Suppose you buy 100 shares of Abolishing Dividend Corporation at the beginning of year 1 for $80. Abolishing Dividend Corporation pays no dividends. The stock price at the end of year 1 is $100, $120 at the end of year 2, and $150 at the end of year 3. The stock price declines to $100 at the end of year 4, and you sell your 100 shares. For the four years, your geometric average return is

 5.57%

Explanation:

Geometric return =

First year return

=

= 25%

Second year return

=

= 20%

Third year return

=

= 25%

Fourth Year return

=

= 33.3%

Geometric return =

Geometric return =

Geometric return =  

Geometric return = 5.57%

15 pounds of apples and 6 cups of flour

a manufacturer of printed circuit boards uses exponential smoothing with trend to forecast monthly demand of its product. at the end of december, the company wishes to forecast sales for january. the estimate of trend through november has been 200 additional boards sold per month. average sales have been around 1000 units per month. the demand for december was 1100 units. the company uses α = 0.20 and β = 0.10. make a forecast including trend for the month of january.