On the equivalence between the APV and the wacc approach in a growing leveraged firm

While in a steady state framework the choice between the wacc approach (Modigliani-Miller, 1963) and the adjusted present value (APV) approach (Myers, 1974) is irrelevant since the two approaches provide the same result, however, in a growing firm context the wacc equation seems to be inconsistent with the APV result. In this paper we propose a simple model to evaluate the tax savings in a growing firm in order to show under which assumptions the two approaches lead to the same results. We demonstrate that the use of the wacc model in a steady-growth scenario gives rise to some unusual assumptions with regard to the discount rates to be used in calculating tax shields. We show that the widely used wacc formula, if used, as it is in most cases, in a growth context, implies that a) debt tax shield related to already existing debt are discounted using k(d); b) debt tax shield related to new debt, due to company's growth, are discounted, according to a mixed procedure, using both k(u) and k(d). We discuss the inconsistency of such a discounting procedure and the preferred features of the APV approach.