Question

In: Finance

6. You have been asked to estimate the beta of a high-technology firm, which has three...

6. You have been asked to estimate the beta of a high-technology firm, which has three divisions with the following characteristics.

Division Beta Market Value

Personal Computers 1.6 $100 million

Software 2.00 $150 million

Computer Mainframes 1.2 $250 million

a. What is the beta of the equity of the firm?

b. If the risk free return is 5% and the spread between the return on all stocks is 5.5%, estimate the cost of equity for the software division?

c. What is the cost of equity for the entire firm?

d. Free cash flow to equity investors in the current year (FCFE) for the entire firm is $7.4 million and for the software division is $3.1 million. If the total firm and the software division are expected to grow at the same 8% rate into the foreseeable future, estimate the market value of the firm and of the software division.

Solutions

Expert Solution

Total Firm value = Value of Personal computers + Value of Software + Value of Computer Mainframes

=100+150+250

=500

Weight of Personal computers = Value of Personal computers/Total Firm Value

= 100/500

=0.2

Weight of Software = Value of Software/Total Firm Value

= 150/500

=0.3

Weight of Computer Mainframes = Value of Computer Mainframes/Total Firm Value

= 250/500

=0.5

Beta of Firm = Weight of Personal computers*Beta of Personal computers+Weight of Software*Beta of Software+Weight of Computer Mainframes*Beta of Computer Mainframes

Beta of Firm = 1.6*0.2+2*0.3+1.2*0.5

Beta of Firm = 1.52

As per CAPM

expected return = risk-free rate + beta * (Market risk premium)

Expected return% = 5 + 2 * (5.5)

Expected return% = 16

As per CAPM

expected return = risk-free rate + beta * (Market risk premium)

Expected return% = 5 + 1.52 * (5.5)

Expected return% = 13.36

firm or enterprise value= recent FCF* (1 + growth rate )/(WACC - growth rate)

Firm/enterprise value = 7.4 * (1+0.08) / (0.1336 - 0.08)

Firm/enterprise value = 149.1 m

Software division value= recent FCF* (1 + growth rate )/(WACC - growth rate)

value = 3.1 * (1+0.08) / (0.16 - 0.08)

value = 41.85 m

jeff jeffy answered 1 year ago

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