Engineering Economic Analysis Chapter 4 Part 2 Gradients

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Engineering Economic Analysis Chapter 4: Part 2 Gradients Engineering Economic Analysis - Ninth Edition

Engineering Economic Analysis Chapter 4: Part 2 Gradients Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 1

Arithmetic Gradient • A uniform increasing amount. • The first cash flow is always

Arithmetic Gradient • A uniform increasing amount. • The first cash flow is always equal to zero. • G = the difference between each cash amount. G = $10 Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 2

Arithmetic Gradient Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University

Arithmetic Gradient Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 3

Arithmetic Gradient • The present amount that is equivalent to an constantly increasing set

Arithmetic Gradient • The present amount that is equivalent to an constantly increasing set of cash flows Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 4

Arithmetic Gradient Present Worth Factor The equivalent present value of a uniformly increasing amount.

Arithmetic Gradient Present Worth Factor The equivalent present value of a uniformly increasing amount. PG = G(P/G, i, n) Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 5

Arithmetic Gradient Uniform Series Factor The equivalent uniform series value of a uniformly increasing

Arithmetic Gradient Uniform Series Factor The equivalent uniform series value of a uniformly increasing amount. AG = G(A/G, i, n) Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 6

Example 1 Let i = 10%. Find P below: Engineering Economic Analysis - Ninth

Example 1 Let i = 10%. Find P below: Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 7

Example 1 Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University

Example 1 Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 8

Example 1 Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University

Example 1 Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 9

Example 1 Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University

Example 1 Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 1 0

Example 1 Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University

Example 1 Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 1 1

Excel for Example 1 • There isn’t an Excel function for the arithmetic gradient

Excel for Example 1 • There isn’t an Excel function for the arithmetic gradient • We can use NPV to find the net present value of a set of flows in time periods 1 to nper • NPV(rate, flows) Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 1 2

Excel for Example 1 Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by

Excel for Example 1 Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 1 3

Geometric Series • Let Ak = the kth payment amount then Ak = A

Geometric Series • Let Ak = the kth payment amount then Ak = A 1(1 + g)k-1 • To translate this back to time zero, want to get P, which is called the geometric series present worth Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 1 4

Example 2 If the 1 st payment is $100 and goes up 20% each

Example 2 If the 1 st payment is $100 and goes up 20% each year, how much are the first five payments? Year 1 2 3 4 5 Amount $100(1. 20) = $100(1 + g) = $120(1. 20) = $100(1 + g)2 = $144(1. 20) = $100(1 + g)3 = $172. 80(1. 20) = $100(1 + g)4 = $207. 36 Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 1 5

Geometric Series Present Worth Factor The equivalent present value of a geometrically increasing amount.

Geometric Series Present Worth Factor The equivalent present value of a geometrically increasing amount. P = A(P/A, g, i, n) – no table for this!!! Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 1 6

Example 3 How much are these five payments worth now at 8% interest? Year

Example 3 How much are these five payments worth now at 8% interest? Year 1 2 3 Amount $100. 00 $120. 00 $144. 00 4 5 $172. 80 $207. 36 Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 1 7

Example 3 • • A 1 = $100 g = 20% i = 8%

Example 3 • • A 1 = $100 g = 20% i = 8% n=5 Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 1 8

Example 3 Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University

Example 3 Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 1 9

Example 3 • Probably, for problems with tables for cash flows, the Output area

Example 3 • Probably, for problems with tables for cash flows, the Output area should be on the left, not below, the input data Engineering Economic Analysis - Ninth Edition Newnan/Eschenbach/Lavelle Copyright 2004 by Oxford University Press, Inc. 2 0