Lesson Return On Investment

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This Lesson (Return On Investment) was created by by Shruti_Mishra(0)

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About Shruti_Mishra: I am a maths graduate from India and am currently persuing masters in Operations Research.

<A HREF="Return_on_investment.wikipedia">Return on Investment</A> (ROI) is an important financial measure which is used to evaluate the efficiency of an investment. Very simply put, ROI is the net gain from an investment as a percentage of the cost (total investment). The formula can be expressed as
<center>
{{{ROI = (Total Gain - Total Cost)/(Total Cost)}}}
</center>
There are a few complexities added to it. For example, ROI doesn't indicate the time period of investment. Also the calculation becomes complex in case the <A HREF="cash_flow.wikipedia">cash inflows</A> (gains) are spread over time. In this case annualized rate of return and <A HREF="yield_(finance).wikipedia">yield</A> are used to evaluate the project.

<b>Annualized Return</b>: Return on investment in a year is known as annual return. However, not all investments produce returns in one year period. Annualized return is an efficient and simple way to evaluate and compare investments with returns spread over different periods of time. In this method the net gain over the whole period is divided by number of years (whole number or fraction) of investment and then by the initial investment. The formula can thus be expressed as:
<center>
{{{ROI = (Total Gain - Total Cost)/(Time Period*Total Cost)}}}
</center>
For example, if an investment returns 16% in 2 years, the annualized return would be 8%. Similarly an investment yielding 0.5% per month would have an annualized return of 6%. A more complex case would be in case of a cash flow spread over few years. A $100 investment yielding the following cash flow:

Year 1: $10
Year 2: $15
Year 3: $12
Year 4: $13

would have an annualized return of {{{(10+15+12+13)/(4*100) = 12.5}}}%

<b>Yield</b>:If the rate of return is based on compounding, then it is called yield. Technically the yield is that rate with which you can discount the future <A HREF="cash_flow.wikipedia">cash flow</A>, to get a <A HREF=lesson-pv.lesson>present value</A> equal to the initial investment.

Example: Consider an investment of $100 which results in cash flow of $10 in first year, $20 in second year and $110 in third year (including the initial investment). Calculate the annualized return and yield on investment.

Solution: The annualized return would be {{{(10+20+110-100)/(3*100)=13.333}}}%
The yield would be that discount rate which will yield the present value of the future cash flows equal to $100. This would be 13.316% since {{{10/(1+0.1316) + 20/(1+0.316)^2 + 110/(1+0.1316)^3 = 100}}}

The difference is very minor but can be large for larger values.