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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

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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.

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