The value of tax shields with a fixed book-value leverage ratio

The value of tax shields depends only on the nature of the stochastic process of the net increases of debt. The value of tax shields in a world with no leverage cost is the tax rate times the current debt plus the present value of the net increases of debt. We develop valuation formulae for a company that maintains a fixed book-value leverage ratio and show that it is more realistic than to assume, as Miles-Ezzell (1980) do, a fixed market-value leverage ratio. We also show that Miles-Ezzell assume that the increase of debt is proportional to the increase of the free cash flows.