A good indicator of the value of a company is the ratio of the price of its stock to its yearly earnings expressed as dividends. This ratio is called the Price to Earnings or P/E ratio. If the price of a stock is $36 and it's earnings are $3.00, by how many cents must the earnings decrease in order that the P/E ratio increases by 20%?

Question

Delaney Weber

Mathematics

30 September, 10:17

A good indicator of the value of a company is the ratio of the price of its stock to its yearly earnings expressed as dividends. This ratio is called the Price to Earnings or P/E ratio. If the price of a stock is $36 and it's earnings are $3.00, by how many cents must the earnings decrease in order that the P/E ratio increases by 20%?

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Davis Munoz · Answer 1

4.92 cents

Step-by-step explanation:

The Price to Earnings or P/E is the ratio of the price of its stock to its yearly earnings expressed as dividends.

The price of a stock is $36 and it's earnings are $3.00

This means the price to earnings ratio,

P/E = 36/3 = 6

Let us express this ratio as percentage. This becomes

36/3 * 100 = 1200%

This means the ratio of price to earnings = 1200%

For an increase of 20%, the ratio of price to earnings will be = 1200 + 20 = 1220%.

Let x be the the value of earnings that would increase the ratio by 20%

36/3 * 100 = 1200%

36/x * 100 = 1220℅

3600/x = 1220

x = 3600/1220 = $2.9508

The amount by which the earnings must decrease in order that the P/E ratio increases by 20% will be

$3 - $2.9508 = $0.0492.

Converting to cents, we multiply by 100. It becomes

0.0492*100 = 4.92 cents