UOP Capital Investment Presentation
Content
Training Services
Capital Investment
Evaluation
EDS 2004/CI-1
Hello and good morning! My name is Joe Weiszmann and I am from the Solutions
and Services Department of UOP. My specialization is the front-end conceptual
design and optimization of refinery and petrochemical complexes. I often evaluate
the economics and profitability of new refinery projects and of refinery revamps or
upgrading projects as part of my work at UOP.
This training class is about capital investment evaluation. For the next three hours, I
would like to tell you about how to evaluate and select capital projects using the
appropriate capital investment evaluation tools.
Outline
Time Value of Money
Investment Evaluation Tools
– Net Present Value (NPV)
– Breakeven analysis
– Internal Rate of Return (IRR)
Project Ranking
– Simple payout
– Mutually exclusive projects
– Sensitivity analysis
– Present value ratio
Cash Flow Analysis
– Examples
Class Problems
EDS 2004/CI-2
We will go through the concept of the time value of money. Next, we will go
through the three most common investment evaluation tools: net present value,
breakeven analysis and internal rate of return.
I will show you which is the correct tool to use for evaluating capital projects.
There are several different techniques used for evaluating capital projects, including
simple payout, mutually exclusive projects, sensitivity analysis, and present value
ratio. We will talk about all of these this morning.
We will then go through a cash flow analysis and work out some examples. We
will finish the class with doing some class and homework problems.
2
Time Line Concept
Income, $
Investment
or Cost, $
Year
50
100
100
0
1
50
50
50
50
2
3
4
5
EDS 2004/CI-3
The time line concept entails organizing the income and investment (or cost) of a
particular project over a selected period of time to be analyzed in terms of the
income received and cost incurred during each individual period of time.
3
Time Line Concept
Income, $
0
50
50
50
50
50
- Cost, $
-100
-100
0
0
0
0
Cash Flow
-100
-50
50
50
50
50
0
1
2
3
4
5
Year
EDS 2004/CI-4
By subtracting the cost from the income, you get the net cash flow for each period
of time. In other words, the cash flow is typically the profit that you make after you
subtract your cost and expenses from the income or revenues.
4
Definition of Cash Flow
Gross revenue or savings
- Operating costs
- Tax costs
- Capital costs
= Cash flow
EDS 2004/CI-5
A more detailed description or definition of cash flow is the money remaining after
you subtract all the operating costs (both variable and fixed), tax costs (everyone
pays some kind of tax?), and capital costs (e.g. for plant, equipment, buildings, etc.,
which are typically amortized via depreciation) from the gross revenues or savings,
i.e. from the revenue received or the savings achieved.
5
Time Value of Money – Example
Putting Money to Work
Invest $100 in Bank A and $100 in Bank B
Bank A pays 20% simple interest at the end of
three years
Bank B pays 10% compound interest for three
years
EDS 2004/CI-6
Here’s an example of the time value of money. Let’s invest $100 M in Bank A and
$100 M in Bank B. Bank A pays 20% simple interest at the end of three years,
while Bank B pays 10% compound interest for three straight years. It is just an
example of the time value of money.
6
Time Value of Money
Bank A
100*1.2=
-$100
Year
0
$120
1
2
3
EDS 2004/CI-7
In Bank A, after 3 years, the $100 investment turns into $120 based on using a
simple interest rate of 20%.
7
Time Value of Money
Bank B
Year
100*1.1=
110*1.1=
121*1.1=
-$100
$110
$121
$133
0
1
2
3
EDS 2004/CI-8
In Bank B, we apply a compound interest rate. This interest rate is different from
the simple one in that it is compounded each and every year.
The interest rate is applied to the investment every year, as long as the money is
kept invested or deposited in the bank.
The value of your $100 with compound interest is calculated using the formula
shown here. After three years, your $100 becomes $133.
8
Investment Evaluation
Investment evaluation will show us if
an investment gives us a good return
on our money.
EDS 2004/CI-9
The next section will introduce the three most common methods of investment
evaluation: net present value, breakeven analysis, and internal rate of return.
9
Cost of Capital
The Cost of Capital (or money) is the rate of
return that could be realized on similar
alternative investments of equivalent risk.
This foregone rate of return is the standard to
which we compare all our investments.
EDS 2004/CI-10
The cost of capital is an important principle that underlies all investment evaluation
work.
What else could we be doing with our money (that would involve only the same
amount of risk)?
10
Investment Evaluation Tools
Net Present Value (NPV)
Breakeven Analysis
Internal Rate of Return (IRR)
EDS 2004/CI-11
Let’s now look at the three most common investment evaluation tools:
Breakeven Analysis, and IRR.
NPV,
11
Net Present Value (NPV)
Net Present Value is the total value of a project,
revenues minus costs, brought backward to the
first year at a specified rate of interest per year.
EDS 2004/CI-12
More explanation (plus examples) are provided on the following slides.
12
Net Present Value (NPV)
(continued)
NPV = Σ Cj / (1 + i) j
where 0 < j < n
j
Cj
I
n
=
=
=
=
Period of time, usually a year
Cash flow in the time period j
Interest rate ( = cost of capital)
Number of time periods, years
EDS 2004/CI-13
The NPV of a project is the summation of all the discounted cash flows over all of
the time periods to be evaluated.
13
Net Present Value (NPV)
(continued)
I want to have $2,000 at the end of 5 years.
The interest rate is 12%.
How much do I have to invest in year 1?
EDS 2004/CI-14
Here is an example. Can anyone tell me the answer?
14
Net Present Value (NPV)
(continued)
Income, $
0
0
0
0
0
2000
- Cost, $
NPV
0
0
0
0
0
Cash Flow
-NPV
0
0
0
0
2000
Year
0
1
2
3
4
5
NPV = 2000 / (1+0.12)5
NPV = $1135 (to be invested at the beginning of the year)
EDS 2004/CI-15
Let’s go through the calculation, step by step, as shown above.
15
Net Present Value (NPV)
(continued)
Another way to look at it:
Income, $
0
0
0
0
0
2000
- Cost, $
X
0
0
0
0
0
Cash Flow
-X
0
0
0
0
2000
Year
0
1
2
3
4
5
To make 12% on my investment:
-X + 2000 / (1+0.12)5 = 0
X = $1135
This is also called the Breakeven Price
EDS 2004/CI-16
The breakeven price is based on determining the initial investment required @ 12%
to obtain @ $2000 at the end of five years.
If you had to invest more than $1135, you would be losing money; if you had to
invest less than $1135, you would be gaining money. However, if you had to invest
exactly $1135, then you would be breaking even. Hence, $1135 is called the
breakeven price in this example.
16
Net Present Value – Example
Income, $
0
50
40
30
20
- Cost, $
100
0
0
0
0
Cash Flow
-100
50
40
30
20
Year
0
1
2
3
4
What is the NPV of this project using a cost of capital of
15%? What is the Breakeven Investment cost?
EDS 2004/CI-17
Here is another example of calculating NPV that I suggest you try working on
(without turning over just yet).
17
Worksheet for NPV Example
NPV = Σ Cj / (1 + i) j
NPV = -100 / (1+0.15)0 +
50 / (1+0.15)1 +
40 / (1+0.15)2 +
30 / (1+0.15)3 +
20 / (1+0.15)4
NPV = -100 + 43 + 30 + 20 + 11
NPV = $4
EDS 2004/CI-18
Please go through the calculation and make sure you could do it yourself.
18
At the beginning of year 1, the value of this project is
$4 at a 15% rate of interest. This means I make
15% interest on my $100 investment over a 4 year
period, plus $4 extra. The interest rate on this
investment is, therefore, greater than 15% per year.
EDS 2004/CI-19
This project is attractive if the cost of capital is 15% (or less). The net present value
of the project is calculated to be plus $4 at a 15% rate of interest.
19
Breakeven Analysis
Breakeven analysis is determining the value of
any parameter which allows a specified rate of
return to be achieved from an investment.
The parameter may be the initial investment
cost, project lifetime, annual revenue, selling
price of a product, or % utilization of plant.
EDS 2004/CI-20
Breakeven analysis can be applied to lots of other parameters, for example the plant
throughput required to just breakeven. See above for other examples of the
parameters that can be studied as part of a breakeven analysis of a project.
20
Breakeven Investment Cost
Income, $
0
50
40
30
20
- Cost, $
X
0
0
0
0
Cash Flow
-X
50
40
30
20
Year
0
1
2
3
4
NPV = 0 = -X / (1+.15)0 + 50 / (1+.15)1 + 40 / (1+.15)2
+ 30 / (1+.15)3 + 20 / (1+.15)4
0 = -X + 43 + 30 + 20 + 11
X = $104
EDS 2004/CI-21
In the breakeven analysis above, we want to find out what our maximum investment
cost should be to just meet our accepted 15% rate of return. This is calculated as
shown above with the NPV set equal to zero.
21
For a Rate of Return of 15% on this investment, I
could invest up to $104. This is then the Breakeven
Investment Cost for this particular project. Any
additional cost would lower the Rate of Return to
less than 15% which would not be acceptable.
EDS 2004/CI-22
This is just another way of saying the same thing.
22
What is the NPV at 20%?
Income, $
0
50
40
30
20
- Cost, $
100
0
0
0
0
Cash Flow
-100
50
40
30
20
Year
0
1
2
3
4
NPV = -100 / (1+.20)0 + 50 / (1+ .20)1 + 40 / (1+ .20)2
+ 30 / (1+ .20)3 + 20 / (1+ .20)4
= -100 + 42 + 28 + 17 + 10
= - $3
The IRR is between 15% and 20%.
EDS 2004/CI-23
Here’s an example that calculates the project NPV at a cost of capital of 20%. The
NPV for this project is now minus $3.
This means that the discount rate used is now too high for this project. You are
asking for too much return from this investment.
The rate of return is thus somewhere between 15% and 20%.
23
Internal Rate of Return (IRR)
Rate of Return or interest rate of a project
Calculated through trial and error
EDS 2004/CI-24
Let’s now talk about internal rate or return or IRR as it is routinely called.
24
Internal Rate of Return (IRR)
(continued)
0 = Σ Cj / (1 + r) j
where 0 < j < n
j
Cj
r
n
=
=
=
=
Period of time, usually a year
Cash flow in time period j
Internal Rate of Return unknown
Number of periods, usually years
Assume a value for “r” and calculate formula.
The project’s IRR is the value of “r” that gives
an answer of zero NPV.
EDS 2004/CI-25
This is the formula for calculating the internal rate of return (IRR) of a project. The
calculation is normally an iterative process, even for a computer.
25
What is the IRR of this project?
0
Income, $
100
100
120
140
- Cost, $
-200
-150
0
0
0
Cash Flow
-200
-50
100
120
140
1
2
3
4
Year
0
at r = 15%
- 200/(1+.15)0 - 50/(1+ .15)1 + 100/(1+ .15)2
+ 120/(1+ .15)3 + 140/(1+ .15)4
- 200 - 43 + 76 + 79 + 80 = - $8
at r = 10%
- 200/(1+.10)0 - 50/(1+ .10)1 + 100/(1+ .10)2
+ 120/(1+ .10)3 + 140/(1+ .10)4
- 200 - 45 + 83 + 90 + 96 = + $24
EDS 2004/CI-26
Here is an example the calculates an IRR of a project. As you can see, it is trial and
error approach.
26
Example – What is the IRR of the
following project?
Income, $
0
30
40
50
- Cost, $
100
0
0
0
Cash Flow
-100
30
40
50
Year
0
1
2
3
EDS 2004/CI-27
Here is another example for you to work on (without turning over just yet).
27
What is the IRR of this Project?
Calculation
at r = 15%
-100/(1+.15)° + 30/(1+.15)1 + 40/(1+.15)2 + 50/(1+.15)3
-100 + 26 + 30 + 33 = - $11
at r = 10%
-100/(1+.10)° + 30/(1+.10)1 + 40/(1+.10)2 + 50/(1+.10)3
-100 + 27 + 33 + 38 = - $2
at r = 8%
-100/(1+.08)° + 30/(1+.08)1 + 40/(1+.08)2 + 50/(1+.08)3
-100 + 28 + 34 + 40 = + $2
The internal rate of return is 9%
EDS 2004/CI-28
Here is the calculation of the internal rate of return (IRR) for this example.
28
Project Ranking
Simple Payout
Mutually Exclusive Projects
Sensitivity Analysis
Present Value Ratio
EDS 2004/CI-29
Let’s now move on and go over methods for ranking and prioritizing projects.
29
Simple Payout
Simple payout is the number of years it will take
to pay back an investment at the initial operating
gross margin. Simple payout takes no account of
inflation, nor of the time value of money.
Example:
– Gross margin in year 1 = $700 MM/year
– Total investment in project = $1,400 MM
– Simple payout = $1,400/$700 = 2 years
EDS 2004/CI-30
Simple payout is (as it says) simple. It is widely used and quite a useful concept,
but beware of the pitfalls explained on the next few slides.
30
Payout Example #1
Project A
Cash Flow
-100
Year
0
50
50
1
2
50
3
NPV @ 15% minimum rate of return = $15
and the IRR ∼ 23%
Payout = 2 years
EDS 2004/CI-31
This is example #1 of using simple payout. Do you agree with the NPV, IRR and
Payout figures worked out above? If yes, then turn over to example #2.
31
Payout Example #2
Project B
Cash Flow
-100
Year
0
100
0
1
2
0
3
NPV @ 15% min rate of return = - $13
and the IRR = 0%
Payout = 1 year
EDS 2004/CI-32
Here again, I suggest you check the NPV, IRR and Payout numbers worked out
above. The point is that the Payout in Example #2 is better (half as long) than in
Example #1, but everything else is obviously much worse.
32
Simple Payout
Simplest economic evaluation method
Takes NO account of the time value of money
Penalizes long term projects
Benefits quick projects
EDS 2004/CI-33
Must emphasize that the Simple Payout approach should not be used as a tool for
making decisions on a project. It is basically a very rough screening tool.
33
Project Ranking
Mutually exclusive alternatives
– Only 1 project can be accepted
Non-mutually exclusive alternatives
– Ranking several projects
EDS 2004/CI-34
It is important to decide up-front whether or not the projects you are evaluating are
mutually exclusive. It affects the correct choice of evaluation method.
A common example of mutually exclusive projects is when there are two or three
different options for revamping of a particular plant. Only one of the revamp
options can be implemented - a decision is required.
34
Mutually Exclusive Alternatives
The goal is to choose the one project that gives the
investors the largest return on their money
– The project with the largest NPV using the minimum
rate of return
– The project with the highest incremental IRR
•
•
•
Calculate each project’s individual IRR; must be
higher than the minimum rate of return
Calculate the incremental IRR between projects; this
too must be higher than the minimum rate of return
The project which has the highest incremental IRR
will give the largest return on the investment
EDS 2004/CI-35
For mutually exclusive projects, beware of using IRR, unless you go through the
whole of the procedure above and calculate the incremental IRR between the
projects as well as all the other numbers as per normal.
35
Mutually Exclusive Alternatives
Project A
Income, $
- Cost, $
Cash Flow
0
100
-100
50
0
50
60
0
60
Year
0
1
2
Project B
Income, $
- Cost, $
Cash Flow
0
200
-200
Year
0
0
0
0
1
0
0
0
2
70
0
70
3
370
0
370
3
EDS 2004/CI-36
Here is an example of two mutually exclusive projects, A and B. Which of these
projects should be implemented?
How should we evaluate this situation? This is not straight forward, but the test
tomorrow will include a question like this.
36
Mutually Exclusive Alternatives
Net Present Value
Project A
at r = 15%
-100/(1+.15)° + 50/(1+.15)1 + 60/(1+.15)2 +
70/(1+.15)3 -100 + 43 + 45 + 46 = + $34
Project B
at r = 15%
-200/(1+.15)° + 370/(1+.15)3 -200 + 243 = + $43
Minimum rate of return is 15%
EDS 2004/CI-37
Please go through the calculations. Do you agree with the NPV numbers shown
above? If not, please ask for further explanation of this.
37
Mutually Exclusive Alternatives
Internal Rate of Return
Project A
at r = 30%
-100/(1+.30)° + 50/(1+.30)1 + 60/(1+.30)2 + 70/(1+.30)3
-100 + 38 + 36 + 32 = + $6
at r = 35%
-100/(1+.35)° + 50/(1+.35)1 + 60/(1+.35)2 + 70/(1+.35)3
-100 + 37 + 33 + 28 = - $2
at r = 33%
-100/(1+.33)° + 50/(1+.33)1 + 60/(1+.33)2 + 70/(1+.33)3
-100 + 38 + 34 + 30 = + $2
EDS 2004/CI-38
Again, please go through the calculations. Find the right IRR number for project A
- it has to be 34% - agreed?
38
Mutually Exclusive Alternatives
Internal Rate of Return
Project B
at r = 20%
-200/(1+.20)° + 370/(1+.20)3 -200 + 214 = + $14
at r = 25%
-200/(1+.25)° + 370/(1+.25)3 -200 + 189 = - $11
at r = 23%
-200/(1+.23)° + 370/(1+.23)3 -200 + 199 = - $1
EDS 2004/CI-39
And for Project B, the IRR is very close to 23% - agreed?
39
Mutually Exclusive Alternatives
Project B
Cash Flow of B
-200
0
0
Year
0
1
2
50
-50
60
-60
1
2
Project A
Cash Flow of A
Cash Flow B-A
Year
-100
-100
0
370
3
70
300
3
EDS 2004/CI-40
Again, please go carefully through the calculation. Check that you agree with all of
the cash flows ( + & - ) shown for project B minus project A.
40
Mutually Exclusive Alternatives
Incremental Rate of Return
Project B - Project A
at r = 15%
-100/(1+.15)° - 50/(1+.15)1 - 60/(1+.15)2 + 300/(1+.15)3
-100 - 43 - 45 + 197 = + $9
at r = 20%
-100/(1+.20)° - 50/(1+.20)1 - 60/(1+.20)2 + 300/(1+.20)3
-100 - 42 - 42 + 174 = - $10
Therefore, the incremental rate of return is approximately
17%, which is above our minimum rate of return. Project B
is the project that will give the highest return on our money.
EDS 2004/CI-41
And finally, one last IRR calculation and the end result is that project B is better
than project A - just like the NPV figures showed us in Slide 37.
The reason for all this is that many people look almost solely at IRR and project A
has the higher IRR but project B is definitely better.
If you are a little confused at this point, go back to Slide 35 and work through the
numbers carefully one more time. It will then become much clearer.
The next slide provides a summary of this project comparison.
41
Project Comparison
Year
Project
A
Project
B
Project
B-A
0
1
2
3
-100
50
60
70
-200
0
0
370
-100
-50
-60
300
80
35
34%
170
43
23%
90
8
17%
Best
IRR
Best
NPV
Net Income
NPV @ 15%
IRR
Winner
is B
EDS 2004/CI-42
When evaluating mutually exclusive projects, you can subtract the cash flows of
project A from those of project B. If the NPV of B minus A is positive, then project
B is the winner. If it is negative, then go with project A.
In summary, always select the project with the higher or highest NPV.
42
Sensitivity Analysis
Year
0
1
2
3
Net Income
NPV @ 15%
IRR
Project
A
-100
50
60
70
Project
B
-200
0
0
370
Project
B-A
-100
-50
-60
300
80
35
34%
170
43
23%
90
8
17%
NPV
62.5
47.6
34.9
23.8
14.2
5.8
Sensitivity Analysis
NPV
119.6
78.0
43.3
14.1
-10.6
-31.6
NPV
57.1
30.3
8.4
-9.7
-24.8
-37.4
Discount Rate
5%
10%
15%
20%
25%
30%
EDS 2004/CI-43
This is an example of a sensitivity analysis (that looks at the effect of the discount
rate on NPV). The next slide is a graphical plot of these numbers.
43
Sensitivity Analysis
(continued)
120
100
80
60
40
20
0
-20
-40
5%
10%
Project A
15%
20%
Project B
25%
30%
Project B-A
EDS 2004/CI-44
Graphically, you can see the range on the x-axis of the cost of capital (up to about
17%) where selecting Project B (the red line) instead of Project A (the blue line)
creates the higher NPV and is, therefore, the better choice.
44
Non-Mutually Exclusive Alternatives
The goal is to rank several potential projects
by economic return to give higher priority to
the projects with highest return on investment
– Present Value Ratio = NPV / PWNC
•
•
NPV = Net Present Value
PWNC = Present Worth Net Cost
(calculated at the minimum rate of return)
EDS 2004/CI-45
The
other situation is when we have a whole set of completely independent projects
.
from which to select and there is enough money to invest in several of them.
Which projects represent the best use of our money available for investment?
45
Present Worth Net Cost (PWNC)
PWNC = Σ Εj / (1 + i) j
where 0 < j < n
j
E
I
n
=
=
=
=
Period of time, usually a year
Expenditure in time period j
Interest rate ( = cost of capital)
Number of time periods, years
EDS 2004/CI-46
The formula only covers the period of time during which expenditure (E) is
incurred. It works out the “Present Worth” of the expenditure or “Net Cost”
required for each of the possible projects.
46
Present Worth Net Cost (PWNC)
Income, $
- Cost, $
Cash Flow
0
-100
-100
Year
0
50
-100
-50
110
0
110
1
2
120
0
120
3
PWNC = +100/(1+.15)° + 50/(1+.15)1
PWNC = $143
EDS 2004/CI-47
Here is an example of calculating the Present Worth Net Cost. Look at the
Cash Flow figures in red above and discount only these two negative numbers
.back to the initial time period to calculate the Present Worth Net Cost.
47
Net Present Value (NPV)
Income, $
- Cost, $
Cash Flow
0
-100
-100
Year
0
50
-100
-50
110
0
110
120
0
120
1
2
3
NPV = -100/(1+.15)° - 50/(1+.15)1 + 110/(1+.15)2 + 120/(1+.15)3
NPV = -100 - 43 + 83 + 79
NPV = + $19
EDS 2004/CI-48
This is the calculation of the project’s NPV exactly as per normal.
48
Present Value Ratio
Income, $
- Cost, $
Cash Flow
0
-100
-100
Year
0
50
-100
-50
1
110
0
110
120
0
120
2
3
Present Value Ratio = Net Present Value / Present Worth Net Cost
Present Value Ratio = 19 / 143 = 0.13
EDS 2004/CI-49
And now the Present Value (PV) Ratio can be calculated as shown above.
49
Non-Mutually Exclusive Alternatives
To rank several projects, order the projects
by their present value ratio
Project
Present
Value Ratio
Rank
A
B
C
D
0.13
1.21
0.37
0.04
3
1
2
4
EDS 2004/CI-50
This is an example of ranking projects based on PV ratio analysis. The higher the
PV ratio the better the project.
50
Project Ranking Example
Project
G
Project
H
-2000
0
2000
5000
-2000
20000
-21000
0
-2000
0
1000
100000
5000
5000
-3000
99000
NPV @ 15%
IRR
2,913
68.2%
2,800
60.1%
(488)
19.2%
64,508
273%
Payout, years
PV ratio
2
1.46
2
1.40
0.1
-0.03
3
>32
Project
E
Project
F
0
1
2
3
-2000
1000
1000
5000
Net Income
Year
EDS 2004/CI-51
There are many interesting points to think about if you go through the example
above comparing projects E, F, G, and H. Simple payout gives a completely wrong
set of answers, whereas, the PV ratio method works perfectly.
51
Cash Flow Analysis
EDS 2004/CI-52
The final section of this session is intended to answer the question - “Where do all
the cash flow numbers come from?” and to lead into a real-life 1999 example of a
residue upgrading refinery project evaluation for you to work on.
52
Cash Flow Analysis
Net Income or Gross Margin
- Expenses
- Taxes
Costs
- Interest
- Capital charges
}
= Net Cash Flow
EDS 2004/CI-53
This definition is critically important. All of the costs must be brought into the
calculation and deducted from the revenue, income, or receipts.
53
Sample Economic Evaluation
$MM(U.S.)
Year
Net Cash Flow
Cum. Cash Flow
0
(350)
(350)
Economic Evaluation:
Net Present Value
Interest rate, i
NPV at i, $MM
Internal Rate of Return
Simple Payout
1
(500)
(850)
2
(79)
(929)
3
365
(564)
4
378
(185)
5
396
211
6
367
578
7
8
9
10
1
381
397
367
383
479
959 1,356 1,723 2,106 2,585
5%
10%
15%
20%
25%
30%
35%
1,604
968
542
250
45
(102)
(209)
26%
4.5 years
EDS 2004/CI-54
Please also refer to the hand-out showing the calculation of the Net Cash Flow
numbers summarized above.
54
Financial Functions in Excel
Net Present Value (NPV)
= NPV (interest rate, cash flow range)
+ cash flow in year 0
Notes: do not discount the cash flow for year 0
cash flow range is for years 1 to n
Internal Rate of Return (IRR)
= IRR (cash flow range, guess of IRR)
Note: cash flow range is for years 0 to n
EDS 2004/CI-55
I suggest you try using these functions the next time you are in Excel.
55
Financial Functions in Lotus
Net present value (NPV)
= @ NPV (i, range) + cash flow in year 0
where i = the minimum rate of return and
range = the cash flows in years 1 to n
Internal Rate of Return
= @ IRR (i, range)
where i = a starting guess for the IRR and
range = the cash flows in years 0 to n
EDS 2004/CI-56
Does anybody still use Lotus? Well just in case there’s someone back there!
56
UOP’s Electric Mop Project
Pilot Production and Test Marketing
– Period of 1 year
– Investment of $125,000
– 50% chance of success
Build Production Plant
– Investment of $1,000,000
– Annual cash flow of $250,000
– or only $75,000 if the test fails
– 20 year project life
High Risk Project
– Use 25% discount factor
Is This A Good Project?
EDS 2004/CI-57
Interesting class problem? The answer is far from being obvious!.
57
NPV Analysis
Cash Flows, $000
Year 0 -125
Year 1 50% of -1000
Year 2 50% of 250
Year 3 50% of 250
…
Year 21 50% of 250
and 50% of 0
and 50% of 0
and 50% of 0
and 50% of 0
Expected
- 125
- 500
125
125
125
NPV = -125 - ( 500 / 1.25 ) + Σ ( 125 / 1.25^t )
NPV = -129.6
Negative NPV = Not A Good Project?
EDS 2004/CI-58
The approach should be to first of all work out the expected cash flow in each
period of time. Then calculate the NPV using an appropriate cost of capital in view
of the risk involved. However, the next slide shows a different approach to this
problem.
58
Decision Tree Analysis
Invest 1,000 in
Full Scale Plant
Success
(50%)
Test
(Invest 125)
Don’t Invest
t = 20
NPV = - 1,000 + Σ ( 250 / 1.15 ^t )
t=1
NPV = 565
Stop NPV = 0
Invest 1,000 in
Full Scale Plant
t = 20
NPV = - 1,000 + Σ (75 / 1.15 ^t )
Failure
(50%)
t=1
NPV = - 531
Don’t Test
Stop
Don’t Invest
Stop NPV = 0
Actual NPV = (-125) + (0.5 * 565)/(1.25) = $101
EDS 2004/CI-59
The right way to analyze the problem is through a decision tree analysis. The key
difference now is that after the test marketing in year 1, there will be much less risk
involved and a lower rate of return would then be acceptable.
59
Capital Investment
Evaluation
EDS 2004/CI-1
Hello and good morning! My name is Joe Weiszmann and I am from the Solutions
and Services Department of UOP. My specialization is the front-end conceptual
design and optimization of refinery and petrochemical complexes. I often evaluate
the economics and profitability of new refinery projects and of refinery revamps or
upgrading projects as part of my work at UOP.
This training class is about capital investment evaluation. For the next three hours, I
would like to tell you about how to evaluate and select capital projects using the
appropriate capital investment evaluation tools.
Outline
Time Value of Money
Investment Evaluation Tools
– Net Present Value (NPV)
– Breakeven analysis
– Internal Rate of Return (IRR)
Project Ranking
– Simple payout
– Mutually exclusive projects
– Sensitivity analysis
– Present value ratio
Cash Flow Analysis
– Examples
Class Problems
EDS 2004/CI-2
We will go through the concept of the time value of money. Next, we will go
through the three most common investment evaluation tools: net present value,
breakeven analysis and internal rate of return.
I will show you which is the correct tool to use for evaluating capital projects.
There are several different techniques used for evaluating capital projects, including
simple payout, mutually exclusive projects, sensitivity analysis, and present value
ratio. We will talk about all of these this morning.
We will then go through a cash flow analysis and work out some examples. We
will finish the class with doing some class and homework problems.
2
Time Line Concept
Income, $
Investment
or Cost, $
Year
50
100
100
0
1
50
50
50
50
2
3
4
5
EDS 2004/CI-3
The time line concept entails organizing the income and investment (or cost) of a
particular project over a selected period of time to be analyzed in terms of the
income received and cost incurred during each individual period of time.
3
Time Line Concept
Income, $
0
50
50
50
50
50
- Cost, $
-100
-100
0
0
0
0
Cash Flow
-100
-50
50
50
50
50
0
1
2
3
4
5
Year
EDS 2004/CI-4
By subtracting the cost from the income, you get the net cash flow for each period
of time. In other words, the cash flow is typically the profit that you make after you
subtract your cost and expenses from the income or revenues.
4
Definition of Cash Flow
Gross revenue or savings
- Operating costs
- Tax costs
- Capital costs
= Cash flow
EDS 2004/CI-5
A more detailed description or definition of cash flow is the money remaining after
you subtract all the operating costs (both variable and fixed), tax costs (everyone
pays some kind of tax?), and capital costs (e.g. for plant, equipment, buildings, etc.,
which are typically amortized via depreciation) from the gross revenues or savings,
i.e. from the revenue received or the savings achieved.
5
Time Value of Money – Example
Putting Money to Work
Invest $100 in Bank A and $100 in Bank B
Bank A pays 20% simple interest at the end of
three years
Bank B pays 10% compound interest for three
years
EDS 2004/CI-6
Here’s an example of the time value of money. Let’s invest $100 M in Bank A and
$100 M in Bank B. Bank A pays 20% simple interest at the end of three years,
while Bank B pays 10% compound interest for three straight years. It is just an
example of the time value of money.
6
Time Value of Money
Bank A
100*1.2=
-$100
Year
0
$120
1
2
3
EDS 2004/CI-7
In Bank A, after 3 years, the $100 investment turns into $120 based on using a
simple interest rate of 20%.
7
Time Value of Money
Bank B
Year
100*1.1=
110*1.1=
121*1.1=
-$100
$110
$121
$133
0
1
2
3
EDS 2004/CI-8
In Bank B, we apply a compound interest rate. This interest rate is different from
the simple one in that it is compounded each and every year.
The interest rate is applied to the investment every year, as long as the money is
kept invested or deposited in the bank.
The value of your $100 with compound interest is calculated using the formula
shown here. After three years, your $100 becomes $133.
8
Investment Evaluation
Investment evaluation will show us if
an investment gives us a good return
on our money.
EDS 2004/CI-9
The next section will introduce the three most common methods of investment
evaluation: net present value, breakeven analysis, and internal rate of return.
9
Cost of Capital
The Cost of Capital (or money) is the rate of
return that could be realized on similar
alternative investments of equivalent risk.
This foregone rate of return is the standard to
which we compare all our investments.
EDS 2004/CI-10
The cost of capital is an important principle that underlies all investment evaluation
work.
What else could we be doing with our money (that would involve only the same
amount of risk)?
10
Investment Evaluation Tools
Net Present Value (NPV)
Breakeven Analysis
Internal Rate of Return (IRR)
EDS 2004/CI-11
Let’s now look at the three most common investment evaluation tools:
Breakeven Analysis, and IRR.
NPV,
11
Net Present Value (NPV)
Net Present Value is the total value of a project,
revenues minus costs, brought backward to the
first year at a specified rate of interest per year.
EDS 2004/CI-12
More explanation (plus examples) are provided on the following slides.
12
Net Present Value (NPV)
(continued)
NPV = Σ Cj / (1 + i) j
where 0 < j < n
j
Cj
I
n
=
=
=
=
Period of time, usually a year
Cash flow in the time period j
Interest rate ( = cost of capital)
Number of time periods, years
EDS 2004/CI-13
The NPV of a project is the summation of all the discounted cash flows over all of
the time periods to be evaluated.
13
Net Present Value (NPV)
(continued)
I want to have $2,000 at the end of 5 years.
The interest rate is 12%.
How much do I have to invest in year 1?
EDS 2004/CI-14
Here is an example. Can anyone tell me the answer?
14
Net Present Value (NPV)
(continued)
Income, $
0
0
0
0
0
2000
- Cost, $
NPV
0
0
0
0
0
Cash Flow
-NPV
0
0
0
0
2000
Year
0
1
2
3
4
5
NPV = 2000 / (1+0.12)5
NPV = $1135 (to be invested at the beginning of the year)
EDS 2004/CI-15
Let’s go through the calculation, step by step, as shown above.
15
Net Present Value (NPV)
(continued)
Another way to look at it:
Income, $
0
0
0
0
0
2000
- Cost, $
X
0
0
0
0
0
Cash Flow
-X
0
0
0
0
2000
Year
0
1
2
3
4
5
To make 12% on my investment:
-X + 2000 / (1+0.12)5 = 0
X = $1135
This is also called the Breakeven Price
EDS 2004/CI-16
The breakeven price is based on determining the initial investment required @ 12%
to obtain @ $2000 at the end of five years.
If you had to invest more than $1135, you would be losing money; if you had to
invest less than $1135, you would be gaining money. However, if you had to invest
exactly $1135, then you would be breaking even. Hence, $1135 is called the
breakeven price in this example.
16
Net Present Value – Example
Income, $
0
50
40
30
20
- Cost, $
100
0
0
0
0
Cash Flow
-100
50
40
30
20
Year
0
1
2
3
4
What is the NPV of this project using a cost of capital of
15%? What is the Breakeven Investment cost?
EDS 2004/CI-17
Here is another example of calculating NPV that I suggest you try working on
(without turning over just yet).
17
Worksheet for NPV Example
NPV = Σ Cj / (1 + i) j
NPV = -100 / (1+0.15)0 +
50 / (1+0.15)1 +
40 / (1+0.15)2 +
30 / (1+0.15)3 +
20 / (1+0.15)4
NPV = -100 + 43 + 30 + 20 + 11
NPV = $4
EDS 2004/CI-18
Please go through the calculation and make sure you could do it yourself.
18
At the beginning of year 1, the value of this project is
$4 at a 15% rate of interest. This means I make
15% interest on my $100 investment over a 4 year
period, plus $4 extra. The interest rate on this
investment is, therefore, greater than 15% per year.
EDS 2004/CI-19
This project is attractive if the cost of capital is 15% (or less). The net present value
of the project is calculated to be plus $4 at a 15% rate of interest.
19
Breakeven Analysis
Breakeven analysis is determining the value of
any parameter which allows a specified rate of
return to be achieved from an investment.
The parameter may be the initial investment
cost, project lifetime, annual revenue, selling
price of a product, or % utilization of plant.
EDS 2004/CI-20
Breakeven analysis can be applied to lots of other parameters, for example the plant
throughput required to just breakeven. See above for other examples of the
parameters that can be studied as part of a breakeven analysis of a project.
20
Breakeven Investment Cost
Income, $
0
50
40
30
20
- Cost, $
X
0
0
0
0
Cash Flow
-X
50
40
30
20
Year
0
1
2
3
4
NPV = 0 = -X / (1+.15)0 + 50 / (1+.15)1 + 40 / (1+.15)2
+ 30 / (1+.15)3 + 20 / (1+.15)4
0 = -X + 43 + 30 + 20 + 11
X = $104
EDS 2004/CI-21
In the breakeven analysis above, we want to find out what our maximum investment
cost should be to just meet our accepted 15% rate of return. This is calculated as
shown above with the NPV set equal to zero.
21
For a Rate of Return of 15% on this investment, I
could invest up to $104. This is then the Breakeven
Investment Cost for this particular project. Any
additional cost would lower the Rate of Return to
less than 15% which would not be acceptable.
EDS 2004/CI-22
This is just another way of saying the same thing.
22
What is the NPV at 20%?
Income, $
0
50
40
30
20
- Cost, $
100
0
0
0
0
Cash Flow
-100
50
40
30
20
Year
0
1
2
3
4
NPV = -100 / (1+.20)0 + 50 / (1+ .20)1 + 40 / (1+ .20)2
+ 30 / (1+ .20)3 + 20 / (1+ .20)4
= -100 + 42 + 28 + 17 + 10
= - $3
The IRR is between 15% and 20%.
EDS 2004/CI-23
Here’s an example that calculates the project NPV at a cost of capital of 20%. The
NPV for this project is now minus $3.
This means that the discount rate used is now too high for this project. You are
asking for too much return from this investment.
The rate of return is thus somewhere between 15% and 20%.
23
Internal Rate of Return (IRR)
Rate of Return or interest rate of a project
Calculated through trial and error
EDS 2004/CI-24
Let’s now talk about internal rate or return or IRR as it is routinely called.
24
Internal Rate of Return (IRR)
(continued)
0 = Σ Cj / (1 + r) j
where 0 < j < n
j
Cj
r
n
=
=
=
=
Period of time, usually a year
Cash flow in time period j
Internal Rate of Return unknown
Number of periods, usually years
Assume a value for “r” and calculate formula.
The project’s IRR is the value of “r” that gives
an answer of zero NPV.
EDS 2004/CI-25
This is the formula for calculating the internal rate of return (IRR) of a project. The
calculation is normally an iterative process, even for a computer.
25
What is the IRR of this project?
0
Income, $
100
100
120
140
- Cost, $
-200
-150
0
0
0
Cash Flow
-200
-50
100
120
140
1
2
3
4
Year
0
at r = 15%
- 200/(1+.15)0 - 50/(1+ .15)1 + 100/(1+ .15)2
+ 120/(1+ .15)3 + 140/(1+ .15)4
- 200 - 43 + 76 + 79 + 80 = - $8
at r = 10%
- 200/(1+.10)0 - 50/(1+ .10)1 + 100/(1+ .10)2
+ 120/(1+ .10)3 + 140/(1+ .10)4
- 200 - 45 + 83 + 90 + 96 = + $24
EDS 2004/CI-26
Here is an example the calculates an IRR of a project. As you can see, it is trial and
error approach.
26
Example – What is the IRR of the
following project?
Income, $
0
30
40
50
- Cost, $
100
0
0
0
Cash Flow
-100
30
40
50
Year
0
1
2
3
EDS 2004/CI-27
Here is another example for you to work on (without turning over just yet).
27
What is the IRR of this Project?
Calculation
at r = 15%
-100/(1+.15)° + 30/(1+.15)1 + 40/(1+.15)2 + 50/(1+.15)3
-100 + 26 + 30 + 33 = - $11
at r = 10%
-100/(1+.10)° + 30/(1+.10)1 + 40/(1+.10)2 + 50/(1+.10)3
-100 + 27 + 33 + 38 = - $2
at r = 8%
-100/(1+.08)° + 30/(1+.08)1 + 40/(1+.08)2 + 50/(1+.08)3
-100 + 28 + 34 + 40 = + $2
The internal rate of return is 9%
EDS 2004/CI-28
Here is the calculation of the internal rate of return (IRR) for this example.
28
Project Ranking
Simple Payout
Mutually Exclusive Projects
Sensitivity Analysis
Present Value Ratio
EDS 2004/CI-29
Let’s now move on and go over methods for ranking and prioritizing projects.
29
Simple Payout
Simple payout is the number of years it will take
to pay back an investment at the initial operating
gross margin. Simple payout takes no account of
inflation, nor of the time value of money.
Example:
– Gross margin in year 1 = $700 MM/year
– Total investment in project = $1,400 MM
– Simple payout = $1,400/$700 = 2 years
EDS 2004/CI-30
Simple payout is (as it says) simple. It is widely used and quite a useful concept,
but beware of the pitfalls explained on the next few slides.
30
Payout Example #1
Project A
Cash Flow
-100
Year
0
50
50
1
2
50
3
NPV @ 15% minimum rate of return = $15
and the IRR ∼ 23%
Payout = 2 years
EDS 2004/CI-31
This is example #1 of using simple payout. Do you agree with the NPV, IRR and
Payout figures worked out above? If yes, then turn over to example #2.
31
Payout Example #2
Project B
Cash Flow
-100
Year
0
100
0
1
2
0
3
NPV @ 15% min rate of return = - $13
and the IRR = 0%
Payout = 1 year
EDS 2004/CI-32
Here again, I suggest you check the NPV, IRR and Payout numbers worked out
above. The point is that the Payout in Example #2 is better (half as long) than in
Example #1, but everything else is obviously much worse.
32
Simple Payout
Simplest economic evaluation method
Takes NO account of the time value of money
Penalizes long term projects
Benefits quick projects
EDS 2004/CI-33
Must emphasize that the Simple Payout approach should not be used as a tool for
making decisions on a project. It is basically a very rough screening tool.
33
Project Ranking
Mutually exclusive alternatives
– Only 1 project can be accepted
Non-mutually exclusive alternatives
– Ranking several projects
EDS 2004/CI-34
It is important to decide up-front whether or not the projects you are evaluating are
mutually exclusive. It affects the correct choice of evaluation method.
A common example of mutually exclusive projects is when there are two or three
different options for revamping of a particular plant. Only one of the revamp
options can be implemented - a decision is required.
34
Mutually Exclusive Alternatives
The goal is to choose the one project that gives the
investors the largest return on their money
– The project with the largest NPV using the minimum
rate of return
– The project with the highest incremental IRR
•
•
•
Calculate each project’s individual IRR; must be
higher than the minimum rate of return
Calculate the incremental IRR between projects; this
too must be higher than the minimum rate of return
The project which has the highest incremental IRR
will give the largest return on the investment
EDS 2004/CI-35
For mutually exclusive projects, beware of using IRR, unless you go through the
whole of the procedure above and calculate the incremental IRR between the
projects as well as all the other numbers as per normal.
35
Mutually Exclusive Alternatives
Project A
Income, $
- Cost, $
Cash Flow
0
100
-100
50
0
50
60
0
60
Year
0
1
2
Project B
Income, $
- Cost, $
Cash Flow
0
200
-200
Year
0
0
0
0
1
0
0
0
2
70
0
70
3
370
0
370
3
EDS 2004/CI-36
Here is an example of two mutually exclusive projects, A and B. Which of these
projects should be implemented?
How should we evaluate this situation? This is not straight forward, but the test
tomorrow will include a question like this.
36
Mutually Exclusive Alternatives
Net Present Value
Project A
at r = 15%
-100/(1+.15)° + 50/(1+.15)1 + 60/(1+.15)2 +
70/(1+.15)3 -100 + 43 + 45 + 46 = + $34
Project B
at r = 15%
-200/(1+.15)° + 370/(1+.15)3 -200 + 243 = + $43
Minimum rate of return is 15%
EDS 2004/CI-37
Please go through the calculations. Do you agree with the NPV numbers shown
above? If not, please ask for further explanation of this.
37
Mutually Exclusive Alternatives
Internal Rate of Return
Project A
at r = 30%
-100/(1+.30)° + 50/(1+.30)1 + 60/(1+.30)2 + 70/(1+.30)3
-100 + 38 + 36 + 32 = + $6
at r = 35%
-100/(1+.35)° + 50/(1+.35)1 + 60/(1+.35)2 + 70/(1+.35)3
-100 + 37 + 33 + 28 = - $2
at r = 33%
-100/(1+.33)° + 50/(1+.33)1 + 60/(1+.33)2 + 70/(1+.33)3
-100 + 38 + 34 + 30 = + $2
EDS 2004/CI-38
Again, please go through the calculations. Find the right IRR number for project A
- it has to be 34% - agreed?
38
Mutually Exclusive Alternatives
Internal Rate of Return
Project B
at r = 20%
-200/(1+.20)° + 370/(1+.20)3 -200 + 214 = + $14
at r = 25%
-200/(1+.25)° + 370/(1+.25)3 -200 + 189 = - $11
at r = 23%
-200/(1+.23)° + 370/(1+.23)3 -200 + 199 = - $1
EDS 2004/CI-39
And for Project B, the IRR is very close to 23% - agreed?
39
Mutually Exclusive Alternatives
Project B
Cash Flow of B
-200
0
0
Year
0
1
2
50
-50
60
-60
1
2
Project A
Cash Flow of A
Cash Flow B-A
Year
-100
-100
0
370
3
70
300
3
EDS 2004/CI-40
Again, please go carefully through the calculation. Check that you agree with all of
the cash flows ( + & - ) shown for project B minus project A.
40
Mutually Exclusive Alternatives
Incremental Rate of Return
Project B - Project A
at r = 15%
-100/(1+.15)° - 50/(1+.15)1 - 60/(1+.15)2 + 300/(1+.15)3
-100 - 43 - 45 + 197 = + $9
at r = 20%
-100/(1+.20)° - 50/(1+.20)1 - 60/(1+.20)2 + 300/(1+.20)3
-100 - 42 - 42 + 174 = - $10
Therefore, the incremental rate of return is approximately
17%, which is above our minimum rate of return. Project B
is the project that will give the highest return on our money.
EDS 2004/CI-41
And finally, one last IRR calculation and the end result is that project B is better
than project A - just like the NPV figures showed us in Slide 37.
The reason for all this is that many people look almost solely at IRR and project A
has the higher IRR but project B is definitely better.
If you are a little confused at this point, go back to Slide 35 and work through the
numbers carefully one more time. It will then become much clearer.
The next slide provides a summary of this project comparison.
41
Project Comparison
Year
Project
A
Project
B
Project
B-A
0
1
2
3
-100
50
60
70
-200
0
0
370
-100
-50
-60
300
80
35
34%
170
43
23%
90
8
17%
Best
IRR
Best
NPV
Net Income
NPV @ 15%
IRR
Winner
is B
EDS 2004/CI-42
When evaluating mutually exclusive projects, you can subtract the cash flows of
project A from those of project B. If the NPV of B minus A is positive, then project
B is the winner. If it is negative, then go with project A.
In summary, always select the project with the higher or highest NPV.
42
Sensitivity Analysis
Year
0
1
2
3
Net Income
NPV @ 15%
IRR
Project
A
-100
50
60
70
Project
B
-200
0
0
370
Project
B-A
-100
-50
-60
300
80
35
34%
170
43
23%
90
8
17%
NPV
62.5
47.6
34.9
23.8
14.2
5.8
Sensitivity Analysis
NPV
119.6
78.0
43.3
14.1
-10.6
-31.6
NPV
57.1
30.3
8.4
-9.7
-24.8
-37.4
Discount Rate
5%
10%
15%
20%
25%
30%
EDS 2004/CI-43
This is an example of a sensitivity analysis (that looks at the effect of the discount
rate on NPV). The next slide is a graphical plot of these numbers.
43
Sensitivity Analysis
(continued)
120
100
80
60
40
20
0
-20
-40
5%
10%
Project A
15%
20%
Project B
25%
30%
Project B-A
EDS 2004/CI-44
Graphically, you can see the range on the x-axis of the cost of capital (up to about
17%) where selecting Project B (the red line) instead of Project A (the blue line)
creates the higher NPV and is, therefore, the better choice.
44
Non-Mutually Exclusive Alternatives
The goal is to rank several potential projects
by economic return to give higher priority to
the projects with highest return on investment
– Present Value Ratio = NPV / PWNC
•
•
NPV = Net Present Value
PWNC = Present Worth Net Cost
(calculated at the minimum rate of return)
EDS 2004/CI-45
The
other situation is when we have a whole set of completely independent projects
.
from which to select and there is enough money to invest in several of them.
Which projects represent the best use of our money available for investment?
45
Present Worth Net Cost (PWNC)
PWNC = Σ Εj / (1 + i) j
where 0 < j < n
j
E
I
n
=
=
=
=
Period of time, usually a year
Expenditure in time period j
Interest rate ( = cost of capital)
Number of time periods, years
EDS 2004/CI-46
The formula only covers the period of time during which expenditure (E) is
incurred. It works out the “Present Worth” of the expenditure or “Net Cost”
required for each of the possible projects.
46
Present Worth Net Cost (PWNC)
Income, $
- Cost, $
Cash Flow
0
-100
-100
Year
0
50
-100
-50
110
0
110
1
2
120
0
120
3
PWNC = +100/(1+.15)° + 50/(1+.15)1
PWNC = $143
EDS 2004/CI-47
Here is an example of calculating the Present Worth Net Cost. Look at the
Cash Flow figures in red above and discount only these two negative numbers
.back to the initial time period to calculate the Present Worth Net Cost.
47
Net Present Value (NPV)
Income, $
- Cost, $
Cash Flow
0
-100
-100
Year
0
50
-100
-50
110
0
110
120
0
120
1
2
3
NPV = -100/(1+.15)° - 50/(1+.15)1 + 110/(1+.15)2 + 120/(1+.15)3
NPV = -100 - 43 + 83 + 79
NPV = + $19
EDS 2004/CI-48
This is the calculation of the project’s NPV exactly as per normal.
48
Present Value Ratio
Income, $
- Cost, $
Cash Flow
0
-100
-100
Year
0
50
-100
-50
1
110
0
110
120
0
120
2
3
Present Value Ratio = Net Present Value / Present Worth Net Cost
Present Value Ratio = 19 / 143 = 0.13
EDS 2004/CI-49
And now the Present Value (PV) Ratio can be calculated as shown above.
49
Non-Mutually Exclusive Alternatives
To rank several projects, order the projects
by their present value ratio
Project
Present
Value Ratio
Rank
A
B
C
D
0.13
1.21
0.37
0.04
3
1
2
4
EDS 2004/CI-50
This is an example of ranking projects based on PV ratio analysis. The higher the
PV ratio the better the project.
50
Project Ranking Example
Project
G
Project
H
-2000
0
2000
5000
-2000
20000
-21000
0
-2000
0
1000
100000
5000
5000
-3000
99000
NPV @ 15%
IRR
2,913
68.2%
2,800
60.1%
(488)
19.2%
64,508
273%
Payout, years
PV ratio
2
1.46
2
1.40
0.1
-0.03
3
>32
Project
E
Project
F
0
1
2
3
-2000
1000
1000
5000
Net Income
Year
EDS 2004/CI-51
There are many interesting points to think about if you go through the example
above comparing projects E, F, G, and H. Simple payout gives a completely wrong
set of answers, whereas, the PV ratio method works perfectly.
51
Cash Flow Analysis
EDS 2004/CI-52
The final section of this session is intended to answer the question - “Where do all
the cash flow numbers come from?” and to lead into a real-life 1999 example of a
residue upgrading refinery project evaluation for you to work on.
52
Cash Flow Analysis
Net Income or Gross Margin
- Expenses
- Taxes
Costs
- Interest
- Capital charges
}
= Net Cash Flow
EDS 2004/CI-53
This definition is critically important. All of the costs must be brought into the
calculation and deducted from the revenue, income, or receipts.
53
Sample Economic Evaluation
$MM(U.S.)
Year
Net Cash Flow
Cum. Cash Flow
0
(350)
(350)
Economic Evaluation:
Net Present Value
Interest rate, i
NPV at i, $MM
Internal Rate of Return
Simple Payout
1
(500)
(850)
2
(79)
(929)
3
365
(564)
4
378
(185)
5
396
211
6
367
578
7
8
9
10
1
381
397
367
383
479
959 1,356 1,723 2,106 2,585
5%
10%
15%
20%
25%
30%
35%
1,604
968
542
250
45
(102)
(209)
26%
4.5 years
EDS 2004/CI-54
Please also refer to the hand-out showing the calculation of the Net Cash Flow
numbers summarized above.
54
Financial Functions in Excel
Net Present Value (NPV)
= NPV (interest rate, cash flow range)
+ cash flow in year 0
Notes: do not discount the cash flow for year 0
cash flow range is for years 1 to n
Internal Rate of Return (IRR)
= IRR (cash flow range, guess of IRR)
Note: cash flow range is for years 0 to n
EDS 2004/CI-55
I suggest you try using these functions the next time you are in Excel.
55
Financial Functions in Lotus
Net present value (NPV)
= @ NPV (i, range) + cash flow in year 0
where i = the minimum rate of return and
range = the cash flows in years 1 to n
Internal Rate of Return
= @ IRR (i, range)
where i = a starting guess for the IRR and
range = the cash flows in years 0 to n
EDS 2004/CI-56
Does anybody still use Lotus? Well just in case there’s someone back there!
56
UOP’s Electric Mop Project
Pilot Production and Test Marketing
– Period of 1 year
– Investment of $125,000
– 50% chance of success
Build Production Plant
– Investment of $1,000,000
– Annual cash flow of $250,000
– or only $75,000 if the test fails
– 20 year project life
High Risk Project
– Use 25% discount factor
Is This A Good Project?
EDS 2004/CI-57
Interesting class problem? The answer is far from being obvious!.
57
NPV Analysis
Cash Flows, $000
Year 0 -125
Year 1 50% of -1000
Year 2 50% of 250
Year 3 50% of 250
…
Year 21 50% of 250
and 50% of 0
and 50% of 0
and 50% of 0
and 50% of 0
Expected
- 125
- 500
125
125
125
NPV = -125 - ( 500 / 1.25 ) + Σ ( 125 / 1.25^t )
NPV = -129.6
Negative NPV = Not A Good Project?
EDS 2004/CI-58
The approach should be to first of all work out the expected cash flow in each
period of time. Then calculate the NPV using an appropriate cost of capital in view
of the risk involved. However, the next slide shows a different approach to this
problem.
58
Decision Tree Analysis
Invest 1,000 in
Full Scale Plant
Success
(50%)
Test
(Invest 125)
Don’t Invest
t = 20
NPV = - 1,000 + Σ ( 250 / 1.15 ^t )
t=1
NPV = 565
Stop NPV = 0
Invest 1,000 in
Full Scale Plant
t = 20
NPV = - 1,000 + Σ (75 / 1.15 ^t )
Failure
(50%)
t=1
NPV = - 531
Don’t Test
Stop
Don’t Invest
Stop NPV = 0
Actual NPV = (-125) + (0.5 * 565)/(1.25) = $101
EDS 2004/CI-59
The right way to analyze the problem is through a decision tree analysis. The key
difference now is that after the test marketing in year 1, there will be much less risk
involved and a lower rate of return would then be acceptable.
59
