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Internal Rate of Return 內部報酬率 張智星 (Roge Jang) 台大資工系 多媒體檢索實驗室.

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Presentation on theme: "Internal Rate of Return 內部報酬率 張智星 (Roge Jang) 台大資工系 多媒體檢索實驗室."— Presentation transcript:

1 Internal Rate of Return 內部報酬率 張智星 (Roge Jang) 台大資工系 多媒體檢索實驗室

2 Scientific Computing: Compounding Intro to IRR Internal rate of return (IRR) Definition: The rate at which an investment breaks even Also known as Annualized effective compounded return rate … Application: Comparison of 2 investment project Reference Wiki 綠角財經筆記

3 Scientific Computing: Compounding IRR Computation IRR satisfies the following equation: Or equivalently:

4 Scientific Computing: Compounding IRR Example An simple example of IRR Cash flow table Equation Year (i)Cash flow (ci)

5 Scientific Computing: Compounding IRR Computed by MATLAB Case 1 Case 2 fun=' /(1+x)+548/(1+x)^2+481/(1+x)^3'; x0=0; r=fzero(fun, x0) fun=' /(1+x/12)^12+548/(1+x/12)^24+481/(1+x/12)^36'; x0=0; r=fzero(fun, x0)

6 Scientific Computing: Compounding Display Intermediate Results fun=' /(1+x/12)^12+548/(1+x/12)^24+481/(1+x/12)^36'; x0=0; opt=optimset('Display', 'iter'); r=fzero(fun, 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-09 interpolation e-13 interpolation e-13 interpolation Zero found in the interval [-0.08, 0.08].....

7 Scientific Computing: Compounding 儲蓄險比較 郵局六年期吉利保險 遠雄好鑽養老保險

8 Scientific Computing: Compounding 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 IRR0.839%  Yearly compounding

9 Scientific Computing: Compounding 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 cashFlowVec=[-16320, , , , , , ]; x0=0; r=irrFind(cashFlowVec, x0)  r=0.839% (Yearly compounding)

10 Scientific Computing: Compounding 年化報酬率 說明一、說明二 說明一說明二 應用:投資比較 方案一: 2 年賺 20%  r=9.54% 方案二: 5 年賺 50%  r=8.45% 方案三: 10 年賺 100%  r=7.18%


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