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Internal Rate of Return 內部報酬率
張智星 (Roger Jang) 台大資工系 多媒體檢索實驗室
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Intro to IRR Internal rate of return (IRR)
Definition: The rate at which an investment plan breaks even Also known as Effective interest rate Annualized effective compounded return rate … Application: Comparison of 2 investment plans Quiz: Definition of IRR in plain texts! The term “internal” indicates it does not take environmental factors (e.g., inflation) into consideration.
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IRR Example Is this investment plan good? Profit=250?
Bank interest rate=2% Bank interest rate=5% What is the equivalent interest rate? NPV: Net present value NPV=121.07 NPV=-51.73
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Definition of IRR in an equation!
IRR Computation IRR satisfies the following equation: Or equivalently: Quiz: Definition of IRR in an equation! Net Present value Cash flow table: NPV NFV Net Future value
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IRR Example An simple example of IRR Cash flow table Equation Year (i)
Cash flow (ci) -1234 1 362 2 548 3 481
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IRR Computed by MATLAB Case 1: Simplified formula
Case 2: Formula used by the banks fcn=' /(1+x)+548/(1+x)^2+481/(1+x)^3'; x0=0; r=fzero(fcn, x0) fcn=' /(1+x/12)^12+548/(1+x/12)^24+481/(1+x/12)^36'; x0=0; r=fzero(fcn, x0)
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Display Intermediate Results
fcn=' /(1+x/12)^12+548/(1+x/12)^24+481/(1+x/12)^36'; x0=0; opt=optimset('Display', 'iter'); r=fzero(fcn, x0, opt) Search for an interval around 0 containing a sign change: Func-count a f(a) b f(b) Procedure initial interval search search search search Search for a zero in the interval [-0.08, 0.08]: Func-count x f(x) Procedure initial interpolation interpolation interpolation e interpolation e interpolation ..... e interpolation Zero found in the interval [-0.08, 0.08]
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Plot NPV as a function of IRR
Function handle to an anonymous function /(1+x/12)^12+548/(1+x/12)^24+481/(1+x/12)^36; x0=0; opt=optimset('Display', 'iter'); r=fzero(npv, x0, opt); ezplot(npv, [0, 0.08]); line(r, npv(r), 'marker', 'o', 'color', 'r'); grid on Note that npv is a function handle Quiz: Can you write a function to find all roots of a given equation in a given interval?
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儲蓄險比較 郵局六年期吉利保險 遠雄好鑽養老保險
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郵局六年期吉利保險 詳細列表 Cash flow table: age of 30, yearly payment
6 年期儲蓄險 - 郵局六年期吉利保險 年度 保費 領回 小計 -16320 1 -16157 2 3 4 5 6 100000 IRR 0.839% Yearly compounding
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Element-wise operation
郵局六年期吉利保險 irrFind.m Main script function r=irrFind(cashFlowVec, x0) x0); function npv=npvCompute(x) n=length(cashFlowVec); npv=sum(cashFlowVec./((1+x).^(0:n-1))); end Note that: npvCompute is a function @npvCompute is a function handle Function of function Element-wise operation Required! cashFlowVec=[-16320, , , , , , ]; x0=0; r=irrFind(cashFlowVec, x0) r=0.839% (Yearly compounding)
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年化報酬率 年化報酬率 應用:投資比較 說明一、說明二 方案一: 2年賺20% r=9.54%
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References References for IRR 綠角財經筆記 A very good example of IRR Wiki
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