# A firm with stock trading at $15.40 expects to distribute a dividend of$0.77. The last dividend...

A firm with stock trading at $15.40 expects to distribute a dividend of$0.77. The last dividend it distributed was $0.70. a) What is the required return on equity implied by the dividend growth model? b) What equity beta does this imply, if the expected market return is 18% and the risk-free rate is 3%? ## Beta: Beta is a financial measure derived by using statistical techniques. It shows the sensitivity of a stock to the market or economy. Beta can be negative or positive depending on the relationship between the stock and the market. In other words, the beta of the stock shows its systematic risk. ## Answer and Explanation: Let us first calculate the growth rate of the dividend which is 0.77 / 0.70 - 1 = 10% a) Required return on equity implied by the dividend growth model Required rate of return is given by Re = D1 / P0 + g where • D1 = dividend expected =$0.77
• P0 = current price of the stock = \$15.40
• g = growth rate of dividends = 10%

Therefore:

Re = 0.77 / 15.40 + 10 = 0.15 or 15%

b) Implication of equity beta

Beta is given by the following CAPM equation

Re = risk-free rate + (market return expected - risk-free rate) * equity beta

15% = 3% + (18% - 3%) * equity beta

Equity beta = 12% / 15% = 0.80

Since beta is less than one, stock is defensive. Using the Systematic Risk Principle & Portfolio Beta

from

Chapter 12 / Lesson 3
2.1K

In this lesson, we'll discuss how investors must understand the systematic risk principle in their portfolio. We'll also explain how investors can measure and define the risk of their portfolios using betas.