compounding returns
(noun)
Returns earned on previous returns. Akin to compounding interest.
Examples of compounding returns 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.
- The internal rate of return (IRR) is another commonly used method for calculating the average return .
-
Calculating the IRR
- Given a collection of pairs (time, cash flow), a rate of return for which the net present value is zero is an internal rate of return.
- Given a collection of pairs (time, cash flow) involved in a project, the internal rate of return follows from the net present value as a function of the rate of return.
- A rate of return for which this function is zero is an internal rate of return.
- Given the (period, cash flow) pairs (n, Cn) where n is a positive integer, the total number of periods N, and the net present value NPV, the internal rate of return is given by r in:
- Because the internal rate of return on an investment or project is the "annualized effective compounded return rate" or "rate of return" that makes the net present value of all cash flows (both positive and negative) from a particular investment equal to zero, then the IRR r is given by the formula:
-
Defining the IRR
- IRR is a rate of return used in capital budgeting to measure and compare the profitability of investments; the higher IRR, the more desirable the project.
- The internal rate of return (IRR) or economic rate of return (ERR) is a rate of return used in capital budgeting to measure and compare the profitability of investments.
- It is also called the "discounted cash flow rate of return" (DCFROR) or the rate of return (ROR).
- The internal rate of return on an investment or project is the "annualized effective compounded return rate" or "rate of return" that makes the net present value (NPV as NET*1/(1+IRR)^year) of all cash flows (both positive and negative) from a particular investment equal to zero.
- Explain how Internal Rate of Return is used in capital budgeting
-
Ranking Investment Proposals
- The internal rate of return on an investment or project is the "annualized effective compounded return rate" or "rate of return" that makes the net present value (NPV as NET*1/(1+IRR)^year) of all cash flows (both positive and negative) from a particular investment equal to zero.
- ARR calculates the return, generated from net income of the proposed capital investment.
- The ARR is a percentage return.
- If the ARR is equal to or greater than the required rate of return, the project is acceptable.
-
Multi-Period Investment
- Multi-period investments require an understanding of compound interest, incorporating the time value of money over time.
- The future value is simply the present value applied to the interest rate compounded one time.
- With multi-periods in mind, interest begins to compound.
- Normalizing expected returns in present value terms (or projecting future returns over multiple time periods of compounding interest) paints a clearer and more accurate picture of the actual worth of a given investment opportunity.
- Time value of money requires an understanding of how return rates impact fixed values over time.
-
Percentage Returns
- This type of return is also called the return on investment (ROI), where the numerator is the dollar return.
- To find the return for the security overall, simply sum the dollar returns and divide by the initial value.
- However, this does not fully take into consideration compounding.
- To do so, analysts use other formulas, like the compound annual growth rate (CAGR):
- Another common method for finding the annual return is to calculate the internal rate of return (IRR).
-
Comparing Interest Rates
- The reason why the nominal interest rate is only part of the story is due to compounding.
- It provides an annual interest rate that accounts for compounded interest during the year.
- The cost of capital is the rate of return that capital could be expected to earn in an alternative investment of equivalent risk.
- In theory, a company will never make an investment if the expected return on the investment is less than their cost of capital.
- Even if a 10% annual return sounds really nice, a company with a 13% cost of capital will not make that investment.
-
Calculating the Yield of a Single-Period Investment
- The yield on an investment is the amount of money that is returned to the owner at the end of the term.
- However, since interest compounds, nominal APR is not a very accurate measure of the amount of interest you actually accrue.
- For example, you may see an ad that says you can get a car loan at an APR of 10% compounded monthly.
- That means that APR=.10 and n=12 (the APR compounds 12 times per year).
- 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.
-
Calculating Values for Different Durations of Compounding Periods
- Since interest generally compounds, it is not as simple as multiplying 1% by 12 (1% compounded each month).
- This atom will discuss how to handle different compounding periods.
- The EAR can be found through the formula in where i is the nominal interest rate and n is the number of times the interest compounds per year (for continuous compounding, see ).
- The equation follows the same logic as the standard formula. r/n is simply the nominal interest per compounding period, and nt represents the total number of compounding periods.
- The effective annual rate for interest that compounds more than once per year.
-
Using the Yield Curve to Estimate Interest Rates in the Future
- For debt contracts, the overall duration of time of the debt security coupled with the interest rate compounded over that time frame will illustrate the overall yield of the security during its lifetime.
- In short, through investor expectations of what the 1-year interest rates will be next year, the current 2-year interest rate can be calculated as the compounding of this year's 1-year interest rate by next year's expected 1-year interest rate.
- As you can see, this is a typical yield curve shape, as the longer the contract is held out the higher the rate of return (with diminishing returns).