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"All our projects are discounted at the same interest rate," says the treasurer of a large company. Would you dispute the advisability of such a procedure?

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Yes I would dispute. There will be different disocunt rates depending on the risk of the project. Risk exists because of the inability of the decision-maker to make perfect forecasts. In formal terms, the risk associated with an investment may be defined as the variability that is likely to occur in the future returns from the investment.
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Wacc is determined.