Understanding Returns

Calculating and Understanding Average Returns

Average returns are commonly found using average ROI, CAGR, or IRR.

The average return on an investment can be calculated in several ways. The three main methods are

1. Return on investment (ROI)
   
   
2. Compound annual growth rate (CAGR)
   
   
3. Internal rate of return (IRR).

For all three methods, the higher the rate, the more desirable the investment.

Return on Investment (ROI)

To calculate the total return on investment (ROI), simply divide the total dollar returns of the investment by the initial value. The average ROI is the arithmetic average: divide the total ROI by the number of periods. If the purchase of a stock led to an ROI of 15% over five years, the average ROI is 3% per year. This is a simple way to calculate the average return.

It is useful for certain securities, such as bonds. If the only source of return on a bond is the coupon payments, then this is an accurate method. A bond purchased at par that pays a 5% coupon per year will return 25% over five years. However, this is a very special case. 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% annually would not be worth 15% more over five years because the gains compound.

Compound Annual Growth Rate (CAGR)

The compound annual growth rate (CAGR) is calculated by the following formula where V_f is the future value, V_i is the initial value, and t is the number of years:

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. The CAGR formula results when solving for i: the interest rate becomes CAGR, FV becomes V_f, PV becomes V_i, and the number of periods is generally assumed to be in years.

CAGR is very useful for finding the rate of return that the investment would have to earn every year for the life of the investment to turn the initial value into the future value over the given time frame.

Internal Rate of Return (IRR)

The internal rate of return (IRR) is another commonly used method for calculating the average return. IRR is the discount rate at which the net present value (NPV) equals 0. Using IRR allows for easy comparison between investment options. It is also known as the effective interest rate.

Internal Rate of Return The IRR is calculated by finding the discount rate at which the investment's NPV equals 0.