Hudson Corporation will pay a dividend of $3.80 per share next year. The company pledges to increase its dividend by 3.40 percent per year indefinitely.

If you require a return of 9.60 percent on your investment, how much will you pay for the company's stock today?

Question

Hudson Corporation will pay a dividend of $3.80 per share next year. The company pledges to increase its dividend by 3.40 percent per year indefinitely.
  
If you require a return of 9.60 percent on your investment, how much will you pay for the company's stock today?

BlackTom AI · Accepted Answer

Apply the Gordon (constant-growth) dividend-discount model: P0 = D1 / (r − g).

1) Relevant knowledge points and concepts
- The Gordon Growth Model values a stock that pays dividends growing at a constant rate forever: P0 = D1 / (r − g). 
- D1 is next year’s dividend, r is the required rate of return, g is the constant growth rate. 
- The model requires r > g so the denominator is positive and the value is finite.

2) Complete reasoning process step by step
- Given D1 = $3.80 (the dividend next year), g = 3.40% and r = 9.60%. 
- Convert percentages to decimals: g = 0.034, r = 0.096. 
- Compute the denominator r − g = 0.096 − 0.034.

3) Calculations with intermediate steps
- r − g = 0.096 − 0.034 = 0.062.
- P0 = D1 / (r − g) = 3.80 / 0.062.
- To compute the division: 3.80 / 0.062 = (3.80 × 1000) / (0.062 × 1000) = 3800 / 62 = 61.29032258...
- Round to two decimal places: P0 = $61.29.

4) Why the correct answer is correct
- The model directly applies because dividends are promised to grow indefinitely at a constant 3.40%, and the required return (9.60%) exceeds the growth rate. Plugging the given D1, r, and g into the Gordon Growth formula yields $61.29, so this is the fair price today that equates the present value of all future growing dividends to the investor’s required return.

5) Why the other options are incorrect (brief)
- $58.84, $63.74 and $59.27 result from arithmetic or rounding mistakes or from misapplying the formula (e.g., using the wrong r or g, or using D0 instead of D1). 
- $28.27 is approximately what you would get if you mistakenly used r + g in the denominator (3.80 / 0.13 ≈ 29.23) or otherwise inverted the sign—an incorrect application of the model.

6) Conclusion confirming the final answer
- Using the Gordon Growth Model and the given inputs yields P0 = $61.29, which matches the provided correct answer.

Hudson Corporation will pay a dividend of $3.80 per share next year. The company pledges to increase its dividend by 3.40 percent per year indefinitely. If you require a return of 9.60 percent on your investment, how much will you pay for the company's stock today? 单项选择题

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