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Fundamentals of Financial Manageme...

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

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BuyFindarrow_forward

Fundamentals of Financial Manageme...

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

PORTFOLIO REQUIRED RETURN Suppose you are the money manager of a $4 million investment fund. The fund consists of four stocks with the following investments and betas:

Stock Investment Beta
A $ 400,000 150
B 600,000 (0.50)
C 1,000,000 1.25
D 2,000,000 0.75

If the market’s required rate of return is 14% and the risk-free rate is 6%, what is the fund’s required rate of return?

Summary Introduction

To determine: The fund’s required rate of return.

The Required Rate of Return:

The required rate of return is the rate, which should be minimum 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

Given,

The risk-free rate is 6%.

The required rate of return on market is 14%.

The value of the investment fund is $4 million.

Calculated,

The value of the beta’s stock is 0.7625 (refer working note).

Compute required rate of return.

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 risk premium.
  • bstock is the value of the stock’s beta.

Substitute 6% for rRF, 14% for rM, and 0.7625 for bstock.

rstock=6%+(14%6%)×0.7625=6%+6.1%=12.1%

The required return on the stock is 12.1%.

Working note:

Calculation of the portfolio weight:

Stock Investment Portfolio Weight
Stock A $400,000 $400,000$4,000,000=0

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