LECTURE-III ECN801

Course Overview

  • Course Title: ECN801 - Principles of Engineering Economics

  • Instructor: Dr. Hakan Toksoy

  • Institution: Toronto Metropolitan University

Chapter 3: Objective Cash Flow Analysis

  • Timing of Cash Flows: Understanding cash flow timing is crucial in economic analysis.

  • Models Covered:

    • Compound Interest Factors for Discrete Compounding

    • Compound Interest Factors for Single Disbursements or Receipts

    • Compound Interest Factors for Annuities

Introduction to Compound Interest Factors

  • Used for evaluating different cash flow patterns including:

    1. Single Disbursement or Receipt

    2. Annuity

    3. Arithmetic Gradient Series

    4. Geometric Gradient Series

Timing of Cash Flows

  • Cash flows can be complex and irregular.

  • Simplified models can help analyze cash flows based on:

    • Discrete models (cash flow/compounding at the end of defined periods)

    • Continuous models (cash flows/compounding occur continuously)

  • Discrete Compounding Assumptions:

    • Equal compounding periods

    • Disbursements/receipts occur at period-end

    • Payments at time 0 occur at the end of time period -1

Common Discrete Cash Flow Patterns

  1. Single Disbursement/Receipt

  2. Annuity: Regular equal disbursements/receipts

  3. Arithmetic Gradient Series: Incremental changes each period

  4. Geometric Gradient Series: Proportional changes each period

Compound Interest Factors for Single Disbursements

  • Future Amount Calculation:

    • Formula: F = P(1 + i)^N

  • Present Worth Factor Calculation:

    • Formula: P = F / (1 + i)^N

Example Application of Interest Tables

  • Example: Future worth of $20,000 at 12% for 15 periods:

    • F = 20,000(1 + 0.12)^{15} = $109,472

    • Present Worth: $20,000 (Future/Present factors)

Present Worth Factor Calculation

  • Present Worth Formula:

    • P = F( P/F, i%, N)

Cash Flow Calculations with Example

  • Future Value Example: Achieving $5,000 from $500 with annual deposits, interest at 7%.

Capital Recovery and Cash Flow Analysis

  • Understand how much needs to be invested annually.

  • Capital Recovery Formula: CR(i) = P(A/P, i%, N) - S(A/F, i%, N)

Capital Cost vs. Operating Cost Analysis

  • Capital Recovery calculations ensure profitability over an asset's lifecycle.

  • Important for making informed financial decisions regarding investments.