Question

The risk-free rate of return is 2 percent, and the expected return on the market is 7.8 percent. Stock A has a beta coefficient of 1.7, an earnings and dividend growth rate of 7 percent, and a current dividend of $3.00 a share. Do not round intermediate calculations. Round your answers to the nearest cent.

What should be the market price of the stock?

$ _____

If the current market price of the stock is $87.00, what should you do?

The stock ___ be purchased.

If the expected return on the market rises to 14.8 percent and the other variables remain constant, what will be the value of the stock?

$_______

If the risk-free return rises to 4 percent and the return on the market rises to 15.7 percent, what will be the value of the stock?

$_______

If the beta coefficient falls to 1.4 and the other variables remain constant, what will be the value of the stock?

$________

Explain why the stock’s value changes in c through e.

The increase in the return on the market ______ the required return and _____ the value of the stock.

The increase in the risk-free rate and the simultaneous increase in the return on the market cause the value of the stock to _____.

The decrease in the beta coefficient causes the firm to become _______ risky as measured by beta, which ______ the value of the stock.

Answer 1

According to capital asset pricing model -

E(Ri) = Rf + ( E(Rm) - Rf ) * beta of security

where,
E(Ri) = Expected return on security i
rf = risk free return
E(Rm) = Expected market return

Here,

Rf = 2 %

E(Rm)= 7.8 %

Beta = 1.7

Expected return = Rf + ( E(Rm) - Rf ) * beta of security

= 2 + ( 7.8 - 2)* 1.7

= 2 + 5.8 * 1.7

= 2 + 9.86

= 11.86 %

Required return = 11.86 %

Now,

1 ) Market price of the stock can be calculated with help of constant dividend growth model-

where, Po is the current market price.
D0= Dividend just paid by company.
g = Growth rate
Ke = cost of equity / required rate of return

Here,

D0 = 3 $

g = 7 %

Ke = 11.86 % ( as calculated above)

Po = 66.05 $ (approx)

market price of the stock = 66.05 $

2 ) The intrinsic value of the share is 66.05 $

If the current market price of the stock is $87.00, the stock should not be purchased.

3 ) If the expected return on the market rises to 14.8 percent keeping other values constant.

Expected return = Rf + ( E(Rm) - Rf ) * beta of security

=  2 + ( 14.8 - 2)* 1.7

= 2 + 12.8 * 1.7

= 2 + 21.76

= 23.76 %

Market price of the stock can be calculated with help of constant dividend growth model-

Here,

D0 = 3 $

g = 7 %

Ke = 23.76 % ( as calculated above)

= 19.15 $ (approx)

4) If the risk-free return rises to 4 percent and the return on the market rises to 15.7 percent

Expected return = Rf + ( E(Rm) - Rf ) * beta of security

=  4 + ( 15.7 - 4)* 1.7

= 4 + 11.7 * 1.7

= 4 + 19.89

= 23.89 %

Market price of the stock can be calculated with help of constant dividend growth model-

Here,

D0 = 3 $

g = 7 %

Ke = 23.89 % ( as calculated above)

= 19.01 $ (approx)

value of the stock = 19.01 $

Hope it helps!