Question text 5Marks Cabcharge Company paid a $1.00 dividend per share last year and is expected to continue to pay out 30% of earnings as dividends for the foreseeable future. If the company is expected to generate a 10% return on equity in the future, and if you require a 15% return on the stock, Calculate the growth rate and value of the stock.Growth rate is Answer 1[select: , 7%, 3%, 5%, 6%, 4%]Value of the stock is Answer 2[select: , $8.58, 13.37, 16.25, 18.72, 15.77]Notes Report question issue Question 9 Notes多项填空题
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Question text 5Marks Cabcharge Company paid a $1.00 dividend per share last year and is expected to continue to pay out 30% of earnings as dividends for the foreseeable future. If the company is expected to generate a 10% return on equity in the future, and if you require a 15% return on the stock, Calculate the growth rate and value of the stock.Growth rate is Answer 1[select: , 7%, 3%, 5%, 6%, 4%]Value of the stock is Answer 2[select: , $8.58, 13.37, 16.25, 18.72, 15.77]Notes Report question issue Question 9 Notes多项填空题

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BlackTom AI · Accepted Answer

Growth rate equals the retention ratio multiplied by return on equity: g = b × ROE. Here the payout ratio is 30%, so the retention ratio b = 1 − 0.30 = 0.70. Therefore g = 0.70 × 0.10 = 0.07, or 7%.

Step-by-step reasoning and calculations:
1. Determine retention ratio: b = 1 − payout = 1 − 0.30 = 0.70.
2. Compute growth rate: g = b × ROE = 0.70 × 0.10 = 0.07 → 7%.
3. Find next year’s dividend (D1) from last year’s dividend (D0 = $1.00): D1 = D0 × (1 + g) = $1.00 × 1.07 = $1.07.
4. Use the Gordon (constant-growth) dividend discount model: P0 = D1 / (r − g), with required return r = 0.15 and g = 0.07.
5. Compute price: P0 = 1.07 / (0.15 − 0.07) = 1.07 / 0.08 = 13.375 → rounded to $13.37.

Why the correct answer is correct:
- The growth rate formula g = retention × ROE is the standard way to convert a company’s reinvestment behavior and profitability into expected dividend/earnings growth. With 70% reinvested and 10% ROE, 7% growth follows directly.
- The Gordon model requires D1 (the dividend one year ahead). Using D1 = $1.07 and the spread r − g = 8% yields the present value $13.375 → $13.37.

Why other options are incorrect (brief):
- Growth = 3% would result from mistakenly treating the 30% payout as the retention (i.e., b = 0.30), which is incorrect given the payout = 30% (retention = 70%).
- The value $8.58 corresponds to that incorrect g = 3% scenario (D1 = $1.03 and P0 = 1.03/0.12 = $8.58).
- The other numeric choices stem from other common mistakes (using D0 instead of D1, wrong retention, or wrong subtraction r − g) and do not follow the correct formulas above.

Conclusion: Growth rate = 7% and value of the stock ≈ $13.37, which matches the provided answers.

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