###
**CFA Practice Question**

The forward P/E ratio of a stock equals 7.1. The company has just released its earnings figures at $12.20 per share. The firm's dividend payout ratio is 28%. If the current stock price is $100, what is its 1-year expected return under the dividend discount model?

A. 19.40%

B. 14.83%

C. neither of these answers

**Explanation:**It is important to remember that the forward P/E ratio is the ratio of the current stock price and next year's expected earnings. The firm's expected earnings next year equal 100/7.1 = $14.09 per share. Since the current earnings equal $12.2, the dividend growth rate equals (14.09/12.2 - 1) = 15.45%. To get the 1-year expected return, first calculate the expected price next year. Under the dividend discount model, the P/E ratio remains constant if the firm makes no policy changes and there are no market disruptions. Therefore, the price next year is expected to be $100*(1 + 15.45%) = $115.45. The dividend next year equals $14.09 * 0.28 = $3.95 per share. Thus, the 1-year expected return (capital gains + dividends) = (P

_{1}+D

_{1})/P

_{0}= (115.45 + 3.95)/100 - 1 = 19.4%.

###
**User Contributed Comments**
14

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

shasha |
growth rate "g" is for both dividend growth and price growth. so P1 = P0*(1+g) = 100*1.1545 |

derekt |
If the P/E ratio is the historical P/E one the growth could be estimated from the information given and used to find next years EPS. |

danlan |
E=100/7.1, g=E/12.2-1, The result is (100*(1+g)+E*0.28)/100-1 =g+E*0.28/100=g+0.28/7.1 |

jerepast |
where does this come from? [dividend growth rate = (NI(n+1)/NI(n) - 1)] |

ontrack |
Try this method: Po/E1=(D1/E1)/k-g Po/E1 is 7.1, g=15.45% as per the soultion given, D1/E1 is .28(also given in Qs). Put in values to get k=19.33%=expected discount rate or returns expected . |

steved333 |
7.1x12.20=86.62 .28x12.20=3.416 100-86.62=13.38 (13.38+3.416)/86.62= .1939 Not hard if you use the STO and RCL buttons on the BAII. |

steved333 |
Just figure out the original price then use the HPY formula of (FV-PV+Div)/PV. |

surob |
looks like it is not that difficult question |

Hervz |
You always have to keep in mind that the dividends are growing at the same pace as the earnings (RR stays th same). - for the purpose of the test, anyway |

serboc |
HERVZ: So your telling me that you can take g (if given) X Eo = E1? |

mekc |
thx ontrack... like that method |

SaeedAlam |
Thanks Steve that really helped it matches with the notes on price multiples! |

dipu617 |
@steved333 Could you please tell us how to use STO and RCL buttons on BA II Plus for this problem? Thank you. |

santibanez |
PER=PayOut/(r-g) Obtain g by estimating E1 first r=(PayOut/PER)+g r=(.28/7.1)+.15447 r=.1938 |