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Getting levered EV from unlevered EV

In the CFAI, it shows an equity only entity EV represents as Vu

To get levered EV -> Vl = Vu + (taxes * new debt)

Shouldn’t the levered EV equal Vl = Vu + [(1-t) * new debt] ?

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No because by adding (taxes * debt) you’re adding The tax shield (The unlevered company does not have The tax shield benefit regarding debt interest)

when you subtract (1-t) you are subtracting The tax shield to calculate the after tax cost of debt