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# Last year the price per share of Stock X increased by k

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Last year the price per share of Stock X increased by k [#permalink]  02 Jan 2006, 20:07
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Last year the price per share of Stock X increased by k percent and the earnings per share of Stock X increased by m percent, where k is greater than m. By what percent did the ratio of price per share to earnings per share increase, in terms of k and m?
A. k/m %
B. (k-m) %
C. [100(k-m)]/(100+k) %
D. [100(k-m)]/(100+m) %
E. [100(k-m)]/(100+k+m) %

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JAI HIND!

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My answer is coming to D. If this is correct I will send the working
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Tony Chandra

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Jai Hind ,

This took me some time mostly to figure out to cancell terms. If there is a better way let me know

From a business perspective they are asking for the increase in P/E ratio.(price to earning ratio or PPS/EPS). Eventhough this does not have a bearing on the problem it will BE good to know what is the purpose of the question.

So = Original Share price
Sn = New share price

Eo = Original EPS
En = New EPS

We are asked to determine the following i.e the increase % in PE Ratio which can be expressed as

Sn/En â€“ So/Eo divided by So/Eo multiplied by 100 to get the increase % â€¦. (A)

Let us build the relationship with K and M

Sn-So/So * 100 = K or

Sn = KSo + 100 So/100 â€¦â€¦. (B)

Similarly

En-Eo/ Eo *100 = M

En = MEo + 100 Eo/100 â€¦â€¦â€¦.(C)

Let us calculate Sn/En first and then substitute in (A)

Sn/En = KSo+ 100So/MEo + 100Eo

For clarity let us calculate the expression

Sn/En â€“ So/Eo =

KSo+ 100So/MEo + 100Eo - So/Eo =

KSo + 100So â€“ Mso â€“ 100So/ MEo+100Eo =

KSo â€“ Mso/MEo + 100Eo = So(K-M)/Eo(M+100)

Continuing further in (A) we get
So(K-M)/Eo(M+100) * Eo/So *100 =

Cancelling Eo and So we are left with the following expression

100(K-M)/M+100 which is D
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Tony Chandra

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In my view, not introducing more variables helps. I took share price to be equal to one and as it asks for ratio. No matter what the share price is it will cancel out anyways. so here is how I did it.

share price after k% increase in share price = (K/100 + 1) * share price and earnings per share by m% increase in share price is (m/100 + 1 ) * Share price

The ratio of increase in price to increase in earning is (k/100 + 1) / (m/100 + 1) = ( K +100 ) / (m + 100)

so finally the increase in ratio, ( [(k+100) / (m+100)] - 1 ) * 100 (to convert to percentage). which yields D as the correct answer.
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D it is

Initial price /Earning ratio =100/100 (Lets say)
New Price /Earning ration = (100+k)/(100+m)
Increase=(100+k)/(100+m)-1 = (k-m)/(100+m)
Increase %= 100(k-m)/(100+m)
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old price ----- p New price P(1 +(k/100))
old earning----e New earning e(1 + (m/100))

old pe = p/e say = T
new pe = T((100+K)/(100+m))

change in pe % = ((new pe -old pe) /old pe) * 100

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