L3 - Discounted Cash Flows

L3 Discounted - Financial Management Fall 2010 Lecture 3 Discounted Cash Flows(I Professor Erica Li Ross School of Business Roadmap of todays class

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Financial Management Fall 2010 Lecture 3: Discounted Cash Flows (I) Professor Erica Li Ross School of Business

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Roadmap of today’s class ! Future value of multiple cash flows ! Present value of multiple cash flows ! Annuity and annuity due ! perpetuity
3 FV of multiple cash flows (I) ! Suppose you invest \$500 in a mutual fund today and \$600 in one year. If the fund pays 9% annually, how much will you have in two years? FV 2 = 500*(1.09) 2 + 600*(1.09) = \$1248.05 ! #\$ % ’(!! ’)!! (!!*%+!#, & - (#.+!( ! )!!*%+!#, - )(.+!! ! /0 & 3

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FV of multiple cash flows (II) ! Suppose you invest \$500 in a mutual fund today and \$600 in one year. If the fund pays 9% annually, how much will you have in two years? 0 1 2 9% 9% \$500 \$600 + \$500 ! (1+9%) = \$545 \$1,145 \$1,145 ! (1+9%) = \$1,248.05 4
Two equivalent ways to calculate FV ! Calculate the future value of each individual cash flow and then sum them up ! Compound the accumulated balance forward one period at a time ! General formula: C 0 C 1 C 2 C T 0 1 2 T FV T = C 0 ( 1 + r ) T + C 1 ( 1 + r ) T " 1 + C 2 ( 1 + r ) T " 2 + ! + C T

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PV of multiple cash flows (I) ! Suppose you expect to receive \$1,000 in one year, and \$500 in two years. Interest rate is 6% for each year. What is the value today of this set of cash flows? 0 1 2 6% 6% \$500 \$1,000 \$1,000/(1+6%) = \$943.40 \$500/(1+6%) 2 = \$445.00 + PV = \$1,388.40 6
PV of multiple cash flows (II) ! Suppose you expect to receive \$1,000 in one year, and \$500 in two years. Interest rate is 6% for each year. What is the value today of this set of cash flows? 0 1 2 6% 6% \$500 \$1,000 \$1,471.70 \$500/(1+6%) = \$471.70 + PV = \$1,471.70/(1+6%) = \$1,388.40 7

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Two equivalent ways to calculate PV ! Calculate the present value of each individual cash flow and then sum them up ! Discount the balance backward one period at a time ! General formula: C 0 C 1 C 2 C T 0 1 2 T PV = C 0 + C 1 1 + r + C 2 ( 1 + r ) 2 + ! + C T ( 1 + r ) T
Your broker’s deal ! Your broker tells you that he gets you a good deal. If you invest \$100 today, you will receive \$40 in one year and \$75 in two years. Suppose you can earn 15% on very similar investments, should you take your broker’s deal?

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10 (Ordinary) Annuities 4 567865 9: 8;6<=>?@ >?5A B9C5 *D, 9>>E778<F ?G GA6 6<; 9: 6?>A H6789; :97 59I6 JK6; <EIL67 9: H6789;5 *M, ! [email protected] >9<5EI67 @9?<5 *6+F+ >?7 @9?<5,1 A9I6 I97GF?F651 6G>+ t=0 1 2 3 T C C C C PV = C 1 + r + C ( 1 + r ) 2 + C ( 1 + r ) 3 + ! + C ( 1 + r ) T FV T = C ( 1 + r ) T " 1 + C ( 1 + r ) T " 2 + C ( 1 + r ) T " 3 + ! + C
11 Shortcut formula " PV of ordinary annuity (at t=0): " C: period payment T: number of payments r: per period interest rate " PVIFA: present value interest factor for annuities " (PV, C, r, T), know any three variables => the 4 th PV = C " 1 # 1 ( 1 + r ) T r \$ % ( ) ) ) ) * C " PVIFA r , T

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This note was uploaded on 12/12/2010 for the course FIN 300 taught by Professor Mishra during the Fall '08 term at University of Michigan.

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L3 Discounted - Financial Management Fall 2010 Lecture 3 Discounted Cash Flows(I Professor Erica Li Ross School of Business Roadmap of todays class

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