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Unformatted text preview: 1 Chapter 2 Time Value of Money 2 Decision DilemmaTake a Lump Sum or Annual Installments A suburban Chicago couple won the Powerball. 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? 3 Option A (Lump Sum) Option B (Installment Plan) 1 2 3 25 $104 M $7.92 M $7.92 M $7.92 M $7.92 M Total=$198 M 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 points 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 N = 0 $100 N = 1 $104 (inflation rate = 4%) N = 0 $100 N = 1 $106 (earning rate =6%) Case 2: Earning power exceeds inflation N = 0 $100 N = 1 $108 (inflation rate = 8%) N = 0 $100 N = 1 $106 (earning rate =6%) Case 1: Inflation exceeds earning power Cost of Refrigerator Account Value N = 0 $100 N = 1 $104 (inflation rate = 4%) N = 0 $100 N = 1 $106 (earning rate =6%) Case 2: Earning power exceeds inflation N = 0 $100 N = 1 $108 (inflation rate = 8%) N = 0 $100 N = 1 $106 (earning rate =6%) Case 1: Inflation exceeds earning power Cost of Refrigerator Account Value 7 $ 8 Elements of Transactions Involving Interest P (principal) : initial amount of money invested or borrowed i (interest rate) : expressed as a percentage per period of time n (interest period) : determines how frequently interest is calculated N (number of interest periods) : duration of transaction A n (a plan for receipts or disbursements) : a particular cash flow pattern F (future amount) : cumulative effects of the interest 9 Which Repayment Plan? End of Year Receipts Payments Plan 1 Plan 2 Year 0 $20,000.00 $200.00 $200.00 Year 1 5,141.85 Year 2 5,141.85 Year 3 5,141.85 Year 4 5,141.85 Year 5 5,141.85 30,772.48 The amount of loan = $20,000, origination fee = $200, interest rate = 9% APR (annual percentage rate) 10 Cash Flow Diagram 11 EndofPeriod Convention Beginning of Interest period End of interest period 1 1 12 Methods of Calculating Interest Simple interest : the practice of charging an interest rate only to an initial sum (principal amount)....
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This note was uploaded on 11/23/2009 for the course ECON econ 320 taught by Professor Cemalettinöztürk during the Spring '09 term at Izmir University of Economics.
 Spring '09
 CEMALETTINöZTüRK

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