In the 4th column, the 78.99 should be 51.45. The column total is correct.
The "1n" (1N) should be "ln" (LN), the natural logarithm function.
Thus, the equation should read CE = -r ln(1 - EU / r).
Also, we missed a typesetting conversion error where minus signs were omitted. Two formulas should show negative utilities for negative outcomes:
U(-$1 million) = -RN$ 1.0517 million
U( -$4 million) = -RN$ 4.9182 million
This always the case: The sign of the utility is always the same as the cashflow NPV. Positive NPVs have a smaller positive utility in RN$. Negative NPV outcomes are more negative, i.e., larger magnitude and negative. In a cost-minimization problem, be sure to use negative values for the outcomes and maximize the EU or CE.
In 1993, I wanted to get some real-to-life numbers for the Wastewater Plant example. A Quick Basic program was hastily built for the purpose. The book describes most of the key assumptions, though many additional variables of the model are missing. Omitted for clarity are assumptions for variables such as inflation rate, cost of debt, cost of equity, depreciation, salvage, and income tax rate. Additionally, I did not detail the calculations.
Several people have contacted me since 1993, wanting to know how the the outcome PV cost numbers were determined (e.g., those in Figure 5.3). I'm pleased that some readers have wanted to work through the calculations to ensure complete understanding. However, my little book isn't the place to detail project economic modeling.
If you really want to see the calculations, contact me and I will be pleased to send you the program listing (with some restrictions). It's not a pretty model, and Quick Basic is obsolete anyway. However, the code is reasonably easy to read despite no supporting documentation. For an eventual 3rd edition book, perhaps I'll rewrite (and improve) this model into Excel or Visual Basic and include a link in the book for interested persons to retrieve the code.
No one has yet asked for a copy of the project model described in Chapter 15, "Optimizing Project Plan Decisions." It is a more interesting model, with formulas describing what happens to activity costs and schedule if the planned activity starts turn out to be too early or too late. There were lots of assumptions in another quickly-constructed and undocumented demonstration model.
This book was reviewed in Project Management Journal (March 2002, p. 59-60). The writer said "The merge bias is developed in an example, yet on page 172 the author instructs the user not to use the result." In case you saw this review and are wondering, the reviewer misinterpreted the text. I wrote in the callout:
"The project manager probably should not use 13.05 (or rounded) days for planning Activity Dís start. The optimal project value will likely be a different planned start for D, and this optimization process is the subject model in Chapter 15."
A major point throughout the book is that the optimal choices of decision variables is the combination that provides the best expected value outcome. Chapter 15 describes
Stochastic variance, Chapter 13's subject, is about getting into trouble if you DO NOT use a stochastic model throughout. Subsidiary-models (e.g., for a sub-grouping of activities) can produce EVs (such as the 13.05 days value above). However improved, these EVs usually cannot be plugged into a higher-level model to get the correct result. Unless sufficiently localized, you will do better by making project decisions using a stochastic model whose major uncertain inputs are probability distributions.
When I wrote these chapters, I was under-appreciating the effect of resource constrains on the critical chain. I'm in-process of writing one or more articles expanding the critical chain effect on a Monte Carlo simulation of the project. Some early notes may be found at: http://www.maxvalue.com/tip110.htm (notes appended to a book review).
Please contact me if you have questions or concerns about anything you have read in the book. E-mail:
Copyright (C) 2006 by John R. Schuyler. Last updated 9-Feb-2013.
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