(Solving a comprehensive problem) Use the end-of-year stock price data in the popup window, to answer the following questions for the Harris and Pinwheel companies.

a. Compute the annual rates of return for each time period and for both firms.

b. Calculate both the arithmetic and the geometric mean rates of return for the entire three-year period using your annual rates of return from part

a.

(Note: you may assume that neither firm pays any dividends.)

c. Compute a three-year rate of return spanning the entire period (i.e., using the ending price for period 1 and ending price for period 4).

d. Since the rate of return calculated in part c is a three-year rate of return, convert it to an annual rate of return by using the following equation:

1+

Three-Year

Rate of Return

=1+

Annual Rate

of Return

3

e. How is the annual rate of return calculated in part d related to the geometric rate of return? When you are evaluating the performance of an investment that has been held for several years, what type of average rate of return (arithmetic or geometric) should you use? Why?

Question content area bottom

Part 1

a. Enter the annual rate of return for each year for Harris in the table below.(Round to two decimal places.)

Part 2

Enter the annual rate of return for each year for Pinwheel in the table below.(Round to two decimal places.)

Time	Value of Harris Stock		Annual Rate of Return		Value of Pinwheel Stock		Annual Rate of Return
1	$9				$22
2	8		11.11	%	33		enter your response here	%
3	14		75.00	%	28		enter your response here	%
4	15		7.14	%	27		enter your response here	%

Part 3

b. The arithmetic average rate of return earned by investing in Harris stock over this period is

enter your response here%.

(Round to two decimal places.)

Part 4

The arithmetic average rate of return earned by investing in Pinwheel stock over this period is

enter your response here%.

(Round to two decimal places.)

Part 5

The geometric average rate of return earned by investing in Harris stock over this period is

enter your response here%.

(Round to two decimal places.)

Part 6

The geometric average rate of return earned by investing in Pinwheel stock over this period is

enter your response here%.

(Round to two decimal places.)

Part 7

c. The three-year rate of return spanning the entire period for Harris is

enter your response here%.

(Round to two decimal places.)

Part 8

The three-year rate of return spanning the entire period for Pinwheel is

enter your response here%.

(Round to two decimal places.)

Part 9

d. The annual rate of return converted from the three-year rate in part c for Harris is

enter your response here%.

(Round to two decimal places.)

Part 10

The annual rate of return converted from the three-year rate in part c for Pinwheel is

enter your response here%.

(Round to two decimal places.)

Part 11

e. How is the annual rate of return calculated in part d related to the geometric rate of return?(Select the best choice below.)

A.

The annual rate of return calculated in part d is nothing but the geometric average rate of return calculated in a different way.

B.

The annual rate of return calculated in part d is nothing but the arithmetic average rate of return calculated in a different way.

C.

The annual rate of return calculated in part d is the same as the geometric rate of return in this problem but this is only a coincidence.

D.

The annual rate of return calculated in part d is not related to the geometric average rate of return.

Part 12

When you are evaluating the performance of an investment that has been held for several years, what type of average rate of return (arithmetic or geometric) should you use? Why?(Select the best choice below.)

A.

Geometric average return better describes the average annual rate of return over a period because it is a simple average, so it answers the question concerning the expected rate of return over a period.

B.

The geometric rate of return should be used. It better describes the average annual rate of return over a period because it compounds at the same rate while the arithmetic rate of return is best used for a single period.

C.

The arithmetic rate of return should be used. It better describes the average annual rate of return over a period because it compounds at the same rate while the geometric rate of return is best used for a single period.

D.

Arithmetic average return better describes the average annual rate of return over a period because it is a simple average, so it answers the question concerning the expected rate of return over a period.