Earnings per Share The earnings per share for Big Lots, Inc. were 1.89 in 2008 and 2.83 in 201

Earnings per Share The earnings per share for Big Lots, Inc....

Key Concepts

Midpoint Formula

The midpoint formula is a specific case of linear interpolation that finds the middle value between two data points by averaging them. When the unknown value lies exactly in the middle of the two known values, the midpoint formula directly provides the estimate. This formula is particularly useful in scenarios where data is evenly spaced, as it simplifies the estimation process by taking the simple average of the endpoints.

Linear Interpolation

Linear interpolation is a mathematical method for estimating an unknown value that falls between two known values on a straight line. Assuming a linear pattern between the data points, it calculates the estimated value by taking a proportionate distance between the known values. This method is useful for filling in missing data in a dataset or making predictions when the change is assumed to be uniform.

Earnings Per Share (EPS)

Earnings per share is a financial metric that represents the portion of a company’s profit allocated to each outstanding share of common stock. It is frequently used as an indicator of a company's profitability and financial health by showing how much money a company makes for each share of its stock, allowing investors to assess the company's financial performance on a per-share basis.

Linear Patterns

A linear pattern in data indicates that the change between values occurs at a constant rate. When values display a linear pattern, the relationship between variables can be described using a straight line, which simplifies the process of predicting intermediate values or making future forecasts based on known data points.

Transcript

00:04 In this exercise, we are asked to find the earnings per share for a company in a certain time.

00:13 So we're told the earnings per share for this company was $1 .89 per share in 2008 and $2 .83 in 2010, and assuming that the earnings per share followed a linear pattern between these two dollars.

00:38 Two times.

00:40 We're asked to use the midpoint formula to estimate the earnings per share in 2009.

00:47 So first, i'm going to plot these two data points we have, and then i'm going to use this plot to estimate what the earnings per share might be, and then i'll use the midpoint formula to get a better estimate for the earnings per share in 2009.

01:13 So we have two data points.

01:16 Here.

01:20 Let's say the x components are time and the y component is earnings per share.

01:29 Then we have 2008, the year 2008, and then $1 .89 or $1 .89 for the earnings per share, as well as 2010, we had an earnings per share of $2 .83.

01:51 And so notice that our x components are much larger than zero.

01:55 Our y components are both positive, and so i'm only going to draw a portion of the first quadrant.

02:02 To do this, i'll draw the right side of the x axis, but i'll make a crucial adjustment.

02:11 I'm going to draw our origin, and then i'll draw a jagged line, indicating that a bunch of values were skipped, and then the point 2008, all the way up to the point 2010.

02:24 Of course, in between these, since we're just dealing with whole number years, we have 2009.

02:36 Now on our y -axis, we're going to range from zero up to, let's say, three.

02:45 We'll divide this into thirds.

02:48 So our first point, 2008, 1 .83, lies about here.

02:55 So 1 .83 is a little bit less than 1 .8, 2.

02:58 And then 2010 2 .83 lies about here.

03:06 2 .83 is a little bit less than 3...

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