To determine: The arithmetic and geometric average return.
Introduction:
Total return refers to the total income from an investment. The total income includes the periodic incomes and the increase or decrease in the value of an asset.
Arithmetic average return refers to the
Geometric average return refers to the return after compounding the average returns for multiple years.
Answer to Problem 21QP
The arithmetic average return is 0.10194 or 10.194% and the geometric average return is 0.0982 or 9.82%.
Explanation of Solution
Given information:
The price of the stock at the end of first year is $58.27. The price of the stock at the end of second year is $67.32, and the dividend paid is $1.10. The price of the stock at the end of third year is $61.46, and the dividend paid is $1.25. The price of the stock at the end of fourth year is $69.32, and the dividend paid is $1.45.
The price of the stock at the end of fifth year is 75.18, and the dividend paid is 1.60. The price of the stock at the end of sixth year is 84.32 and the dividend paid is 1.75.
The formula to calculate the total percentage returns:
The formula to calculate the arithmetic average return:
Where,
“∑Xi” refers to the total of observations,
“Xi” refers to each of the observations from X1 to XN (as “i” goes from 1 to “N”),
“N” refers to the number of observations.
The formula to calculate the geometric average return:
Where,
“R” is the annual returns for the investment,
“T” is the years of returns.
Compute the percentage return for the second year:
The closing price of the stock is $67.32, and the beginning price is $58.27. The dividend received in the second year is $1.10.
Hence, the percentage return for Year 2 is 0.1741 or 17.41%.
Compute the percentage return for the third year:
The closing price of the stock is $61.46, and the beginning price is $67.32. The dividend received in the second year is $1.25.
Hence, the percentage return for Year 3 is 0.0684 or 6.84%.
Compute the percentage return for the fourth year:
The closing price of the stock is $69.32, and the beginning price is $61.46. The dividend received in the second year is $1.45.
Hence, the percentage return for Year 4 is 0.1515 or 15.15%.
Compute the percentage return for the fifth year:
The closing price of the stock is $75.15, and the beginning price is $69.32. The dividend received in the second year is $1.60.
Hence, the percentage return for Year 5 is 0.10718 or 10.718%.
Compute the percentage return for the sixth year:
The closing price of the stock is $84.32, and the beginning price is $75.18. The dividend received in the second year is $1.75.
Hence, the percentage return for Year 6 is 0.1448 or 14.48%.
Compute the arithmetic average return:
The return for the second year is 16.45 percent, the return for the third year is 9.29 percent, the return for the fourth year is (8.57 percent), the return for the fifth year is 14.15 percent, and the return for the sixth year is 16.29 percent.
Hence, the arithmetic average return is 0.10194 or 10.194%.
Compute the geometric average return:
Hence, the geometric average return is 0.0982 or 9.82%.
Want to see more full solutions like this?
Chapter 10 Solutions
Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
- A stock has had the following year-end prices and dividends: Year Price Dividend 1 $43.33 2 48.31 $0.54 3 57.23 0.57 4 45.31 0.80 5 52.23 0.85 6 61.31 0.93 What are the arithmetic and geometric returns for the stock? (Do not round intermediate calculations. Round the final answers to 2 decimal places.) Arithmetic return Geometric return % %arrow_forwardA stock had the following year-end prices and dividends: Year Price Dividend 0 $ 58.75 — 1 68.56 $ 1.14 2 61.78 1.33 3 70.20 1.49 What was the arithmetic average return for the stock?arrow_forwardA stock has had the following year-end prices and dividends: Year Price Dividend 1 $ 64.43 — 2 71.30 $ .62 3 77.10 .67 4 63.37 .73 5 73.31 .82 6 80.75 .89 What are the arithmetic and geometric returns for the stock? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Arithmetic average return % Geometric average return %arrow_forward
- 1. A stock has had the following year-end prices and dividends: Year Price ($) Dividend ($) 94.17 92.21 1.05 96.1 1.2 96.3 1.57 94.16 1.66 96.46 1.69 What is the geometric average return for the stock? Answer as a percentage to two decimals (if you get -0.0435, you should answer -4.35).arrow_forwardA stock has had the following year-end prices and dividends: Year 0 1 2 3 4 5 Price $ 32.00 34.18 35.18 33.68 36.02 39.13 Dividend $ 0.15 0.29 0.32 0.33 0.39 What are the arithmetic and geometric returns for the stock? Note: Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Arithmetic return Geometric return % %arrow_forwardA stock has had the following year-end prices and dividends: Year Price Dividend 0 $ 43.29 - 1 48.27 $ .48 2 57.19 .51 3 45.27 .60 4 52.19 .65 5 61.27 .73 What are the arithmetic and geometric average returns for the stock? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Arithmetic average return % Geometric average return %arrow_forward
- A stock has had the following year-end prices and dividends: Year 0 1 2 3 4 5 Price $16.50 18.68 19.68 18.18 20.52 23.63 Dividend $ 0.15 0.35 0.37 0.38 0.45 What are the arithmetic and geometric returns for the stock? Note: Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.arrow_forward1. A stock has had the following year-end prices and dividends: Dividend ($) Year 1 2 3 4 5 6 Price ($) 93.75 94.42 95.5 93.24 94.65 97.9 1.38 1.36 1.72 1.76 1.95 What is the geometric average return for the stock? Answer as a percentage to two decimals (if you get -0.0435, you should answer -4.35).arrow_forwardA stock has had the following year-end prices and dividends: Year Price Dividend 1 $ 64.93 — 2 71.80 $ .72 3 77.60 .77 4 63.87 .83 5 74.31 .92 6 85.75 .99 What are the arithmetic and geometric returns for the stock? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)arrow_forward
- A stock had the following year-end prices and dividends. What is the geometric average annual return on this stock Time Price Dividend 0 $23.19 ? 1 $24.90 $0.23 2 $23.18 $0.24 3 $24.86 $0.25arrow_forwardA stock has had the following year-end prices and dividends: Year Price Dividend 1 $ 64.23271.10 $.58 3 76.90.63 4 63.17 .69 5 72.91.78 6 78.75 .85 What are the arithmetic and geometric returns for the stock? Note: Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.arrow_forwardA stock has had the following year-end prices and dividends: Price $64.68 Year 1 2 3 4 6 71.55 77.35 63.62 73.81 83.25 Dividend Arithmetic average return Geometric average im $.67 .72 .78 .87 94 What are the arithmetic and geometric returns for the stock? Note: Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e. 1%arrow_forward
- Managerial AccountingAccountingISBN:9781337912020Author:Carl Warren, Ph.d. Cma William B. TaylerPublisher:South-Western College Pub