Given the following information, what is the sustainable growth rate?

Total Assets = $1500
Current Liabilities = $396
Long-Term Liabilities = $902
Total Equity = $202
Sales = $644
COGS = $208
Operating Expenses = $310
Net Income = $112
Retained Earnings = $70
Dividends = $42

Question

Given the following information, what is the sustainable growth rate?

Total Assets = $1500
Current Liabilities = $396
Long-Term Liabilities = $902
Total Equity = $202
Sales = $644
COGS = $208
Operating Expenses = $310
Net Income = $112
Retained Earnings = $70
Dividends = $42

BlackTom AI · Accepted Answer

We start by restating what we’re calculating: the sustainable growth rate (SGR), which is typically defined as SGR = ROE × retention ratio.
Option-by-option analysis helps ensure understanding of the core components.
Option A: 34.65%. This value aligns with the standard calculation using ROE and the retention ratio. First, compute ROE as Net Income divided by Equity: ROE = 112 / 202 ≈ 0.5545 (55.45%). Next, determine the retention ratio: Retained earnings = Net Income − Dividends = 112 − 42 = 70, so retention ratio = 70 / 112 = 0.625 (62.5%). Multiply ROE by retention: 0.5545 × 0.625 ≈ 0.3466, or 34.66%. Rounding to two decimals gives 34.65%, which matches this option. The math is consistent with the definitions.
Option B: 147.85%. This figure is far outside plausible SGR values given typical ROE and retention inputs here. It would require an ROE or retention ratio well above 1, which isn’t the case with the provided numbers (ROE ≈ 55% and retention ≈ 62.5%). Therefore this option is incorrect.
Option C: 16.71%. This result would imply either a much smaller ROE or retention ratio than what the data yield. Since ROE ≈ 55% and retention ≈ 62.5%, the product is around 34.7%, not 16.7%, so this option miscalculates one of the components or misapplies the formula.
Option D: 24.50%. While closer to the correct ballpark, it still underestimates the SGR given the actual components. If you recompute carefully (ROE ≈ 55.45%, retention ≈ 62.5%), the product is about 34.7%, not 24.5%, so this is incorrect.
To recap the key checks: the sustainable growth rate uses ROE and the retention ratio. ROE = Net Income / Total Equity = 112 / 202 ≈ 0.5545. Retention ratio = (Net Income − Dividends) / Net Income = 70 / 112 = 0.625. Multiply: 0.5545 × 0.625 ≈ 0.3466 ≈ 34.65%. Options B, C, and D fail because they do not reproduce this correct product given the inputs, whether by overestimating, underestimating, or misapplying either ROE or the retention ratio.

Given the following information, what is the sustainable growth rate? Total Assets = $1500 Current Liabilities = $396 Long-Term Liabilities = $902 Total Equity = $202 Sales = $644 COGS = $208 Operating Expenses = $310 Net Income = $112 Retained Earnings = $70 Dividends = $42单项选择题

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