green electric energy lecture 14
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Lecture 14
Engineering Economics
Professor Tom OverbyeDepartment of Electrical and
Computer Engineering
ECE 333
Green Electric Energy
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Announcements
Be reading Chapter 5
Homework 6 is due Oct 22. It is 4.9, 5.2, 5.4, 5.6, 5.11
Wind Farm field trip will be on Nov 5 from about 8am to 4pm turn in forms to sign up.
Campus Wind Turbine Project: Let your voice be heard! If you would like to email your student senators
with your wind turbine views some folks to talk with are Bradley Tran (president-iss@illinois.edu), Bobby
Gregg (bobby.gregg@gmail.com), Melanie Cornell (cornell4@illinois.edu)
mailto:president-iss@illinois.edumailto:bobby.gregg@gmail.commailto:cornell4@illinois.edumailto:cornell4@illinois.edumailto:bobby.gregg@gmail.commailto:president-iss@illinois.edu -
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The economic evaluation of a renewable energy resourcerequires a meaningful quantification of cost elements
fixed costs
variable costs We use engineering economics notions for this purpose
since they provide the means to compare on a consistent
basis
two different projects; or, the costs with and without a given project
Energy Economic Concepts(From Prof. Gross)
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loanP for 1 yearrepayP+ iP = P(1 + i) at the end of 1 year
year0 P
year 1 P(1 + i)
loanP forn years
year0 P
year 1 (1 + i) P repay/reborrowyear 2 (1 + i)2P repay/reborrow
year 3 (1 + i)3P repay/reborrow
.
yearn (1 + i)nP repay
Simple Example
M M M
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Compound Interest
e.o.p. amount owed interest for
next period
amount owed for next period
0 P Pi P + Pi = P(1+i)
1 P(1+i) P(1+i) i P(1+i) + P(1+i) i = P(1+i)2
2 P(1+i)2 P(1+i)2 i P(1+i)2 + P(1+i)2 i = P(1+i)3
3 P(1+i)3 P(1+i)3 i P(1+i)3 + P(1+i)3 i = P(1+i)4
n-1 P(1+i)n-1 P(1+i)n-1 i P(1+i)n-1 + P(1+i)n-1 i = P(1+i)n
n P(1+i)n
M M
The value in the last column for the e.o.p. (k-1) provides the value in
the first column for the e.o.p.k(e.o.p. is end of period)
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Terminology/Overview
Cash flow diagrams
Common conversion factors Present Value- (P|A,i%,n) and (P|F,i%,n) Future Value- (F|A,i%,n) and (F|P,i%,n)
Capital Recovery Factor- (A|P,i%,n)
Incoming cash flow
Outward cash flows
0 1 2 3 4
Present
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Cash Flows
A cash flow is a transfer of an amount At from one
entity to another at e.o.p. time t
A cash-flow set corresponds to the set
of times
The convention for cash flows is + inflow
outflow
Each cash flow has (1) amount, (2) time, and (3) sign
{ }1 2, , , ...,0 n A A A A{ },1,2,...,0 n
I take out a loan
I make equal repayments
0 1 2 3 4
Ex.
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Cash Flows
Given a cash-flow set we
define the future worthFnof the cash flow set at e.o.y.
n as
{ }1 2, , , ...,0 n A A A A
( )1n n tn tt 0
F A i
== +
0 1 2 t n 2 nn 2
A0 A1 A2 At An-2 An-1 An
. . . . . .
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Cash Flows
Note that each cash flow At in the set contributesdifferently toF
n
( )( )( )( )
1
1 1
2
2 2
1
1
1
1
n
0 0
n
n
n t
t t
n n
A A i
A A i
A A i
A A i
A A
+ + + +
M M
M M
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Discount Rate
The interest rate i is typically referred to as thediscount rate and is denoted by d
In converting a future amount F to a present worth
P we can view the discount rate as the interest ratethat can be earned from the best investment
alternative
A postulated savings of $10,000 in a project in 5
years is worth at present
( ) 555 10,000 1 P F d = = +
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Discount Rate
Ford = 0.1, P = $6,201,while ford = 0.2, P = $4,019
In general, the lower the discount factor, the
higher the present worth The present worth of a set of costs under a given
discount rate is called the life-cycle costs
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Cash Flow Example
0 1 3
$ 2,000
$ 3,000
F5=?
year
2 4 5
$ 2,000
Find the future worth of cash flows at the end of year 5
Answer: outflow of $2571
d = %12
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Cash Flows
Single-payment compound amount factor-
Single-payment present worth factor-
n is typically in years and need not be an integer value
( ) 11 i +@ ( )1 nn i = +( )1 ni
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Cash Flows
We define thepresent worthPof the cash flow set as
Note that
( )1n n ttt tt 0 t 0
P A A i
= == = +
( )
( ) ( ) ( )
1
1 1 1
1
nt
t
t 0
n
t n nt
t 0
P A i
A i i i
=
=
= +
= + + + 1 4 4 2 4 4 3
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Cash Flows
or equivalently
( ) ( )1 1n
n
nn n t
t
t 0
F
P i A i
== + +
142 431 4 42 4 43
( )1 nnF i P+This is the lump equivalent sum at the end of n periods.
Fis thefuture worth, andPis thepresent worth
nnF
contd
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Example 1
Consider a loan of$4,000 at 8% interest to be repaid intwo installments
$ 1,000 and interest at the e.o.y. (end of year) 1
$ 3,000 and interest at the e.o.y. 4
The cash flows are e.o.y. 1: 1000 + 4000 (.08) = $ 1,320
e.o.y. 4: 3000 (1 + .08 )
3
= $ 3,779.14 Note that the loan is made in year0 presentdollars,
but the repayments are in year 1 and
year 4future dollars
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Example 2
Given that
Then we say that for the cost of money of 12%,PandFare equivalent in the sense that $1,000 todayhas the same worth as $1,762.34 in 5 years
1, 000 .12 P $ i =and
( ) ( )5 51 1, 000 1 .12 1, 762.34 P i $ $ F = + = =
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Example 3
Consider an investment that returns
$1,000 at the e.o.y. 1
$2,000 at the e.o.y. 2
i = 10%
We evaluateP
rate at which
money can befreely lent or
borrowed
( ) ( )1 22
1, 000 1 .1 2, 000 1 .1
909.9 1, 652.09 2, 561.98
P $ $
$ $ $
= + + +
= + =142 43 142 43
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Net Present Value (NPV) for Example 3
Next, suppose that this investment requires $ 2,400now. At 10%, the investment has a net present value
(NPV) of
NPV = $ 2,561.98 $ 2,400 = $ 161.98
0 1 2
$ 2,561.98$ 1,000 $ 2,000
year
NPV=$ 161.98 {
$ 2,400
0 1 2
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Uniform Cash Flow Set
Consider the cash-flow set with
Such a set is called an equal payment cash flow set Each payment can be thought of as a future value and
the results will be the same
We compute the present worth
1,2,...,t A A t n={ }1 2, , , ...,0 n A A A A
2 1
1 1
1 ...n n
t t n
t
t t
P A A A = =
= = + + + +
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Uniform Cash Flow Set, cont.
Now, for , we have the identity
It follows that
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