Transcript Lecture Presentation

-------------------------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
One
dollar
today
$ + time = $$$
TIMING OF INFLOWS AND OUTFLOWS
Future cash inflows
time
Present
Future cash outflows
Cash Flow Diagram graphically shows relationships
BASIC TERMINOLOGY


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
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
i Period 
i % Yearly .01
nPerYear
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
APR  (1  iPeriod )
CONTINUOUS
i %Yearly .01
APR  e
n per _ year
1
1
PRESENT vs. FUTURE VALUE

Dollars today are worth more than the same amount of
dollars in the future
P

F
(1  i Period )
nTotal
$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
$120
P
12  $113.03
(1.005)
PRESENT vs. FUTURE VALUE
How Many Periods?

How many years does it take to double your money
if the APR=9%
SOLVING
2 P
P
n
(1.09)
ln 2
n
 8.043 years
ln(109
. )
LOG FUNCTION WORKS TOO
PRESENT vs. FUTURE VALUE
What interest rate is needed?
What interest rate is needed to make $200 grow to
$1000 in ten years, if interest is paid yearly?
SOLVING
ie
$1000
$200 
10
(1  i )
ln(1000 200)
10
 1 .1746  17.46%
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
n
A  (1  (1  i ) )
P
i
PRESENT VALUE OF EQUAL
PAYMENTS


$10 monthly payments for one year
interest rate is 6% per year = .005 per month
$10  (1  (1.005)
P
.005
12
)
 $116.09
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
$100000.0075
A
 360  $804.62
(1  (1.0075)
)
Note in 30 years, $289,663 will be paid in
payments
MATHEMATICAL BASIS
A SERIES OF PAYMENTS IS BROKEN DOWN INTO
SUMS OF INFINITE
A STRINGS OF PAYMENTS
etc.
P1=A/i
Subtract
P2=A/(i(1+i) n)
A
P=P1-P2
A
etc.
PRESENT VALUE
OF INCREASING AMOUNTS
A+3B
A+2B
A=$15 & B=$10
4A+6B=$120
i=.06/4=.015
n=4 (quarterly)
A+B
A
Present
n 1
n
A  (1  (1  i ) )
P

i
Future
B  (  (1  i )  k  (n  1)  (1  i )  n )
k 1
i
3
4
$15  (1  (1015
. ) )
P

.015
$10  (  (1015
. )  k  3  (1015
. ) 4 )
k 1
.015
 $114.91
ECONOMIC COMPARISON


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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
EV .35 0.15 4.20 2.301  13
.
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