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**CFA Practice Question**

A junior analyst with Smith, Kleen & Beetchnutty is performing an analysis of Microscam Incorporated. Assume the following information:

r (the required rate of return) = 21% per year

EPS = $3.10

D0 = $0.68

g (the expected growth rate of dividends)= 20% per year

r (the required rate of return) = 21% per year

EPS = $3.10

D0 = $0.68

Using this information, what is the P/E ratio for Microscam shares?

A. 24.32

B. 26.32

C. 15.82

**Explanation:**By dividing each side of the infinite period dividend discount equation by the EPS figure, it is possible to determine the P/E ratio. This is illustrated as follows:

P/E = (D1 / EPS)/(r - g)

Where: D1 = the dividend at t1, EPS = the earnings per share calculation for t1

Manipulating the infinite period dividend discount model to solve for the P/E is a rather intuitive process. Consider the fact that an investment's value is truly nothing more than the present value of all future returns. Dividing both sides of the infinite period dividend discount model equation should yield the appropriate multiple, or "earnings multiplier." This is the price-to-earnings ratio. In this example, we are provided all of the necessary information. However, the dividend at t1 must be calculated manually by multiplying D0 by (1 + growth rate). This will yield a figure of $0.816 for D1. Now that D1 has been determined, we can solve for the P/E. Imputing all the given information into the equation provided above will yield the following: P/E = ($0.816 / $3.10) / (21% - 20%) = 26.32.

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**User Contributed Comments**
10

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

dimos |
Any comments about the following approach? Since P=Do(1+g)/k-g=81.6 and EPS=3.1 then we know that P=EPS*(P/E)...P/E=81.6/3.1=26.32 Am I correct? |

eddeb |
that's exactly the same! |

chuong |
this EPS is the current year (EPS0) how the formular D1/EPS0 reflect the payout ration (must be D1/EPS1). We don't know ESP1. |

HoyaPaul |
how do you know to use d1 and not d0? |

nsmwaura |
The formula calls for D1 always |

steved333 |
Thanks, Analyst Notes. This one's a cinch. |

cahiz84 |
How do you know the EPS is from t1 or t0? |

nzdavid |
D1=D0*1.2=0.68*1.2=0.816. P0=D1/k-g=0.816/.01=$81.6. P/E=81.6/3.1=$26.32. |

shoara |
As far as I can understand 3.1 is current EPS and not EPS t+1. If one is trying to calcilate current price and uses D(t+1) by multiplying 0.68*(1+0.20%) then EPS in t+1 shoudl also be 3.1*(1+20%). That thrue me off. |

alles |
How can you assume that dividends will grow and earnings won't (the forward payout ratio will be higher) ? |