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
-
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).
-
Interest Compounded Continuously
- The amount of interest earned increases with each compounding period.
- Compound interest is not linear, but exponential in form.
- This time we use compound interest instead.
- To highlight this, we return the the examples we did prior and now consider how much money is in each account after 50 years.
- The formula for compound interest with the number of compounding periods going to infinity yields the formula for compounding continuously.
-
Alkyl Halide Occurrence
- Halogen containing organic compounds are relatively rare in terrestrial plants and animals.
- Synthetic organic halogen compounds are readily available by direct halogenation of hydrocarbons and by addition reactions to alkenes and alkynes.
- Some halogen compounds, shown in the box. have been used as pesticides, but their persistence in the environment, once applied, has led to restrictions, including banning, of their use in developed countries.
- Because DDT is a cheap and effective mosquito control agent, underdeveloped countries in Africa and Latin America have experienced a dramatic increase in malaria deaths following its removal, and arguments are made for returning it to limited use. 2,4,5-T and 2,4-D are common herbicides that are sold by most garden stores.
- Other organic halogen compounds that have been implicated in environmental damage include the polychloro- and polybromo-biphenyls (PCBs and PBBs), used as heat transfer fluids and fire retardants; and freons (e.g.
-
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.
-
The Role of Prokaryotes in Ecosystems
- The movement of carbon is via carbon dioxide, which is removed from the atmosphere by land plants and marine prokaryotes and is returned to the atmosphere via the respiration of chemoorganotrophic organisms, including prokaryotes, fungi, and animals.
- A large amount of available carbon is found in land plants, which are producers that use carbon dioxide from the air to synthesize carbon compounds.
- Consumers such as animals use organic compounds generated by producers, releasing carbon dioxide to the atmosphere.
- In this case, the cycle is based on one-carbon compounds.
- This methane moves into the zone above the sediment, which is richer in oxygen and supports bacteria called methane oxidizers that oxidize methane to carbon dioxide, which then returns to the atmosphere.