Did you know? – Forecasting and budgeting
14 Forecasting 77 mins
14.1 The following four data pairs have been obtained: (1, 5), (2, 6), (4, 9), (5, 11). Without carrying out any calculations, which of the following correlation coefficients best describes the relationship between x and y?
A –0.98 B –0.25 C 0.98
D 0.25 (2 marks)
14.2 A company's management accountant is analysing the reject rates achieved by 100 factory operatives working in identical conditions. Reject rates, Y%, are found to be related to months of experience, X, by this regression equation: Y = 20 – 0.25X. (The correlation coefficient was r = –0.9.)
Using the equation, what is the predicted reject rate for an operative with 12 months' experience? A 17%
B 19% C 20%
D 23% (2 marks)
14.3 A regression equation Y = a + bX is used to forecast the value of Y for a given value of X. Which of the following increase the reliability of the forecast?
(i) A correlation coefficient numerically close to 1
(ii) Working to a higher number of decimal places of accuracy
(iii) Forecasting for values of X outside the range of those used in the sample (iv) A large sample is used to calculate the regression equation
A (i) only B (i) and (ii) only C (i) and (iii) only
D (i) and (iv) only (2 marks)
14.4 If x = 12, y = 42, x2 = 46, y2 = 542, xy = 157 and n = 4, what is the correlation coefficient?
A 0.98 B –0.98 C 0.26
D 0.008 (2 marks)
14.5 Using data from twelve European countries, it has been calculated that the correlation between the level of car ownership and the number of road deaths is 0.73. Which of the statements shown follow from this?
(i) High levels of car ownership cause high levels of road deaths
(ii) There is a strong relationship between the level of car ownership and the number of road deaths (iii) 53% of the variation in the level of road deaths from one country to the next can be explained by
the corresponding variation in the level of car ownership
(iv) 73% of the variation in the level of road deaths from one country to the next can be explained by the corresponding variation in the level of car ownership
A (i) and (ii) only B (i) and (iii) only C (ii) and (iii) only
14.6 The regression equation Y = 3 + 2X has been calculated from 6 pairs of values, with X ranging from 1 to 10. The correlation coefficient is 0.8. It is estimated that Y = 43 when X = 20. Which of the following are true?
(i) The estimate is not reliable because X is outside the range of the data (ii) The estimate is not reliable because the correlation is low
(iii) The estimate is reliable
(iv) The estimate is not reliable because the sample is small A (i) and (ii) only
B (i) and (iii) only C (ii) and (iv) only
D (i) and (iv) only (2 marks)
14.7 In calculating the regression equation linking two variables, the standard formulae for the regression coefficients are given in terms of X and Y. Which of the following is true?
A X must be the variable which will be forecast B It does not matter which variable is which C Y must be the dependent variable
D Y must be the variable shown on the vertical axis of a scatter diagram (2 marks)
14.8 A company uses regression analysis to establish a total cost equation for budgeting purposes. Data for the past four months is as follows:
Month Total cost Quantity produced
$'000 $'000 1 57.5 1.25 2 37.5 1.00 3 45.0 1.50 4 60.0 2.00 200.0 5.75
The gradient of the regression line is 17.14. What is the value of a?
A 25.36 B 48.56 C 74.64
D 101.45 (2 marks)
14.9 Regression analysis is being used to fine the line of best fit (y = a + bx) from eleven pairs of data. The calculations have produced the following information:
x = 440, y = 330, x2 = 17,986, y2 = 10,366 and xy = 13,467
What is the value of 'a' in the equation for the line of best fit (to 2 decimal places)? A 0.63
B 0.69 C 2.33
D 5.33 (2 marks)
14.10 Which of the following is a feasible value for the correlation coefficient? A – 2.0
B – 1.2 C 0
14.11 Over an 18-month period, sales have been found to have an underlying linear trend of y = 7.112 + 3.949x, where y is the number of items sold and x represents the month. Monthly deviations from trend have been calculated and month 19 is expected to be 1.12 times the trend value.
What is the forecast number of items to be sold in month 19? A 91
B 92 C 93
D 94 (2 marks)
14.12 Based on the last 15 periods the underlying trend of sales is y = 345.12 – 1.35x. If the 16th period has a seasonal factor of –23.62, assuming an additive forecasting model, what is the forecast for that period, in whole units?
A 300 B 301 C 324
D 325 (2 marks)
14.13 Unemployment numbers actually recorded in a town for the second quarter of the year 2000 were 4,700. The underlying trend at this point was 4,300 people and the seasonal factor is 0.92. Using the multiplicative model for seasonal adjustment, what is the seasonally-adjusted figure (in whole numbers) for the quarter?
A 3,932 B 3,956 C 5,068
D 5,109 (2 marks)
14.14 Monthly sales have been found to follow a linear trend of y = 9.82 + 4.372x, where y is the number of items sold and x is the number of the month. Monthly deviations from the trend have been calculated and follow an additive model. In month 24, the seasonal variation is estimated to be plus 8.5. What is the forecast number of items to be sold in month 24? (to the nearest whole number.) A 106
B 115 C 123
D 152 (2 marks)
14.15 Which of the following are necessary if forecasts obtained from a time series analysis are to be reliable? (i) There must be no unforeseen events
(ii) The model used must fit the past data (iii) The trend must be increasing
(iv) There must be no seasonal variation A (i) only
B (i) and (ii) only C (i), (ii) and (iii) only
D (i), (ii), (iii) and (iv) (2 marks)
14.16 What is the purpose of seasonally adjusting the values in a time series? A To obtain an instant estimate of the degree of seasonal variation B To obtain an instant estimate of the trend
C To ensure that seasonal components total zero
14.17 The following data represents a time series: X 36 Y 41 34 38 42
A series of three point moving averages produced from this data has given the first two values as 38 and 39. What are the values of (X, Y) in the original time series?
A (38, 39) B (38, 40) C (40, 38)
D (39, 38) (2 marks)
14.18 Using an additive time series model, the quarterly trend (Y) is given by Y = 65 + 7t, where t is the quarter (starting with t = 1 in the first quarter of 20X5). If the seasonal component in the fourth quarter is –30, what is the forecast for the actual value for the fourth quarter of 20X6, to the nearest whole number?
A 63 B 546 C 85
D 91 (2 marks)
14.19 The trend for monthly sales ($Y) is related to the month (t) by the equation Y = 1,500 – 3t where t = 1 in the first month of 20X8. What are the forecast sales (to the nearest dollar) for the first month of 20X9 if the seasonal component for that month is 0.92 using a multiplicative model?
A $1,377 B $17,904 C $1,344
D $1,462 (2 marks)
14.20 Which of the following are necessary if forecasts obtained from a time series analysis are to be reliable? (i) The trend must not be increasing or decreasing
(ii) The trend must continue as in the past (iii) Extrapolation must not be used
(iv) The same pattern of seasonal variation must continue as in the past A (i) only
B (i) and (ii) only C (ii) and (iv) only
D (i) and (iii) only (2 marks)
14.21 Under which of the following circumstances would a multiplicative model be preferred to an additive model in time series analysis?
A When a model easily understood by non-accountants is required B When the trend is increasing or decreasing
C When the trend is steady
D When accurate forecasts are required (2 marks)
14.22 A company's annual profits have a trend line given by Y = 20t – 10, where Y is the trend in $'000 and t is the year with t = 0 in 20X0.
What are the forecast profits for the year 20X9 using an additive model if the cyclical component for that year is –30?
A $160,000 B $140,000 C $119,000
14.23 In January, the unemployment in Ruritania is 567,800. If the seasonal factor using an additive time series model is +90,100, what is the seasonally-adjusted level of unemployment (to the nearest whole number)?
A 90,100 B 477,700 C 567,800
D 657,900 (2 marks)
14.24 The following statements relate to Paasche and Laspeyre indices.
(i) Constructing a Paasche index is generally more costly than a Laspeyre index
(ii) With a Laspeyre index, comparisons can only be drawn directly between the current year and the base year
Which statements are true? A Both statements are true B Both statements are false C (i) is true and (ii) is false
D (ii) is true and (i) is false (2 marks)
14.25 The following information is available for the price of materials used at P Co. Laspeyre index for price in 20X5 (with base year of 20X0) 150.0 Corresponding Paasche index 138.24 What is Fisher's ideal index?
A 12.00 B 16.98 C 144.00
D 288.24 (2 marks)
14.26 A large bag of cement cost $0.80 in 20X3. The price indices are as follows. 20X3 91
20X4 95 20X5 103 20X6 106 How much does a bag of cement cost in 20X6?
A $0.69 B $0.85 C $0.93
D $0.95 (2 marks)
14.27 Four years ago material X cost $5 per kg and the price index most appropriate to the cost of material X stood at 150.
The same index now stands at 430.
What is the best estimate of the current cost of material X per kg? A $1.74
B $9.33 C $14.33
14.28 Six years ago material M cost $10 per kg and the price index most appropriate to the cost of material M was 130. The same index now stands at 510.
What is the best estimate of the current cost of material M per kg? A $2.55
B $29.23 C $39.23
D $51.00 (2 marks)
14.29 Which of the following are common applications of spreadsheets used by management accountants? (i) Variance analysis
(ii) Cash flow budgeting and forecasting (iii) Preparation of financial accounts A (i) and (ii) only
B (i) and (iii) only C (ii) and (iii) only
D (i), (ii) and (iii) (2 marks)
14.30 A spreadsheet is unlikely to be used for which of the following tasks? A Cash flow forecasting
B Monthly sales analysis by market C Writing a memo
D Calculation of depreciation (2 marks)
14.31 The following question is taken from the December 2012 exam paper. The following data relates to a company's overhead cost.
Time
(units) Output Overheadcost ($) Priceindex
2 years ago 1,000 3,700 121 Current year 3,000 13,000 155
Using the high low technique, what is the variable cost per unit (to the nearest $0.01) expressed in current year prices?
A $3.22
B $4.13
C $4.65
D $5.06 (2 marks)
14.32 The following question is taken from the June 2013 exam paper. An additive time series has the following trend and seasonal variations: Trend Y=4,000 + 6X where Y= sales in units
X is the number of quarters, with the first quarter of 2014 being 1, the second quarter of 2014 being 2 etc. Seasonal variation
Quarter 1 2 3 4
Quarterly variation (units) –4 –2 +1 +5
What is the forecast sales volume for the fourth quarter of 2015?
A 4,029
B 4,043
C 4,048
D 4,053 (2 marks)