payback period, Net Present Value (NPV), discounted payback and Internal Rate of Return (IRR). The results of the five investment appraisal techniques may not be similar because of differences in their approaches and calculations. However, it is advantageous to use more than one investment appraisal technique and understand the importance and problems of each method before making a final decision.