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L2: Time Value of Money

L2: Time Value of Money. ECON 320 Engineering Economics Mahmut Ali GOKCE Industrial Systems Engineering Computer Sciences. Chapter 2 Time Value of Money. Interest: The Cost of Money Economic Equivalence Interest Formulas – Single Cash Flows Equal-Payment Series

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L2: Time Value of Money

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  1. L2: Time Value of Money ECON 320 Engineering Economics Mahmut Ali GOKCE Industrial Systems Engineering Computer Sciences

  2. Chapter 2Time Value of Money • Interest: The Cost of Money • Economic Equivalence • Interest Formulas – Single Cash Flows • Equal-Payment Series • Dealing with Gradient Series • Composite Cash Flows. Power-Ball Lottery

  3. Decision Dilemma—Take a Lump Sum or Annual Installments • A suburban Chicago couple won the Power-ball. • They had to choose between a single lump sum $104 million, or $198 million paid out over 25 years (or $7.92 million per year). • The winning couple opted for the lump sum. • Did they make the right choice? What basis do we make such an economic comparison?

  4. What Do We Need to Know? • To make such comparisons (the lottery decision problem), we must be able to compare the value of money at different point in time. • To do this, we need to develop a method for reducing a sequence of benefits and costs to a single point in time. Then, we will make our comparisons on that basis.

  5. Time Value of Money • Money has a time value because it can earn more money over time (earning power). • Money has a time value because its purchasing power changes over time (inflation). • Time value of money is measured in terms of interest rate. • Interest is the cost of money—a cost to the borrower and an earning to the lender

  6. Delaying Consumption

  7. Which Repayment Plan?

  8. Cash Flow Diagram

  9. End-of-Period Convention Interest Period 0 1 End of interest period Beginning of Interest period 0 1

  10. Methods of Calculating Interest • Simple interest: the practice of charging an interest rate only to an initial sum (principal amount). • Compound interest: the practice of charging an interest rate to an initial sum and to any previously accumulated interest that has not been withdrawn.

  11. Simple Interest • P = Principal amount • i = Interest rate • N = Number of interest periods • Example: • P = $1,000 • i = 8% • N = 3 years

  12. Simple Interest Formula

  13. Compound Interest • Compound interest: the practice of charging an interest rate to an initial sum and to any previously accumulated interest that has not been withdrawn.

  14. Compound Interest • P = Principal amount • i = Interest rate • N = Number of interest periods • Example: • P = $1,000 • i = 8% • N = 3 years

  15. Compounding Process $1,080 $1,166.40 0 $1,259.71 1 $1,000 2 3 $1,080 $1,166.40

  16. $1,259.71 2 1 0 3 $1,000

  17. Compound Interest Formula

  18. Some Fundamental Laws The Fundamental Law of Engineering Economy

  19. Compound Interest “The greatest mathematical discovery of all time,” Albert Einstein

  20. Practice Problem: Warren Buffett’s Berkshire Hathaway • Went public in 1965: $18 per share • Worth today (August 22, 2003): $76,200 • Annual compound growth: 24.58% • Current market value: $100.36 Billion • If he lives till 100 (current age: 73 years as of 2003), his company’s total market value will be ?

  21. Market Value • Assume that the company’s stock will continue to appreciate at an annual rate of 24.58% for the next 27 years.

  22. EXCEL Template • In 1626 the Indians sold Manhattan Island to Peter Minuit • Of the Dutch West Company for $24. • If they saved just $1 from the proceeds in a bank account • that paid 8% interest, how much would their descendents • have now? • As of Year 2003, the total US population would be close to • 275 millions. If the total sum would be distributed equally • among the population, how much would each person receive?

  23. Excel Solution FV(8%,377,0,1) = $3,988,006,142,690

  24. Excel Worksheet FV(8%,377,0,1) = $3,988,006,142,690

  25. Practice Problem • Problem Statement If you deposit $100 now (n = 0) and $200 two years from now (n = 2) in a savings account that pays 10% interest, how much would you have at the end of year 10?

  26. Solution F 0 1 2 3 4 5 6 7 8 9 10 $100 $200

  27. Practice problem • Problem Statement Consider the following sequence of deposits and withdrawals over a period of 4 years. If you earn 10% interest, what would be the balance at the end of 4 years? ? $1,210 1 4 0 2 3 $1,500 $1,000 $1,000

  28. ? $1,210 0 1 3 2 4 $1,000 $1,000 $1,500 $1,100 $1,000 $2,981 $1,210 $2,100 $2,310 + $1,500 -$1,210 $1,100 $2,710

  29. Solution

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