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

14th Edition
Eugene F. Brigham + 1 other
ISBN: 9781285867977

Solutions

Chapter
Section Fundamentals of Financial Manageme...

14th Edition
Eugene F. Brigham + 1 other
ISBN: 9781285867977
Textbook Problem

CAPM AND REQUIRED RETURN HR Industries (HRI) has a beta of 1.8, while LR Industries’ (LRI) beta is 0.6. 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.

The required rate of return:

The required rate of return is the minimum rate, which should be earned on an investment to keep that investment running in the market. 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 1.8.

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

The risk-free rate is 6%.

The expected rate of inflation falls by 1.5 percentage points.

The real risk-free rate remains constant.

The required return on market falls to 10.5%.

The value of beta remains constant.

Calculation of the new risk-free rate:

Newrisk-freerate=Realrisk-freerateInflationrate=6%1.5%=4.5%

The new risk-free rate is 4.5%.

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

The formula to calculate the required rate of return is:

rstock=rRF+(rMrRF)×bstock

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 1.8 for bstock in the above formula.

rstock=4.5%+(10.5%4.5%)×1.8=4.5%+10.8%=15

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