Contemporary Engineering Economics Time Value of Money Lecture No. 4 Chapter 3 Contemporary Engineering Economics Copyright © 2016

Chapter Opening Story Take a Lump Sum or Annual Installments Dearborn couple claimed Missouri’s largest jackpot: $293.75 million in 2012. They had two options. Option 1: Take a lump sum cash payment of $192.37 M. Option 2: Take an annuity payment of $9.79 M a year for 30 years. Which option would you recommend?

What Do We Need to Know? Be able to compare the value of money at different points in time. A method for reducing a sequence of benefits and costs to a single point in time

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).

The Market Interest Rate Interest is the cost of money, a cost to the borrower and a profit to the lender. Time value of money is measured in terms of market interest rate, which reflects both earning and purchasing power in the financial market.

Cash Flow Diagram (A Graphical Representation of Cash Transactions over Time) Borrow $20,000 at 9% interest over 5 years, requiring $200 loan origination fee upfront. The required annual repayment is $5,141.85 over 5 years. n = 0: $20,000 n = 0: $200 n = 1 ~ 5: $5,141.85

End-of-Period Convention Convention: Any cash flows occurring during the interest period are summed to a single amount and placed at the end of the interest period. Logic: This convention allows financial institutions to make interest calculations easier.

Methods of Calculating Interest Simple interest: Charging an interest rate only to an initial sum (principal amount) Compound interest: Charging an interest rate to an initial sum and to any previously accumulated interest that has not been withdrawn Note: Unless otherwise mentioned, all interest rates used in engineering economic analyses are compound interest rates.

Simple Interest Formula P = $1,000, i = 10%, N = 3 years $1,000 1 $100 = $1,300 End of Year Beginning Balance Interest Earned Ending Balance $1,000 1 $100 $1,100 2 $1,200 3 $1,300

Compound Interest Formula P = $1,000, i = 10%, N = 3 years End of Year Beginning Balance Interest Earned Ending Balance $1,000 1 $100 $1,100 2 $110 $1,210 3 $121 $1,331

Compounding Process $1,100 $1,210 $1,331 1 $1,000 2 3 $1,100 $1,210

The Fundamental Law of Engineering Economy

Warren Buffett’s Berkshire Hathaway Went public in 1965: $18 per share Worth today (May 29, 2015): $214,800 per share Annual compound growth: 20.65% Current market value: $179.5 billion If his company continues to grow at the current pace, what will be his company’s total market value when he reaches 100? (He is 85 years old as of 2015.) Assume that the company’s stock will continue to appreciate at an annual rate of 20.65% for the next 15 years. The stock price per share at his 100th birthday would be F = 214,800(1 + 0.2065)15 = $3,588,758

Example 3.2: Comparing Simple with Compound Interest In 1626, American Indians sold Manhattan Island to Peter Minuit of the Dutch West Company for $24. Given: If they saved just $1 from the proceeds in a bank account that paid 8% interest, how much would their descendents have in 2010? Find: As of 2015, the total U.S. population would be close to 308 million. If the total sum would be distributed equally among the population, how much would each person receive?

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