Chapter 4, Problem 30QP

EFN [LO2] Define the following:

$\begin{array}{l}\text{S}=\text{Previous}\text{year's}\text{sales}\\ \text{A}=\text{Total}\text{assets}\\ \text{E}=\text{Total}\text{equity}\\ g=\text{Projected}\text{growth}\text{in}\text{sales}\\ \text{PM}=\text{Profit}\text{margin}\\ b=\text{Retention}\text{(plowback)}\text{ratio}\end{array}$

Assuming all debt is constant, show that EFN can be written as follows:

$\text{EFN}=-\text{PM(S)}b+(\text{A}-\text{PM(S)}b)\times g$

Hint: Asset needs will equal A × g. The addition to retained earnings will equal PM(S)b × (1 + g).