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Cost of debt and discount rate

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In the weighted cost-of-capital, why is the cost of debt always calculated as an after-tax cost, or debt percent * (1-tax rate)?

Briefly explain how the discount rate, or the cost-of-capital, be used to represent the risk associated with a particular investment opportunity?

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In the weighted cost-of-capital, why is the cost of debt always calculated as an after-tax cost, or debt percent * (1-tax rate)?
It is always taken after tax cost as the interest is tax deductible. Hence debt reduces a company's tax liability because interest payments are deductible expenses. Thus they are taken after tax. On the other hand, dividend paid on the equity is not tax deductible. Hence there is no reduction of tax liablity in case of cost of preference stock and equity stock.

Briefly explain how the ...

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