# Course 10 ROR

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Rate of Return Analysis

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Rate of Return Definition: A relative percentage method whichmeasures the yield as a percentage ofinvestment over the life of a project

Example : Vincent Goghs painting Irises John Whitney Payson bought the art at\$80,000.

John sold the art at \$53.9 million in 40years later. What is the rate of return on Johnsinvestment?

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Rate of Return

Given : P =\$80,000, F = \$53.9M, and N = 40years

Find : i Solution :

\$80,000

\$53.9M

\$53. \$80, ( ).

9 000 117 68%

40 M i

i

0

40

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In 1970, when Wal-Mart Stores, Inc.went public, an investment of 100shares cost \$1,650. That investmentwould have been worth \$13,312,000on January 31, 2000.

What is the rate of return on thatinvestment?

Meaning of Rate of Return

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Solution:

0

30

\$13,312,000

\$1,650

Given : P = \$1,650F = \$13,312,000N = 30

Find i :

\$13,312,000 = \$1,650 (1 + i )30i = 34.97%

N i P F )1(

Rate of Return

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Suppose that you invested that amount(\$1,650) in a savings account at 6% per year.Then, you could have only \$9,477 on January,2000.

What is the meaning of this 6% interest here?

This is your opportunity cost if putting moneyin savings account was the best you can do atthat time!

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So, in 1970, as long as you earn more than 6%interest in another investment, you will take that

investment.Therefore, that 6% is viewed as a minimumattractive rate of return (or required rate of

return).

So, you can apply the following decision rule, tosee if the proposed investment is a good one.

ROR > MARR

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Why ROR measure is sopopular?

This project will bring in a 15% rate of return oninvestment.

This project will result in a net surplus of\$10,000 in NPV.

Which statement is easier tounderstand?

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Calculating ROR

PW of benefit = PW of cost PW of benefit - PW of cost = 0

NPW = 0 PW of benefit/ PW of cost = 1 EUAB EUAC = 0

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Example

1. An \$ 8200 investment returned \$ 2000 per yearover a five year useful life. What was the rate ofreturn on the investment?

2. Given the cash flow below, calculate rate ofreturn. Year Cash flow01

2345

-\$100+\$20

+\$30+\$20+\$40+\$40

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ROR Calculation For Double Alternatives

When there are two alternatives, RORanalysis is performed by computing theincremental ROR - ROR- on thedifference between the alternatives.

To decide ho w to proceed, the calculatedROR (internal rate of return) is comparedwith a preselected minimum attractive rate

of return, MARR. This is the same value of i used for PW

and AW analysis.

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The Minimum Attractive Rateof Return (MARR) The MARR is a minimum return the

company will accept on the money itinvests

The MARR is usually calculated byfinancial analysts in the company andprovided to those who evaluate projects

The value of MARR depends on : cost ofborrowed money, cost of capital andopportunity cost (choose the highest one)

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Guidance

Increment of investment : If ROR MARR, choose the higher cost

alternative.

If ROR < MARR, choose the lower costalternative.

Increment of borrowing :

If ROR MARB, the increment is acceptable If ROR > MARB, the increment is notacceptable

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Incremental Rate of ReturnAnalysisPWB = A (P/A, 6%, 20) = A (11.47)MARR = 6% (given) All projects are initially acceptable because IRR < MARR

A B C D ECost 4000 2000 6000 1000 9000EUAB (A) 639 410 761 117 785

PWB 7330 4700 8730 1340 9000IRR 15% 20% 11% 10% 6%P/A 6.26 4.88 7.88 8.55 11.47

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Incremental Analysis1. Rank from lowest cost to highest cost2. Start with two lowest cost alternatives3. Compare increments using MARR criteria4. Repeat until a winner is determined

D B A C ECost 1000 2000 4000 6000 9000EUAB (A) 117 410 639 761 785

Increment B-D A-B C-A E-Aincr. Cost 1000 2000 2000 5000incr. UAB 293 229 122 146incr. ROR 29% 10% 2% < 0%Keep B A A AP/A 3.413 8.73 16.393 34.236

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Example

1. Which one would you select, if the MARR is 6%.

2. A manufacturer of boys pants is considering purchasing anew sewing machine. Determine which machine shouldbe selected if the MARR is 10% per year.

Year Alt 1 Alt 2

01

-\$10+\$15

-\$20+\$28

Semiautomatic Fully automatic

Initial cost Annual benefitSVUseful life,years

\$200\$95\$50

6

\$700\$120\$150

12

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Perbandingan antara MetodeNPV dan IRR

Apabila ada satu proyek yang independen maka NPV dan IRR akanselalu memberikan rekomendasi yang sama untuk menerima ataumenolak usulan proyek tersebut.

Tapi apabila ada proyek2 yang mutually exclusive, NPV dan IRR tidakselalu memberikan rekomendasi yg sama.

Ini disebabkan oleh dua kondisi:1. Ukuran proyek berbeda . Yg satu lebih besar daripada yg lain2. Perbedaan waktu . Waktu dari aliran kas dari dua proyek berbeda.

Intinya: untuk proyek2 yg mutually exclusive, pilih proyek dengan NPVyang tertinggi.

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Choosing an Analysis Method

DependsMoreFor comparisonROR

DependsLessRequired forcalculation AW

DependsLessRequired forcalculation

PW

ExplanationComputations*MARRMethod

Do what the Organization requires. Occasionally augmentwith alternate methods where the method adds beneficialinformation.

*Not an issue when using a spreadsheet.

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