Lecture No. 23
Chapter 7
Contemporary Engineering Economics
Copyright © 2010
Contemporary Engineering Economics, 5th edition, © 2010
Chapter Opening Story
 Mr. Clean Takes Car-
Wash Gig:
 Proctor & Gamble
wants to enter carwash franchise
business - $35
billion industry.
 Initial investment
required by a
franchise operator $500,000.
 Average monthly
sales - $6,800 or
$3,800 profit per
month.
 At Issue: What is the
return on investment on
car-wash franchise
Contemporary Engineering Economics, 5
operation?
th
edition © 2010
Rate of Return
 What it is: Interest
earned on your
invested capital, or
commonly known as
internal rate of
return (IRR)
 A Simple Example:
The interest earned
on your savings
account is the rate of
return on your
deposits.
 Investopedia® says:
IRRs can also be compared
against prevailing rates of
return in the securities market.
If a firm can't find any projects
with IRRs greater than the
returns that can be generated
in the financial markets, it may
simply choose to invest its
retained earnings into the
market.
Contemporary Engineering Economics, 5th edition © 2010
Investing in WalMart Stock
In October 1,1970,
when Wal-Mart
Stores, Inc. went
public, an
investment of 100
shares cost $1,650.
That investment
would have been
worth $10,053,632
on September 30,
2009. What is the
rate of return on
this investment?
Contemporary Engineering Economics, 5th edition © 2010
Wal-Mart Investment Problem
 Given:
 Cash Flow Diagram
 P = $1,650
$10,053,632
 F = $10,053,632
 N = 29 years
 Find: i
 Formula to Use:
 F = P(1 +
1970
2009
i)N
 $10,053,632 = $1,650(1 +
i)29
$1,650
 i = 25.04%
Contemporary Engineering Economics, 5th edition © 2010
How Good the Wal-Mart Investment Was and
What to Compare with?
If you took out $1,650 from
your savings account and
invested in Wal-Mart stock,
you could have
 $10,053,632
 Or equivalent to earning
25.04% interest on your
savings account.
If you did not invest $1,650 in
Wal-Mart stock, what could
use your money for?
 If the best you could do was
to leave the money in the
savings account to earn 6%
interest over 29 years, you
will have $16,010.
 What is the meaning of 6%
interest? This will be your
opportunity cost rate or
minimum return required
for any investment.
Contemporary Engineering Economics, 5th edition © 2010
Is This a Good investment?
 In 1970, as long as you could earn more than a 6%
interest in another investment opportunity, you would
take that investment.
 Therefore, that 6% is viewed as a minimum
attractive rate of return (or required rate of return).
This is the interest rate used in NPW analysis.
 So, to see if the proposed investment is a good one,
you adopt the following decision rule.
ROR (25.04%) > MARR(6%)
Contemporary Engineering Economics, 5th edition © 2010
Why ROR measure is so popular?
 This project will bring in a 15% rate of return
on investment.
 This project will result in a net surplus of
$10,000 in NPW.
Which statement is easier to understand?
Contemporary Engineering Economics, 5th edition © 2010
Definition 1: Interest Earned on Loan Balance
• Rate of return (ROR) is defined as the interest
rate earned on the unpaid (outstanding) balance
of an installment loan.
• Example: A bank lends $10,000 and receives
annual repayment of $4,021 over 3 years. The
bank is said to earn a return of 10% on its loan of
$10,000.
Contemporary Engineering Economics, 5th edition © 2010
Loan Balance Calculation:
A = $10,000 (A/P, 10%, 3)
= $4,021
Year
0
1
2
3
Unpaid
balance
at beg.
of year
-$10,000
-$10,000
-$6,979
-$3,656
Return on
unpaid
balance
(10%)
-$1,000
-$698
-$366
Payment
received
Unpaid
balance
at the end
of year
+$4,021
+$4,021
+$4,021
-$10,000
-$6,979
-$3,656
0
A return of 10% on the amount still
outstanding at the beginning of each year
Contemporary Engineering Economics, 5th edition © 2010
Definition 2: Break-Even Interest Rate
• Rate of return (ROR) is the break-even interest rate,
i*, which equates the present worth of a project’s cash
outflows to the present worth of its cash inflows.
• Mathematical Relation:
PW (i * )  PW (i * )cash inflows  PW (i * )cash outflows
0
• Example:
PW(10%)  10,000  $4,021(P / A,10%,3)  0
Contemporary Engineering Economics, 5th edition © 2010
Definition 3: Return on Invested Capital –
Internal Rate of Return
• The internal rate of return (IRR) is the interest rate
earned on the unrecovered project balance of the
investment such that, when the project terminates, the
unrecovered project balance will be zero.
•Example: A company invests $10,000 in a computer system
which results in equivalent annual labor savings of $4,021 over 3
years. The company is said to earn a return of 10% on its
investment of $10,000.
Contemporary Engineering Economics, 5th edition © 2010
Return on Invested Capital
 The firm earns a 10% rate of return on funds that remain
internally invested in the project. Since the return is internal
to the project, we call it internal rate of return.
0
Project Balance
1
2
3
Beginning Project Balance
-$10,000
-$6,979
-$3,656
Return on Invested Capital
-$1,000
-$698
-$366
Payment Received
-$10,000
$4,021
$4,021
$4,021
Ending Project Balance
-$10,000
-$6,979
-$3,656
$0
Contemporary Engineering Economics, 5th edition © 2010