Given the following information: profit margin = 10%; sales = $100; retention ratio = 40%; assets = $200; equity multiplier = 2.0. If the firm maintains a constant debt-equity ratio and no new equity is used,

what is the maximum growth rate? (Assume a constant profit margin.)

To find the maximum growth rate, we need to calculate the return on equity (ROE), which is the product of the profit margin, retention ratio, and equity multiplier.

Step 1: Calculate ROE
ROE = Profit Margin * Retention Ratio * Equity Multiplier

Given:
Profit Margin = 10% (0.10)
Retention Ratio = 40% (0.40)
Equity Multiplier = 2.0

ROE = 0.10 * 0.40 * 2.0 = 0.08

Step 2: Calculate the maximum growth rate

The maximum growth rate can be calculated using the sustainable growth rate formula:

Growth Rate (g) = ROE * (1 - Dividend Payout Ratio)

Since the firm maintains a constant debt-equity ratio and no new equity is used, the Dividend Payout Ratio would be equal to 1 - Retention Ratio. Therefore:

Dividend Payout Ratio = 1 - Retention Ratio = 1 - 0.40 = 0.60

Growth Rate (g) = ROE * (1 - Dividend Payout Ratio)
= 0.08 * (1-0.60)
= 0.08 * 0.40
= 0.032

Therefore, the maximum growth rate is 3.2%.