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
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 Big-Sale Stores Inc. in 2011 and sold his shares for a total
of $2,800 in 2014. The ROI on Joe’s holdings in Big-Sale would be $800/$2,000,
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 multi-year
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)
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
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.)
formula to calculate the Present Value is:
PV = FV / (1+r)n
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)?
Future Value (FV) is $900,
interest rate (r) is 10%, which is 0.10
as a decimal, and
number of years (n) is 3.
Present Value of $900 in 3 years
PV = FV / (1+r)n
PV = $900 / (1 + 0.10)3
PV = $900 / 1.103
PV = $676.18 (to nearest cent)
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%
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 / 1.063
PV = $755.66 (to nearest cent)
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, 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.
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
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
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%.
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
interest NPV = $0
have discovered the Internal Rate of Return.
It is 14% for that
14% made the NPV zero.
Internal Rate of Return (IRR)
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:
PV = $100 / 1.10 = $90.91
PV = $100 / 1.102 = $82.64
PV = $100 / 1.103 = $75.13
(final payment): PV = $2,500 / 1.103 = $1,878.29
those up gets:
= -$2,000 + $90.91 + $82.64 + $75.13 + $1,878.29 = $126.97
Example: (continued) at 12% interest rate
PV = $100 / 1.12 = $89.29
PV = $100 / 1.122 = $79.72
PV = $100 / 1.123 = $71.18
(final payment): PV = $2,500 / 1.123 = $1,779.45
those up gets:
= -$2,000 + $89.29 + $79.72 + $71.18 + $1,779.45 = $19.64
close. Maybe 12.4%?
Example: (continued) at 12.4% interest rate
PV = $100 / 1.124 = $88.97
PV = $100 / 1.1242 = $79.15
PV = $100 / 1.1243 = $70.42
(final payment): PV = $2,500 / 1.1243 = $1,760.52
those up gets:
= -$2,000 + $88.97 + $79.15 + $70.42 + $1,760.52 = -$0.94
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
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
Maybe the amounts involved are quite
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 = -$3.48
Thus the IRR is about 10%. And so the other investment (where the IRR was
12.4%) is better. Doing your calculations in a spreadsheet is great as you can
easily change the interest rate until the NPV is zero. You also get to see the
influence of all the values, and how sensitive the results are to changes
(which is called "sensitivity analysis").
If the cost of attracting capital (the
weighted average cost of capital) is higher than the revenues you make on this
capital expressed in internal rate of return (return projected in % or IRR),
then the project throws good money at bad money. In other words, the IRR >
 If one wants
not to go through the examples. Calculating
the NPV starts with setting the discount rate. The discount rate is nothing
more than the costs of risk. That is the risk-free rate of interest and add to
this the risk premium. Say investment is US$ 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