Rate of Return Analysis

Anastasia L. Maukar

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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? 2

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 into 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.

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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 $10,053,632 on September 30, 2009. What is the rate of return on this investment?

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Wal-Mart Investment ProblemGiven:

P = $1,650F = $10,053,632N = 29 years

Find: iFormula to Use:

F = P(1 + i)N

$10,053,632 = $1,650(1 + i)29

i = 25.04%

Cash Flow Diagram

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$10,053,632

$1,650

19702009

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

$10,053,632Or 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.

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Is This a Good investment?

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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%)

Why ROR measure is so popular?

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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?

Definition 1: Interest Earned on Loan Balance

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• 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.

Loan Balance Calculation:

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A = $10,000 (A/P, 10%, 3)= $4,021

Unpaid Return on Unpaid balance unpaid balanceat beg. balance Payment at the end

Year of year (10%) received of year

0123

-$10,000-$10,000

-$6,979-$3,656

-$1,000 -$698 -$366

+$4,021+$4,021+$4,021

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

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A return of 10% on the amount still outstanding at the beginning of each year

Definition 2: Break-Even Interest Rate

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• 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 outflowsPW ( ) PW ( ) PW ( )

0i i i

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

Definition 3: Return on Invested Capital – Internal Rate of Return

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• 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.

Return on Invested CapitalThe 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.

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0 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

Project Balance

CALCULATING RATE OF RETURN

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Example 5.1• An $8200 investment returned $2000 per year

over a 5-year useful life. What was the rate of return on the investment?

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Example 5.2

• An investment resulted in the following cash flow. Compute the rate of return :

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Year Csh Flow

0 -$700

1 +100

2 +175

3 +250

4 +325

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Example 5.3

• Calculate the rate of return on the investment on the following cash flow

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Year Csh Flow

0 -$100

1 +20

2 +30

3 +20

4 +40

5 +40

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Example 5.4• A new corporate bond was initially sold by a

stockbroker to an investor for $1000. The issuing corporation promised to pay the bondholder $40 interest on the $1000 face value of the bond every 6 months, and to repay the $1000 at the end of 10 years. After one year the bond was sold by the original buyer for $950

(a)What rate of return did the original buyer receive on his investment?

(b) What rate of return can the new buyer (paying$950) expect to receive if he keeps the bond for its remaining 9-year life?

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RATE OF RETURN ANALYSIS

• We compute a rate of return (more accurately called internal rate of return)from the cash flow. To decide how to proceed, the calculated rate of return is compared with a preselected minimum attractive rate of return, or simply MARR. This is the same value of i used for present worth and annual cash flow analysis

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RATE OF RETURN ANALYSIS

• When there are two alternatives, rate of return analysis is performed by computing the incremental rate of return-IRR-on the difference between the alternative

• Since we want to look at increments of investment, the cash flow for the difference between the alternatives is computed by taking the higher initial-cost alternative minus the lower initial cost alternative

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RATE OF RETURN ANALYSIS

• If ∆IRR is the same or greater than the MARR, choose the higher-cost alternative.

• If ∆IRR is less than the MARR, choose the lower-cost alternative

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RATE OF RETURN ANALYSIS

Example:• If an electromagnet is installed on the input conveyor of a coal-

processing plant, it will pick up scrap metal in the coal. The removal of this metal will save an estimated $1200 per year in costs associated with machinery damage due to metal. The electromagnetic equipment has an estimated useful life of 5 years and no salvage value. Two suppliers have been contacted: – Lease co will provide the equipment in return for

three beginning-of-year annual payments of $1000 each;

– Saleco will provide the equipment for $2783. • If the MARR is 10%, which supplier should be selected?

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RATE OF RETURN ANALYSIS

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Example 2

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Example 3• A firm is considering which of two devices to install

to reduce costs in a particular situation. Both devices cost $1000, and both have useful lives of 5 years and no salvage value. Device A can be expected to result in $300 savings annually. Device B will provide cost savings of $400 the first year but will decline $50 annually ,making the second-year savings $350, the third-year savings $300, and so forth.

• For a 7% MARR, which device should the firm purchase?

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Example 4

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Exercise 1

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Exercise 2

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If the owner wants a miniumum attractive rate of returnon his investment 6%, which of the 2 alternatives would you recommend?

The owner of a corner lot wants to find a use that will yield a desirable return on his investment. After much study and calculation, the owner decides that the two best alternatives are:

Build Gas Station

Build Soft Ice Cream Stand

First Cost $80,000 $120,000

Annual property taxes 3,000 5,000

Annual Income 11,000 16,000

Life of Building, in years 20 20

Salvage value 0 0

Exercise 3

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Exercise 4

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Exercise 5

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Two mutually exclusive alternatives are being considered.

If the minimum attractive rate of return is 8%, which alternative should be selected? Solve the problem by:a.Present Worth Analysisb.Annual Cash Flow Analysisc.Rate of return analysis

Year A B

0 -$2,500 -$6,000

1 +746 +1,664

2 +746 +1,664

3 +746 +1,664

4 +746 +1,664

5 +746 +1,664