Suppose a firm has a net profit margin of 15%, sales of $155 million, assets of $312 million, and owner’s equity of $223. If the dividend payout ratio is 10%, what is the firm’s sustainable growth rate?

Question

BlackTom AI · Accepted Answer

Begin by identifying the key financial relationships involved: sustainable growth rate (g) is commonly calculated as g = ROE × retention ratio, where retention ratio b equals 1 minus the dividend payout ratio.

Step 1: Compute net income from the given net profit margin and sales. Net income = net profit margin × sales = 0.15 × 155 million = 23.25 million.

Step 2: Determine return on equity (ROE). ROE = Net income / Shareholders' equity = 23.25 million / 223 million ≈ 0.1043, i.e., about 10.43%.

Step 3: Find the retention ratio. With a dividend payout ratio of 10%, the retention ratio b = 1 − 0.10 = 0.90.

Step 4: Calculate the sustainable growth rate g = ROE × b = 10.43% × 0.90 ≈ 9.387%, which rounds to about 9.38%.

Step 5: Confirm the units and rounding. Each intermediate figure is consistent in absolute terms (millions for incomes and equity, percentages for margins and ROE), and rounding to two decimals yields g ≈ 9.38%.

Summary check: The approach relies on standard stylized facts of sustainable growth in the dupla framework (retention drives growth via reinvested earnings, scaled by profitability as ROE). If any piece is altered (e.g., payout ratio or margins), the final g would shift accordingly.

Suppose a firm has a net profit margin of 15%, sales of $155 million, assets of $312 million, and owner’s equity of $223. If the dividend payout ratio is 10%, what is the firm’s sustainable growth rate?Single choice

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