Lecture02 - FINM2401 Financial Management $50 $50 $50 $50...

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FINM2401 Financial Management Time Value of Money Lecture 2 2 $50 $50 $50 $50 $50 $50 Regular Periodic Payments ( ) ( ) ( ) ( ) ( ) = + + + + + 2 3 4 5 6 50 50 50 50 50 50 1.02 1.02 1.02 1.02 1.02 1.02 PV 0 1 2 3 4 5 6 Quarters An annuity – equal, regular payments 3 Present Value of an Annuity ( ) - - + = 1 1 n per per r PV A r $50 $50 $50 $50 $50 $50 0 1 2 3 4 5 6 Quarters 4 Present Value of an Annuity ( ) - - + = 6 1 1 .02 50 .02 PV $50 $50 $50 $50 $50 $50 0 1 2 3 4 5 6 Quarters
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5 Try it out… pentasterisk6 You win $2 million, and can choose from the following payout schedules: pentasterisk5 $2 million NOW pentasterisk5 $172,000 per month for 12 months starting 1 month from now pentasterisk6 Which is the best alternative? pentasterisk5 Assume your opportunity cost is 7% p.a. compounded monthly 6 Solution 0 1 2 3 4 5 6 7 8 9 10 11 12 7 Future Value of an Annuity Suppose you save $100 per month from the time you start work until you retire. If you earn 6% interest (r nom ) per year, and you work for 40 years, how much will you have saved? (Compound monthly) ( ) + - = 1 1 n per n per r FV A r 8 Future Value of an Annuity ( ) × + - = + - = 12 40 480 .06 1 1 12 100 .06 12 1 .005 1 100 .005 FV
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9 Try it out… pentasterisk6 You want to be able to buy a $250,000 yacht when you retire in 20 years pentasterisk5 If you make quarterly payments into your bank account, how much must each payment be? (first payment 3 months from now) pentasterisk5 Assume your bank account pays 7% p.a. compounded quarterly 10 Solution 11 Compounding Periods and Effective Interest Rate Formula assumes compounding at same frequency as payments If compounding is more or less frequent than payments, use “effective” periodic interest rate For quarterly payments, compounded monthly with a nominal rate of 12% p.a. + - = 3 .12 1 1 3.0301% 12 12 Compounding Periods and Effective Interest Rate Suppose you deposit $100 per quarter in an account paying 12% p.a. compounded monthly. After 8 quarters, what will your account balance be? ( ) - = 8 1.030301 1 100 .030301 FV
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13 Solution 0 1 2 3 4 5 6 7 8 9 10 11 12 To use annuity formula compute “effective quarterly rate” 14 Matching Cash Flows With Formulas 1.
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