# Question: Companies vary greatly in size This variation can hide how

Companies vary greatly in size. This variation can hide how well a company is performing. A retailer, for instance, reports \$500 million in profits for the past year. That would be a good year for Foot Locker stores, but not for Wal-Mart whose profit was \$16 billion in 2010. Rather than look at the raw profit numbers, analysts consider financial ratios that adjust for the size of the company.
A popular ratio is the return on assets, defined as
Return on Assets = Net Income/Total Assets
Net income is another name for profits, and the total assets of a company is the value of everything it owns that is used to produce profits. The return on assets indicates how much profit the company generates relative to the amount that it invested to make that profit. It’s a bit like interest on a savings account. Five percent interest means that you make \$5 for every \$100 saved. Similarly, if the return on assets is 0.05, then the company profits \$5 for each dollar of assets it owns. A company with losses rather than profits has a negative return on assets.
The data table for this exercise gives the total assets and net income reported by 179 retailers in the United States.
Motivation
(a) Why would it be helpful to describe management’s performance using return on assets rather than both net income and total assets?
(b) What are the units of the return on assets?
(c) Describe how a firm might use the return on assets as a yardstick for the performance of its management.
(d) Are there other ratios that might serve a similar purpose, or is this the only ratio that will be useful?
Method
(e) What plots will be useful for summarizing the distribution of return on assets and for showing if this distribution is bell-shaped?
(f) Why is it useful to have a bell-shaped distribution for the return on assets rather than one that is very skewed?
Mechanics
(g) Describe histograms of the variables Net Income and Total Assets. Are these skewed or bell shaped?
(h) Identify any exceptional outliers in these two distributions.
(i) Produce a histogram and boxplot for the return on assets. Describe the shape of this distribution.
(j) Is the company that is the major outlier on total assets also an outlier in terms of return on assets? Explain.
Message
(k) Summarize the distribution of the return on assets for these retailers.
(l) On the basis of the distribution of the return on assets, would a return on assets larger than 0.1 (10%) indicate that a retailer is having a good year in 2010?

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