PRESENT VALUE TABLEPresent value of $1, that is where r = interest rate; n = number of periods untilpayment or receipt.1 r n Periods(n)Interest rates (r)1%2%3%4%5%6%7%8%9%10%10.9900.9800.9710.9620.9520.9430.9350.9260.9170.90920.9800.9610.9430.9250.9070.8900.8730.8570.8420.82630.9710.9420.9150.8890.8640.8400.8160.7940.7720.75140.9610.9240.8880.8550.8230.7920.7630.7350.7080.68350.9510.9060.8630.8220.7840.7470.7130.6810.6500.62160.9420.8880.8370.7900.74607050.6660.6300.5960.56470.9330.8710.8130.7600.7110.6650.6230.5830.5470.51380.9230.8530.7890.7310.6770.6270.5820.5400.5020.46790.9140.8370.7660.7030.6450.5920.5440.5000.4600.424100.9050.8200.7440.6760.6140.5580.5080.4630.4220.386110.8960.8040.7220.6500.5850.5270.4750.4290.3880.350120.8870.7880.7010.6250.5570.4970.4440.3970.3560.319130.8790.7730.6810.6010.5300.4690.4150.3680.3260.290140.8700.7580.6610.5770.5050.4420.3880.3400.2990.263150.8610.7430.6420.5550.4810.4170.3620.3150.2750.239160.8530.7280.6230.5340.4580.3940.3390.2920.2520.218170.8440.7140.6050.5130.4360.3710.3170.2700.2310.198180.8360.7000.5870.4940.4160.3500.2960.2500.2120.180190.8280.6860.5700.4750.3960.3310.2770.2320.1940.164200.8200.6730.5540.4560.3770.3120.2580.2150.1780.149 Periods(n)Interest rates (r)11%12%13%14%15%16%17%18%19%20%10.9010.8930.8850.8770.8700.8620.8550.8470.8400.83320.8120.7970.7830.7690.7560.7430.7310.7180.7060.69430.7310.7120.6930.6750.6580.6410.6240.6090.5930.57940.6590.6360.6130.5920.5720.5520.5340.5160.4990.48250.5930.5670.5430.5190.4970.4760.4560.4370.4190.40260.5350.5070.4800.4560.4320.4100.3900.3700.3520.33570.4820.4520.4250.4000.3760.3540.3330.3140.2960.27980.4340.4040.3760.3510.3270.3050.2850.2660.2490.23390.3910.3610.3330.3080.2840.2630.2430.2250.2090.194100.3520.3220.2950.2700.2470.2270.2080.1910.1760.162110.3170.2870.2610.2370.2150.1950.1780.1620.1480.135120.2860.2570.2310.2080.1870.1680.1520.1370.1240.112130.2580.2290.2040.1820.1630.1450.1300.1160.1040.093140.2320.2050.1810.1600.1410.1250.1110.0990.0880.078150.2090.1830.1600.1400.1230.1080.0950.0840.0790.065160.1880.1630.1410.1230.1070.0930.0810.0710.0620.054170.1700.1460.1250.1080.0930.0800.0690.0600.0520.045180.1530.1300.1110.0950.0810.0690.0590.0510.0440.038190.1380.1160.0980.0830.0700.0600.0510.0430.0370.031200.1240.1040.0870.0730.0610.0510.0430.0370.0310.026 The Chartered Institute of Management Accountants 2010Cumulative present value of $1 per annum, Receivable or Payable at the end of each year for nyears r r )(11 n Periods(n)Interest rates (r)1%2%3%4%5%6%7%8%9%10%10.9900.9800.9710.9620.9520.9430.9350.9260.9170.90921.9701.9421.9131.8861.8591.8331.8081.7831.7591.73632.9412.8842.8292.7752.7232.6732.6242.5772.5312.48743.9023.8083.7173.6303.5463.4653.3873.3123.2403.17054.8534.7134.5804.4524.3294.2124.1003.9933.8903.79165.7955.6015.4175.2425.0764.9174.7674.6234.4864.35576.7286.4726.2306.0025.7865.5825.3895.2065.0334.86887.6527.3257.0206.7336.4636.2105.9715.7475.5355.33598.5668.1627.7867.4357.1086.8026.5156.2475.9955.759109.4718.9838.5308.1117.7227.3607.0246.7106.4186.1451110.3689.7879.2538.7608.3067.8877.4997.1396.8056.4951211.25510.5759.9549.3858.8638.3847.9437.5367.1616.8141312.13411.34810.6359.9869.3948.8538.3587.9047.4877.1031413.00412.10611.29610.5639.8999.2958.7458.2447.7867.3671513.86512.84911.93811.11810.3809.7129.1088.5598.0617.6061614.71813.57812.56111.65210.83810.1069.4478.8518.3137.8241715.56214.29213.16612.16611.27410.4779.7639.1228.5448.0221816.39814.99213.75412.65911.69010.82810.0599.3728.7568.2011917.22615.67914.32413.13412.08511.15810.3369.6048.9508.3652018.04616.35114.87813.59012.46211.47010.5949.8189.1298.514 Periods(n)Interest rates (r)11%12%13%14%15%16%17%18%19%20%10.9010.8930.8850.8770.8700.8620.8550.8470.8400.83321.7131.6901.6681.6471.6261.6051.5851.5661.5471.52832.4442.4022.3612.3222.2832.2462.2102.1742.1402.10643.1023.0372.9742.9142.8552.7982.7432.6902.6392.58953.6963.6053.5173.4333.3523.2743.1993.1273.0582.99164.2314.1113.9983.8893.7843.6853.5893.4983.4103.32674.7124.5644.4234.2884.1604.0393.9223.8123.7063.60585.1464.9684.7994.6394.4874.3444.2074.0783.9543.83795.5375.3285.1324.9464.7724.6074.4514.3034.1634.031105.8895.6505.4265.2165.0194.8334.6594.4944.3394.192116.2075.9385.6875.4535.2345.0294.8364.6564.4864.327126.4926.1945.9185.6605.4215.1974.9887.7934.6114.439136.7506.4246.1225.8425.5835.3425.1184.9104.7154.533146.9826.6286.3026.0025.7245.4685.2295.0084.8024.611157.1916.8116.4626.1425.8475.5755.3245.0924.8764.675167.3796.9746.6046.2655.9545.6685.4055.1624.9384.730177.5497.1206.7296.3736.0475.7495.4755.2224.9904.775187.7027.2506.8406.4676.1285.8185.5345.2735.0334.812197.8397.3666.9386.5506.1985.8775.5845.3165.0704.843207.9637.4697.0256.6236.2595.9295.6285.3535.1014.870 May 2010 2 Performance OperationsFORMULAEPROBABILITY A B = A or B.A B = A and B (overlap).P(B A) = probability of B, given A.Rules of AdditionIf A and B are mutually exclusive:P(A B) = P(A) + P(B) If A and B are not mutually exclusive: P(A B) = P(A) + P(B) – P(A B)Rules of MultiplicationIf A and B are independent: P(A B) = P(A) * P(B)If A and B are not independent: P(A B) = P(A) * P(B | A)E(X) = (probability * payoff)DESCRIPTIVE STATISTICSArithmetic Meanxnx ffxx (frequency distribution)Standard DeviationnxxSD )( 22 2xffxSD (frequency distribution)INDEX NUMBERSPrice relative = 100 * P1/P0 Quantity relative = 100 * Q1/Q0Price: 100 xP P ww1 oQuantity: 100 x1QQ wwo TIME SERIESAdditive ModelSeries = Trend + Seasonal + RandomMultiplicative ModelSeries = Trend * Seasonal * RandomMay 2010 3 Performance OperationsFINANCIAL MATHEMATICSCompound Interest (Values and Sums)Future Value S, of a sum of X, invested for n periods, compounded at r% interestS = X[1 + r]nAnnuityPresent value of an annuity of £1 per annum receivable or payable for n years, commencing in oneyear, discounted at r% per annum:PV =nr r ]1[11 1PerpetuityPresent value of £1 per annum, payable or receivable in perpetuity, commencing in one year,discounted at r% per annum:PV =1rLEARNING CURVEYx = aXbwhere:Yx = the cumulative average time per unit to produce X units;a = the time required to produce the first unit of output;X = the cumulative number of units;b = the index of learning.The exponent b is defined as the log of the learning curve improvement rate divided by log 2.INVENTORY MANAGEMENTEconomic Order QuantityEOQ =o hCD2C where:Co=cost of placing an orderCh=cost of holding one unit in Inventory for one yearD=annual demand May 2010 4 Performance Operations

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