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Effective Annual Rates when Loan Interest is Paid
The term “effective annual rate” (EAR) is very often explained with reference to the compounding of a nominal or stated rate using the formula: For example, if the stated rate is 12% p.a., compounded quarterly, then the EAR is (1.03)^4 -1 i.e. around 12.6% p.a. These explanations are potentially ambiguous, since they do not make …
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Challenges in Risk Identification
This is a follow-on article to the one “Key Stages in Modelling Risk and Uncertainty” and focusses on some of the challenges in the risk identification stage. Risk identification involves identifying which factors of a real-lie situation affect the outcome (whose risk we are trying to assess, such as the value of a contract, the …
Key Stages in Modelling Risk and Uncertainty
The modelling of risk and uncertainty should involve several stages. These are summarised in this note. It is important to note that each stage is important, and if not performed adequately, the quality of the results, conclusions and decisions could be severely affected to the point that the analysis is wrong, very inaccurate or misleading. …
Using Macros with @RISK – Fixing Samples
One the most important features of @RISK is the ability to embed Excel macros within the simulation. That is, for a macro the be run at every iteration of a simulation. If one has a model that requires a macro to be run whenever the model’s input values are changed, then this functionality will be …
Maximising Project Value Through Phasing and Real Options Approaches
Projects can often be divided into phases. As well as to help set targets, milestones and plan resources, the phasing of projects is very useful if there are critical points at which a project may fail, or its direction should be adapted or modified in some way. The modularisation of projects into sub-projects (modules), allows …
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Real Options: Simple Example
The term “Real Option” refers to an additional decision possibility that is created in any real-life situation if the scope of the permitted decision alternatives is extended in some way. Real options are most frequently discussed in the context of situations in which there is uncertainty. However, there is no requirement for uncertainty to be …
Using Risk Modelling and Monte Carlo Simulation in Cash Flow Valuation: Role and Benefits
Since 1989, I have been using risk modelling combined with Monte Carlo simulation to improve the robustness, transparency and accuracy of cash flow valuation models. This powerful approach is still underused for reasons that can be debated elsewhere. Here, I briefly summarise the key reasons that drive the improvement in the valuation when using such …
Some Challenges in Using IRR (Part II)
The IRR rule can also be misleading or inapplicable if the cash flow profiles change sign and if one relies on the default settings for the Excel IRR function. Consider a “base case” project where one could invest $100 this year to earn $120 next year (cash profile -100, 120), so that the IRR is …
Some Challenges in Using IRR in Decision Support (Part I)
The use of the internal rate of return in decision-making can be rather subtle and may even be misleading. For example, the decision rule: “For independent projects, accept the project if the IRR is above the required rate of return” is often stated as the core rule. However, the following demonstrates the general principle that …
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