Question

Suppose that the consensus forecast of security analysts of NoWork Inc. is that earnings next year will be E1= $5.00 per share. The company tends to plow back 60% of its earnings and pay the rest as dividends. The CFO estimates that the company’s growth rate will be 8% from now on.

(a) If your estimate of the company’s required rate of return is 12%, what is the equilibrium price of the stock?

(b) Suppose there is uncertainty about the growth rate. With 50% probability the growth rate will be 6%, with 50% probability the growth rate will be 10%. What are the respective market values under the two growth rates? What must be the price of the stock, given that both growth rates have equal probability?

(c) Under the probabilities in (b) the expected growth rate of the firm is 8%. Howcome the valuation in part (b) is different from the valuation in part (a)?

Answer 1

a. Equilibrium Price = Dividend next year/(required rate - growth rate)

Dividend next year = Earning's(1-earnings retained) = 5*(1-0.60) = $2

Equilibrium Price = 2/(12%-8%) = $50

Hence, the equilibrium price is $50.

b. Price with 6% growth rate = 2/(12%-6%) = $33.34

Price with 10% growth rate = 2/(12%-10%) = $100

Expected Price = 0.50*33.34 + 0.50*100 = 16.67 + 50 = $66.67.

c.

The increase in price due to 10% growth rate is higher than increase in price due to 6% growth rate. Therefore, the impact on the dividend is larger in 10% because of denominator being small i.e. 0.02.

If we were to calculate expected return first and than value the share, growth rate would have been 8% and answer would have been same as (a). However, since the valuation done on the basis of adjusting the price and not adjusting the rate, we are getting a different valuation simply because 10% growth rate has more impacti on the price than 6%.

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