MSci261-2007-Ch_3

# MSci261-2007-Ch_3 - Chapter 3 Cash flow analysis MSci 261...

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Chapter 3 1 Chapter 3 Chapter 3     MSci 261: Engineering Economics: Financial Management for Engineers Spring 2007 Instructor: Bon Koo Instructor: Bon Koo Cash flow analysis Cash flow analysis

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Chapter 3 2 Overview Overview Pattern and timing of cash flow are complicated and irregular. Some flows are constant, others fluctuate. It can be paid weekly, monthly, quarterly, yearly, etc. E.g., initial investment cost, operational costs (wage, electricity, etc.), prepaid expenses (rent, lease) For project evaluation or comparison, cash flow should be converted into a common time period. We will study different types of cash flow and learn the methods of evaluating them in different timings.
Chapter 3 3 1. Types of cash flow 1. Types of cash flow Single, one-time cash flow Compound amount factor (F/P, i, N) Present worth factor (P/F, i, N) Annuity Constant flow Future worth: Sinking fund factor (A/F, i, N) vs. Uniform series compound amount factor (F/A, i, N) Present worth: Capital recovery factor (A/P, i, N) vs. Series present worth factor (P/A, i, N) Changing flow Arithmetic gradient series : change by a constant amount Geometric gradient series : change by a constant proportion

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Chapter 3 4 1.1 Graphs of cash flow (1) 1.1 Graphs of cash flow (1) Single cash flow Annuity: constant flow P F 0 1 2 N 0 1 2 3 N-1 A A A A N F P
Chapter 3 5 1.1 Graphs of cash flow (2) 1.1 Graphs of cash flow (2) Arithmetic gradient series Geometric gradient series 0 1 2 3 N A(1+g) A(1+g) 2 4 A A(1+g) 3 A(1+g) N-1 0 1 2 3 N A’+ G A’+ 2G A’+ 3G 4 A’+ (N-1)G A’

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Chapter 3 6 1.2 Basic assumptions 1.2 Basic assumptions Discrete cash flow (vs. continuous cash flow) Compounding periods are of equal length Each cash flow occurs at the end of period End of period 1 = beginning of period 2 “Now” is period 0 (i.e., end of period -1)
Chapter 3 7 2. Single cash flow (1) 2. Single cash flow (1) Examples: initial investment, salvage value at a future date, etc. We will study the relation between the future worth (F) and the present worth (P). Should be able to convert cash flow into different point of time. P 0 1 N 2 F

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Chapter 3 8 2. Single cash flow (2) 2. Single cash flow (2) Compound amount factor (F/P, i, N) Convert current worth P into future worth F Given P, i and N periods, what is F? F = P(1 + i) N If interest is compounded m times per year, F = P(1 + i/m) mN (F/P, i, N) = (1 + i) N Present worth factor (P/F, i, N) Convert future value F into present value P N
Chapter 3 9 Examples 2-1: P and F Examples 2-1: P and F If \$1,000 is deposited to a bank this year, what is the value at the end of 10 years, with i = 12%? P = 1,000; N = 10; i = 0.12

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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_3 - Chapter 3 Cash flow analysis MSci 261...

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