You are considering the purchase of Miller Manufacturing, Inc.'s ordinary shares. The shares are selling for $21.00 per share. The next dividend is expected to be $2.10, and you expect the dividend to keep growing at a constant rate. If the share returns 15% p.a., calculate the annual growth rate of dividends.

Question

You are considering the purchase of Miller​ Manufacturing, Inc.'s ordinary shares. The shares are selling for​ $21.00 per share. The next dividend is expected to be​ $2.10, and you expect the dividend to keep growing at a constant rate. If the share returns​ 15% p.a., calculate the annual growth rate of dividends.

BlackTom AI · Accepted Answer

We start by restating the given data to keep the scenario clear: the current share price P0 is 21.00, the next dividend D1 is 2.10, and the required return (cost of equity) r is 15% or 0.15. The dividends are expected to grow at a constant rate g, which implies the Gordon Growth Model applies: P0 = D1 / (r - g).

Option a. 5%: This would yield r - g = 0.15 - 0.05 = 0.10. Plugging into the model, D1 / (r - g) = 2.10 / 0.10 = 21, which matches the given price. This is consistent, so 5% is a viable growth rate.

Option b. 3%: If g = 0.03, then r - g = 0.12, and the model gives P0 = 2.10 / 0.12 = 17.50. This does not equal the observed price of 21, so 3% is inconsistent with the data.

Option c. 8%: If g = 0.08, then r - g = 0.07, and P0 = 2.10 / 0.07 ≈ 30.0. This is far higher than the actual price, so 8% cannot be correct given the inputs.

Option d. 10%: If g = 0.10, then r - g = 0.05, and P0 = 2.10 / 0.05 = 42.0. This again greatly exceeds the observed price, indicating 10% growth is not supported by the data.

In this kind of valuation, the key relation is P0 = D1 / (r - g). Only the growth rate that makes the denominator equal to 2.10 / 21 = 0.10 (i.e., r - g = 0.10) will be internally consistent with the provided price, dividend, and required return. This leads to g = r - 0.10 = 0.15 - 0.10 = 0.05, or 5%.

MCD2170 Foundations of Finance - Trimester 3 - 2025

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MCD2170 Foundations of Finance - Trimester 3 - 2025

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类似问题

Company ABC’s ordinary shares are currently selling at​ $24.00 per share. The company is expected to pay a dividend of​ $1.92 per share, which is predicted to grow at ​ 4% per annum forever. What is the​ share's expected rate of​ return?

Company ABC’s ordinary shares are currently selling at​ $24.00 per share. The company is expected to pay a dividend of​ $1.92 per share, which is predicted to grow at ​ 4% per annum forever. What is the​ share's expected rate of​ return?

Is the following statement true or false? Déjà vu’ just paid a cash dividend of $0.20 per share. Investors require a 16% return from investments such as this. If the dividend is expected to grow at a steady 8% per year. The share will be worth $2.70 in five years?[Fill in the blank]

Is the following statement true or false? Déjà vu’ just paid a cash dividend of $0.20 per share. Investors require a 16% return from investments such as this. If the dividend is expected to grow at a steady 8% per year. The share will be worth $2.70 in five years?[Fill in the blank]

The two-stage dividend growth model evaluates the current price of a stock based on the assumption a stock will:

更多留学生实用工具

希望你的学习变得更简单

Company ABC’s ordinary shares are currently selling at $24.00 per share. The company is expected to pay a dividend of $1.92 per share, which is predicted to grow at 4% per annum forever. What is the share's expected rate of return?

Company ABC’s ordinary shares are currently selling at $24.00 per share. The company is expected to pay a dividend of $1.92 per share, which is predicted to grow at 4% per annum forever. What is the share's expected rate of return?