accaf5业绩管理performancemanagement上(编辑修改稿)

accaf5业绩管理performancemanagement上(编辑修改稿)内容摘要：

+ (3 50) = 270 Forecast sales are $270,000 This 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 $420,00 This is an extrapolation outside the sample range and may be inaccurate. Test your understanding 2 Regression 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: Σ x = 440, Σ y = 330, Σ x2 = 17,986, Σ y2 = 10,366 and Σ xy = 13,467 Find 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 Using the data from illustration 2 above: r2 = Thus % 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 analysis A 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. The four ponents of a time series are: The trend – this describes the longterm 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 (6 10,600 – 2402) (6 355,000 – 1,4402) 6 60,600 – 240 1,440 r = =… (n∑ x2 – (∑ x)2) (n∑ y2 – (∑ y)2) n∑ xy – ∑ x∑ y r = Sales, costs, revenues, etc. Time period 14 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 analysis This is performed by carrying out two distinct steps: establishing the longterm underlying trend establishing 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 model This 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 model Actual = Trend SV factor The SV will be expressed in proportional terms, . 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 100112 = 11,200. Test your understanding 3 A pany has found that the trend in the quarterly sales of its furniture is well described by the regression equation y = 150 + 10x where y equals quarterly sales ($000) x = 1 represents the first quarter of 20 0 x = 2 represents the second quarter of 20 0 x = 5 represents the first quarter of 20 1, etc. It has also been found that, based on a multiplicative model, . Sales = Trend Seasonal Random The mean seasonal quarterly index for its furniture sales is as follows: Quarter 1 2 3 4 Seasonal index 80 110 140 70 Explain the meaning of this regression equation, and set of seasonal index numbers. Using the regression equation, estimate the trend values in the pany‟s furniture sales for each quarter of 20 5 Using the seasonal index, prepare sales forecasts for the pany‟s quarterly furniture sales in 20 5 State what factors might cause your sales forecasts to be in error. Test your understanding 4 The 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 factor May 116 June 107 July 94 August 82 September 106 Prepare a forecast for the number of customers in each of the months May to September, 16 Year 2. 5 Average growth models Strategic 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 models Sales are forecast to increase, on average, by 2% per quarter. Sales are currently $250,000 pa. Calculate the budgeted sales figures for each quarter of the forthing year. Show how you could have found the average growth rate given the final figure. Solution Sales ($) Quarter 1 ($250,000/4 ) 63,750 Quarter 2 ($63,750 ) 65,025 Quarter 3 ($65,025 ) 66,326 Quarter 4 ($66,325 ) 67,652 $262,753 The problem may be to find the average growth rate given the original and final sales figure. Let g = the unknown growth rate 0 = the original figure F = the final figure n = number of periods of growth F = O(1 +。