ACCA F5 业绩管理Perance Management（上）.doc

ACCA F5教材PERFORMANCEMANAGEMENT教材（下）Test your understanding 12Original budgetFlexed budgetActualVariancesSales1002001964 adverseVariable costs(30)(60)(62)2 adverseFixed costs(10)(15)(16)1 adverseProfit601251187 adverseTest your understanding 13(a)Flexible budgetActualVarianceNumber of units sold (000) 720 270 80$000$000$000Sales1,1521,071 (81)Variable cost of salesMaterials18914445Labour270288(18)Overheads36360Fixed labour cost 100 94 6 595 562 33Gross profit 557 509 (48)Selling and distribution costsFixed7283(11)Variable1621539Administration costsFixed1841768Variable 54 54 472 466 6Net profit 85 43 (42)Possible reasonsSales (adverse) the volume variance is favourable so the adverse variance must be due to price being less than planned.Materials (favourable) could be due to bulk purchase, resulting in a lower unit price.Variable labour (adverse) could be due to inefficient working by direct labour.Fixed labour (favourable) could be due to employees leaving and not being replaced.Fixed selling overheads (adverse) could be due to additional fixed advertising costs.Variable selling overheads (favourable) could be due to lower running costs of distribution vehicles.Fixed administration overheads (favourable) better computer systems reduces the number of accountants needed!Note: There are many other possible reasons for the variances.(b) The original statement was of no use as there are volume variances comparing 640,000 units with 720,000 units. To be fair, the budget needs to be flexed to the actual level of 720,000 in order to compare like with like.(c) (i) Problems of forecasting with flexible budgets include the following:General problems: These must be overcome in any budgeting system, e.g. predicting volume and other internal estimates along with macroeconomic factors such as inflation and the interest rate.Separation of fixed and variable costs: Whereas separating out a gas bill between standing charge and usage is relatively straightforward, labour is more convoluted especially if pay structure is complicated and involves an element of both (e.g. piece rate plus fixed bonuses).Nature of fixed costs: In the long-term, all costs are variable. An apparently fixed cost will turn out to be a stepped cost, e.g. the need to hire a new machine once output reaches a certain level.Historical information: Standards must be kept up to date as much as possible but the past is not necessarily an indicator the future, e.g. increased mechanisation may alter the standard times taken.(ii)ChangeActivity level ($000):640760120Overheads ($000)3237Stepped cost (1)32364Variable cost per unit =0.0333Fixed cost=32 - 0.0333 640=10.667Therefore flexed budget for 720 would be ($000)Fixed cost 10.667Variable cost (720 0.0333) 24.000 34.667Test your understanding 14The mobile phone market is intensely competitive so a company will need sophisticated systems to gather information about the market and competitors. The market is also fast changing so a rolling budget approach may be suitable to keep budget target up to date. It will be very important to incorporate the latest information into budgets and a participative approach will be important as production managers and sales managers may have local knowledge which would improve the budgeting process. Test your understanding 15Internal information will be required from the:Sales department relating to volume and estimated collection periodsthe production manager will estimate material, labour and overhead usagethe purchasing manager will estimate material prices and payment termshuman resources will forecast pay rates, bonus payments and overtime requirements.The finance office may forecast payments of interest, dividends and general office costs.External information may be required relating to forecast interest rates, tax rates, payment terms for tax, exchange rates, inflation, etc.Test your understanding 16An analysis of overheads should be carried out to determine the proportion that have identifiable cost drivers which differ from the normal volume related cost drivers which may be used when carrying out incremental budgeting. If a substantial volume of overhead is non-volume related then implementing ABB may lead to more accurate planning and control.Issues, which should then be considered include:the development or purchase of a suitable computer system to support an ABB process;training of staff to operate and interpret the information produced;development of an implementation plan and whether this should run in tandem with the existing process for a trial period.Test your understanding 17AdvantagesIssues, which should then be considered include:Standard format can be used which is easily understood throughout the organisation.What-if? analysis can be carried out easily to test different assumptions.Cash budget can be linked to other functional budgets and the income statement and balance sheet so that changes can be linked between budgets.Look up tables can be used so that, for example, if price levels change these can be input in one place in the spreadsheet and the effects can be carried throughout the budget.Different managers may be able to input information into the spreadsheet if it is held on a shared drive.Dangers:If there is an error in the cash budgeting model this may be overlooked and the organisation will be using inaccurate information.Information may be accidentally changed or deleted.Data used will still be forecast and subject to a high degree of uncertainty. There is a danger that it will be used incorrectly.Chapter 8Quantitative analysisChapter learning objectivesUpon completion of this chapter you will be able to:explain and evaluate the use of high/low analysis to separate the fixed and variable elements of total costexplain and evaluate the use of regression analysis to separate the fixed and variable elements of total costexplain the use of time series analysis as a forecasting techniquepredict a future value from time series analysis data using both the additive and proportional dataexplain the use of a simple average growth model as a forecasting techniqueexplain the use of judgement and experience in forecastingexplain the learning curve effectestimate the learning effect and apply this to a budgetary problemcalculate production times when the learning curve has reached a steady stateexplain the limitations of the learning curve model.QUANTITATIVEANALYSISHIGH LOW ANALYSISLEARNING CURVEMODELTIME SERIESANALYSISREGRESSIONANALYSISREGRESSIONANALYSIS1 High/low analysisA method of analysing a semi-variable cost into its fixed and variable elements based on an analysis of historical information about costs at different activity levels.The approach is as follows:Step 1Select the highest and lowest activity levels, and their costs.(Note: do not take the highest and lowest costs).Step 2Find the variable cost/unit.Variable cost/unit = Step 3Find the fixed cost, using either the high or low activity level.Fixed cost = Total cost at activity level Total variable costThe high-low method has the enormous advantage of simplicity. It is easy to understand and easy to use.The limitations of the high-low method are:It assumes that activity is the only factor affecting costs.It assumes that historical costs reliably predict future costs.It uses only two values, the highest and the lowest, so the results may be distorted due to random variations in these values.Illustration 1 Hi/low analysisCost data for six months to 31 December 208 is as follows:MonthUnitsInspection costs$July3402,240August3002,160September3802,320October4202,400November4002,360December360The variable element of a cost item is estimated by calculating the unit cost between high and low volumes during a period.Six months to 31/128UnitsProducedInspectioncosts$Highest month4202,400Lowest month3002,160Range 120 240Variable cost per unit=$240/120 = $2 per unitFixed inspection costs are, therefore:$2,400 (240 units $2)=$1,560 per monthOr 2,160 (300 units $2)=$1,560 per monthi.e. the relationship is of the form y=$1,560 + $2x.Test your understanding 1Output (Units)Total cost ($)2007,0003008,0004009,000Find the variable cost per unit.Find the total fixed cost.Estimate the total cost if output is 350 units.Estimate the total cost if output is 600 units.2 Regression analysisRegression involves using historical data to find the line of best fit between two variables (one dependent on the other), and use this to predict future values.The dependent variable is y and must always be on the vertical axis.The independent variable is x and always goes on the horizontal axis.Scatter diagramxyxxxxxThe scatter of the points is caused by the other factors affecting y. Our objective is to find the best line (the line of best fit) through the centre of this diagram.Equation of a straight lineThe equation of a straight line is:y = a + bxwhere:a is the intercept: the y value when x equal zero, andb is the gradient or slope: the change in y when x increases by one unitIf b is negative, the line will be downwards sloping as x increases, y decreases. This is called a negative relationship.To find the line of best fit we need to calculate a and b using the historical data for x and y. The formulae for these are:b =nxy - xyNx2a =y- bxnnwhere n = sample sizeBoth of these formulae are given in the examination.Illustration 2 Regression analysisA company has recorded expenditure on advertising and resulting sales for six months as follows:MonthAdvertisingExpenditureSalesxy$000$000March20170April40240May50260June60300July30220August40250Required:Plot the data on a scatter diagram and comment.Calculate the line of best fit through the data, and interpret your values of a and b.Forecast sales when advertising expenditure is:$50,000$100,000and comment on your answers.Solution(a)Sales($000)30025020015010 20 30 40 50 60Advertising expenditure($000)xxxxxxThere appears to be a positive linear relationship between advertising expenditure and sales.(b)xyxyx2y2201703,40040028,900402409,6001,60057,6005026013,0002,50067,6006030018,0003,60090,000302206,60090048,4004025010,0001,60062,5002401,44060,60010,600355,000b=6 60,600 240 1,440=18,000= 36 10,600 24026,000a = - 3 = 120Line is: y = 120 + 3xThis means that when advertising expenditure is zero, sales will be $120,000, and for every $1 spent on advertising, sales will increase by $2.(c) (i) Advertising is $50,000 x = 50; y = 120 + (3 50) = 270Forecast sales are $270,000This is an interpolation within the sample range of values and is likely to be fairly accurate. (ii) Advertising is $100,000x = 100; y = 120 + (3 100) = 420.Forecast sales are $420,00This is an extrapolation outside the sample range and may be inaccurate.Test your understanding 2Regression analysis is being used to find the line of best fit (y = a + bx) from 11 pairs of data. The calculations have produced the following information:x = 440, y = 330, x2 = 17,986, y2 = 10,366 and xy = 13,467Find the equation of the line of best fit using regression analysis.Use your equation to forecast the value of y if x = 42.Note: You may recall form paper F2 that the strength of the linear relationship between the two variables (and hence the usefulness of the regression line equation) can be assessed by calculating the correlation coefficient (“r”) and the coefficient of determination (“r2”), where(nx2 (x)2) (ny2 (y)2)nxy xyr =Using the data from illustration 2 above:(6 10,600 2402) (6 355,000 1,4402)6 60,600 240 1,440r =0.97849r2 = 0.957Thus 95.7% of the observed variation is sales can be explained as being due to changes in the advertising spend. This would give strong assurances that the forecasts made using the regression equation are valid.3 Time series analysisA time series is a series of figures relating to the changing value of a variable over time. The data often conforms to a certain pattern over time. This pattern can be extrapolated into the future and hence forecasts are possible. Time periods may be any measure of time including days, weeks, months and quarters.Sales,costs,revenues,etc.Time periodThe four components of a time series are:The trend this describes the long-term general movement of the data.Seasonal variations a regular variation around the trend over a fixed time period, usually one year.Cyclical variations economic cycle of booms and slumps.Residual variations irregular, random fluctuations in the data usually caused by factors specific to the time series. They are unpredictable.In examination problems there is generally insufficient data to evaluate the cyclical variations, hence, they are ignored. The residual influences are also, effectively, ignored. They should actually be eliminated by using some averaging techniques.The numerical analysisThis is performed by carrying out two distinct steps:establishing the long-term underlying trendestablishing the regular seasonal variations.You will not be asked to derive the time series relationship. Instead you could be given this information and asked to forecast future sales.The additive modelThis is based upon the idea that each actual result is made up of two influences.Actual = Trend + Seasonal Variation (SV)The SV will be expressed in absolute terms.The multiplicative modelActual = Trend SV factorThe SV will be expressed in proportional terms, e.g. if, in one particular period the underlying trend was known to be $10,000 and the SV in this period was given as +12%, then the actual result could be forecast as:$10,000 = 11,200.Test your understanding 3A company has found that the trend in the quarterly sales of its furniture is well described by the regression equation y = 150 + 10xwhere y equals quarterly sales ($000) x = 1 represents the first quarter of 200 x = 2 represents the second quarter of 200 x = 5 represents the first quarter of 201, etc.It has also been found that, based on a multiplicative model, i.e. Sales = Trend Seasonal RandomThe mean seasonal quarterly index for its furniture sales is as follows:Quarter1234Seasonal index8011014070Explain the meaning of this regression equation, and set of seasonal index numbers.Using the regression equation, estimate the trend values in the companys furniture sales for each quarter of 205Using the seasonal index, prepare sales forecasts for the companys quarterly furniture sales in 205State what factors might cause your sales forecasts to be in error.Test your understanding 4The number of customers to a health centre has been increasing and it is estimated that the underlying trend is for an increase of 50 customers each month. However, the numbers fluctuate depending on the month of the year.The underlying trend value for customers in December Year 1 is 4,300.SVs for some of the months are: SV factorMay 116June 107July 94August 82September 106Prepare a forecast for the number of customers in each of the months May to September, Year 2.5 Average growth modelsStrategic plans may incorporate an objective of a target average growth of profit or sales over a number of years. There may also be requirements for a target average growth rate of productivity over a number of years.Illustration 6 Average growth modelsSales are forecast to increase, on average, by 2% per quarter. Sales are currently $250,000 pa. Calculate the budgeted sales figures for each quarter of the forthcoming year.Show how you could have found the average growth rate given the final figure.SolutionSales ($)Quarter 1($250,000/4 1.02)63,750Quarter 2($63,750 1.02)65,025Quarter 3($65,025 1.02)66,326Quarter 4($66,325 1.02) 67,652 $262,753The problem may be to find the average growth rate given the original and final sales figure.Let g = the unknown growth rate0 = the original figureF = the final figuren = number of periods of growthF = O(1 + g)nIn this problem $67,652 = $62,500(1 + g)3So g = ($67,652/62,500)1/3 1 = 2.0%Test your understanding 5A company is producing a budget relating to a new product to be introduced. Sales volume is expected to be 1,000 units in the first quarter of the year and is forecast to grow by 10% per quarter. The sale price is to be set at $125 initially but will be reduced by 5% each quarter. Variable costs per unit are forecast to be $65 initially b