A firm has a retention ratio of 45 percent and a sustainable growth rate of 6.2 percent. The capital intensity ratio is 1.2 and the debt-equity ratio is .64. What is the profit margin?

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Quizplus · Accepted Answer

The sustainable growth rate (SGR) formula is SGR = ROE * b, where ROE is the return on equity and b is the retention ratio (the portion of earnings retained rather than paid out as dividends). The ROE can also be expressed as the profit margin (PM) times the asset turnover (AT) times the equity multiplier (EM), or ROE = PM * AT * EM. Given the capital intensity ratio (CIR) is the inverse of the asset turnover (AT = 1/CIR), and the equity multiplier (EM) can be calculated from the debt-equity ratio (DE) as EM = 1 + DE, we can rearrange the SGR formula to solve for the profit margin (PM).Given:- Retention ratio (b) = 45% or 0.45- Sustainable growth rate (SGR) = 6.2% or 0.062- Capital intensity ratio (CIR) = 1.2 (thus, AT = 1 / CIR = 1 / 1.2)- Debt-equity ratio (DE) = 0.64 (thus, EM = 1 + DE = 1.64)First, calculate ROE using SGR = ROE * b:ROE = SGR / b = 0.062 / 0.45 = 0.1378 or 13.78%Then, calculate PM using ROE = PM * AT * EM:PM = ROE / (AT * EM) = 0.1378 / (1 / 1.2 * 1.64) = 0.1378 / (0.8333 * 1.64) ≈ 0.0949 or 9.49%

A Firm Has a Retention Ratio of 45 Percent and a Sustainable