Question

Below are the prices on the first and last day of the year for Netflix common stock for several recent years.

Year   First Day   Last Day 2017   124.96   191.96 2016   109.00       123.80 2015   49.15           114.38 2014   52.40            48.80

Netflix paid no dividends over this period. Calculate the return that an investor would have earned in each calendar year. What is the average of these annual​ returns? Next, calculate the average annual growth rate in Netflix stock from the first day of 2014 to the last day of 2017. Compare these two answers.

The rate of return for 2017 is _____​%. ​(Enter as a percentage and round to the nearest whole​ percent.)

The rate of return for 2016 is _____​%.​(Enter as a percentage and round to the nearest whole​ percent.)

The rate of return for 2015 is _____​%. ​(Enter as a percentage and round to the nearest whole​ percent.)

The rate of return for 2014 is _____​%.​(Enter as a percentage and round to the nearest whole​ percent.)

The average of these returns is _____​%.​(Enter as a percentage and round to two decimal​ places.)

The average annual growth rate is _____% ​(Enter as a percentage and round to two decimal​ places.)

Answer 1

1. Year = 2017

Price first day (P₀) = 124.96

Price last day (P₁) = 191.96

Capital Gain yield for the year or Return for the year = (P₁ - P₀) / P₀

Return = (191.96 - 124.96) / 124.96 = 67 / 124.96 = 0.54 or 54%

The rate of return for 2017 is 54%.

2. Year = 2016

Price first day (P₀) = 109

Price last day (P₁) = 123.80

Capital Gain yield for the year or Return for the year = (P₁ - P₀) / P₀

Return = (123.80 - 109) / 109 = 14.80 / 109 = 0.14 or 14%

The rate of return for 2016 is 14%.

3. Year = 2015

Price first day (P₀) = 49.15

Price last day (P₁) = 114.38

Capital Gain yield for the year or Return for the year = (P₁ - P₀) / P₀

Return = (114.38 - 49.15) / 49.15 = 65.23 / 49.15 = 1.33 or 133%

The rate of return for 2015 is 133%.

4. Year = 2014

Price first day (P₀) = 52.40

Price last day (P₁) = 48.80

Capital Gain yield for the year or Return for the year = (P₁ - P₀) / P₀

Return = (48.80 - 52.40) / 52.40 = -3.60 / 52.40 = -0.07 or -7%

The rate of return for 2014 is -7%.

5. Average of these returns = (Sum of the returns) / (Number of years)

Average = (-7 + 133 + 14 + 54) / 4 = 194 / 4 = 48.50%

The average of these returns is 48.50%.

6. Average annual growth rate or Compounded annual growth rate = [ Ending price / Beginning price] ^{(1 / # years)} - 1

Ending price = 191.96

Beginning price = 52.40

# years or Number of years = 4

AAGR = [191.96 / 52.40] ^(1/4) - 1 = [3.66] ^(0.25) - 1 = 1.38 - 1 = 0.38 or 38%

The average annual growth rate is 38%.