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**Rate of Return Analysis**

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Introduction Rate of Return is the rate of interest at which the benefits are equivalent to the cost. ROR analysis is the most frequently used method in industry, as the resulting ROR is readily understood. The difficulties in selecting a suitable interest rate to used in present worth and annual worth analysis is avoided.

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**Rate of Return Example: Vincent Gogh’s painting “Irises”**

Definition: A relative percentage method which measures the yield as a percentage of investment over the life of a project Example: Vincent Gogh’s painting “Irises” John Whitney Payson bought the art at $80,000. John sold the art at $53.9 million in 40 years later. What is the rate of return on John’s investment?

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**Rate of Return Given: P =$80,000, F = $53.9M, and N = 40 years Find: i**

Solution: $53.9M 40 $80,000

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**Meaning of Rate of Return**

In 1970, when Wal-Mart Stores, Inc. went public, an investment of 100 shares cost $1,650. That investment would have been worth $13,312,000 on January 31, 2000. What is the rate of return on that investment?

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**Solution: Given: P = $1,650 F = $13,312,000 N = 30 Find i:**

30 $1,650 Given: P = $1,650 F = $13,312,000 N = 30 Find i: $13,312,000 = $1,650 (1 + i )30 i = 34.97% 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 money in savings account was the best you can do at that 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 minimum attractive rate of return (or required rate of return). So, you can apply the following decision rule, to see if the proposed investment is a good one. ROR > MARR

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**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 NPV. Which statement is easier to understand?

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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 An $ 8200 investment returned $ 2000 per year over a five year useful life. What was the rate of return on the investment? Given the cash flow below, calculate rate of return. Year Cash flow 1 2 3 4 5 -$100 +$20 +$30 +$40

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**ROR Calculation For Double Alternatives**

When there are two alternatives, ROR analysis is performed by computing the incremental ROR -ΔROR- on the difference between the alternatives. To decide ho w to proceed, the calculated ROR (internal rate of return) is compared with 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 Rate of Return (MARR)**

The MARR is a minimum return the company will accept on the money it invests The MARR is usually calculated by financial analysts in the company and provided to those who evaluate projects The value of MARR depends on : cost of borrowed money, cost of capital and opportunity cost (choose the highest one)

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**Increment of investment :**

Guidance Increment of investment : If ΔROR ≥ MARR, choose the higher cost alternative. If ΔROR < MARR, choose the lower cost alternative. Increment of borrowing : If ΔROR ≤ MARB, the increment is acceptable If ΔROR > MARB, the increment is not acceptable

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**Incremental Rate of Return Analysis**

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

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**Incremental Analysis 1. Rank from lowest cost to highest cost 2**

Incremental Analysis 1. Rank from lowest cost to highest cost 2. Start with two lowest cost alternatives 3. Compare increments using MARR criteria 4. Repeat until a “winner” is determined

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

A manufacturer of boy’s pants is considering purchasing a new sewing machine. Determine which machine should be selected if the MARR is 10% per year. Year Alt 1 Alt 2 1 -$10 +$15 -$20 +$28 Semiautomatic Fully automatic Initial cost Annual benefit SV Useful life,years $200 $95 $50 6 $700 $120 $150 12

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**Perbandingan antara Metode NPV dan IRR**

Apabila ada satu proyek yang independen maka NPV dan IRR akan selalu memberikan rekomendasi yang sama untuk menerima atau menolak usulan proyek tersebut. Tapi apabila ada proyek2 yang mutually exclusive, NPV dan IRR tidak selalu memberikan rekomendasi yg sama. Ini disebabkan oleh dua kondisi: Ukuran proyek berbeda. Yg satu lebih besar daripada yg lain Perbedaan waktu. Waktu dari aliran kas dari dua proyek berbeda. Satu proyek aliran kasnya terjadi pada tahun2 awal sementara yg proyek yg lain aliran kasnya terjadi pada tahun2 akhir Intinya: untuk proyek2 yg mutually exclusive, pilih proyek dengan NPV yang tertinggi.

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**Choosing an Analysis Method**

Depends More For comparison ROR Less Required for calculation AW PW Explanation Computations* MARR Method *Not an issue when using a spreadsheet. Do what the Organization requires. Occasionally augment with alternate methods where the method adds beneficial information.

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Contemporary Engineering Economics, 4 th edition, © 2007 Rate of Return Analysis Lecture No. 24 Chapter 7 Contemporary Engineering Economics Copyright.

Contemporary Engineering Economics, 4 th edition, © 2007 Rate of Return Analysis Lecture No. 24 Chapter 7 Contemporary Engineering Economics Copyright.

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