### CFA Practice Question

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

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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