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