-------------------------- ENGR 300 Dept. of Computer Science and Engineering

-------------------------- ENGR 300 Dept. of Computer Science and Engineering University of Bridgeport, CT 06601

NET PRESENT VALUE - NPV • Measures inflows vs. outflows • Today’s dollars • Cradle to Grave

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

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

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

QUALITATIVE ANALYSIS • Complex Factors • Risks • External Factors

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

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

DECISIONS CAN BE INFLUENCED BY THE TIME VALUE OF MONEY Will be worth more in the future Present Future $ + time = $$$ One dollar today

TIMING OF INFLOWS AND OUTFLOWS Future cash inflows • time • Future cash outflows Present Cash Flow Diagramgraphically shows relationships

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

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

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

COMPOUNDING FORMULAS FIXED PERIODS CONTINUOUS

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

PRESENT vs. FUTURE VALUE Find Present given the Future Value • $120 one year from now is worth $113.03 today • n=12 periods or monthly • Yearly interest rate is 6%, per month is .005

PRESENT vs. FUTURE VALUE How Many Periods? • How many years does it take to double your money if the APR=9% SOLVING LOG FUNCTION WORKS TOO

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

PRESENT VALUE(P) OF A SERIES OF AMOUNTS • n = number of payments of amount A • i=interest rate per period (decimal) • A= amount of each payment

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)

AMOUNT OF A LOAN PAYMENT • P=$100,000 • i=9% per year = .0075 per month • n=360 monthly payments Note in 30 years, $289,663 will be paid in payments

MATHEMATICAL BASIS A SERIES OF PAYMENTS IS BROKEN DOWN INTO SUMS OF INFINITE STRINGS OF PAYMENTS A etc. P1=A/i Subtract A P2=A/(i(1+i) n) etc. A P=P1-P2

PRESENT VALUEOF INCREASING AMOUNTS A+3B A+2B A+B A=$15 & B=$10 4A+6B=$120 i=.06/4=.015 n=4 (quarterly) A Present Future

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

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

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

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

EXPECTED VALUE Saturdays, the following probabilities exist • .35 won’t 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

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

-------------------------- ENGR 300 Dept. of Computer Science and Engineering