Consider the following three stocks. (a) Stock A is expected to provide a dividend of $10 a share forever. (b) Stock B is expected to pay a dividend of $5 next year. The dividend growth is expected to be 4% per year forever. (c) Stock C is expected to pay a dividend of $5 next year. The dividend is expected to grow by 20% annually for 5 years (i. e., until year 6) and then become zero forever. If the discount rate for each stock is 10 %, which stock is the most valuable?

The stock A is most valuable as the fair value of Stock A is $100 which is more than the fair value of Stock B ($83.33) and Stock C ($34.28).

Explanation:

to calculate the fair price of the stocks, we will use the DDM or dividend discount model. The DDM bases the value of a stock on the present value of the expected future dividends from the stock.

Let r be the discount rate which is 10%.

a.

The stock is like a perpetuity as it pays a constant dividend after equal intervals of time and for an indefinite period.

The price of this stock can be calculated as,

Price or P0 = Dividend / r

P0 = 10 / 0.1 = $100

b.

The constant growth model of DDM can be used to calculate the price of this stock as its dividends are growing at a constant rate forever.

P0 = D1 / r - g

Where,

D1 is the dividend for the next period r is the cost of equity or discount rate g is the growth rate in dividends

P0 = 5 / (0.1 - 0.04)

P0 = $83.33

c.

The price of this stock can be calculated using the present of dividends.

P0 = 5 / (1+0.1) + 5 * (1+0.2) / (1+0.1) ^2 + 5 * (1+0.2) ^2 / (1+0.1) ^3 +

5 * (1+0.2) ^3 / (1+0.1) ^4 + 5 * (1+0.2) ^4 / (1+0.1) ^5 + 5 * (1+0.2) ^5 / (1+0.1) ^6

P0 = $34.28