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NE 364
Engineering EconomyLecture 3
Money-Time Relationships and Equivalence
(Part 1: Single Payment)
1
Time
F
P
NE 364 Engineering Economy
Money − Time Value
Capital refers to wealth in the form of money or
property that can be used to produce more wealth.
Engineering economy studies involve the
commitment of capital for extended periods of time.
A dollar today is worth more than a dollar one or
more years from now.
3NE 364 Engineering Economy
Return to capital or Interest
Interests and profit are payments for the risk the investor takes in letting another use their capital.
Any project or venture must provide a sufficient return to be financially attractive to the suppliers of money or property.
4NE 364 Engineering Economy
Simple InterestWhen interest earned or charged is not accumulated.
I = P * N * i
P = principal amount lent or borrowed
N = number of interest periods (e.g., years, months,…)
i = interest rate per interest period
The total amount repaid at the end of N interest periods is
F = P + I.
5NE 364 Engineering Economy
Example on Simple Interest
If $5,000 were loaned for five years at a simple interest
rate of 7% per year, the interest earned would be
I = $5,000 * 5 * 0.07 = $1,750
So, the total amount repaid at the end of five years
would be
F = P + I = $5000 + $1,750 = $6,750
NE 364 Engineering Economy 6
Compound InterestWhenever the interest charge for any interest period is
based on the
remaining principal amount + any accumulated interest
charges
up to the beginning of that period, the interest is said to
be compound.
NE 364 Engineering Economy 7
Compound Interest Calculations
for $1,000 at 10%
Period
(1)
Amount owed
at beginning of
period
(2)=(1)x10%
Interest
amount for
period
(3)=(1)+(2)
Amount owed
at end of
period
1 $1,000 $100 $1,100
2 $1,100 $110 $1,210
3 $1,210 $121 $1,331
8
Compound interest is commonly used in personal and professional financial
transactions.
NE 364 Engineering Economy
Cash-flow Diagram
10
Horizontal Line is the Time Scale
Arrow Down=
Expenses
Arrow Up=
Receipts
The Cash-flow is dependent on the point of view
NE 364 Engineering Economy
Example on Cash-flow Before evaluating the economic merits of a proposed
investment, the XYZ Corporation insists that its engineers develop a cash-flow diagram of the proposal.
An investment of $10,000 can be made
that will produce uniform annual revenue of $5,310 for five years and
then have a market (recovery) value of $2,000 at the end of year (EOY) five.
Annual expenses will be $3,000 at the end of each year for operating and maintaining the project.
Draw a cash-flow diagram for the five-year life of the project.
Use the corporation's viewpoint.
11NE 364 Engineering Economy
Cash-flow Calculation Rules
• Rule 1: Cash flows cannot be added or
subtracted unless they occur at the same time.
• Rule 2: To move a cash flow forward in time by
one time unit, multiply the magnitude of the cash
flow by (1 + i), where i is the interest rate.
• Rule 3: to move a cash flow backward in time by
one time unit, divide the magnitude of the cash
flow by (1 + i).
NE 364 Engineering Economy 14
Arithmetic on Cash flow
0 1 2 3 4 5 6
Time (years)i%
P
Multiply by (1+i) Compounding
Divide by (1+i) Discounting
NE 364 Engineering Economy 15
Arithmetic on Cash flow
0 1 2 3 4 5 6
Time (years)
P*(1+i)
Multiply by (1+i) Compounding
Divide by (1+i) Discounting
i%
NE 364 Engineering Economy 16
Arithmetic on Cash flow
0 1 2 3 4 5 6
Time (years)
P*(1+i)2
Multiply by (1+i) Compounding
Divide by (1+i) Discounting
i%
NE 364 Engineering Economy 17
Arithmetic on Cash flow
0 1 2 3 4 5 6
Time (years)
P*(1+i)3
Multiply by (1+i) Compounding
Divide by (1+i) Discounting
i%
NE 364 Engineering Economy 18
Single Payment (cont.) If an amount of P dollars is invested at a point in time
with interest rate i%, the amount will grow to a future
amount :
after period one
P+Pi =P(1+i)
after period two
P(1+i)+P(1+i)i=P(1+i)[1+i]=P(1+i)2
19NE 364 Engineering Economy
Single Payment (cont.) After period 3
P(1+i)2
+ P(1+i)2
i= P(1+i)2
[1+i]= P(1+i)3
After period N:
P(1+i)N-1
+ P(1+i)N-1
i= P(1+i)N-1
[1+i]= P(1+i)N
Hence ,
F=P(1+i)N
NE 364 Engineering Economy 20
We can apply compound interest formulas
to “move” cash flows along the cash flow
diagram.
NE 364 Engineering Economy 21
Example on Compound Interest
Estimating the Future
You decide to invest $2,500 at the bank. The bank
offers 8% yearly interest rate.
How much will you have in six years?
F=$2,500 * (1+ 0.08)6 = $3,967.19
NE 364 Engineering Economy 22
Example on Compound Interest
Estimating the Present
An investor (owner) has an option to purchase a tract of
land that will be worth $10,000 in six years.
If the value of the land increases at 8% each year, how
much should the investor be willing to pay now for this
property?
P = $10,000 * (1+ 0.08)− 6 = $6301.70
NE 364 Engineering Economy 23
Example on Compound Interest
Estimating the Future
using Discrete Compounding Tables
You decide to invest $2,500 at the bank. The bank
offers 8% yearly interest rate.
How much will you have in six years?
F=$2,500 * (F/P, 8%, 6)
NE 364 Engineering Economy 26
Example on Compound Interest
Estimating the Future
using Discrete Compounding Tables
You decide to invest $2,500 at the bank. The bank
offers 8% yearly interest rate.
How much will you have in six years?
F=$2,500 * (F/P, 8%, 6)
= $2,500 * 1.5869
=$3,967.25
NE 364 Engineering Economy 28
Example on Compound Interest
Estimating the Present
using Discrete Compounding Tables
An investor (owner) has an option to purchase a tract of
land that will be worth $10,000 in six years.
If the value of the land increases at 8% each year, how
much should the investor be willing to pay now for this
property?
P = $10,000 * (P/F, 8%, 6)
29NE 364 Engineering Economy
Example on Compound Interest
Estimating the Present
using Discrete Compounding Tables
An investor (owner) has an option to purchase a tract of
land that will be worth $10,000 in six years.
If the value of the land increases at 8% each year, how
much should the investor be willing to pay now for this
property?
P = $10,000 * (P/F, 8%, 6)
= $10,000 * 0.6302
=$6302.00
31NE 364 Engineering Economy
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