MSci261-2007-Ch_5

# MSci261-2007-Ch_5 - Chapter 5 Comparison method 2 MSci 261:...

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Chapter 5 1 Chapter 5 Chapter 5 Comparison method 2 Comparison method 2 MSci 261: Managerial and Engineering Economics Spring 2007 Instructor: Bon Koo

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Chapter 5 2 Overview Overview In this chapter, we will study another method of comparing projects, called the internal rate of return (IRR). It is a commonly used, but slightly complicated method. There’s a reason that this method has its own chapter! In contrast to PW or AW method, IRR is expressed as a rate (%), which makes the comparison of project easy. We will heavily use the linear interpolation method to calculate the IRR. (You may want to refresh your memory!) All of the four comparison methods have value in particular circumstances, and you need to understand when to use which method.
Chapter 5 3 1. Internal rate of return (1) 1. Internal rate of return (1) How do we measure the performance of an investment? We can calculate a “rate of return” per dollar invested. For example, if I invested \$100 today and earn \$150 next year, the rate of return is 50%. Internal rate of return (IRR) The “internal” implies that the return depends only on cash flows due to the specific investment. (We will learn external rate of return later.) Definition: “the interest rate at which a project breaks even” That is, we find the interest rate at which the set of benefit equals cost.

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Chapter 5 4 1. Internal rate of return (2) 1. Internal rate of return (2) Formal definition The interest rate i * that satisfies the following condition A negative IRR means that the project is losing money How to calculate IRR? 1. Calculate the benefits (B) and costs (C) of a project, either as present worth or annual worth 2. Solve for i* with PW(B) = PW(C) or AW(B) = AW(C). * * 0 0 (1 ) (1 ) N N n n n n n n B C i i = = = + +
Chapter 5 5 Examples 1-1: IRR (1) Examples 1-1: IRR (1) If a new window, costing \$8,000 now, saves \$400 per year in energy cost for the next 30 years, what is the IRR? Use the present worth calculation PW (C) = 8,000 PW (B) = 400 (P/A, i*, 30) 8,000 = 400 (P/A, i*, 30) (P/A, i*, 30) = 20 Linear interpolation

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Chapter 5 6 Examples 1-1: IRR (2) Examples 1-1: IRR (2) Use the annual worth calculation AW (C) = 8,000 (A/P, i*, 30) AW (B) = 400 8,000 (A/P, i*, 30) = 400 (A/P, i*, 30) = 0.05 Linear interpolation (A/P, 2%, 30) = 0.0446 and (A/P, 3%, 30) = 0.0512
7 Examples 1-2: IRR (1) Examples 1-2: IRR (1) An ad campaign will cost \$2 million for planning and \$400,000 per year for 6 years. It is expected to increase revenues permanently by \$400,000 per year. Additional revenues will be gained with \$200,000 in the first year, declining by \$50,000 per year to zero in the 5 th year. What is the IRR of this investment? Let’s use the present worth calculation.

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## This note was uploaded on 03/13/2009 for the course MSCI 261 taught by Professor Bonkoo during the Spring '09 term at Waterloo.

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MSci261-2007-Ch_5 - Chapter 5 Comparison method 2 MSci 261:...

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