The price to earnings ratio of the pharmaceutical industry on a stock

Let P = 10 & Q = 15 (Pharmaceutical company price to earnings ratio)

Percentage increase = (5/10)*100 = 50% = Z

Let A = 12 & Q = 15 (company X price to earnings ratio)

Percentage increase = 3*100/12 = 25% = Y

The percentage increase in the price to earnings ratio of company X (Y) less than that of the pharmaceutical industry (Z)
= Y*100/Z = 25*100/50 = 50%..

Putting values in options
A) (aq-pb)*100/a(q-p)
=> (12*15-10*15)*100/12(15-10)
=> (180-150)*100/12*5
=> 30*100/60
=> 50 (Matcing)

B) (bq-ap)*100/b(q-p)
=> (15*15-12*10)*100/12(15-10)
=> (225-120)*100/12*5
=> 105*100/60
=> 175 (Not Matcing)

C) (bq-ap)*100/b(p-q)
=> (15*15-12*10)*100/12(15-10)
=> (225-120)*100/12*5
=> 105*100/-60
=> -175 (Not Matcing)

D) (aq-pb)*100/a(p-q)
=> (12*15-10*15)*100/12(10-15)
=> (180-150)*100/12*-5
=> 30*100/-60
=> -50 (Not Matcing)

IMO A

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IMO C

Pharmaceutical Industry :
P/E (Start 2014) = p ; P/E (End 2014)= q
% change Y= (q-p)/p *100

Company X :
E/P (Start 2014) = a ; E/P (End 2014)= b
P/E (Start 2014) = 1/a ; P/E (End 2014)=1/ b
% change X= (1/b - 1/a)/1/a *100 = (a-b)/b *100

Req % = (X-Y)/Y * 100
X-Y = (a-b)/b *100 - (q-p)/p *100 = (ap- qb)/bp
(X-Y)/Y = (ap- qb)/bp*(q-p)/p = (ap- qb)/b(q-p)

(X-Y)/Y*100 = (qb-ap)/b(p-q) *100
Ans . C

Ans E

Percentage increase in price to Earning for X=

(1/a-1/b)/ 1/a........<1>

Percent increase in pharmaceutical =
(q-p)/p..........,,,,,,,....<2>

The difference in percentage = 1-2

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IMO E.

I took values as

P...................... Q
100...................150.

Percentage increase = 50.


Next if earning : price = a........b

Then price : earning ratio increase from
1/a ...... To...... 1/b

Let 1/a = 5 and 1/b = 6.

Percentage increase = 100/5 = 20.

The question then becomes by what percentage is 20 less than 50.

= 150 percent.

Edit: I did a mistake in calculation here. It should be (50-20)/50 = 60%
So i need tp find option which gives 60 and putting the values pf a,b,p,q.
Silly of me

So we need to plug values of a, b, p, q and answer must be 150.

None satisfy.

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parma:
p begin of 2014
q end of 2014
increase in value= q-p
percentage increase=(q-p)/p

company X:
a begin of 2014
b end of 2014
increase in value=b-a
percentage increase=(b-a)/a

so,
[(q-p)/p - (b-a)/a]/(q-p)/p
on solving, we get
(aq-pb)*100/a(q-p)
Ans A

Where can you make a mistake..
Not taking proper base for % calculations.
Reading a and as ;price to earnings ratio' instead of 'earnings to price ratio'.


% increase = \(\frac{q-p}{p}*100\)



So E to P is a and b, and P tp E will be 1/a and 1/b
% increase = \(\frac{(\frac{1}{b})-(\frac{1}{a})}{(\frac{1}{a})}*100=\frac{\frac{a-b}{ab}}{\frac{1}{a}}*100=\frac{a-b}{b}*100\)


% decrease = \(\frac{\frac{q-p}{p}*100-\frac{a-b}{b}*100}{\frac{q-p}{p}*100}*100=\frac{\frac{b(q-p)-p(a-b)}{pb}}{\frac{q-p}{p}}=\frac{bq-bp-ap+bp}{b(q-p)}=\frac{bq-ap}{b(q-p)}\)

B

The price to earnings ratio of the pharmaceutical industry on a stock exchange was p at the beginning of the year 2014 and q at the end of the year 2014. Company X, which was a pharmaceutical company had its earnings to price ratio equal to a at the beginning of the year 2014 and b at the end of the year 2014. By what percentage was the percentage increase in the price to earnings ratio of company X less than that of the pharmaceutical industry?


Let us take values for all the variables
a=2, b=1, p=3 and q=9


% increase = \(\frac{q-p}{p}*100=\frac{9-3}{3}*100=200%\)



So E to P is a and b, and P to E will be 1/a and 1/b
% increase = \(\frac{(\frac{1}{1})-(\frac{1}{2})}{(\frac{1}{2})}*100=100%\)


% decrease = \(\frac{200-100}{200}*100=50%\)

Let us test the choices now..

A. \(\frac{aq - pb}{a(q - p)}*100=\frac{2*9-1*3}{2(9-3)}*100=125%\)

B. \(\frac{bq - ap}{b(q - p)}*100=\frac{1*9-2*3}{1(9-3)}*100=50%\)...YES

C. \(\frac{bq - ap}{b(p - q)}*100=\frac{1*9-2*3}{1(3-9)}*100=-50%\)

D. \(\frac{aq - pb}{a(p - q)}*100=\frac{2*9-1*3}{2(3-9)}*100=5-125%\)

E. None of the above

B

The price to earnings ratio of the pharmaceutical industry on a stock exchange was p at the beginning of the year 2014 and q at the end of the year 2014. Company X, which was a pharmaceutical company had its earnings to price ratio equal to a at the beginning of the year 2014 and b at the end of the year 2014. By what percentage was the percentage increase in the price to earnings ratio of company X less than that of the pharmaceutical industry?


---------------------------------2014 Start --------------------------------------2014 end

Indusry Price/Earnings-----------p-----------------------------------------------q-------

Company Price/Earnings---------1/a--------------------------------------------1/b-------

% change in industry = \( \frac{ ((q-p) * 100)}{ p }\)

% change in industry = ((1/b)-(1/a)) * 100)/ (1/a) =\( \frac{((a-b) * 100)}{ b }\)

so change percentage in the percentage increase in the price to earnings ratio of company X less than that of the pharmaceutical industry


= { \( \frac{ ((q-p) * 100)}{ p }\) - \( \frac{((a-b) * 100)}{ b }\) } / { \( \frac{((q-p) * 100)}{ p }\) }

= \(\frac{(bq - pa ) }{ b (q-p)}\)

Hence B may be the correct choice .

The price to earnings ratio of the pharmaceutical industry on a stock exchange was p at the beginning of the year 2014 and q at the end of the year 2014. Company X, which was a pharmaceutical company had its earnings to price ratio equal to a at the beginning of the year 2014 and b at the end of the year 2014. By what percentage was the percentage increase in the price to earnings ratio of company X less than that of the pharmaceutical industry?

The price to earning : (pharmaceutical industry)
--> At the beginning of the year 2014 - p
--> At the end of the year 2014 - q

the percentage increase ...of the pharmaceutical industry= \(\frac{100(q - p)}{p }\)

The price to earning : (Company X)
--> At the beginning of the year 2014 - \(\frac{1}{a}\)
--> At the end of the year 2014 - \(\frac{1}{b}\)

the percentage increase ...of company X = \( \frac{(\frac{1}{b}-\frac{1}{a})}{\frac{1}{a}} 100= \frac{100(a - b)}{b}\)

Since the question stem tells us that the percentage increase ...of the pharmaceutical industry is greater than that of the company X,

\(\frac{\frac{100(q - p)}{p} -\frac{100(a - b)}{b}}{\frac{100(q - p)}{p}}*100= \frac{\frac{(bq -bp- ap+bp)}{bp}}{\frac{(q - p)}{p}}*100= \frac{(bq- ap)}{b(q - p)}*100\)

Answer (B)

does values decreases in earning to price ratio? as you took value of b ( at the end of year 2014) less than that of A? or is it because of reversed no. kindly explain the concept of earnings to price and price to earnings ratio.
thankyou

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