Consider first the determination of the optimal ratio of outside equity to debt, So/B. To do
this let us hold the size of the firm constant. V, the actual value of the firm for a given size, will
depend on the agency costs incurred, hence we use as our index of size V*, the value of the firm
at a given scale when agency costs are zero. For the moment we also hold the amount of outside
financing (B+So), constant. Given that a specified amount of financing (B+So) is to be obtained
externally our problem is to determine the optimal fraction E* º o
* S /(B + So ) to be financed with
equity.