when calculating the value of a geared firm , we would add value of a ungeared firm and the present value of tax shield which I saw is calculated by multiplying Debt and tax rate.
my question is do we do this because we are assuming the debt is perpetual? what if the debt is a fixed rate 5 year debt?
That is one way you could be expected to value a firm, but it would help to see the wording of the particular question.
However, assuming that we are asked to take an APV approach then we would assume that the debt would be replaced as it matured and that therefore the gearing would be maintained and the interest payable in perpetuity.