###
**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 * 1.1

^{2}* 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*1.1

^{2}/1.14

^{2}+ 25.17/1.14

^{2}= $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 Contributed Comments**
8

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 |