IE 5325 Advanced Economic Analysis

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IE 5325Advanced Economic Analysis

• Week 7
• Compound Interest
• Cash Flow Analysis

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Time Value of Money

• Amount and timing
• Interest rate
• Taxes and inflation
• Investments made NOW have their impact in the
  FUTURE

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Interest

• Simple interest
• Interest is calculated independently for each
  period
• Compound interest
• Interest is calculated for each period and added
  to the principal amount

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Single-Sum Transactions

• Compound Interest Assumed
• End-of-year cash flows assumed
• Calculate Future Value given Present Value
• Calculate Present Value given Future Value

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Example 1Future Worth (Compounding)

• 10,000 is invested now at 5. What is it worth
  10 years from now?

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Example 2Present Worth (Discounting)

• I wish to invest a sum now that will grow to
  50,000 in ten years at 6. How much do I need
  to invest?

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Cash Flow Series

• Equivalent present and future value of a series
• Uniform series (annuity)
• Equal annual payments for n years
• Annual value
• Present value
• Future value

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Example 3 Amortization

• I wish to pay off a 100,000 loan with equal
  annual payments over 10 years at 6 interest.
  What are my payments?

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Example 4Series Compound Amount

• I can pay 12,000 per year for the next 15 years
  toward my retirement. How much will I have when
  I retire if my fund pays 4?

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Example 5Series Present Worth

• I can afford to pay 10,000 per year for a house
  for 30 years at 5. How much house can I afford?

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Example 6 Annuity

• I will have 750,000 saved when I retire. If I
  live 30 years and my fund earns 4, how much can
  I draw each year?

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Example 7 Sinking Fund

• I need another 250,000 in my retirement account
  before I retire in ten years. How much do I need
  to put in each year if the fund pays 4?

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Gradient Series

• Arithmetic Gradient Series
• Increases or decreases by the same amount each
  period
• Geometric Gradient Series
• Increases or decreases by the same percentage
  each period

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Comparing Cash Flows

• Equivalence
• Cash flow profiles are equivalent if their values
  at a common point in time are equal
• It is common to compare present values

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Typical Cash Flow Pattern
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Net Investment

• Initial investment
• Less any recoveries
• Later required investments
• Working capital increases

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Net Operating Inflows

• Benefits of the investment
• Must be net, not gross
• Reduced by additional costs
• Affected by depreciation and taxes
• May be uniform or varying

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Economic Life

• Physical life
• Technological life
• Depreciation life
• Economic life

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Residual (Terminal) Value

• Salvage value of equipment
• Disposal costs
• Released working capital

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Interest Rate

• Cost of capital
• Expected rate of return
• Effect of income taxes
• Interest paid is deductible
• Additional profits are taxable
• Minimum attractive rate of return (MARR)

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Where do I get the numbers?

• Estimates of cost
• Estimates of future benefits
• Economic life estimate
• Residual value estimate
• Interest rate

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Chapter 7a Summary

• Compound interest
• Single sum (F-P) transactions
• Uniform annual series (A-P, A-F)
• Typical cash flow patterns
• Definitions of economic quantities
• Estimating economic quantities