### CFA Practice Question

A high-growth firm is expected to have a dividend growth of 10% for the next 2 years. It is then expected to stabilize at 4%. The firm has just paid a dividend of \$2 and investors require a rate of return of 14%. The market price of the firm's stock is:
A. \$23.16
B. \$19.68
C. \$23.46
Explanation: Since the dividends do not grow at a constant rate, you cannot directly apply the Dividend Discount Model valuation formula. However, note that 2 years from now, looking into the future, you will see a constant growth rate of 4% and the dividend 3 years from now will be \$2 * 1.12 * 1.04 = \$2.517. Therefore, the stock price 2 years from now, using the required rate of return of 14%, will equal P = 2.517/(14% - 4%) = \$25.17. Thus, the current stock price equals 2*1.1/1.14 + 2*1.12/1.142 + 25.17/1.142 = \$23.16. Note that you must be very careful about the time line. In the Dividend Discount Model valuation formula, the price at time t uses the dividend paid at time (t+1). That's the reason we had to use the dividend paid in year 3 to calculate the price at the end of year 2.

User Comment
Will1868 What about a multi-stage DDM?
Tomas This is a multi-stage DDM, first stage with a growth of 10% and second with a growth of 4%.
Dinosaur its not the cash flow for the third year, its the selling price of the security after 2 years.
pups01 You could also do:
D1 = 2(1.1) = 2.2
D2 = 2(1.1*1.1) = 2.42

Using CF function,
CF0 = 0
CF1 = 2.2
CF2 = 27.59 (i.e. 2.42 + 25.17)
I = 14.0
CPT NPV = 23.16
indrayudha thanks pups01, that should save valuable minutes.
Procbaby1 It's not DDM because the dividend stabilize at 4%. It does NOT grow at 4%.
Procbaby1 just kidding...
birdperson thanks Pup! very helpful way to speed up the problem