# Determining Stock Price and Equilibrium Expected Growth Rate

Problem 1

A stock is expected to pay a dividend of $0.75 at the end of the year. The required rate of return is rs = 10.5%, and the expected constant growth rate is g = 6.4%. What is the stock's current price?

Problem 2

A share of common stock just paid a dividend of $1.00 (D0 = $1.00). If the expected long-run growth rate for this stock is 5.4%, and if investors' required rate of return is 11.4%, what is the stock price?

Problem 3

Assume that a company will pay a dividend of D1 = $1.25 per share on its common stock at the end of the year, and that this dividend is expected to grow at a constant rate of 6.00% per year in the future. The company's beta is 1.15, the market risk premium is 5.50%, and the risk-free rate is 4.00%. What is the company's current stock price (P0)?

Problem 4

Your research leads you to believe a company's common stock will pay a dividend of $1.25 per share at the end of the year (D1 = $1.25). The stock currently sells for $32.50 per share, and your required rate of return is 10.5%. The dividend is expected to grow at some constant rate, g, forever. What is the equilibrium expected growth rate, g?

Problem 5

A dividend of D0 = $1.32 has just been paid to you on a share of common stock. You (and other analysts) expect the company's dividend to grow by 30% this year, by 10% in Year 2, and at a constant rate of 5% in Year 3 and each year thereafter. The required return on this low-risk stock is 9.00%. What is your best estimate of the stock's current market value (your belief as to the stock's intrinsic value)?

Problem 6

A company is presently enjoying relatively high growth because of a surge in the demand for its new product. The CFO expects earnings and dividends to grow at a rate of 25% for the next 4 years, after which competition will probably reduce the growth rate in earnings and dividends to zero, i.e., g = 0. The company's last dividend, D0, was $1.25, its beta is 1.20, the market risk premium is 5.50%, and the risk-free rate is 3.00%. Based on this information, what is the current price of the common stock?

#### Solution Preview

PROBLEM 1

Expected dividend $0.75

Required rate of return 10.50%

Expected constant growth rate 6.40%

Stock price = Expected dividend/(Required rate of return - Expected constant growth rate)

Stock price= $18.29

PROBLEM 2

Paid Dividend (D0) $1

Expected constant growth rate 5.40%

Required rate of return 11.40%

Stock price = [Paid Dividend *(1+Expected constant growth rate)]/(Required rate of return - Expected constant growth rate)

Stock price = $17.57

PROBLEM 3

Expected dividend $1.25

Expected constant growth rate 6%

Beta 1.15

Market risk premium 5.50%

Risk free rate 4%

First, compute the required rate of return

Required rate of return = Risk free rate + Beta*Market risk premium

Required rate of return= 10.325%

Second, compute for the stock price

Stock price ...

#### Solution Summary

The expert determines the stock price and equilibrium expected growth rates.