Return On Investments (ROI)
The calculation of the ROI is notcomplicated, relatively easy to interpret, and has a range of applications. Ifan investment’s ROI is not positive, or if other opportunities with higher ROIsare available, these signals can help investors eliminate or select the bestoptions.
For example, suppose Joe invested$1,000 in Slice Pizza Corp. in 2010 and sold his shares for atotal of $1,200 one year later. To calculate his return on his investment, hewould 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 couldcompare his investment in Slice Pizza with his other projects. Suppose Joe alsoinvested $2,000 in Big-Sale Stores Inc. in 2011 and sold his shares for a totalof $2,800 in 2014. The ROI on Joe’s holdings in Big-Sale would be $800/$2,000,or 40%.
Examples like Joe's (above) revealsome limitations of using ROI, particularly when comparing investments. Whilethe ROI of Joe’s second investment was twice that of his first investment, thetime between Joe’s purchase and sale was one year for his first investment andthree years for his second. Joe could adjust the ROI of his multi-yearinvestment accordingly. Since his total ROI was 40%, to obtain his averageannual ROI, he could divide 40% by 3 to yield 13.33%. With this adjustment, itappears that although Joe’s second investment earned him more profit, his firstinvestment was the more efficient choice.
ROI can be used in conjunctionwith Internal Rate of Return, which takes in account aproject’s time frame. The Internal Rate of Return is the interest rate that makes the Net Present Value zero. A "guess andcheck" method is the common way to find the Internal Rate of Return, hencelet us start with the Net Present Value to see how it works.
Present Value (PV)
PresentValue (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 moneyin future.
Example: Let us say you can get 10% interest on your money. $1,000now earns $1,000 x 10% = $100 ina 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.)
Theformula to calculate the Present Value is:
PV = FV / (1+r)n
PV isPresent Value
FV isFuture Value
r is theinterest rate (as a decimal, so 0.10, not 10%)
n is thenumber of years
Example: Alex promises you $900 in 3 years, what is the PresentValue (using a 10% interest rate)?
TheFuture Value (FV) is $900,
Theinterest rate (r) is 10%, which is 0.10as a decimal, and
Thenumber of years (n) is 3.
ThePresent Value of $900 in 3 yearsis:
PV = FV / (1+r)n
PV = $900 / (1 + 0.10)3
PV = $900 / 1.103
PV = $676.18 (to nearest cent)
Noticethat $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%
Theinterest rate (r) is now 6%, which is 0.06as a decimal:
PV = FV / (1+r)n
PV = $900 / (1 + 0.06)3
PV = $900 / 1.063
PV = $755.66 (to nearest cent)
When weonly get 6% interest, then $755.66 nowis as valuable as $900 in 3 years
Net Present Value (NPV)
The formula to calculate NPV is not too complex if one remembersto work out the PV of every amount,[1] then addand 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 andsubtract the PVs you pay.
Example: You invest $500 now, and get back $570 next year. Use an InterestRate of 10% to work out the NPV.
Youinvest $500 now, so PV = −$500.00 MoneyIn: $570 next year. PV = $570 /(1+0.10)1 = $570 / 1.10. PV = $518.18 (to nearest cent). And the Net Amount is: Net PresentValue = $518.18 − $500.00 = $18.18. So,at 10% interest, that investment has NPV= $18.18
Your choice of interest rate changes things! Example: Sameinvestment, but work out the NPV using an Interest Rate of 15%.You invest $500 now, so PV = -$500.00
MoneyIn: $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. Ithas gone negative!
What Interest Rate can make the NPV exactly zero? Example: Try again,but the interest Rate is 14%.
Youinvest $500 now, so PV = -$500.00. MoneyIn: $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 wehave discovered the Internal Rate of Return.It is 14% for thatinvestment.
Because14% made the NPV zero.
Internal Rate of Return (IRR)
TheInternal Rate of Return is the interestrate 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 / 1.102 = $82.64
Year 3:PV = $100 / 1.103 = $75.13
Year 3(final payment): PV = $2,500 / 1.103 = $1,878.29
Addingthose 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 / 1.122 = $79.72
Year 3:PV = $100 / 1.123 = $71.18
Year 3(final payment): PV = $2,500 / 1.123 = $1,779.45
Addingthose up gets:
NPV= -$2,000 + $89.29 + $79.72 + $71.18 + $1,779.45 = $19.64
Gettingclose. 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 / 1.1242 = $79.15
Year 3:PV = $100 / 1.1243 = $70.42
Year 3(final payment): PV = $2,500 / 1.1243 = $1,760.52
Addingthose up gets:
NPV= -$2,000 + $88.97 + $79.15 + $70.42 + $1,760.52 = -$0.94
That isgood enough! The IRR is 12.4%. Ina way it is saying "this investment could earn 12.4%" (assuming itall goes according to plan!).
The Internal Rate of Return is a good way of judging an investment. The bigger thebetter!
Using the Internal Rate of Return (IRR)
The IRR is a goodway of judging different investments. First of all, the IRR should be higherthan the cost of funds (WACC). If it costs you 8% to borrow money, then an IRRof only 6% is not good enough!
It is also useful when investments are quitedifferent.
Maybe the amounts involved are quitedifferent.
Or maybe one has high costs at the start, andanother has many small costs over time etc…
Example: instead of investing $2,000like above, you could also invest 3 yearly sums of $1,000 to gain $4,000 in the4th 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 = -$3.48
Thus the IRR is about 10%. And so the other investment (where the IRR was12.4%) is better. Doing your calculations in a spreadsheet is great as you caneasily change the interest rate until the NPV is zero. You also get to see theinfluence of all the values, and how sensitive the results are to changes(which is called "sensitivity analysis").
If the cost of attracting capital (theweighted average cost of capital) is higher than the revenues you make on thiscapital expressed in internal rate of return (return projected in % or IRR),then the project throws good money at bad money. In other words, the IRR >WACC.
[1] If one wantsnot to go through the examples. Calculatingthe NPV starts with setting the discount rate. The discount rate is nothingmore than the costs of risk. That is the risk-free rate of interest and add tothis the risk premium. Say investment is US$ 10,000. The discount rate is 10%and the expected return n year 1 is US$ 12,000. What is the NPV? US$ 909. Trueor false.
