Lecture02c - FINM2401 Financial Management Time Value of...

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Unformatted text preview: 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 P V 1 2 3 4 5 6 Quarters An annuity –equal, regular payments 3 Present Value of an Annuity ( )- - + = 1 1 n p e r p e r r P V A r $50 $50 $50 $50 $50 $50 1 2 3 4 5 6 Quarters 4 Present Value of an Annuity ( )- - + = 6 1 1.02 50 .02 P V $50 $50 $50 $50 $50 $50 1 2 3 4 5 6 Quarters = $280.07 5 Try it out… p You win $2 million, and can choose from the following payout schedules: P $2 million NOW P $172,000 per month for 12 months starting 1 month from now p Which is the best alternative? P Assume your opportunity cost is 7% p.a. compounded monthly 6 r p e r = 0.07/12 = 0.005833 $172k $172k $172k $172k $172k $172k $172k $172k $172k $172k $172k $172k Solution 1 2 3 4 5 6 7 8 9 10 11 12 PV of $2m today is $2m. Compare this to PV of $172k/month. ( )- - + = 12 1 1.005833 172,000 .005833 P V = $1,987,824.66 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 p e r n p e r r F V A r 8 Future Value of an Annuity ( ) × +- = +- = 1240 480 .06 1 1 12 100 .06 12 1.005 1 100 .005 F V = $199,149.07 9 Try it out… p You want to be able to buy a $250,000 yacht when you retire in 20 years P If you make quarterly payments into your bank account, how much must each payment be? (first payment 3 months from now) P Assume your bank account pays 7% p.a. compounded quarterly 10 = 171.793824 n = 20x4 = 80 r p e r = 0.07/4 = 0.0175 F V = 250,000 Solution ( ) +- = 1 1 n p e r n p e r r F V A r ( ) - = 80 1.0175 1 250,000 0.0175 A = $1455.23 A 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 F V = $890.18 Turn back to lecture 1 slide 38 13 Solution $700 $700 $700 $700 1 2 3 4 5 6 7 8 9 10 11 12 To use annuity formula compute “effective quarterly rate” 3 11.015075 700 700 0.015075 P V- - = + Monthly rate = 0.5% in one quarter $1 becomes (1.005)in one quarter $1 becomes (1....
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This note was uploaded on 03/13/2010 for the course ECON econ1010 taught by Professor Margretfinch during the Three '08 term at Griffith.

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Lecture02c - FINM2401 Financial Management Time Value of...

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