Lecture no23 rate of return

Rate of Return AnalysisLecture No... Rate of Return • Investopedia ® says: IRRs can also be compared against prevailing rates of return in the securities market.. What it is : Interes

Rate of Return Analysis

Lecture No 23 Chapter 7 Contemporary Engineering Economics

Copyright © 2016

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

• 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

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)

A Simple Example : The

interest earned on your

savings account is the

rate of return on your

deposits.

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

$1,650

1970

2014

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.

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.

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%)

Why is ROR measure so popular?

of return on the investment.

surplus of $10,000 in NPW.

Which statement is easier to

understand?

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

Loan Balance Calculation:

A = $10,000 (A/P, 10%, 3)

= $4,021

0

1

2

3

$0 -$10,000

-$6,979 -$3,656

-$1,000 -$698 -$366

+$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

Unpaid Loan

Balance at Beginning of Year

Return on Unpaid Balance (10%)

Payment Received from Borrower

Unpaid Loan Balance at End of Year

n

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 :

cash inflows cash outflows

PW ( ) PW ( ) PW ( )

0



PW(10%)  10,000$4,021(P/ A,10%,3) 0

Definition 3: Return on Invested Capital:

Internal Rate of Return

(IRR) is the interest rate

investment such that when

the project terminates, the

unrecovered project

balance will be zero.

a computer system, which results in

equivalent annual labor savings of

$4,021 over 3 years The company is

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