Question

Two stocks each currently pay a dividend of $2.20 per share. It is anticipated that both firms’ dividends will grow annually at the rate of 2 percent. Firm A has a beta coefficient of 0.95 while the beta coefficient of firm B is 0.72.

If U.S. Treasury bills currently yield 3.4 percent and you expect the market to increase at an annual rate of 8 percent, what are the valuations of these two stocks using the dividend-growth model? Do not round intermediate calculations. Round your answers to two decimal places.

Stock A:

Stock B:

Answer 1

Current Value

Stock A

$    38.89

Stock B

$    47.64

Working:

As per dividend growth model, current value of stock is the present value of future dividends.

Step-1:Calculation of expected rate of return

As per Capital Asset pricing model(CAPM),

Expected rate of return

=

Rf+Beta*(Rm-Rf)

Where,

Rf

Risk free rate

So, as per CAPM, expected rate of return of,

Rm

Market return

Stock A

=

3.40%

+

0.95

*

(8%-3.4%)

=

7.77%

Stock B

=

3.40%

+

0.72

*

(8%-3.4%)

=

6.71%

Step-2:Calculation of current value of stocks

As per dividend valuation method,

current value of stock

=

D0*(1+g)/(Ke-g)

Where,

D0

Current dividend

So, current value of:

g

Growth rate in dividends

Ke

Expected rate of return

Stock A

=

2.20*(1+0.02)/(0.0777-0.02)

Where,

=

$    38.89

D0

$       2.20

g

2%

Ke

7.77%

Stock B

=

2.20*(1+0.02)/(0.0671-0.02)

Where,

=

$    47.64

D0

$       2.20

g

2%

Ke

6.71%