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**CFA Practice Question**

Consider the following annual growth forecasts for a common stock:

Growth after year 3 = 15%

Growth in years 1-3 = 25%

Growth after year 3 = 15%

Assuming that the last dividend was $2.25 per share, and the required rate of return is 20% per year, what is the value of this common stock?

A. $63.78

B. $58.23

C. $65.82

**Explanation:**To determine the value of a common stock experiencing temporary supernormal growth, use the following equation: {V = {[d

_{0}x (1 + gs)

^{1}] / k} + {[d

_{1}x (1 + gs)

^{2}} + ... {d

_{n}x (1 + gs)

^{n}} + {[d

_{n}x (1 + gs)

^{n}x (1 + gn] / (k - g)} / (1 + k)

^{n}}}

where: V = the value of common stock at t

_{0}, d

_{0}= the dividend at t

_{0}, d

_{1}= the dividend at t

_{1}, d

_{n}= the dividend at tn, g

_{s}= the supernormal rate of growth, gn = the normal rate of growth, n = the time period "n", and k = the required rate of return.

In this example, there is a supernormal growth period of three years, during which the growth rate of this common stock is expected to grow at 25% annually. After this period of supernormal growth, the growth rate is anticipated to settle to a "normal" rate of 15%, and this rate is expected to remain stable indefinitely. The calculation of the value of this common stock is illustrated as follows: {V = {[$2.25 x (1.25)

^{1}] / (1.20)} + {[$2.25 x (1.25)

^{2}] / (1.20)

^{2}} + {[$2.25 x (1.25)

^{3}] / (1.20)

^{3}}{{[$2.25 x (1.25)

^{3}x (1.15)

^{1}]/ (0.20 - 0.15)}/ (1.20)

^{3}} which can be deduced to the following: {V = [$2.34375 + $2.441406 + $2.543132 + $58.492025] = $65.82}

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**User Contributed Comments**
19

User |
Comment |
---|---|

dealsoutlook |
long question and pretty hard as well |

mulira |
try this PCS= Div1/1+0.2+Div2/(1.02)^2+div3/(1.02)^3 +div4+ PCS4/(1.02)^4. Where PCS4 = Div5/rce-g grow div 1,2,3 by 25% and div4 by 15%. |

jackwez |
D1!!! everytime!!! D1!!! |

StanleyMo |
i was thinking should the after year 3 aka year 4 divide by (1.2)^4 rather than 3. |

cwa4 |
StanleyMo, I thought the same and missed the q. On pg. 133 footnote b of reading 56 it describes why this year is used. In this case the third year is used because the valuation of the remaining stream is made at the end of the third year to reflect the dividend in year 4 and all future dividends. |

tommyguard3 |
how are we supposed to remember this? anyone have any tricks? |

tommyguard3 |
Only thing I found still isn't great V = DoGs Nose over Kats Nose & DoGs Need of Goons over Kats without Goon over Kats Nose -> V=(D x (1+gs)^n)/(1+k)^n)...+ (D x (1+gs)^n x (1+gn)/(k-g))/(1+k)^n |

mary11 |
sigh... that is harder then the formula. |

moneyguy |
Goon dogs cats birds fig tree driveway cats goon nose orange juice kitchen floor dogs cats solve for dog |

mjwoulf |
90 seconds...come on! |

SKIA |
nice one, moneyguy |

jjhigdon |
Yea, the time is the most challenging part of this one. Easy and basic concept, but I made a math error somewhere trying to do it quickly... |

kaulin |
Find your dividends: D1:2.8125 D2:3.515625 D3:4.3945 D4:5.05371 Discount D4 to get price@T=3...5.05371/.2-.15 put into cash flow in calculator, use k (.2) as irr and solve for NPV CF0:0 CF1:2.8125 CF2:3.515625 CF3:4.3945+101.074=105.46875 |

asalonga7 |
questions like these are the ones i would hope to get part marks for while in school - sometimes multiple choice sucks |

praj24 |
Kaulin you LEGEND! |

thebkr7 |
@Kaulin YOU SAVED THE DAY!!! |

merc5559 |
@Kaulin!!! |

Cain621 |
Thank you Kaulin |

atlootah |
@Kaulin ur a G |