Percentage Returns
Percentage returns show how much the value of the investment has changed in proportion to the size of the initial investment.
Learning Objective

Calculate an investment's percentage return using CAGR
Key Points
 Total percentage returns divide the dollar returns by the initial value of the investment. This is also the return on investment (ROI).
 Annual returns show the percentage by which the value of the asset changes in each individual year.
 Average annual percentage returns can be calculated by dividing ROI by the number of years, or by other methods such as the compound annual growth rate (CAGR) or internal rate of return (IRR).
Terms

compound annual growth rate
CAGR. A method for finding the average annual return of an investment.

internal rate of return
IRR. The rate of return on an investment which causes the net present value of all future cash flows to be zero.

return on investment
ROI. The dollar return of the investment divided by the initial value.
Full Text
The conventional way to express the return on a security (and investments in general) is in percentage terms. This is because it does not only matter how much money was earned on the investment, it matters how much was earned in proportion to the cost.
There are two types of percentage returns: total and annual. Total returns calculate how much the value of the investment has changed since it was first purchased, while annual returns calculate how much the value changed each year. When the length of time of the investment is one year, the total and annual returns are equivalent.
Total Returns
The total percentage return is based off of the final value (V_{f}), the initial value (V_{i}), and all dividend payments or additional incomes (D). If the investment is a security such as a stock, the final value is the sales price, the initial value is the purchase price, and D is the sum of all dividends received.
$Return\quad =\quad \frac { V_{ f }{ V }_{ i }+D }{ { V }_{ i } }$
This type of return is also called the return on investment (ROI), where the numerator is the dollar return.
Annual Returns
In , the ROI is calculated for each individual year by dividing the dollar return by the initial value of $1,000. To find the return for the security overall, simply sum the dollar returns and divide by the initial value. The ROI can be annualized by dividing by the number of years between the purchase and sale of the security. This is the arithmetic mean of the return.
Cash Flow Return
The ROI is the percentage return, and is calculated by dividing the dollar return by the initial value of the investment ($1,000).
However, this does not fully take into consideration compounding. To do so, analysts use other formulas, like the compound annual growth rate (CAGR):
$CAGR={ \left( \frac { V_{ f } }{ { V }_{ i } } \right) }^{ \frac { 1 }{ t } }1$
In this case, the only variable that differs from the previous formula is t, which is the number of years between the beginning and end of the investment. CAGR is a way of measuring the return per year. It is widely used because it allows for the easy comparison of the growth rates of multiple investments.
Another common method for finding the annual return is to calculate the internal rate of return (IRR). Recall that the IRR is the discount rate at which the net present value (NPV) equals 0.
Key Term Reference
 Assets
 Appears in these related concepts: Secured vs. Unsecured Funding, Defining LongLived Assets, and Defining the Marketing Objectives
 Stock
 Appears in these related concepts: Ownership Nature of Stock, Advantages of Private Financing, and Financial Instruments
 asset
 Appears in these related concepts: Goodwill Impairment, Shifts in the Money Demand Curve, and Balance Sheets
 discount
 Appears in these related concepts: The Discount Rate, Par Value at Maturity, and Present Value, Multiple Flows
 discount rate
 Appears in these related concepts: Discounted Cash Flow Approach, The Discount Rate, and The Federal Reserve and the Financial Crisis of 2008
 dividend
 Appears in these related concepts: Investor Preferences, Accounting for Preferred Stock, and Division and Factors
 growth rate
 Appears in these related concepts: The Valuation of Stocks, Calculating Perpetuities, and Discounted Dividend vs. Corporate Valuation
 investment
 Appears in these related concepts: Functions of Corporate Finance, The Role of the Financial System, and GDP Equation in Depth (C+I+G+X)
 net present value
 Appears in these related concepts: Other Considerations in Capital Budgeting, The Role of Financial Managers, and CostBenefit Analysis
 present value
 Appears in these related concepts: Capital Leases vs. Operating Leases, Calculating Values for Different Durations of Compounding Periods, and Present Value and the Time Value of Money
 proportion
 Appears in these related concepts: Methods of Paying Dividends, Dividend Payments and Earnings Retention, and Seasoned Equity Offering
 return
 Appears in these related concepts: Dollar Returns, Comparing the Fields of Finance, Economics, and Accounting, and Disadvantages of the Payback Method
 sales
 Appears in these related concepts: Overview of Merchandising Operations, Additional Funds Needed (AFN), and Repurchasing Stock
 securities
 Appears in these related concepts: Secondary Market Organizations, Types of Market Organizations, and The United States Banking System
 security
 Appears in these related concepts: Advantages of Public Financing, Pricing a Security, and Underwriter
 variable
 Appears in these related concepts: What is a Linear Function?, Math Review, and Introduction to Variables
Sources
Boundless vets and curates highquality, openly licensed content from around the Internet. This particular resource used the following sources: