Question

Two stocks each currently pay a dividend of $1.75 per share. It is anticipated that both firms’ dividends will grow annually at the rate of 3 percent. Firm A has a beta coefficient of 0.88 while the beta coefficient of firm B is 1.35.

1. If U.S. Treasury bills currently yield 2.4 percent and you expect the market to increase at an annual rate of 8.7 percent, what are the valuations of these two stocks using the dividend-growth model?

2. Why are your valuations different?

3. If stock A’s price were $51 and stock B’s price were $42, what would you do?

Answer 1

For applying dividend-growth model, we need the following three informations:

1) Expected Dividend per share which is already given: $1.75 per share

2) Growth rate in Dividend which is also already given= 3%

3) Required rate of return/Cost of capital which is missing for both the Firms. So, we should now find out this by using CAPM formula. Which is as follows:

Ra= Rrf + Ba (Rm - Rrf) for Firm A

Where Ra= Required rate of return/cost of capital for Firm A

Rrf= Risk free rate of return = 2.4

Rm= Market rate of return= 8.7

Ba= Beta co-efficient for Firm A= 0.88

By putting these values in above formula, we will get the Required rate of return for Firm A

Ra= 0.024 + 0.88 (0.087 - 0.024)

Ra= 0.07944= 7.944%

Rb= Rrf + Bb (Rm - Rrf) for Firm B

Where Ra= Required rate of return/cost of capital for Firm B

Rrf= Risk free rate of return = 2.4

Rm= Market rate of return= 8.7

Ba= Beta co-efficient for Firm B= 1.35

By putting these values in above formula, we will get the Required rate of return for Firm B

Rb= Rrf + Bb (Rm - Rrf)

Rb= 0.024 + 1.35 (0.087 - 0.024)

Rb= 0.10905= 10.905%

Now, we have required rate of return for both the firms: Firm A= 7.944% AND Firm B= 10.905%

Now, we will apply, Dividend Growth Model where Stock Value= D1 divided by (K-G) for Firm A

Where D1= Expected Dividend= $1.75

K= Required rate of return= 0.07944

G= Growth rate in Dividend= 3%= 0.03

Putting figures in above formula, stock value of Firm A= 35.3964

Now, again we will apply, Dividend Growth Model for Firm B where Stock Value= D1 divided by (K -G)

=$1.75 divided by (0.10905 - 0.03)

= $22.137

Stock Value of Firm B= $22.137