a b GE(General Erectrics) 9 4 irr (JAPLA 2009/12) Example1 120 P = C r + C 2 (1 + r) C t 1 (1 + r) t 1 + C t + F (1 + r) t 10

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1 1 SHIMURA Masato CF *1 irr irr irr(inner rate of return)function is able to written only few lines,and it is very powerful and useful for simulate unprofitable business model NPV(Net Present Value) 2. IRR Inner Rate of Return) NVP IRR NVP IRR 1. *1 SHIMURA Masato Japan APL Association

2 a b GE(General Erectrics) 9 4 irr (JAPLA 2009/12) Example1 120 P = C r + C 2 (1 + r) C t 1 (1 + r) t 1 + C t + F (1 + r) t r 100 = r + 5 (1 + r) (1 + r) 3 = 100(1 + r)3 + 5(1 + r) 2 + 5(1 + r) (1 + r) r 295r 2 100r 3 = 0 100(r 3 + 3r 2 + 3r + 1) 5(r 2 + 2r + 1) 5(r + 1) J (p.) Newton a mk_poly_sum _ _285 _295 _100

3 1 3 b mk_poly_sum=:3 : 0 NB. make polynominal coefficient. +/ y *."1. pascal <: # y ) pascal=:3 : :!/ i. >: y NB. Pascal triangles c J (p.) ;}. p. 35 _285 _295 _100 _ j _ j_ %( 2. irr J J addon require jpath addons/finance/interest/interest.ijs irr irr _ xirr extended irr xirr ,: _ irr, xirr EXCEL CF irr _ CF irr _ CF irr _100 _5 _5 95 _ CF

4 1 4 irr _100 _5 _5 85 _ mk_poly_sum _100 _5 _5 95 _15 _315 _305 _100 f = x 303x 2 100x 3 p. mk_poly_sum _100 _5 _ _100 _1.5j _1.5j_ _ NB. -5% 1.3 J irr J addon finance interest.i js irr NB. internal rate of return by newton-raphson iteration. NB. form: t irr cf NB. t = optional initial trial value (decimal rate) NB. cf = cash flow starting at time 0 NB. tolerance 1e_5, max iterations 15 NB. result is decimal interest rate, or error message irr=: 3 : 0 0 irr y : t=. %>:x cf=.,y tol=. 1e_5 max=. 15 if. 2>#cf do. cash flow must have at least two elements return. end. if. -. *./_1 1 e.*cf do. no sign change in cash flow return. end. cf=. (.cf),:.1.cf*i.#cf while. tol< t-r=. t-%/t#.cf do. t=. r if. 0=max=. <:max do. iterations exceeded return. end. end. <:%r

5 1 5 ) irr (JAPLA 2010/3) ( ) P(x) = dp(x) dx = M{nx n 1 + (n 1)x n x + 1} = M(n(n 1), (n 2),, 3, 2, 1) (x n 1, x n 2,, x 2, x, 1) 2 cf*i.#cf cf=. (.cf),:.1.cf*i.#cf while. tol< t-r=. t-%/t#.cf do. t=. r J Grammar % >: +1 1 <: 1 1 # copy copy. less 1 *. And e. memberso f = equal CF 5% irr _ CF 5% irr irr _100 _5 _5 _5 _5 _5 _5 _5 _5 95 _0.05

6 2 CF 6 2 CF 2.1 CF 1. CF irr CF irr irr J irr (iteration) 15 (tolelance) 1e_ (2) irr _100 _5 _5 _5 _5 _5 _5 _5 _5 95 _0.05 script Script irr 30

7 2 CF CF 1. irr irr 25 irr _100 _5 _5 _5 _5 _5 _5 _5 _5 25 _ irr _100 _5 _5 _5 _5 _5 _5 _5 _5 24 iterations exceeded max irr _100 _5 _5 _5 _5 _5 _5 _5 _5 21 _ irr _100 _5 _5 _5 _5 _5 _5 _5 _5 20 NaN error: irr tol< t-r=.t-%/t #.cf % 25-5 mk_poly_sum _100 _5 _5 _5 _5 _5 _5 _5 _5 20 _120 _1080 _4020 _9030 _13230 _13020 _8580 _3645 _905 _100 f = x 4020x x x x x x 7 905x 8 100x $ ; >}. p. mk_poly_sum _100 _5 _5 _5 _5 _5 _5 _5 _5 20 _1.7973j _1.7973j_ _1.4204j _1.4204j_ _ j _ j_ _ j _ j_ _ case 15( $ ; >}. p. mk_poly_sum _100 _5 _5 _5 _5 _5 _5 _5 _5 10 _1.7453j _1.7453j_ _ j _ j_ _ j _ j_ _ j _ j_ _ % + ( -5)

8 2 CF $ ; >}. p. mk_poly_sum _100 _5 _5 _5 _5 _5 _5 _5 _5 5 _1.7015j _1.7015j_ _ j _ j_ _ j _ j_ _ j _ j_ _ % 3 3 $ ; >}. p. mk_poly_sum _100 _5 _5 _5 _5 _5 _5 _5 _5 0 _ j _ j_ _ j _ j_ _ j _ j_ _1 _ j _ j_ case 0 (add -5) 3 3 $ ; >}. p. mk_poly_sum _100 _5 _5 _5 _5 _5 _5 _5 _5 _5 _ _ j _ j_ _ j _ j_ _ j _ j_ _ j _ j_ (2) irr _100,(10#_5),95 _ {: 0.03 layer_ganri (10#5);.>: i

9 2 CF 9 +/ a a=._5+ -{:"1 ; {: 0.03 layer_ganri (10#5);.>: i.10 irr _100,(a),95 _ % irr _100,(a),45 _ (3) 5 irr _100 _5 _5 _5 _5 _5 _5 _5 _5 _5 95 _ , irr _100 _5 _5 _5 _5 _35 _5 _5 _5 _5 130 _ (-7.8%) irr _100 _5 _5 _5 _5 _35 _5 _5 _5 _5 95 _ irr _100 _5 _5 _5 _5 _35 _5 _5 _5 _5 80 _ irr _100 _5 _5 _5 _5 _35 _5 _5 _5 _5 45 _

10 irr irr 5% 0.05 irr _ % (-11%) irr _ _ % irr _100, 10# % irr _100, 20# % irr _100, 30#3.33 _ e_5 NB % irr _100, 50# % irr _100, 100#1 0 References 3 JAPLA 2010/3 (JAPLA 2009/12)

11 3 11 Miscellance J JAPLA HP

1 SHIMURA Masato polynomial irr.xirr EXCEL irr

1 SHIMURA Masato polynomial irr.xirr EXCEL irr 1 SHIMURA Masato 2009 12 8 1 2 1.1................................... 2 1.2 polynomial......................... 4 2 irr.xirr EXCEL 5 2.1 irr............................................. 5 2.2 d f, pv...........................................