Question

Assume a firm has net income in 20x9 of 20 and its end-of-year 20x8 total assets were 450. Further assume that the firm has a standing requirement to maintain a debt/equity ratio of 0.8, and that its managers are prohibited from further borrowing or stock issuance.

a. What is this firm's maximum sustainable growth rate?
b. If the firm pays 6 of the 20 net income as a dividend, and plans to maintain this payout ratio into the future, now what is its maximum sustainable growth rate?
c. If the firm uses 12 of the 20 net income to repurchase some of its outstanding shares, and plans to maintain the use of this ratio of net income for future repurchases, now what is its maximum sustainable growth rate?
d. If the firm takes action as described in parts b) and c), what would its maximum sustainable growth rate be?

Answer 1

a. The firm's maximum sustainable growth rate is 4.44%. b. With a dividend payout ratio of 30%, the maximum sustainable growth rate is 3.11%. c. With a net income ratio of 40% for share repurchases, the maximum sustainable growth rate is 1.78%. d. With both dividend payments and share repurchases, the maximum sustainable growth rate is 0.44%.

Step-by-step explanation:

a. To determine the firm's maximum sustainable growth rate, we need to use the formula:

Growth Rate = Return on equity (ROE) x Retention Ratio

ROE can be calculated as Net Income / Total Assets. In this case, ROE = 20 / 450 = 0.0444 or 4.44%.

The retention ratio is calculated as 1 - Dividend Payout Ratio. Since the firm is not paying any dividends, the retention ratio is 1, or 100%.

Using these values, the maximum sustainable growth rate is:

Growth Rate = 4.44% x 100% = 4.44%

b. If the firm pays 6 of the 20 net income as a dividend, the dividend payout ratio is 6 / 20 = 0.3 or 30%. The retention ratio is 1 - Dividend Payout Ratio = 1 - 0.3 = 0.7 or 70%. Using these values, the maximum sustainable growth rate is:

Growth Rate = 4.44% x 70% = 3.11%

c. If the firm uses 12 of the 20 net income for share repurchases, the retention ratio is 8 / 20 = 0.4 or 40%. Using these values, the maximum sustainable growth rate is:

Growth Rate = 4.44% x 40% = 1.78%

d. If the firm both pays 6 of the 20 net income as a dividend and uses 12 of the 20 net income for share repurchases, the retention ratio is 2 / 20 = 0.1 or 10%. Using this value, the maximum sustainable growth rate is:

Growth Rate = 4.44% x 10% = 0.44%