The APV method conceptually is well accepted. The primary benefit of the APV method is that it separates the value derived from operations from the value derived from other sources such as tax shields, ancillary revenues/cash flows. However, there are some concerns. The criticism of the APV method are:

First, the APV method’s manner of computing the cost of debt can be reconciled with the cost of equity only when the cost of debt is assumed to be the risk-free rate. This is not true in practice.

Second, the APV method assumes that the tax shield benefits are universal. This may not be the case across the world. Tax rates and tax codes are different in different countries.  

Third, theoretically, the APV method should also consider the cost of distress that comes with taking on debt. However, most APV models ignore the cost of distress or assume it is zero due to the challenges involved in estimating the cost of distress.