- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 2. Time Value of Money in Finance
- Subject 3. Equity Instruments and the Time Value of Money

###
**CFA Practice Question**

Young Company does not currently pay any dividends. An analyst forecasts that Young Company will pay its first dividend of $0.50 per share at the end of year 5 and that the dividend payout will grow at the rate of 12% per year in perpetuity. If the required rate of return on Young company stock is 13%, the current value of its stock would be closest to ______.

A. $27.14

B. $30.67

C. $50.00

**Explanation:**The infinite-period DDM would give the price at the end of year 4:

E(P

_{4}) = E(D

_{5}) / (k - g) = $0.50 / (0.13 - 0.12) = $50.00.

The value today would be P

_{0}= E(P

_{4}) / (1+k)

^{4}= $50.00 / (1.13)

^{4}= $30.67.

###
**User Contributed Comments**
18

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

Carol1 |
remember use 4 years discount to calculate PV |

aroman21 |
why use 4 and not 5? |

anju |
the given first dividend is at end of year 5, but we can compute share value at end of year 4 only as we need next year dividend (D1). This is the reason for discounting to pv based on 4 year time frame. |

Nathan |
It says right there that this cash flow is 5 years in the future. If this dividend were paid at the beginning of year 5 then of coursee I would use 4 years. Can someone point to a reliable source? |

sevaa1 |
Right, the CF is at year 5. In this case our CF is D5. But the formula says that we use D5, we get P4 - by definition. |

CoffeeGirl |
0.5 is D5. P4 = 50 P1 = 50 / (1.13^4) = 30.67 |

dimanyc |
"Right, the CF is at year 5. In this case our CF is D5" Not right. CF is at end of year 5, so 50 is actually P at beginning of 5. I think we need to discount 5 times to get back to the time now. |

heinzlive |
Source: Reading 46 5.2. page 316: It sounds a little bit confusing but paying dividend in 5 years from now means that it is the next years dividend (D5 = D4 * (1+g))Then computing the TV of D4 * (1+g) = 0,50/(0,13-0,12), then discounting 4 periods back to t=0 with 1/(1 + 0,13)^4 |

scottharris |
Gordon growth model: value this year = next years dividend / (r -g) So if dividends start in 5 years the value calculated by GGM is in 4 years, and is therefore discounted back 4 years. |

aggabad |
The question is: If currently we are at the end of the year then all the calculations make sense but what if we are at the beginning of the year now? Is the answer going to be the same? |

olagbami |
I think from the stand point of the question, the current time is end of year one. |

yxten1 |
the number of years is a classical trap. yet i fell for it. sigh... |

Cesarnew |
this Q asks about PV of payments 5 years from now. So, IMO, we should calculate the terminal value in year 5: 0,5*1.12/(0.13-0.12). Add 0,5 div, as we are going to receive it as well and discount (terminal+0,5) using 5 periods. I came to B this way. |

Tony1234 |
don't worry yxten1. it got me too. better now than on the exam though. |

Paulvw |
Got me too. D'oh! |

Nakata |
Why do we not add the dividend in time 5? |

birdperson |
look at CoffeeGirl's answer - it is spot on. |

bruno5104 |
Using in time 5 gives me 30.39. Using in time 4 gives me the answer... oh God |