Multiple choice general knowledge math & puzzles

An analyst gathers the following information about two companies for the year ending 31 December 2008: Company 1 Company 2 Dividend payout ratio 37.5% 40.0% Return on assets 12% 10.0% Financial leverage 1.6 2.0 Which of the following best describes the expected growth rate of Company 1? The expected growth rate of Company 1 compared to Company 2 is

  1. lower.

  2. greater.

  3. the same

  4. none of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The sustainable growth rate formula is g = ROA × Financial Leverage × (1 - payout ratio). For Company 1: 12% × 1.6 × (1 - 0.375) = 12% × 1.6 × 0.625 = 12%. For Company 2: 10% × 2.0 × (1 - 0.40) = 10% × 2.0 × 0.60 = 12%. Both companies have identical expected growth rates of 12%. Despite different individual ratios, the combined effect produces the same result.

AI explanation

To determine the expected growth rate of Company 1 compared to Company 2, we need to consider the given information about dividend payout ratio, return on assets, and financial leverage.

The growth rate of a company can be estimated using the sustainable growth rate (SGR) formula:

SGR = (Return on Assets) × (1 - Dividend Payout Ratio) × (Financial Leverage)

Let's calculate the SGR for Company 1 and Company 2:

SGR1 = (12%)(1 - 37.5%)(1.6) = 7.2% SGR2 = (10.0%)(1 - 40.0%)(2.0) = 12.0%

Comparing the SGRs, we can see that the SGR for Company 1 is 7.2%, and the SGR for Company 2 is 12.0%.

Since the SGR for Company 1 is lower than the SGR for Company 2, we can conclude that the expected growth rate of Company 1 is lower than that of Company 2.

Therefore, the correct answer is A) lower.

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