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Atelier des Lumieres – Fantastic!
Pere La Chaise Cemetery - huge, free, interesting
Roland Garros, Horticulture Gardens
Pompidou – Dora Maar, Prehistory
New homework due Wednesday
More on stocks
Present Worth Analysis, Annual Equivalent
Internal Rate of Return

2. Quiz Results

3. Quiz Results

4. Recommendations
Atelier des Lumieres
Projecting pictures with music on 30 foot walls in a football field sized building – stay as long as you like – about a one hour show- fantastic!
38 rue saint Maur – buy ticket on line

6. Pere Lachaise Cemetary
Jim Morrison, Chopin

7. Dora Maar (1907 – 1997)

8. Selling short and options
Definition – stock in street name – the broker holds the stock and the company does not know that you are the owner
Selling short – sell someone else’s stock hoping that it goes down and you can buy it back cheaper and replace it. No actual transfer of stock ownership happens
Without dividend – trading a stock without the associated dividend
Put - An option contract giving the owner the right, but not the obligation, to sell a specified amount of an underlying security at a specified price (strike price) within a specified time. This is the opposite of a call option, which gives the holder the right to buy shares.

9. CHAPTER 5 PRESENT WORTH ANALYSIS
PROJECT CASH FLOWS
PAYBACK PERIOD
NET PRESENT WORTH
CAPITALIZED EQUIVALENT METHOD
MUTUALLY EXCLUSIVE ALTERNATIVES
PROJECT LIVES

10. PROJECT CASH FLOWS INVESTMENTS ARE MADE EARLY IN THE PROJECT
BENEFITS ARE EXPECTED OVER A PERIOD OF YEARS IN THE FUTURE
LOAN CASH FLOW - PAYMENTS RECEIVED BY THE LENDER
PROJECT CASH FLOW - INCOME LESS EXPENSES
PAYBACK PERIOD - THE TIME THAT IT TAKES TO RECOVER THE ORIGINAL COST, e.g., A WAREHOUSE COSTS $4M TO BUILD AND YIELDS A PROFIT OF $500,000/YEAR. THE PAYBACK IS 8 YEARS. THIS IS THE SIMPLEST ANALYSIS
DISCOUNTED PAYBACK PERIOD – REDUCE THE VALUE OF THE INVESTMENT BY THE DISCOUNT RATE

11. PROJECT CASH FLOWS (CONTINUED)
FOR UNEQUAL CASH FLOWS, DETERMINE THE TIME WHEN CASH FLOW EQUALS THE INITIAL INVESTMENT
SALVAGE VALUE - WHAT YOU CAN GET FOR USED EQUIPMENT
THE SALVAGE VALUE OF THE OLD EQUIPMENT IS SUBTRACTED FROM THE INITIAL INVESTMENT
DO NOT USE PAYBACK PERIOD FOR COMPARING PROJECTS, -- ONLY FOR ROUGH SCREENING

12. NET PRESENT WORTH
DISCOUNTED CASH FLOW TECHNIQUES (DCF)
ONE SUCH METHOD IS NET PRESENT WORTH (NPV or NPW)
BRING ALL INVESTMENTS AND BENEFITS BACK TO TIME ZERO
COMPARE THEM
COMPARE TO OTHER ALTERNATIVES
SELECT LARGEST PRESENT WORTH PROJECT

13. NET PRESENT WORTH
WHAT INTEREST RATE DO WE USE?
COMPANIES DETERMINE WHAT THEY CALL:
MINIMUM ATTRACTIVE RATE OF RETURN (MARR)
MANY COMPANIES INSIST ON A HIGH RATE OF RETURN BECAUSE THEY HAVE LIMITED RESOURCES AND WANT TO INVEST IN THE BEST PROJECTS
NET PRESENT WORTH SHOULD BE POSITIVE TO ACCEPT A PROJECT
NPW = 0 MEANS YOU ARE MAKING MONEY AT MARR!
INVESTMENT POOL - ALL AVAILABLE FUNDS FOR INVESTMENT
IF THERE ARE NO FUNDS, THEY MUST BE BORROWED

14. Example

15. CAPITALIZED EQUIVALENT METHOD
APPLIES TO LONG HORIZONS OR PERPETUAL INVESTMENTS
COMPUTING THE PRESENT WORTH OF AN INFINITE SERIES IS CALLED THE CAPITALIZATION OF THE PROJECT’S COST
APPLYING L’HOPITAL’S RULE TO THE (P/A,i,N), WE GET A/i
SO THE PRESENT WORTH OF A SERIES OF CONSTANT PAYMENT STRETCHING OUT TO INFINITE IS A/i

16. Capitalized Equivalent Method

17. MUTUALLY EXCLUSIVE ALTERNATIVES
IF ONE ALTERNATIVE IS SELECTED, ALL OTHERS ARE REJECTED
“DO NOTHING’ IS AN ALTERNATIVE
REVENUE PROJECT -- INCOME DEPENDS ON THE CHOICE OF THE ALTERNATIVE
SERVICE PROJECT -- REVENUES ARE THE SAME REGARDLESS OF THE CHOICE OF ALTERNATIVE

18. PROJECT LIVES
ANALYSIS PERIOD, STUDY PERIOD OR PLANNING HORIZON:
TIME PERIOD OVER WHICH THE IMPACT OF THE PROJECT WILL BE EVALUATED
WE HAVE TO CONSIDER:
REQUIRED SERVICE PERIOD
USEFUL LIFE OF THE PROJECT
FOR MULTIPLE PROJECTS WE MUST COMPARE THEM OVER AN EQUAL TIME SPAN

19. PROJECT LIVES (CONTINUED)
EXAMPLES
PROJECT LIVES LONGER THAN ANALYSIS PERIOD (5.11)
PROJECT LIVES SHORTER THAN ANALYSIS PERIOD (5.10)
ANALYSIS PERIOD = LONGEST LIFE (5.12)
UNEQUAL LIVES - LOWEST COMMON MULTIPLE METHOD (5.13)

20. Example 5.11 – Project lives longer than the analysis period
THIS ONE IS VERY STRAIGHT FORWARD:
WE ANALYZE FOR THE LENGTH OF TIME THAT WE ARE INTERESTED IN. WHATEVER THE EQUIPMENT IS WORTH AT THE END OF THE ANALYSIS PERIOD, WE CONSIDER AS SALVAGE VALUE

21. Example 5.10 Project lives shorter than analysis period
THIS EXAMPLE HAS TWO OPTIONS, ONE THAT WILL LAST 3 YEARS, THE OTHER 4. UNFORTUNATELY WE HAVE TO PLAN FOR 5 YEARS.
WE HAVE TO CHOOSE AN APPROACH THAT WILL FILL IN THE LAST TWO YEARS OF THE FIRST OPTION, AND THE LAST YEAR OF THE SECOND OPTION

22. Example 5.12 Analysis period = longest life

23. Example 5.13 Unequal lives - lowest common multiple method
Option A has a life of 3 years, Option B 4 years.
We use a lowest common denominator (12) as the analysis period
For each option we calculate NPV and the end of its life and then repeat the investment until we have reached the common denominator

24. A FUN NOTE TO END ON (GARY LARSEN) “Notice all the computation, theoretical scribbling, and lab equipment, Norm … Yes, curiosity killed these cats

25. Annual Equivalent
CALCULATE THE NPW, THEN CONVERT TO THE ANNUAL EQUIVALENT
Examples 6.1 and 6.2

26. Contemporary Engineering Economics
Incremental Analysis
Lecture No. 13
Chapter 7
Contemporary Engineering Economics
Copyright © 2006
Contemporary Engineering Economics, 4th edition, © 2007

27. Comparing Mutually Exclusive Alternatives Based on IRR
Issue: Can we rank the mutually exclusive projects by the magnitude of its IRR?
n A1 A2
-$1,000 -$5,000
$2,000 $7,000
100% > %
$818 < $1,364 1
IRR
PW (10%)

28. Contemporary Engineering Economics, 4th edition, © 2007
Who Got More Pay Raise?
Bill
Hillary
10% 5%
Contemporary Engineering Economics, 4th edition, © 2007

29. Can’t Compare without Knowing Their Base Salaries
Bill
Hillary
Base Salary
$50,000
$200,000
Pay Raise (%)
10% 5%
Pay Raise ($)
$5,000
$10,000
For the same reason, we can’t compare mutually exclusive projects based on
the magnitude of its IRR. We need to know the size of investment and its timing
of when to occur.

30. Incremental Investment
Project A1
Project A2
Incremental Investment (A2 – A1) 1
-$1,000
$2,000
-$5,000
$7,000
-$4,000
$5,000
ROR
PW(10%)
100%
$818
40%
$1,364
25%
$546
Assuming a MARR of 10%, you can always earn that rate from other investment source, i.e., $4,400 at the end of one year for $4,000 investment.
By investing the additional $4,000 in A2, you would make additional $5,000, which is equivalent to earning at the rate of 25%. Therefore, the incremental investment in A2 is justified.

31. Incremental Analysis (Procedure)
Step 1: Compute the cash flow for the difference between the projects (A,B) by subtracting the cash flow of the lower investment cost project (A) from that of the higher investment cost project (B).
Step 2: Compute the IRR on this incremental investment (IRR ).
Step 3: Accept the investment B if and only if
IRR B-A > MARR
B-A
NOTE: Make sure that both IRRA and IRRB are greater than MARR.

32. Example 7.10 - Incremental Rate of ReturnB1 B2
B2 - B1 1 2 3
-$3,000
1,350
1,800
1,500
-$12,000
4,200
6,225
6,330
-$9,000
2,850
4,425
4,830
IRR
25%
17.43%
15%
Given MARR = 10%, which project is a better choice?
Since IRRB2-B1=15% > 10%, and also IRRB2 > 10%, select B2.

33. IRR on Increment Investment: Three Alternatives
Step 1: Examine the IRR for each
project to eliminate any project
that fails to meet the MARR.
Step 2: Compare D1 and D2 in pairs.
IRRD1-D2=27.61% > 15%,
so select D1. D1 becomes the
current best.
Step 3: Compare D1 and D3.
IRRD3-D1= 8.8% < 15%,
so select D1 again.
Here, we conclude that D1 is the best
alternative. n D1 D2 D3
-$2,000
-$1,000
-$3,000 1
1,500
800 2
1,000
500
2,000 3
IRR
34.37%
40.76%
24.81%

34. Practice Problem
You are considering four types of engineering designs. The project lasts 10 years with the following estimated cash flows. The interest rate (MARR) is 15%. Which of the four is more attractive?
Project A B C D
Initial cost
$150
$220
$300
$340
Revenues/Year
$115
$125
$160
$185
Expenses/Year
$70
$65
$60
$80
IRR (%)
27.32
24.13
31.11
28.33

35. Example 7.13 Incremental Analysis for Cost-Only Projects
Items
CMS Option
FMS Option
Annual O&M costs:
Annual labor cost
$1,169,600
$707,200
Annual material cost
832,320
598,400
Annual overhead cost
3,150,000
1,950,000
Annual tooling cost
470,000
300,000
Annual inventory cost
141,000
31,500
Annual income taxes
1,650,000
1,917,000
Total annual costs
$7,412,920
$5,504,100
Investment
$4,500,000
$12,500,000
Net salvage value
$500,000
$1,000,000

36. Incremental Cash Flow (FMS – CMS)
CMS Option
FMS Option
Incremental
(FMS-CMS)
-$4,500,000
-$12,500,000
-$8,000,000 1
-7,412,920
-5,504,100
1,908,820 2 3 4 5 6
$2,408,820
Salvage
+ $500,000
+ $1,000,000

37. Solution:

38. Summary
Rate of return (ROR) is the interest rate earned on unrecovered project balances such that an investment’s cash receipts make the terminal project balance equal to zero.
Rate of return is an intuitively familiar and understandable measure of project profitability that many managers prefer to NPW or other equivalence measures.
Mathematically we can determine the rate of return for a given project cash flow series by locating an interest rate that equates the net present worth of its cash flows to zero. This break-even interest rate is denoted by the symbol i*.

39. Internal rate of return (IRR) is another term for ROR that stresses the fact that we are concerned with the interest earned on the portion of the project that is internally invested, not those portions that are released by (borrowed from) the project.
To apply rate of return analysis correctly, we need to classify an investment into either a simple or a nonsimple investment.
A simple investment is defined as one in which the initial cash flows are negative and only one sign change occurs in the net cash flow, whereas a nonsimple investment is one for which more than one sign change occurs in the net cash flow series.
Multiple i*s occur only in nonsimple investments. However, not all nonsimple investments will have multiple i*s either.

40. For a pure investment, the solving rate of return (i
For a pure investment, the solving rate of return (i*) is the rate of return internal to the project; so the decision rule is:
If IRR > MARR, accept the project.
If IRR = MARR, remain indifferent.
If IRR < MARR, reject the project.
IRR analysis yields results consistent with NPW and other equivalence methods.
For a mixed investment, we need to calculate the true IRR, or known as the “return on invested capital.” However, if your objective is simply to make an accept or reject decision, it is recommended that either the NPW or AE analysis be used to make an accept/reject decision.
To compare mutually exclusive alternatives by the IRR analysis, the incremental analysis must be adopted.