Cost and Time Value of $$

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Cost and Time Value of

• Prof. Eric Suuberg
• ENGINEERING 90

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Cost and Time Value Lecture

• What is our goal?
• To gain an understanding of what is and what is
  not a good project to undertake from a
  financial point of view.
• What are our tools?
• Material presented by Prof. Crawford
• Discounting / Time Value of Money
• Tax Savings through Depreciation

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So, what are we starting today?

• Go through some of the fun math for Present
  Value Calculations
• Do a teaching example of purchasing a machine
  for a manufacturing plant
• Talk about costs both the obvious kind as well
  as the non-obvious types
• Time value of money calculations
• Cost Comparisons
• Depreciation
• Put it all together inc. continuous
  discounting and after-tax cost comparisons

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Have I Got a Deal for You

• Would you be interested in investing in a company
  that has 1 million in annual sales?

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What More Would You Like to Know?

• Annual operating expenses (salaries, raw
  materials, etc.)
• Suppose these were 900,000/yr
• Are you interested? (Come on - Ive got to know
  now. There are a lot of people interested)

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Profit

• Profit Sales (revenues) - expenses (costs)
• Basis for taxation - What goes into the
  calculation is of great interest to Uncle Sam

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In Our Example

• Profit 1,000,000/yr - 900,000/yr
  100,000/yr
• Is this a good business?

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What Would You be Willing to Pay Me for this
Business?

• 1 million?
• 2 million?
• How do you decide?
• This is one of the questions that we will answer
  in this part of the course.

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Present Value Calculations

• Essential element of evaluating a business
  opportunity
• Different variants
• Simple discounting
• Replacement and abandonment
• Venture Worth, Present Value, Discounted Cash
  Flow Rate of Return

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What information do we need?

• Investment (Capital assets, working capital)
• Lifetime and Salvage Values
• Operating Costs
• Fixed
• Variable
• Interest Rate
• Tax Rate
• Depreciation Method
• Revenues

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Capital Investment -
Facility

• Purchased Process Equipment
• Field Constructed Equipment
• Wiring, Piping, Instrumentation
• Construction, Installation Costs
• Site Preparation, Buildings
• Storage Areas
• Utilities
• Services (Cafeterias, Parking lots, etc.)
• Contingency

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Capital Investment- Manufacturing

• Costs of process equipment may represent only 25
  of actual investment!
• Costs of process equipment scale according to the
  six-tenths rule
• C2/C1 (Q2/Q1)0.6
• See, for example
• Cost and Optimization Engineering by F.C. Jelen
  and J.H. Black, McGraw-Hill, 1983.

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Other Items

• Working Capital
• Raw materials and supplies inventory
• Finished goods in stock and Work in Progress
• Accounts Receivable, Taxes payable
• Operating Costs
• Labor and Raw Materials
• Utilities and Maintenance
• Royalties
• Fixed Costs
• Insurance, rent, debt service, some taxes

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Time Value of Money

• 1 today is more valuable than the promise of 1
  tomorrow
• Has nothing to do with inflation
• Discounting is the term used to describe the
  process of correcting for the reduced value of
  future payments
• Discount rate is the return that can be earned
  on capital invested today

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Future Worth of an Investment

• P Principal
• i Annual Interest Rate
• S Future value of investment
• Compound Interest Law
• S1 P (1i) at the end of one year
• S2 S1(1i) P(1i)2 at end of year 2
• Sn P (1i)n at end of year n

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Present Value of a Future Amount

• P Sn / (1 i)n
• Sn (1 i)-n
• (1 i)-n Present Value Factor or
• Discount Factor
• The promise of 1 million at a time 50 years in
  the future _at_ i 15/yr
• P 1,000,000(10.15)-50 923

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Simple Example

• What is the PV of 10.00 today if I promise to
  give it to you in fifteen years, given a discount
  rate of 20?
• PV 10(1.20)-15
• .65
• Not enough to buy a soda these days

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Take Home Message

• Not all dollars of profit are the same
• Those that come earlier are worth more

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Start with Simple Example from Everyday Life

• Do you buy the better made equipment with the
  higher price tag? or the low first cost equipment
  that has high maintenance?

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Cost Comparisons

• What are we doing here?
• Comparing one project to another
• Deciding to buy the expensive computer that has
  free maintenance versus the cheap one that makes
  you pay for service

vs.
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Simple Cost Comparisons

• Strategy
• Reduce costs (and/or revenues) to a common
  instant, usually the present time
• Work on full year periods
• approximate costs or revenues which occur over
  the year as single year-end amounts
• Basic Rule All comparisons must be performed on
  an equal time period basis

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Unequal Lifetime Cost Comparisons

• Repeatability Assumption (to get to same time
  basis)
• Annuity Comparison
• Co-termination assumption

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First Some Useful Mathematical Machinery

• Uniform periodic annual payments (annuities)
• Projects frequently generate recurring income or
  cost streams on an annual basis

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Discounting a Series of Payments
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Discounting a Series of Payments cont
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Capital Recovery Factor
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Future Equivalents of Annuities
Link to summary of useful formulae
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Examples

• What future payment N years from now shall I
  accept in return for an investment of P now,
  given I could instead invest my money elsewhere
  (e.g. a bank) and earn i /yr?
• What set of annual revenues for N years will
  entice me to invest P, given the same
  alternative as above?

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Examples

• What price should I pay for an investment which
  returns X/yr for N years, if i /yr is available
  to me in a bank?
• What annual interest rate (bank, etc.) would be
  required to make an investment returning S in N
  years on a present investment of P?

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A Simple Replacement Problem

• Process to be operated for 4 years and then
  junked
• Do you buy a new low-maintenance machine now or
  not???

DATA (neglect tax effects)
Options Stick w/old Buy newPurchase
Price () 0 4000Operating Cost (/yr)
2000 500Lifetime (yrs) 4 4
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Cash Flow Time Lines
OLD
NEW
4
3
2
0
1
500
500
500
4000
500
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The Key Role of Interest Rates

• If management demands i 10 /yrPold6340,
  Pnew5585 new is better choice

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Note

• In a replacement problem like this you could have
  added revenues to the analysis, but no need to do
  so if they are the same for both options.

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Financial Comparisons with Unequal Lifetimes

• Simple Example Choose between 2 pieces of
  equipment, one of which is better built and has a
  longer lifetime
• N is not the same for both
• Not a fair comparison with N2 unless process is
  to be shut down and both options have no residual
  value

20 year life
Well Built
Poorly Built
2 year life
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What to Do?

• Option 1 - Repeatability

Well Built
20 year life
(Buy 1)
(Buy 10)
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Option 2 - Annualized Costs

• Convert the investment and maintenance for both
  options into a single annual payment

i 0.15 / yr
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Annualized Cost of Alternative 1
Now

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Annualized Cost of Alternative 2
1000

0
0
1
2
3
1
3
2
1000
20,000
1000
1000
9472
9472
9472
In this case, choose alternative 1 because yearly
cost is lower.