Lecture Presentation

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-------------------------- ENGR 300 Dept. of
Computer Science and Engineering University of
Bridgeport, CT 06601
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NET PRESENT VALUE - NPV

• Measures inflows vs. outflows
• Todays dollars
• Cradle to Grave

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NET PRESENT VALUE - NPV

• Not only accounts for the Costs of Inflows and
  Outflows, but for their timing
• Sales Revenues
• Loan Payments
• Development Costs
• Ramp Up and Production Costs
• Marketing and Support Costs
• Disposal Costs

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SENSITIVITY ANALYSIS
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• Answers What If? Questions
• Helps in Making Project Tradeoffs
• Cost is a Critical Factor in Design

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SENSITIVITY ANALYSIS

• Project Parameters can be Varied
• Development Time
• Project Loading
• Interest Rates
• Sales Price
• Product Quality

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QUALITATIVE ANALYSIS

• Complex Factors
• Risks
• External Factors

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DEPRECIATION

• Only a portion of the cost of an asset can be
  deducted for tax purposes in one year
• Tangible Assets decrease in value over time
• Cars
• Equipment
• Buildings

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DEPRECIATION METHODS

• An Asset has an Initial and a Salvage Value at
  the start and end of its service life
• The Book Value is the remaining undepreciated
  value of the asset
• Straight Line Method (equal amounts)
• Accelerated Cost Recovery System
• Modified Accelerated Cost Recovery System

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DECISIONS CAN BE INFLUENCED BY THE TIME VALUE
OF MONEY
Will be worth more in the future
Present
Future
time
One dollar today
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TIMING OF INFLOWS AND OUTFLOWS
Future cash inflows
time
Future cash outflows
Present
Cash Flow Diagram graphically shows relationships
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BASIC TERMINOLOGY

• P Present value (NPV in Today's Dollars)
• F Future value (Tomorrows Dollars)
• n Number of compounding periods between
  present and future
• A uniform Amount received or paid out each
  compounding period

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INTEREST RATE

• The reward that investors demand for accepting
  delayed payment
• Sometimes referred to as the Discount Rate
• n is the number of periods per year
• Must convert the yearly percentage rate to its
  decimal equivalent rate

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COMPOUNDING OF INTEREST

• ANNUAL PERCENTAGE RATE (APR) INCREASES WITH
  SHORTER PERIODS OF COMPOUNDING
• 12 Yearly 12 APR
• 3 Quarterly 12.55 APR
• 1 Monthly 12.68 APR
• Continuous 12.75 APR

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COMPOUNDING FORMULAS
FIXED PERIODS
CONTINUOUS
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PRESENT vs. FUTURE VALUE

• Dollars today are worth more than the same amount
  of dollars in the future
• 1000 today will grow to 3300.39 in 10 years at
  12 compounded monthly

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PRESENT vs. FUTURE VALUE Find Present given the
Future Value

• 120 one year from now is worth 113.03 today
• n12 periods or monthly
• Yearly interest rate is 6, per month is .005

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PRESENT vs. FUTURE VALUE How Many Periods?

• How many years does it take to double your money
  if the APR9

SOLVING
LOG FUNCTION WORKS TOO
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PRESENT vs. FUTURE VALUEWhat interest rate is
needed?
What interest rate is needed to make 200 grow to
1000 in ten years, if interest is paid yearly?
SOLVING
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(No Transcript)
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PRESENT VALUE(P) OF A SERIES OF AMOUNTS

• n number of payments of amount A
• iinterest rate per period (decimal)
• A amount of each payment

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PRESENT VALUE OF EQUAL PAYMENTS

• 10 monthly payments for one year
• interest rate is 6 per year .005 per month

Present Value is greater than one single
payment of 120 after a year (in that case, P was
113.03)
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AMOUNT OF A LOAN PAYMENT

• P100,000
• i9 per year .0075 per month
• n360 monthly payments

Note in 30 years, 289,663 will be paid in
payments
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MATHEMATICAL BASIS
A SERIES OF PAYMENTS IS BROKEN DOWN INTO SUMS OF
INFINITE STRINGS OF PAYMENTS
A
etc.
P1A/i
Subtract
A
P2A/(i(1i) n)
etc.
A
PP1-P2
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PRESENT VALUEOF INCREASING AMOUNTS
A3B
A2B
AB
A15 B10 4A6B120 i.06/4.015 n4
(quarterly)
A
Present
Future
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ECONOMIC COMPARISON

• Decisions often include comparisons of economic
  costs/benefits of alternative actions
• Inflows/Outflows may occur at several different
  times
• Time-value of money must be considered

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ALTERNATIVES WITH EQUAL LIVES

• For each alternative, compute the Net Present
  Value (NPV)
• Compute P for all inflows
• Compute P for all outflows
• NPV SP(inflows) - SP(outflows)
• Alternative with highest NPV is the best choice
  from an economic viewpoint

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ALTERNATIVES WITH UNEQUAL LIVES

• For each alternative, compute the equivalent
  uniform cost per period (EUC/P)
• Assume identical replacement at end of life
• Compute A for all inflows
• Compute A for all outflows
• EUC/P SA(outflows) - SA(inflows)
• Alternative with lowest EUC/P is the best choice
  from an economic viewpoint

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DEALING WITH RISK AND UNCERTAINTY

• Use Expected Value (EV) for inflows and outflows
  with estimated uncertainties
• EV (p1)(V1) (p2 )(V2) ....... (pn)(Vn)
• pn is the probability that a value will be Vn
• where p1 p2 ....... pn 1
• Calculate NPV or EUC/P based on expected values

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EXPECTED VALUE

• Saturdays, the following probabilities exist
• .35 wont study at all
• .15 will study for 4 hours
• .20 will study for 2 hours
• .30 will study for 1 hour

1.3 IS THE EXPECTED NUMBER OF HOURS OF STUDY
ON A TYPICAL SATURDAY
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WHAT IF?

• What If questions can be supported by doing a
  sensitivity analysis.
• Take one variable at a time, holding others
  fixed, make small changes in that variable
  observe effect on NPV or on EUC/P
• Spreadsheet program is useful for this purpose
  and doing time value of money calculations