compound annual growth rate

(noun)

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

Related Terms

Examples of compound annual growth rate in the following topics:

  • Calculating and Understanding Average Returns

    • Average ROI generally does not calculate the actual average rate of return, because it does not incorporate compounding returns.
    • A stock that appreciates by 3% per year would not actually be worth 15% more over 5 years, because the gains compound.
    • CAGR stands for compound annual growth rate.
    • CAGR, unlike average ROI, does consider compounding returns.
    • CAGR is derived from the compounding interest formula, FV=PV(1+i)t, where PV is the initial value, FV is the future value, i is the interest rate, and t is the number of periods.

  • Percentage Returns

    • However, this does not fully take into consideration compounding.
    • To do so, analysts use other formulas, like the compound annual growth rate (CAGR):
    • 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.

  • Impacts of Productivity on Output

    • From 1964-65 to 1999-2000, labor productivity in Australia's market sector grew at a compound annual rate of 2.4%.
    • The contribution of growing capital intensity of IT to growth in labor productivity has been generally rising over time.
    • Nevertheless, there is one criterion by which we can generalize the rate of success in production.
    • When there is productivity growth, even the existing commitment of resources generates more output and income.
    • Over long periods of time, small differences in rates of productivity growth compound, such as interest in a bank account, and can make an enormous difference to a society's prosperity.

  • Long Run Growth

    • Over long periods of time even small rates of growth, like a 2% annual increase, have large effects.
    • The large impact of a relatively small growth rate over a long period of time is due to the power of compounding.
    • A growth rate of 2.5% per annum leads to a doubling of the GDP within 29 years, while a growth rate of 8% per annum (an average exceeded by China between 2000 and 2010) leads to a doubling of GDP within 10 years.
    • Divide 72 by the percentage annual growth rate to get a rough estimate of the number of years until the number doubles.
    • Growth in GDP can be significant, especially when annual growth rates are fairly consistent.

  • Calculating Values for Different Durations of Compounding Periods

    • Finding the Effective Annual Rate (EAR) accounts for compounding during the year, and is easily adjusted to different period durations.
    • For example, the interest rate could be 12% compounded monthly, but one period is one year.
    • But suppose you want to convert the interest rate into an annual rate.
    • The effective annual rate (EAR) is a measurement of how much interest actually accrues per year if it compounds more than once per year.
    • The effective annual rate for interest that compounds more than once per year.

  • Compounding Frequency

    • Financial analysts always define an interest rate as an annual term, called the Annual Percentage Rate (APR).The APR come from the Federal Reserve's regulation that helps prevent fraud.For example, do you consider a 1% interest rate a good interest rate to charge a borrower?
    • Unfortunately, we do not know the time period this interest rate applies to because the time period was omitted.If the 1% is annual, then it is an excellent interest rate for a loan.However, if it is daily, subsequently, this rate is terrible.Borrower took money from a loan shark.For this book, we define all interest rates in annual terms, unless otherwise stated.
    • Banks and finance companies usually calculate interest payments and deposits monthly.Thus, we adjust the present value formula for different time units.If you refer to Equation 11, we add a new variable, m, the compounding frequency while APR is the interest rate in annual terms.In the monthly case, m equals 12 because a year has 12 months.
    • For example, you deposit $10 in your bank account for 20 years that earns 8% interest (APR), compounded monthly.Consequently, we calculate your savings grow into $49.27 in Equation 12: If your bank compounded your account annually, then you would have $46.61.
    • We can convert any compounding frequency into an APR equivalent interest rate, called the effective annual rate (EFF).From the previous example, we convert the 8% APR interest rate, compounded monthly into an annual rate without compounding, yielding 8.3%.We show the calculation in Equation 13.The EFF is the standard compounding formula removing the years and the present value terms.

  • Calculating the Yield of a Single-Period Investment

    • Another common way of calculating yield is to determine the Annual Percentage Rate, or APR.
    • To find the effective APR, the actual amount of interest you would accrue per year, we use the Effective Annual Rate, or EAR.
    • Interest usually compounds, so there is a difference between the nominal interest rate (e.g. monthly interest times 12) and the effective interest rate.
    • The Effective Annual Rate is the amount of interest actually accrued per year based on the APR. n is the number of compounding periods of APR per year.
    • The Annual Percentage Yield is a way or normalizing the nominal interest rate.

  • Comparing Interest Rates

    • Variables, such as compounding, inflation, and the cost of capital must be considered before comparing interest rates.
    • The reason why the nominal interest rate is only part of the story is due to compounding.
    • The last section went through one method for finding the amount of interest that actually accrues: the Effective Annual Rate (EAR).
    • It provides an annual interest rate that accounts for compounded interest during the year.
    • Even if a 10% annual return sounds really nice, a company with a 13% cost of capital will not make that investment.

  • Abiotic Factors Influencing Plant Growth

    • Primary production is the synthesis of organic compounds from atmospheric or aqueous carbon dioxide.
    • Annual biomass production is directly related to the abiotic components of the environment.
    • Environments with the greatest amount of biomass have conditions in which photosynthesis, plant growth, and the resulting net primary productivity are optimized.
    • Conversely, dry and cold environments have lower photosynthetic rates and, therefore, less biomass.
    • However, warm and wet climates have the greatest amount of annual biomass production.

  • Expected Dividends and Constant Growth

    • Valuations rely heavily on the expected growth rate of a company; past growth rate of sales and income provide insight into future growth.
    • Valuations rely very heavily on the expected growth rate of a company.
    • Calculating the future growth rate requires personal investment research.
    • Derived from the compound interest formula using the present value of a perpetuity equation, SPM is an alternative to the Gordon Growth Model.
    • It assumes that dividends will increase at a constant growth rate (less than the discount rate) forever.