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Fundamentals of Financial Manageme...

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

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BuyFindarrow_forward

Fundamentals of Financial Manageme...

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

PORTFOLIO REQUIRED RETURN Suppose you are the money manager of a $4.82 million investment fund. The fund consists of four stocks with the following investments and betas:

Stock Investment Beta
A $ 460,0000 1.50
B 500,000 (0.50)
C 1,260,000 125
D 2,600,000 0.75

If the market’s required rate of return is 8% and the risk-free rate is 4%, 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 the 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 4%.

The required rate of return on market is 8%.

The value of the investment fund is $4.82 million.

Calculated,

The value of the beta’s stock is 0.822 (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=4%+(8%4%)×0.822=4%+4%×0.822=4%+3.288%=7.288%

Working note:

Calculation of the portfolio weight:

StockInvestmentPortfolio Weight
Stock A$460,000 $460,000$4,820,000=0

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