Required Rate of Return and Present Value of Growth Opportunities Suppose that t

Question

Required Rate of Return and Present Value of Growth Opportunities
Suppose that the stock of Kandi Technologies is currently trading at $10 per share. Earnings per share in
the coming year are expected to be $2. The company has a policy of paying out 50% of its earnings each
year in dividends. The rest is retained and invested in projects that earn a 20% rate of return per year
(ROE = 0.20).

(a) Using the constant-growth DDM calculate the required rate of return of an investor in Kandi
Technologies who purchases the stock at $10.

(b) Calculate the Present Value of Growth Opportunities (PVGO). You may assume that the current
trading price of the stock of $10 reflects its intrinsic value.

(c) What would happen to the stock price of Kandi Technologies if the company cut the dividend payout
ratio is cut to 0.25? Assume the required return on equity is the same as the answer you calculated in Part
(a).

Explanation / Answer

a. As per DDM, stock price = D1/(r - g) where r is the required rate of return and g is the growth rate.

D1 = 50% * 2 = $1
stock price = $10

g = ROE * (1-payout rate) = 20% * (1-0.50) = 10%

Thus, $10 = 1/(r - 0.10)
r - 0.10 = 1/10 = 0.10

r = 0.10 + 0.10 = 0.20 or 20%

Thus, the investors required rate of return is 20%

b. Share price = PVGO + EPS in year 1/required rate of return

Thus, 10 = PVGO + 2/0.20 = PVGO + 10

Thus, PVGO = 0

(PVGO is also = ROE - required rate of return = 20%-20% = 0)

c. If dividend payout = 25%, D1 = 0.25 * 2 = $0.50
g = ROE*(1-payout rate) = 20%*(1-0.25) = 20%*0.75 = 15%

stock price = 0.50/(0.20-0.15) = 0.50/0.05 = $10
The stock price will remain the same as growth rate of dividend will increase.

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