Lecture no23 rate of return

Rate of Return Analysis
Lecture No. 23
Chapter 7
Contemporary Engineering Economics
Copyright © 2016

Contemporary Engineering Economics, 6 th edition
Park

Copyright © 2016 by Pearson Education, Inc.
All Rights Reserved


Chapter Opening Story - Investing in
Wal-Mart 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
$15,384,576 on September
30, 2014, after nine times
stock splits for 2 for 1.
What would be the rate of
return on this investment?
Contemporary Engineering Economics, 6 th edition
Park

• WMT Split History Table
• Date

Ratio
• 08/25/1975 2 for 1
• 12/17/1980 2 for 1
• 07/12/1982 2 for 1
• 07/11/1983 2 for 1
• 10/07/1985 2 for 1
• 07/13/1987 2 for 1
• 07/09/1990 2 for 1
• 02/26/1993 2 for 1
• 04/20/1999 2 for 1
Copyright © 2016 by Pearson Education, Inc.
All Rights Reserved


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 in the
market.

Contemporary Engineering Economics, 6 th edition
Park

Copyright © 2016 by Pearson Education, Inc.
All Rights Reserved


Wal-Mart Investment Problem
• Given:
• P = $1,650
• F = $15,384576
• N = 44 years
• Find: i
• Formula to Use
• F = P(1 + i)N
• $15,384,576 =
$1,650(1 + i)44
• i = 23.09%

Contemporary Engineering Economics, 6 th edition
Park

• Cash Flow Diagram

$15,384,576

1970
2014

$1,650

Copyright © 2016 by Pearson Education, Inc.
All Rights Reserved


How Good Was the Wal-Mart Investment and
What Can It Be Compared with?
If you took out $1,650 from your savings
account and invested in Wal-Mart stock,
you could have

• $15,384,576
• Or the equivalent to
earning 23.09%
interest each year
on your savings
account over 44
years.

Contemporary Engineering Economics, 6 th edition
Park

If you did not invest $1,650 in Wal-Mart
stock, what could you use your money

for?

• If the best you could do
was to leave the money
in a savings account to
earn 6% interest over 44
years, you would have
$21,426.
• What is the meaning of
6% interest? This will be
your opportunity cost
rate or minimum return
required for any
investment.
Copyright © 2016 by Pearson Education, Inc.
All Rights Reserved


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 commonly used in NPW
analysis.
 So to see if the proposed investment is
a good one, you adopt the following

decision rule:
ROR (23.09%) > MARR(6%)

Contemporary Engineering Economics, 6 th edition
Park

Copyright © 2016 by Pearson Education, Inc.
All Rights Reserved


Why is ROR measure so popular?
 This project will bring in a 15% rate
of return on the investment.
 This project will result in a net
surplus of $10,000 in NPW.

Which statement is easier to
understand?

Contemporary Engineering Economics, 6 th edition
Park

Copyright © 2016 by Pearson Education, Inc.
All Rights Reserved


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 an 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, 6 th edition
Park

Copyright © 2016 by Pearson Education, Inc.
All Rights Reserved


Loan Balance Calculation:
A = $10,000 (A/P, 10%, 3)
= $4,021

n

0
1
2
3

Unpaid Loan
Return on
Balance at
Unpaid
Beginning of Year Balance (10%)

$0
-$10,000
-$6,979
-$3,656

$0
-$1,000
-$698
-$366

Payment
Received
from Borrower

Unpaid Loan
Balance at
End of Year

-$10,000
+$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, 6 th edition
Park

Copyright © 2016 by Pearson Education, Inc.
All Rights Reserved


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
PW (i * )  PW (i * )cash inflows
 PW (i * )cash outflows
Relation:
0

• Example:
PW(10%)  10,000 $4,021(P/ A,10%,3)  0
Contemporary Engineering Economics, 6 th edition
Park

Copyright © 2016 by Pearson Education, Inc.
All Rights Reserved

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 ofCopyright
10%
on its
Contemporary Engineering Economics, 6 edition
© 2016 by Pearson Education, Inc.
Park
All Rights Reserved
investment of $10,000.
th


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.

Contemporary Engineering Economics, 6 th edition
Park

Copyright © 2016 by Pearson Education, Inc.
All Rights Reserved