Question

The price-earnings ratio (P/E ratio) is a commonly used measure of how overpriced or underpriced a company's stock is. There are a number of different statistics about a company's stock. One of these statistics is a measure of future growth. To examine the relationship between P/E and the measure of future growth (FG), you run a simple regression and get the equation: P/E = 3 + 0.9FG. The R^2 for this model is 18% and the standard error is 5. Another model was run using a measure of dividends (D) to explain the P/E. This gives the equation: P/E = 1.6 + 13.2D. a) Give a managerial interpretation for the coefficients 3 and 0.9. b) A particular company has a value of 15 on the measure of future growth. Its P/E ratio is 4.5. What would you conclude about the company's P/E? Briefly explain. c) Since 13.2 is greater than 0.9, can you conclude that the P/E ratio has a stronger relationship to dividends than future growth? If not, what would you need to know to conclude which variable has a stronger relationship to the P/E ratio? Briefly explain.

          The price-earnings ratio (P/E ratio) is a commonly used measure of how overpriced or underpriced a company's stock is. There are a number of different statistics about a company's stock. One of these statistics is a measure of future growth. To examine the relationship between P/E and the measure of future growth (FG), you run a simple regression and get the equation:

P/E = 3 + 0.9FG.

The R^2 for this model is 18% and the standard error is 5. Another model was run using a measure of dividends (D) to explain the P/E. This gives the equation:

P/E = 1.6 + 13.2D.

a) Give a managerial interpretation for the coefficients 3 and 0.9.
b) A particular company has a value of 15 on the measure of future growth. Its P/E ratio is 4.5. What would you conclude about the company's P/E? Briefly explain.
c) Since 13.2 is greater than 0.9, can you conclude that the P/E ratio has a stronger relationship to dividends than future growth? If not, what would you need to know to conclude which variable has a stronger relationship to the P/E ratio? Briefly explain.

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Added by Michael R.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Jon Southam

10/08/2022

Step 1

9 in the equation P/E = 3 + 0.9FG. The coefficient 3 represents the intercept, which is the P/E ratio when the measure of future growth (FG) is zero. The coefficient 0.9 represents the slope, indicating that for every unit increase in future growth, the P/E ratio Show more…

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The price-earnings ratio (P/E ratio) is a commonly used measure of how overpriced or underpriced a company's stock is. There are a number of different statistics about a company's stock. One of these statistics is a measure of future growth. To examine the relationship between P/E and the measure of future growth (FG), you run a simple regression and get the equation: P/E = 3 + 0.9FG. The R^2 for this model is 18% and the standard error is 5. Another model was run using a measure of dividends (D) to explain the P/E. This gives the equation: P/E = 1.6 + 13.2D. a) Give a managerial interpretation for the coefficients 3 and 0.9. b) A particular company has a value of 15 on the measure of future growth. Its P/E ratio is 4.5. What would you conclude about the company's P/E? Briefly explain. c) Since 13.2 is greater than 0.9, can you conclude that the P/E ratio has a stronger relationship to dividends than future growth? If not, what would you need to know to conclude which variable has a stronger relationship to the P/E ratio? Briefly explain.

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Transcript

00:01 Right, so we're kind of price to earnings ratios, and we have someone who made some equations, linear regression, the models, i should say, for price to earnings based on future growth and dividends.

00:14 And based on the future growth, we want to interpret 3 and 9, or it's actually 0 .9.

00:22 Let's fix that.

00:23 0 .9.

00:25 So the way we interpret this, it's our good friend, it's our good linear equation, y equals, and that.

00:33 Plus b but statistics we usually write it as a plus b x if it's a linear equation you might even see it as beta not plus beta 1x something like that either way it's the same thing your slope is is the coefficient on the x and the constant is your intercept so it's just kind of picture of that so here's a graph intercept will be here whatever that number is zero comma in this case three and this is interpreting that three here.

01:10 This is the, when there's no future growth, no units of future growth, the price for earnings ratio is three.

01:15 That's how we interpret that.

01:17 And the point nine, let's graph something here.

01:21 So here's a general line.

01:25 You go here and make this big.

01:29 So here's delta x, delta y.

01:33 Because slope is, that's what slope is.

01:36 Change in y, no, change in x.

01:42 So when delta x is 1, delta y is whatever this number is.

01:47 In this case, it's 0 .9.

01:48 And so what it means is for every one unit increase of future growth, the price or earnings ratio will go up by 0 .9.

01:58 All right, so is that.

02:05 So there are our interpretations.

02:07 And now we're given that a particular company has a value of 15 on the measures of future growth.

02:12 So let's make a prediction of that.

02:14 Price to earnings is 3 plus 0 .9 times 15, which equals 16 .5.

02:26 And then, but we're told that its ratio, is the actual ratio is it's 4 .5.

02:32 So we use the standard error and see how far away we are from the mean.

02:40 So the actual is 4 .5, minus the expected value, which is 16 .5.

02:47 Divided by the standard error with five.

02:50 This gives us negative 2 .38...

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