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Return

The word return is used in many ways in finance. For a start we might mention cash return, return on capital, and overall return. In these contexts, return will be measured as a percentage of the amount invested. To keep things simple, we shall, in all that follows, refer to yearly return, i.e. the amount earned over the course of a year on some sum invested at the beginning of the year. Imagine that you purchase 1 share of XYZ Corporation for $100. During the year, the corporation pays out dividends totaling $5.00 per share. Your cash return in this case would be 5%, i.e. 5/100. Your return on capital would depend on the price of the stock at the end of the year. If, for example, ...view middle of the document...

The mathematics of return. We may use the following simple formula to calculate the overall return for any asset that we might own, during any year that we own it,

1.

Where = overall return on any asset during the year t

= the price of the asset at the end of the year

= the price of the asset at the beginning of the year

= the cash generated by the asset during the year.

Thus, in the example above, where XYZ is priced at $100 at the beginning of the year, rises to $110 by the end of the year, and pays a dividend of $5, we have,

or 15% 2.

Now consider the same stock, XYZ, with the most recent 10 years of price and dividend data presented in table 1.

TABLE 1

year | Beginning price | Ending price | Dividend | return % |

92 | $50.00 | 55.00 | 2.00 | ? |

93 | 55.00 | 58.00 | 2.00 | |

94 | 58.00 | 65.00 | 2.50 | |

95 | 65.00 | 60.00 | 2.50 | |

96 | 60.00 | 70.00 | 3.00 | |

97 | 70.00 | 75.00 | 3.00 | |

98 | 75.00 | 80.00 | 3.00 | |

99 | 80.00 | 90.00 | 3.50 | |

00 | 90.00 | 100.00 | 4.00 | |

01 | 100.00 | 110.00 | 5.00 | 15.00 |

Before reading further, see if you can calculate the overall return for each of the nine years from 1992 thru the year 2000. Consider, for instance, the year 1998. During that year, the holder of XYZ stock would have reaped $5.00 in capital appreciation and a $3.00 dividend for a total gain of $8.00 against a base (the beginning of year value) of $75.00, resulting in a return of 10.67% (8 divided by 75). You should fill out the rest of the table, and check your answers against those provided in table 3 below.

Before moving on, we mention some of the other contexts in which the word return is used. Consider for instance return on equity (ROE), return on investment (ROI), return on assets (ROA, means the same as ROI), and return on sales. In every case, the return is measured in percentage terms, although, of course, it can be presented in decimal form as well. (Thus 13.24% = .1324). We shall have ample opportunity to consider these concepts in the finance class that follows.

Expected Return

As you may recall from elementary statistics, there are many ways to calculate an average, including the mean, the median, and the mode. The mean (sometimes called the arithmetic mean) is the average that most of us are familiar with, and the one that we shall focus on. A student who has gotten a 55, a 65, and a 90 on the first three exams in a semester probably does not need a calculator to conclude that they are carrying a 70 average into the next exam. Even so, we shall find it useful to...

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