# Copyright (C) 2020-2023 Koen Derks # This program is free software: you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation, either version 3 of the License, or # (at your option) any later version. # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the # GNU General Public License for more details. # You should have received a copy of the GNU General Public License # along with this program. If not, see . context("Benchmark against Appendix C (AICPA 2017)") # Audit Guide: Audit Sampling [https://future.aicpa.org/cpe-learning/publication/audit-sampling-audit-guide-OPL] # Retrieved on 28-04-2021 from https://onlinelibrary.wiley.com/doi/pdf/10.1002/9781119448617.app3 test_that(desc = "(id f10-v0.4.0-t1) Test Monetary Unit Sample Sizes for 5 percent risk of overreliance (AICPA 2017 - Appendix C: Table C-1)", { riskOfIncorrectAcceptance <- c(rep(5, 6), rep(10, 5), rep(15, 5), rep(20, 5), rep(25, 5), rep(30, 4), rep(35, 4), rep(50, 4)) / 100 ratioExpectedTolerable <- c(seq(0, 0.5, 0.1), 0, seq(0.2, 0.5, 0.1), 0, seq(0.2, 0.5, 0.1), 0, seq(0.2, 0.5, 0.1), 0, seq(0.2, 0.5, 0.1), 0, seq(0.2, 0.6, 0.2), 0, seq(0.2, 0.6, 0.2), 0, seq(0.2, 0.6, 0.2)) tolerableMisstatement <- c(0.5, 0.3, 0.1, 0.08, 0.06, 0.05, 0.04, 0.03, 0.02, 0.01, 0.005) sampleSizeMatrix <- matrix(NA, nrow = length(riskOfIncorrectAcceptance), ncol = length(tolerableMisstatement) + 3) colnames(sampleSizeMatrix) <- c("Risk", "Expected", tolerableMisstatement, "Taints") sampleSizeMatrix[, 1] <- riskOfIncorrectAcceptance sampleSizeMatrix[, 2] <- ratioExpectedTolerable for (i in seq_len(nrow(sampleSizeMatrix))) { for (j in seq_along(tolerableMisstatement)) { jfaRes <- planning(conf.level = (1 - sampleSizeMatrix[i, 1]), expected = tolerableMisstatement[j] * sampleSizeMatrix[i, 2], likelihood = "poisson", materiality = tolerableMisstatement[j]) sampleSizeMatrix[i, j + 2] <- jfaRes[["n"]] } sampleSizeMatrix[i, 14] <- ceiling(jfaRes[["x"]] * 100) / 100 } aicpaMatrix <- matrix(data = NA, nrow = length(riskOfIncorrectAcceptance), ncol = length(tolerableMisstatement) + 3, byrow = FALSE) colnames(aicpaMatrix) <- c("Risk", "Expected", tolerableMisstatement, "Taints") aicpaMatrix[, 1] <- riskOfIncorrectAcceptance aicpaMatrix[, 2] <- ratioExpectedTolerable aicpaMatrix[, 3:14] <- matrix( c( 6, 10, 30, 38, 50, 60, 75, 100, 150, 300, 600, 0, 8, 13, 37, 46, 62, 74, 92, 123, 184, 368, 736, 0.37, 10, 16, 47, 58, 78, 93, 116, 155, 232, 463, 925, 0.93, # For taints of highest materiality percentage AICPA gives 0.93 but correct value is 0.92000000000000004 12, 20, 60, 75, 100, 120, 150, 200, 300, 600, 1199, 1.80, 17, 27, 81, 102, 135, 162, 203, 270, 405, 809, 1618, 3.24, 24, 39, 116, 145, 193, 231, 289, 385, 577, 1154, 2308, 5.77, 5, 8, 24, 29, 39, 47, 58, 77, 116, 231, 461, 0, 7, 12, 35, 43, 57, 69, 86, 114, 171, 341, 682, 0.69, # For taints of highest materiality percentage AICPA gives 0.69 but correct value is 0.68000000000000005 9, 15, 44, 55, 73, 87, 109, 145, 217, 433, 866, 1.30, 12, 20, 58, 72, 96, 115, 143, 191, 286, 572, 1144, 2.29, 16, 27, 80, 100, 134, 160, 200, 267, 400, 799, 1597, 4.00, # For taints of highest materiality percentage AICPA gives 4 but correct value is 3.9900000000000002 4, 7, 19, 24, 32, 38, 48, 64, 95, 190, 380, 0, 6, 10, 28, 35, 46, 55, 69, 91, 137, 273, 545, 0.55, # For taints of highest materiality percentage AICPA gives 0.55 but correct value is 0.55000000000000004 7, 12, 35, 43, 57, 69, 86, 114, 171, 341, 681, 1.03, # For taints of highest materiality percentage AICPA gives 1.03 but correct value is 1.02 9, 15, 45, 56, 74, 89, 111, 148, 221, 442, 883, 1.77, 13, 21, 61, 76, 101, 121, 151, 202, 302, 604, 1208, 3.02, 4, 6, 17, 21, 27, 33, 41, 54, 81, 161, 322, 0, 5, 8, 23, 29, 38, 46, 57, 76, 113, 226, 451, 0.46, # For taints of highest materiality percentage AICPA gives 0.46 but correct value is 0.45000000000000001 6, 10, 28, 35, 47, 56, 70, 93, 139, 277, 554, 0.84, # For taints AICPA gives 0.84 but correct value is 0.82999999999999996 8, 12, 36, 45, 59, 71, 89, 118, 177, 354, 707, 1.42, # For taints of highest materiality percentage AICPA gives 1.42 but correct value is 1.4099999999999999 10, 16, 48, 60, 80, 95, 119, 159, 238, 475, 949, 2.38, # For taints of highest materiality percentage AICPA gives 2.28 but correct value is 2.3700000000000001 3, 5, 14, 18, 24, 28, 35, 47, 70, 139, 278, 0, 4, 7, 19, 24, 32, 38, 48, 64, 95, 190, 380, 0.38, 5, 8, 23, 29, 39, 46, 58, 77, 115, 230, 460, 0.69, 6, 10, 29, 37, 49, 58, 73, 97, 145, 289, 578, 1.16, 8, 13, 38, 48, 64, 76, 95, 127, 190, 380, 760, 1.90, 3, 5, 13, 16, 21, 25, 31, 41, 61, 121, 241, 0, 4, 6, 17, 21, 27, 33, 41, 54, 81, 162, 323, 0.33, # For taints of highest materiality percentage AICPA gives 0.33 but correct value is 0.32000000000000001 5, 8, 24, 30, 40, 48, 60, 80, 120, 239, 477, 0.96, # For taints of highest materiality percentage AICPA gives 0.96 but correct value is 0.94999999999999996 9, 15, 43, 54, 71, 85, 107, 142, 213, 425, 850, 2.55, 3, 4, 11, 14, 18, 21, 27, 35, 53, 105, 210, 0, 3, 5, 14, 18, 23, 28, 35, 46, 69, 138, 276, 0.28, # For taints of highest materiality percentage AICPA gives 0.28 but correct value is 0.28000000000000003 4, 7, 20, 25, 34, 40, 50, 67, 100, 199, 397, 0.80, # For taints of highest materiality percentage AICPA gives 0.80 but correct value is 0.79000000000000004 7, 12, 34, 43, 57, 68, 85, 113, 169, 338, 676, 2.03, 2, 3, 7, 9, 12, 14, 18, 24, 35, 70, 139, 0, 2, 3, 9, 11, 15, 18, 22, 29, 44, 87, 173, 0.18, # For taints of highest materiality percentage AICPA gives 0.18 but correct value is 0.17000000000000001 3, 4, 12, 15, 19, 23, 29, 38, 57, 114, 228, 0.46, 4, 6, 17, 22, 29, 34, 43, 57, 85, 170, 340, 1.02 ), ncol = length(tolerableMisstatement) + 1, nrow = length(riskOfIncorrectAcceptance), byrow = TRUE ) expect_equal(sampleSizeMatrix, aicpaMatrix, tolerance = 0.01) })