Q:

Which of the following statements are true with respect to price-earnings (P/E) multiples?
I. During a recession, P/E multiples will generally increase.
II. As the growth prospects of a company increases, holding everything else constant, its P/E will also rise.
III. As the required rate of return expected from a company decreases, holding everything else constant, its P/E will also decrease.
IV. During a period of decreasing interest rates, P/E ratios will generally decrease, holding everything else constant.

A) I and IV only
B) I and II only
C) II, III and IV only
D) II and IV only

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A:

The reason choice I is true is because during a recession, corporate earnings will generally fall faster than their respective stock prices. Remember, the price of a stock is supposed to reflect all future cash flows. The earnings (which is the denominator) would only be reflective of the current recessionary environment. We can see how P/E multiples are affected by looking at the following:
First, we know that

 P0 = D1 (k - g)

To calculate P/E, simply divide both sides by Earnings (E):

 P0 Â  = D1/E E (k - g)

Where: k is the required rate of return, and
Â Â Â Â Â Â Â Â Â Â  g is the growth rate in earnings and dividends.
Therefore, II is correct because as "g" increases, the denominator will get smaller and the whole term gets bigger. III is incorrect because when "k" drops, the denominator will get smaller and thus the whole term will get bigger. IV is incorrect because as interest rates decrease, investors will generally reduce their required rate of return. As we have seen, this will boost the P/E ratio.

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