# Executives at XYZ Corporation realize that they have too much liquid assets. They want to use...

## Question:

Executives at XYZ Corporation realize that they have too much liquid assets. They want to use this cash to buy a company that has decent returns to maximize their asset utilization. They find two companies they can buy, and want to decide if they should acquire company A or Company B. The expected returns from both companies depending on the state of the economy are shown in the table below. Each state of the economy is equally likely to happen.

State of the economy | Return on company A (%) | Return on company B (%) |

Worse than expected | 7.3% | -4.7% |

Expected | 11.5% | 5.4% |

Better than expected | 16.6% | 24.3% |

Calculate the expected rate of return, and standard deviation of each company.

## Expected Return and Risk

For investment decisions, two evaluation criteria are 1) expected return, and 2) risk. Expected returns can be forecast using a variety of techniques, including scenarios. Risk can be assessed using measures of variability or distribution of expected returns.

## Answer and Explanation:

The expected return and standard deviation of return for each company is given in the table:

Company A | Company B | |
---|---|---|

Expected Return | 11.80% | 8.33% |

Standard Deviation | 3.802 | 12.019 |

The calculation of the expected return is simply the mean (average) of the three values for each company:

- Company A expected return = (7.3% + 11.5% + 16.6%) / 3 = 11.80%
- Company B expected return = (-4.7% + 5.4% + 24.3%) / 3 = 8.33%

The calculation of the standard deviation requires taking the difference of each scenario return from the expected return, squaring those figures (eliminates negative values), taking the average of the squares, and the taking the square root. For Company A:

Scenario | Return | Difference from Expected Return(11.80%) | Squared Value |
---|---|---|---|

Worse | 7.3% | -4.5% | 20.25 |

Average | 11.5% | -0.3% | 0.09 |

Better | 16.6% | 4.8% | 23.04 |

Average of Squared Values | 14.46 | ||

Square Root = Standard Deviation | 3.80 |

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