Question

a)

Assume you purchased a share of stock for $80 on January 1, 2008 and sold the share of stock for $30 on December 31, 2012. If the stock paid no dividends what your average yearly growth rate?

(not -21.8 or -21.75)

b)

Assume you purchase a stock which grows at 10% the first year, 5% the second year and lost 2% the third year. What is your average annual growth rate?

(not 4.33 or 5.67)

c)

Assume you purchased a stock for $100 today and it went up by 90% in the first year and dropped by 50% the second year. Assume no dividends. What is your average annual growth rate?

(not -2.469 or -2.5)

Answer 1

a)

1st Jan 2008 to 31st Dec 2012 is 5yrs therefore n is 5

Beginning stock price is $80; Ending value given as $30

Average yearly growth rate = ((Ending value/ beginning value)^(1/n)) - 1

((30/80)^(1/5)) - 1

0.821875914 - 1

-0.17812409 or -17.81%

Answer: Average yearly growth rate is -17.81%

b)

Here each year's rate of return is given

The stock which grows at 10% in the first year, 10% can be written in the decimal form as 0.10, therefore the growth is (1+ 0.10) = 1.10

Similarly, 5% the second year will be 1.05 and lost 2% the third year since it is a loss, it will be represented with a subtraction (1-0.02) = 0.98

Average yearly growth rate = (Year 1 return * Year 2 return * Year 3 return) - 1

Average yearly growth rate = (1.10 * 1.05 * 0.98) - 1

Average yearly growth rate = 1.1319 - 1

Average yearly growth rate = 13.19%

Answer: Average yearly growth rate is 13.19%

c)

Here though the beginning dollar value is provided, each year's rate of return is also given

The stock which grows at 90% in the first year, 90% can be written in the decimal form as 0.90, therefore the growth is (1+ 0.90) = 1.90

50% drop in the second year will be will be represented with a subtraction (1-0.50) = 0.50

Average yearly growth rate = (Year 1 return * Year 2 return) - 1

Average yearly growth rate = (1.90 * 0.50) - 1

Average yearly growth rate = 0.95 - 1

Average yearly growth rate = -0.05 or -5%

Answer: Average yearly growth rate is -5%