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

2. 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?
WMT Split History Table
DateRatio
08/25/ for 1
12/17/ for 1
07/12/ for 1
07/11/ for 1
10/07/ for 1
07/13/ for 1
07/09/ for 1
02/26/ for 1
04/20/ for 1

3. Rate of Return 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.
What it is: Interest earned on your invested capital, or commonly known as internal rate of return (IRR)
ASimple Example: The interest earned on your savings account is the rate of return on your deposits.

4. 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%
Cash Flow Diagram
$15,384,576
1970
2014
$1,650

5. How Good Was the Wal-Mart Investment and What Can It Be Compared with?
If you did not invest $1,650 in Wal-Mart stock, what could you use your money for?
If you took out $1,650 from your savings account and invested in Wal-Mart stock, you could have
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.
$15,384,576
Or the equivalent to earning % interest each year on your savings account over 44 years.

6. 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%)

7. 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 $10,000in NPW.
Which statement is easier to understand?

8. Definition 1: Interest Earned on Loan Balance
Rate of return (ROR) is defined as the interest rate earned on the unpaid (outstanding) balanceof 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.

9. Loan Balance Calculation:
A = $10,000 (A/P, 10%, 3)
= $4,021
Unpaid Loan
Balance at
Beginning of Year
Return on
Unpaid
Balance (10%)
Payment
Received
from Borrower
Unpaid Loan
Balance at
End of Year n 1 2 3 $0
-$10,000
-$6,979
-$3,656 $0
-$10,000
-$10,000
-$6,979
-$3,656 $0
-$1,000
-$698
-$366
+$4,021
A return of 10% on the amount still outstanding at the beginning of each year

10. 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:
Example:

11. 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.

12. 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.