Interest_Formulas

Interest_Formulas - Interest Formulas IE 226 1 Setting the...

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1 Interest Formulas Interest Formulas IE 226 IE 226 2 Setting the Stage Setting the Stage We will describe a project’s finances through cash flow diagrams Eventually, we will have to determine whether a project is acceptable or which of a set of projects is best Must be able to convert cash flow diagrams for comparison and analysis Interest allows us to do the conversions
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3 Key Concepts Economic Equivalence: two cash flow diagrams are equivalent if we do not prefer one over the other. Interest factors: allow for the conversion of a cash flow diagram into another equivalent cash flow diagram Analyze different cash flows utilizing: Interest factor equations and tables Spreadsheets 4 Economic Equivalence Economic Equivalence When two cash flow diagrams are economically equivalent , we are indifferent as to which we choose. To fairly compare two different cash flow diagrams, we must convert each into something similar ( compare apples to apples !) Equivalence depends on: Magnitude of the cash flow(s) Timing of the cash flow(s) Interest rate(s) over the relevant time periods
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5 Conversions Conversions Most cash flows follow a pattern: Single cash flow Repeated (equal sized) cash flows Fixed amount of growth each period • Arithmetic Gradient Percentage amount of growth each period • Geometric Gradient Interest factors allow for quick conversions between these types of cash flow diagrams 6 Assumptions Assumptions Interest is compounded per period. The interest rate does not change over time. The timing of cash flows coincides with the interest rate compounding period. All cash flows occur at the end of the time period unless otherwise specified. Time period zero is an arbitrary starting point.
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7 Notation P represents cash flows at time zero for now (or previous to other variables) F represents cash flows at time period N A denotes repeated cash flows of equal value G represents the constant increase in cash flows in each consecutive period g represents the periodic growth rate i represents the periodic interest rate 8 Compound Amount Factors Compound Amount Factors Goal : to transform a set of cash flows into an economically equivalent single cash flow, F , in the future (time period N ) Compounding refers to money moving forward in time (growing with a positive interest rate).
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9 Single Payment Analysis Single Payment Analysis Assuming periodic interest i 0 1 2 3 . . . . . . . . . . . . . . N P 0 1 2 3 . . . . . . . . . . . . . . N F Equivalent by the Compound Amount Factor Question: If I place ( P ) into an account, how much ( F ) do I accumulate N periods later? 10 What is What is F given given P ? We know this from compound interest: Single payment compound amount factor F = P (1 + i ) N = P ( F / P , i , N ) ( F/P, i, N ) is the shorthand notation
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11 Example Example Continental Airlines announced the purchase 10 Boeing 787s for the price of $1.3 billion.
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Interest_Formulas - Interest Formulas IE 226 1 Setting the...

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