How much should you be willing to pay for one share of stock if the company just paid an $0.80 annual dividend (D0), the dividends increase by 4% annually and you require an 8% rate of return?

Question

BlackTom AI · Accepted Answer

First, identify the stock valuation approach given: with a constant growth in dividends, the Gordon growth model applies, where P0 = D1 / (r - g).

Option 1: $19.23. To assess, compute D1 = D0 × (1 + g) = 0.80 × 1.04 = 0.832. Then P0 = 0.832 / (0.08 − 0.04) = 0.832 / 0.04 = 20.80. The value 19.23 would imply a denominator around 0.04 and a smaller numerator, or a different model; as given, this is not consistent with the Gordon model.

Option 2: $20.00. This would correspond to P0 = 20.00, which would require D1 = P0 × (r − g) = 20.00 × 0.04 = 0.80. Since D1 is actually 0.832, this option ignores the growth in dividends and thus is incorrect under the Gordon framework.

Option 3: $20.40. If P0 = 20.40, then D1 would need to be 20.40 × (0.04) = 0.816. However, the actual D1 is 0.832, so this price does not match the required discounting of a growing dividend stream at r = 8% with g = 4%.

Option 4: $20.80. This result comes directly from applying the Gordon growth formula: D1 = 0.80 × 1.04 = 0.832, and P0 = 0.832 / (0.08 − 0.04) = 0.832 / 0.04 = 20.80. This price correctly prices the stock given a perpetual 4% dividend growth and an 8% required return.

In summary, each incorrect option either ignores the dividend growth, misapplies the formula, or uses inconsistent arithmetic, while the fourth option faithfully implements P0 = D1 / (r − g) with D1 = 0.832, r = 8%, and g = 4%.

How much should you be willing to pay for one share of stock if the company just paid an $0.80 annual dividend (D0), the dividends increase by 4% annually and you require an 8% rate of return?单项选择题

类似问题

ABC, Inc. just paid a dividend of $2. ABC expects dividends to grow at 10% annually forever. The return on shares like ABC, Inc. is typically around 12%. What is the most you would pay for ABC’s share?

ALP’s most recent dividend was $2.00 per share and is selling today for $70. The dividend is expected to grow at 7% per year for the foreseeable future. Should you purchase the share if the market return is 10% on investments with comparable risk?

Using a dividend discount model, find the intrinsic value (price at time zero) for a firm whose expected dividend is $1.92 and growth in dividends for year 2, 3, and 4 is 23.2% and constant growth afterwards is 0.54%. The cost of equity is 9.21%. (Answer in 2 decimal places, 6.21 for $6.21).

Using a dividend discount model, find the intrinsic value (price at time zero) for a firm whose expected dividend is $1.37 and growth in dividends for year 2, 3, and 4 is 13.8% and constant growth afterwards is 1.42%. The cost of equity is 6.67%.

AWSM has just paid a dividend of $1.24 and is expected to increase the future dividends at a rate of 3% per year indefinitely. If you, as a shareholder, require 12% per year, what is the current price per share?

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单