   Chapter 8, Problem 15P Fundamentals of Financial Manageme...

15th Edition
Eugene F. Brigham + 1 other
ISBN: 9781337395250

Solutions

Chapter
Section Fundamentals of Financial Manageme...

15th Edition
Eugene F. Brigham + 1 other
ISBN: 9781337395250
Textbook Problem

CAPM AND REQUIRED RETURN HR Industries (HRI) has a beta of 1.6; LR Industries’ (LRI) beta is 0.8. The risk-free rate is 6%, and the required rate of return on an average stock is 13%. The expected rate of inflation built into rRF falls by 1.5 percentage points; the real risk-free rate remains constant; the required return on the market falls to 10.5%; and all betas remain constant. After all of these changes, what will be the difference in the required returns for HRI and LRI?

Summary Introduction

To determine: The difference between the required return.

Introduction:

The required rate of return:

The minimum rate which should be earned on an investment to keep that investment running in the market is the required rate of return. When the required return is earned, only then the users and the companies invest in that particular investment.

Explanation

For Company H:

Given,

The value of beta is 1.6.

The required rate of return on an average stock is 13%.

The risk-free rate is 6%.

The expected rate of inflation decreases by 1.5 percentage points.

The real risk-free rate is constant.

The required return on market declines to 10.5%.

The value of beta remains constant.

Calculation of the required rate of return for stock of Company H:

The formula to compute the required rate of return is:

rstock=rRF+(rMrRF)×bstock (I)

Where,

• rstock is the required return on the stock,
• rRF is the risk-free return,
• rM is the market return and
• bstock is the value of the stock’s beta.

Substitute 4.5% for rRF , 10.5% for rM , and 1.6 for bstock in the equation (I).

rstock=4.5%+(10.5%4.5%)×1.6=4.5%+6%×1.6=4.5%+9.6%=14.1%

The required return on the stock of Company H is 14.1%.

For Company L:

Given,

The value of beta is 0.8.

The required rate of return on an average stock is 13%.

The risk-free rate is 6%.

The expected rate of inflation decreases by 1.5 percentage points.

The real risk-free rate remains the same.

The required return on market declines to 10.5%.

The value of beta remains constant

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