## Description

**Question:**

The following gives dividend and share price of JBS. Your required to calculate

The Annual Rate of Return

The Expected (Average rate of return)

The Variance

The Standard Deviation of return

YEAR |
Dividend per share |
Closing Share Price |

1 | 2.50 | 12.50 |

2 | 2.50 | 14.50 |

3 | 2.50 | 17.50 |

4 | 3.00 | 16.75 |

5 | 3.00 | 18.45 |

6 | 3.25 | 22.25 |

7 | 3.50 | 23.50 |

8 | 3.50 | 27.75 |

9 | 3.50 | 25.50 |

10 | 3.75 | 27.95 |

11 | 3.75 | 31.30 |

**Answer:**

Here first we, calculate the dividend yield ratio in percentage and it is computed as follows and this can be considered as the annual returns to the investor as dividends have been paid annually.

dividend yield = dividends per share / share price(here closing price)

Using the dividend yield later we calculate the average rate of return. But there is a bit of ambiguity in question in part b where expected return(average return is asked). To calculate the expected return we calculate the CAGR of the dividend yields and then predict the further rate. By the average rate simply we get the average rate of annual returns. So in the following table Dividend yield has been shown and expected dividend yield for the upcoming year has been predicted and also the average rate.

Year | dividend-yield(%) |

1 | 20.00 |

2 | 17.24 |

3 | 14.29 |

4 | 17.91 |

5 | 16.26 |

6 | 14.61 |

7 | 14.89 |

8 | 12.61 |

9 | 13.73 |

10 | 13.42 |

11 | 11.98 |

Now the average rate is average of the above dividend yield = **15.18%**

CAGR = [(11.98/20.00)^(1/12)] – 1. So CAGR = -4.55%

Expected annual return for 12th year = 11.98*(1+(-.0455)) = **11.435%**

For variance we simply apply the formula and taking data from the above table we get the value = **0.00054**

For standard deviation we simply take the non-negative square root of variance **= 0.02323**.

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