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ECON320_2_TimeValueOfMoney - Chapter 2 Time Value of Money...

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1 Chapter 2  Time Value of Money
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2 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?
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3 Option A (Lump Sum) Option B (Installment Plan) 0 1 2 3 25 $104 M $7.92 M $7.92 M $7.92 M $7.92 M Total=$198 M
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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.
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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
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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
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7 $
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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
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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 0 Year 2 5,141.85 0 Year 3 5,141.85 0 Year 4 5,141.85 0 Year 5 5,141.85 30,772.48 The amount of loan = $20,000, origination fee = $200, interest rate = 9% APR (annual percentage rate)
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10 Cash Flow Diagram
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11 End-of-Period Convention Beginning of Interest period End of interest period 0 1 1 0
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12 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.
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13 Simple Interest P = Principal amount i = Interest rate N = Number of interest periods Example: P = $1,000 i = 8% N = 3 years End of Year Beginning Balance Interest earned Ending Balance 0 $1,000 1 $1,000 $80 $1,080 2 $1,080 $80 $1,160 3 $1,160 $80 $1,240
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14 Simple Interest Formula ( ) where = Principal amount = simple interest rate = number of interest periods = total amount accumulated at the end of period F P iP N P i N F N = + $1,000 (0.08)($1,000)(3) $1,240 F = + =
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15 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.
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