3. Suppose that a company’s dividends are expected to grow at a constant rate gd

Question

3. Suppose that a company’s dividends are expected to grow at a constant rate gd forever, and the price of the stock of the company is expected to grow at a constant rate of gp forever. The interest rate is constant, denoted by R. Compute the dividend next period if gd = 0.01, i.e., 10%.

(a) (10 points) Suppose the next period’s dividend is $10, gd = 0.02, gp = 0, and R = 0.04.

(b) (8 points) What goes wrong if we assume that the growth rate of the stock price exceeds the interest rate, i.e., gp > R? (c) (7 points) Using your answer to part (b), carefully explain why stock-market bubbles cannot last forever.

Explanation / Answer

a)

Current Price=10/(0.04-0.02)=500

b)

Lets say the current price is P0, next years price is P1 and next dividend is D1 and the next to next dividend is D2

gd is growth rate in dividends

gp is growth rate in price

r is cost of equity

We know, according to constant growth model, Current Price=Next DIvidend/(cost of equity-growth rate)

P0=D1/(r-gd)

Now if gd>R, price will become negative which is impossible

c)

P0=D1/(r-gd)

P1=D2/(r-gd)=D1*(1+gd)/(r-gd)

=>P0*(1+gp)=D1*(1+gd)/(r-gd)

=>P0=D1*(1+gd)/((r-gd)*(1+gp))

So, 1+gd /1+gp will tend to 1..growth in price will approximate growth in dividends

As dividends cannot keep on increasing and go beyond R or cost of equity and as price rise is approximately equal to dividend growth, the prices cannot keep on increase and the stock market bubbles cannot last forever

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