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masha68 [24]
3 years ago
12

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%?
Mathematics
1 answer:
gulaghasi [49]3 years ago
3 0

Answer:

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

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Answer:

a) (0.5256,0.5944)  

c) Criticism is invalid

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 560

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\hat{p} = 0.56

a) 90% Confidence interval:

\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

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Putting the values, we get:

0.56\pm 1.64(\sqrt{\dfrac{0.56(1-0.56)}{560}}) = 0.56\pm 0.0344\\\\=(0.5256,0.5944)

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