Question

The common stock Dell Co. is trading at $21 per share. The company has paid a constant dividend of $2 per share. However, the company has just announced new investments that the market did not know about. The market expects that with these new investments, the dividends should grow at 2 percent per year forever.

Assuming that the cost of equity remains the same, what will be the price of the stock after the announcement?

Answer 1

P = D₁ / (r-g) is the formula used to calculate the price of stock using dividend discount model.

Here,

P is the Price of Stock

D₁ is the value of next year's dividend

r is the cost of equity

g is the growth rate of dividends.

We may use the formula discussed to figure out cost of equity by substituting known values before investments were made. The growth in dividends was zero (dividends were constant).

Hence, P = D₁ / (r-g) would imply 21 = 2 / (r-0)

21 = 2/r

21 r = 2

r = 2/21.

We may now use this r (cost of equity) which remains constant post investments to arrive at new stock price by using the same formula.

P = D₁ / (r-g)

where D₁= current dividend * (1+g)

i.e D₁= 2*(1+0.02)

D₁= 2*1.02 = 2.04

Now P = D₁ / (r-g) would imply P = 2.04 / ( (2/21) - 0.02 ) = 2.04 / 0.075238 = $27.11

Therefore, after announcement, the price of the stock is $ 27.11