1. Rate of Return Analysis
Lecture No. 23
Chapter 7
Contemporary Engineering Economics
Copyright © 2010
Contemporary Engineering Economics, 5th edition, © 2010

2. Chapter Opening Story Mr. Clean Takes Car- Wash Gig:
Proctor & Gamble wants to enter car-wash 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 operation?
Contemporary Engineering Economics, 5th edition © 2010

3. Rate of Return Investopedia® says:
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

4. Investing in Wal-Mart Stock
In October 1,1970, when Wal-Mart Stores, Inc. went public, an investment of 100 shares cost $1, That investment would have been worth $10,053,632 on September 30, What is the rate of return on this investment?
Contemporary Engineering Economics, 5th edition © 2010

5. Wal-Mart Investment Problem
Given:
P = $1,650
F = $10,053,632
N = 39 years
Find: i
Formula to Use:
F = P(1 + i)N
$10,053,632 = $1,650(1 + i)39
i = 25.04%
Cash Flow Diagram
$10,053,632
1970
2009
$1,650
Contemporary Engineering Economics, 5th edition © 2010

6. 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
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 39 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.
$10,053,632
Or equivalent to earning 25.04% interest on your savings account.
Contemporary Engineering Economics, 5th edition © 2010

7. 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

8. 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

9. 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

10. Loan Balance Calculation:
A = $10,000 (A/P, 10%, 3)
= $4,021
Unpaid Return on Unpaid
balance unpaid balance
at beg. balance Payment at the end
Year of year (10%) received of year 1 2 3
-$10,000
-$6,979
-$3,656
-$10,000
-$6,979
-$3,656
-$1,000
-$698
-$366
+$4,021
A return of 10% on the amount still outstanding at the beginning of each year
Contemporary Engineering Economics, 5th edition © 2010

11. 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:
Contemporary Engineering Economics, 5th edition © 2010

12. 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

13. 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, 5th edition © 2010