2Chapter 2 Time Value of Money Interest: The Cost of MoneyEconomic EquivalenceInterest Formulas – Single Cash FlowsEqual-Payment SeriesDealing with Gradient SeriesComposite Cash Flows.Power-Ball Lottery
3Decision 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?
4Option A(Lump Sum)Option B(Installment Plan)12325$104 M$7.92 M
5What 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.
6Time Value of MoneyMoney 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
13End-of-Period Convention Interest Period1End of interestperiodBeginning ofInterest period1
14Methods 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practice of charging an interest rate to an initial sum and to any previously accumulated interest that has not been withdrawn.
15Simple Interest P = Principal amount i = Interest rate N = Number of interest periodsExample:P = $1,000i = 8%N = 3 yearsEnd of YearBeginning BalanceInterest earnedEnding Balance$1,0001$80$1,0802$1,1603$1,240
17Compound InterestCompound interest: the practice of charging an interest rate to an initial sum and to any previously accumulated interest that has not been withdrawn.
18Compound Interest P = Principal amount i = Interest rate N = Number of interest periodsExample:P = $1,000i = 8%N = 3 yearsEnd of YearBeginning BalanceInterest earnedEnding Balance$1,0001$80$1,0802$86.40$1,166.403$93.31$1,259.71
22Some Fundamental LawsThe Fundamental Law of Engineering Economy
23“The greatest mathematical discovery of all time,” Albert Einstein Compound Interest“The greatest mathematical discovery of all time,”Albert Einstein
24Practice Problem: Warren Buffett’s Berkshire Hathaway Went public in 1965: $18 per shareWorth today (August 22, 2003): $76,200Annual compound growth: 24.58%Current market value: $ BillionIf he lives till 100 (current age: 73 years as of 2003), his company’s total market value will be ?
25Market ValueAssume that the company’s stock will continue to appreciate at an annual rate of 24.58% for the next 27 years.
26EXCEL TemplateIn 1626 the Indians sold Manhattan Island to Peter MinuitOf the Dutch West Company for $24.If they saved just $1 from the proceeds in a bank accountthat paid 8% interest, how much would their descendentshave now?As of Year 2003, the total US population would be close to275 millions. If the total sum would be distributed equallyamong the population, how much would each person receive?
31? 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??$1,2101423$1,500$1,000$1,000