Topic outline


Return On Investments (ROI)
The calculation of the ROI is not complicated, relatively easy to interpret, and has a range of applications. If an investment’s ROI is not positive, or if other opportunities with higher ROIs are available, these signals can help investors eliminate or select the best options.
For example, suppose Joe invested $1,000 in Slice Pizza Corp. in 2010 and sold his shares for a total of $1,200 one year later. To calculate his return on his investment, he would divide his profits ($1,200  $1,000 = $200) by the investment cost ($1,000), for a ROI of $200/$1,000, or 20%. With this information, he could compare his investment in Slice Pizza with his other projects. Suppose Joe also invested $2,000 in BigSale Stores Inc. in 2011 and sold his shares for a total of $2,800 in 2014. The ROI on Joe’s holdings in BigSale would be $800/$2,000, or 40%.
Examples like Joe's (above) reveal some limitations of using ROI, particularly when comparing investments. While the ROI of Joe’s second investment was twice that of his first investment, the time between Joe’s purchase and sale was one year for his first investment and three years for his second. Joe could adjust the ROI of his multiyear investment accordingly. Since his total ROI was 40%, to obtain his average annual ROI, he could divide 40% by 3 to yield 13.33%. With this adjustment, it appears that although Joe’s second investment earned him more profit, his first investment was the more efficient choice.
ROI can be used in conjunction with Internal Rate of Return, which takes in account a project’s time frame. The Internal Rate of Return is the interest rate that makes the Net Present Value zero. A "guess and check" method is the common way to find the Internal Rate of Return, hence let us start with the Net Present Value to see how it works.
Present Value (PV)
Present Value (PV) is the current value of the project. It is important to bring future value to current (today's) value because money at present is more valuable than money in future.
Example: Let us say you can get 10% interest on your money. $1,000 now earns $1,000 x 10% = $100 in a year. Your $1,000 now becomes $1,100 in a year's time.
(In other words: $1,100 next year is only worth $1,000 now.)
The formula to calculate the Present Value is:
PV = FV / (1+r)^{n}
PV is Present Value
FV is Future Value
r is the interest rate (as a decimal, so 0.10, not 10%)
n is the number of years
Example: Alex promises you $900 in 3 years, what is the Present Value (using a 10% interest rate)?
The Future Value (FV) is $900,
The interest rate (r) is 10%, which is 0.10 as a decimal, and
The number of years (n) is 3.
The Present Value of $900 in 3 years is:
PV = FV / (1+r)^{n}
PV = $900 / (1 + 0.10)^{3}
PV = $900 / 1.10^{3}
PV = $676.18 (to nearest cent)
Notice that $676.18 is a lot less than $900. It is saying that $676.18 now is as valuable as $900 in 3 years (at 10%).
Example: try that again, but use an interest rate of 6%
The interest rate (r) is now 6%, which is 0.06 as a decimal:
PV = FV / (1+r)^{n}
PV = $900 / (1 + 0.06)^{3}
PV = $900 / 1.06^{3}
PV = $755.66 (to nearest cent)
When we only get 6% interest, then $755.66 now is as valuable as $900 in 3 years
Net Present Value (NPV)
The formula to calculate NPV is not too complex if one remembers to work out the PV of every amount,[1] then add and subtract them to get the NPV. For each amount (either coming in, or going out) work out its PV, then add the PVs you receive and subtract the PVs you pay.
Example: You invest $500 now, and get back $570 next year. Use an Interest Rate of 10% to work out the NPV.
You invest $500 now, so PV = −$500.00 Money In: $570 next year. PV = $570 / (1+0.10)^{1} = $570 / 1.10. PV = $518.18 (to nearest cent). And the Net Amount is: Net Present Value = $518.18 − $500.00 = $18.18. So, at 10% interest, that investment has NPV = $18.18
Your choice of interest rate changes things! Example: Same investment, but work out the NPV using an Interest Rate of 15%. You invest $500 now, so PV = $500.00
Money In: $570 next year: PV = $570 / (1+0.15)^{1} = $570 / 1.15. PV = $495.65 (to nearest cent). Net Present Value = $495.65  $500.00 = $4.35. So, at 15% interest, that investment has NPV = $4.35. It has gone negative!
What Interest Rate can make the NPV exactly zero? Example: Try again, but the interest Rate is 14%.
You invest $500 now, so PV = $500.00. Money In: $570 next year: PV = $570 / (1+0.14)^{1} = $570 / 1.14. PV = $500 (exactly) Net Present Value = $500 − $500.00 = $0
At 14% interest NPV = $0
And we have discovered the Internal Rate of Return. It is 14% for that investment.
Because 14% made the NPV zero.
Internal Rate of Return (IRR)
The Internal Rate of Return is the interest rate that makes the NPV zero. The "guess and check" method is the common way to find it.
Example: Invest $2,000 now, receive 3 yearly payments of $100 each, plus $2,500 in the 3rd year.
Try 10% interest:
Now: PV = $2,000
Year 1: PV = $100 / 1.10 = $90.91
Year 2: PV = $100 / 1.10^{2} = $82.64
Year 3: PV = $100 / 1.10^{3} = $75.13
Year 3 (final payment): PV = $2,500 / 1.10^{3} = $1,878.29
Adding those up gets:
NPV = $2,000 + $90.91 + $82.64 + $75.13 + $1,878.29 = $126.97
Example: (continued) at 12% interest rate
Now: PV = $2,000
Year 1: PV = $100 / 1.12 = $89.29
Year 2: PV = $100 / 1.12^{2} = $79.72
Year 3: PV = $100 / 1.12^{3} = $71.18
Year 3 (final payment): PV = $2,500 / 1.12^{3} = $1,779.45
Adding those up gets:
NPV = $2,000 + $89.29 + $79.72 + $71.18 + $1,779.45 = $19.64
Getting close. Maybe 12.4%?
Example: (continued) at 12.4% interest rate
Now: PV = $2,000
Year 1: PV = $100 / 1.124 = $88.97
Year 2: PV = $100 / 1.124^{2} = $79.15
Year 3: PV = $100 / 1.124^{3} = $70.42
Year 3 (final payment): PV = $2,500 / 1.124^{3} = $1,760.52
Adding those up gets:
NPV = $2,000 + $88.97 + $79.15 + $70.42 + $1,760.52 = $0.94
That is good enough! The IRR is 12.4%. In a way it is saying "this investment could earn 12.4%" (assuming it all goes according to plan!).
The Internal Rate of Return is a good way of judging an investment. The bigger the better!
Using the Internal Rate of Return (IRR)
The IRR is a good way of judging different investments. First of all, the IRR should be higher than the cost of funds (WACC). If it costs you 8% to borrow money, then an IRR of only 6% is not good enough!
It is also useful when investments are quite different.
Maybe the amounts involved are quite different.
Or maybe one has high costs at the start, and another has many small costs over time etc…
Example: instead of investing $2,000 like above, you could also invest 3 yearly sums of $1,000 to gain $4,000 in the 4th year ... should you do that instead? It is easiest to use a spreadsheet. You will find that 10% is pretty close. At 10% interest rate NPV = $3.48
Thus the IRR is about 10%. And so the other investment (where the IRR was 12.4%) is better. Doing your calculations in a spreadsheet is great as you can easily change the interest rate until the NPV is zero. You also get to see the influence of all the values, and how sensitive the results are to changes (which is called "sensitivity analysis").
If the cost of attracting capital (the weighted average cost of capital) is higher than the revenues you make on this capital expressed in internal rate of return (return projected in % or IRR), then the project throws good money at bad money. In other words, the IRR > WACC.
[1] If one wants not to go through the examples. Calculating the NPV starts with setting the discount rate. The discount rate is nothing more than the costs of risk. That is the riskfree rate of interest and add to this the risk premium. Say investment is US$ 10,000. The discount rate is 10% and the expected return n year 1 is US$ 12,000. What is the NPV? US$ 909. True or false.
