Assume that Lamar Company’s 15% required return resulted from a risk-free rate of 9%, a market…

Assume that Lamar Company’s 15% required return resulted from a risk-free rate of 9%, a market return of 13%, and a beta of 1.50. Substituting into the capital asset pricing model, Equation 7.9, we get a required return,ks, of 15%:

KS = 9% + [1.50 X (13% – 9%)] = 15%

With this return, the value of the firm was calculated in the example above to be $18.75.

Now imagine that the financial manager makes a decision that, without changing expected dividends, causes the firm’s beta to increase to 1.75. Assuming that RF and km remain at 9% and 13%, respectively, the required return will increase to 16% (9% + [1.75  X (13% – 9%)]) to compensate stockholders for the increased risk. Substituting D1= $1.50, ks=0.16, and g = 0.07 into the valuation equation, Equation 7.5, results in a share value of $16.67 [$1.50÷(0.16- 0.07)]. As expected, raising the required return, without any corresponding increase in expected return, causes the firm’s stock value to decline. Clearly, the financial manager’s action was not in the owners’ best interest.

 

Equation 7.9

 

KS  = RF + [b × (km – RF)]

 

Equation 7.5

 

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