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Unformatted text preview: ISE 504 (Spring 2008) Lecture Notes Part I square6 Equivalence (Ch 13) square6 Microsoft Excel (Appendix A) square6 Effective Interest Rates (Ch 4) Equivalence (Chapters 13) Cash Flow Diagrams Period Amount (5,000) 1 1,000 2 (7,000) 3 5,000 4 10,000 i% Cash Flow Diagrams square6 A nice tool for keeping ourselves straight when working on equivalence problems square6 ALWAYS have an interest rate square6 Periods square6 Can represent any unit of time square6 Usually months, quarters, or years depends on problem square6 End of period convention square6 All cash flows are assumed to happen at the end of the period. square6 Sign depends on perspective If I loan you $100 to be paid back next month My Perspective Your Perspective 0% 0% Spend $10k today to save $10k per year for 5 years i% Symbols square6 t = time in periods square6 i = the interest rate per period square6 n = the number of compounding periods square6 P = a present (earlier) sum of money square6 F = a future (later) sum of money square6 A = a uniform series of payments square6 G = a linearly increasing series of payments square6 g = geometrically increasing series of payments P P P P F A G 3G 2G 4G 1 1 ) 1 ( + n g A From Blank & Tarquin MARR square6 Minimum Attractive (Acceptable) Rate of Return square6 Simple model borrowing and investment rate of return are the same square6 Set by corporate leadership square6 Usually high; ~18% typical square6 Risk square6 Uncertainty square6 Entrepreneurship square6 Investments usually arent liquid Compound Interest One period: Two period: Three period: i) P(1 F 1 + = 2 2 i) P(1 i) i)](1 [P(1 F + = + + = 3 2 3 i) P(1 i) ](1 i) [P(1 F + = + + = n i P F ) 1 ( + = The most important equation in this course.. learn it, know it, live it! Solving for each variable ) 1 ln( ) ln( ) ln( 1 ) ln( ) ln( exp ) 1 ( ) 1 ( i P F n n P F i i F P i P F n n + =  = + = + = Be careful when calculating n. Example find F given P square6 On September 28, 1999 you deposit $100 in account which pays 0.5% interest per month. On October 1, 2002 the account was worth: 36 F=? $100 i=0.5% $119.67 (1.005) 100 i) (1 P F 36 n = = + = Example find P given F square6 How much should you invest now to have $100,000 in 18 years if i = 14% per year? 18 $100k P=? i=14% $9456 (1.14) 100,000 i) (1 F P 18 n = = + = Example square6 A relative purchased a bond for you when you were born. The terms of the bond were 8% per year for 20 years. You cashed the bond at maturity for $4660.95 to pay your tuition. How much was it worth when you were 10? 20 F=$4660.95 ? P=? 10 $2158.92 (1.08) 95 . 660 4 i) (1 F P 10 n = = + = Moral: P doesnt have to be at zero....
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This note was uploaded on 04/18/2008 for the course ISE 504 taught by Professor Pierson during the Spring '08 term at Ohio State.
 Spring '08
 Pierson

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