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1 Complex Cash Flows 1. Break complex flows into simpler patterns: Match to P, F, A, G, or g patterns 2. Convert individual patterns to either P or F equivalent 3. Convert P and F equivalents to the same point in time Use P/F or F/P factors 4. Combine the equivalent cash flows at the same point in time (compute the net equivalent)

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2 Example 1: Find the Year 5 equivalent of all cash flows, at an interest rate of 12% per year: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 $ 1 000 $ 2 000 YR 5 = ? YR 5 = – [$1000 (F/A,12%,4) (F/P,12%,2) + $2000 (P/A,12%,7) (P/F,12%,1)] = – [$1000 (4.7793) (1.2544) + $2000 (4.5638) (.8929)] = – [$5995 + $8150] = – $ 14 145

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3 Example 2: Find the net cash flow (x), if the interest rate is 18% per year: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 $ 800 x = ? $ 700 $ 950 X = $700 (F/P,18%,7) + $700 (F/P,18%,4) – $800 (F/A,18%,2) (F/P,18%,8) – $950 (F/A,18%,2) (F/P,18%,1) – $800 (P/A,18%,3) = $2230 + $1357 – $6556 – $2444 – $1739= $ – 7 152

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4 Example 3: Add P, F, A, G, and g cash flows, then pick a point in time (x) and find the net flow, if interest is 8% per year: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

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