Management Accounting - Forecasting

 

Management Accounting

Forecasting

 

Part A: Discussing basic concepts of forecasting including demand forecasting and stating different methods of forecasting.

Part B: 18 Illustrations with Solutions.

Part A

What is Forecasting?

Forecasting is a scientifically calculated guess. It is basic to all planning activity –

1)         Whether it is national, regional, organisational, or functional planning; and

2)         Whether it is a long-range plan or a short- range plan.

 

The scientific basis of forecasting lies in studying past, present and future trends, present and future actions and their effects. What happened in the past is relevant to what is happening now and what could happen in the future. Thus, forecasting takes into account all the three dimensions of time – past, present and future. In spite of all the calculations, forecasting remains a calculated guess. Errors are bound to be there, but it remains the foundation for management planning.

 

Many tend to think that forecasting is important only for marketing planning and not for production, because the figures for production planning are received from marketing planning anyway. This is an erroneous view. Production planning need not necessarily follow marketing planning. There are many situations where production plans and marketing planning have to be done together and many other situations where production planning may be done separately from marketing planning. Therefore, forecasting is a very important activity for production planning, be it strategic or tactical.

 

Methods of Forecasting

The most effective, popular and important methods of forecasting are:

1.         Least Squares Method

2.         Simple Moving Average Method

3.         Weighted Moving Average Method

4.         Exponential Smoothing Method

5.         Trend-Adjusted Exponential Smoothing Method

 

We shall now explore these methods including the relevant formulas by solving some illustrations as follows.

Part B

Management Accounting

Forecasting

Selected Problems and Solutions

 

Illustration: 1

Following table gives the demand (in million tonne) for iron ore during the years 2000 to 2010. Find the forecast of the demand for the years 2011 and 2012 using the Method of Least Squares for forecasting.

Year	Demand
2000	10
2001	12
2002	13
2003	16
2004	14
2005	16
2006	20
2007	25
2008	22
2009	30
2010	35

 

Solution: 1

Illustration: 2

Following table gives the annual exports (in US$ million) of automobile parts of a company in India. The figures for the past 8 years are as follows:

Year	Exports
2002	124
2003	130
2004	142
2005	154
2006	165
2007	179
2008	185
2009	153

 

Compute the forecast for the year 2010 using 5-year Simple Moving Average Method.

 

Solution: 2

Illustration: 3

Following table gives the annual exports (in US$ million) of automobile parts of a company in India. The figures for the past 8 years are as follows:

Year	Exports
2002	124
2003	130
2004	142
2005	154
2006	165
2007	179
2008	185
2009	153

 

Compute the forecast for the year 2010 using 3-year Weighted Moving Average Method. Weights are given as follows:

History	Weight
3 years ago	0.2
2 years ago	0.3
Last year	0.5

 

Solution: 3

Illustration: 4

Data on exports (in US$ million) of an Indian Company are as follows:

Year	Exports
2006	165
2007	179
2008	185
2009	153

 

If the forecast made for the year 2006 was US$ 173 million, using Exponential Smoothing Method with Alpha value of 0.2, make a forecast for the year 2010.

Solution: 4

Illustration: 5

Following table gives the annual exports (in US$ million) of automobile parts of a company in India. The figures for the past 8 years are as follows:

Year	Exports
2002	124
2003	130
2004	142
2005	154
2006	165
2007	179
2008	185
2009	153

 

Make the forecast for the year 2010 using Exponential Smoothing Method and taking α = 0.3.

 

Solution: 5

Illustration: 6

Demand values for the four quarters of the years 2010 to 2013 are observed as given in the table below:

Year	Quarter 1	Quarter 2	Quarter 3	Quarter 4
2010	92	117	104	82
2011	96	124	109	87
2012	101	131	115	92
2013	107	140	124	99

Find the seasonal indices for each of the quarters and forecast the demand for the Quarter 2 of the year 2014 and for the Quarter 1 of the year 2015.

 

Solution: 6

Illustration: 7

The demand for a product in each of the last five months is shown below.

Month	1	2	3	4	5
Demand	13	17	19	23	24

 

Use a 2-month moving average to generate a forecast for demand in month 6. Apply exponential smoothing with a smoothing constant of 0.9 to generate a forecast for demand in month 6. Which of these two forecasts do you prefer and why?

 

Solution: 7

Illustration: 8

The table below shows the demand for a new aftershave in a shop for each of the last 7 months.

Month	1	2	3	4	5	6	7
Demand	23	29	33	40	41	43	49

 

Calculate a 2-month moving average for month two to seven. What would be your forecast for the demand in month eight? Apply exponential smoothing with a smoothing constant of 0.1 to derive a forecast for the demand in month eight. Which of the two forecasts for month eight do you prefer and why?

 

Solution: 8

Illustration: 9

The table below shows the demand for a particular brand of razor in a shop for each of the last nine months.

Month	1	2	3	4	5	6	7	8	9
Demand	10	12	13	17	15	19	20	21	20

 

Calculate a 3-month moving average for month three to nine. What would be your forecast for the demand in month ten? Apply exponential smoothing with a smoothing constant of 0.3 to derive a forecast for the demand in month ten. Which of the two forecasts for month ten do you prefer and why?

 

Solution: 9

Illustration: 10

The table below shows the demand for a particular brand of fax machine in a department store in each of the last twelve months.

Month	Demand
1	12
2	15
3	19
4	23
5	27
6	30
7	32
8	33
9	37
10	41
11	49
12	58

 

Calculate the 4-month moving average for months 5 to 12. What would be your forecast for the demand in month 13? Apply exponential smoothing with a smoothing constant of 0.2 to derive a forecast for the demand in month 13. Which of the two forecasts for month 13 do you prefer and why?

 

Solution: 10

Illustration: 11

The table below shows the demand for a particular brand of microwave oven in a department store in each of the last twelve months.

Month	Demand
1	27
2	31
3	29
4	30
5	32
6	34
7	36
8	35
9	37
10	39
11	40
12	42

 

Make 6-month moving average forecast for the demand in month 13? Apply exponential smoothing with a smoothing constant of 0.7 to derive a forecast for the demand in month 13. Which of the two forecasts for month 13 do you prefer and why?

 

Solution: 11

Illustration: 12

The table below shows the temperature (degrees C), at 11 p.m., over the last ten days:

Day	Temperature
1	1.5
2	2.3
3	3.7
4	3.0
5	1.4
6	-1.3
7	-2.4
8	-3.7
9	-0.5
10	1.3

 

Make 3-day moving average forecast for the temperature at 11 p.m. on day 11? Apply exponential smoothing with a smoothing constant of 0.8 to derive a forecast for the temperature at 11 p.m. on day 11. Which of the two forecasts for the temperature at 11 p.m. on day 11 do you prefer and why?

 

Solution: 12

Illustration: 13

The table below shows the sales of a toy robot over the last 11 months.

Month	Sales
1	3651
2	4015
3	3874
4	3501
5	3307
6	3105
7	2986
8	3100
9	3209
10	3450
11	3507

 

Estimate a 4-month moving average forecast for the sales in month 12? Apply exponential smoothing with a smoothing constant of 0.9 to derive a forecast for the sales in month 12. Which of the two forecasts for month 12 do you prefer and why?

 

Solution: 13

Illustration: 14

The table below shows the movement of the price of a commodity over 12 months.

Month	Price
1	25
2	30
3	32
4	33
5	32
6	31
7	30
8	29
9	28
10	28
11	29
12	31

 

Make a 6 month moving average forecast for month 13? Apply exponential smoothing with smoothing constants of 0.7 and 0.8 to derive forecasts for month 13. Which of the two forecasts based on exponential smoothing for month 13 do you prefer and why?

 

Solution: 14

Illustration: 15

Given the following information, make a forecast for May using exponential smoothing with trend.

 

Month	January	February	March	April
Demand	700	760	780	790

 

For exponential smoothing with trend, assume that the previous forecast (for January) including trend was 800 units and the previous trend component was 50 units. Also α=0.30 and b= 0.10.

 

Solution: 15

Illustration: 16

The following are quarterly data for the past two years. From these data, prepare a forecast for the upcoming year using suitable methods.

Period	Actual
1	300
2	540
3	885
4	580
5	416
6	760
7	1191
8	760

 

 

Solution: 16

Illustration: 17

The following table contains the demand from the last 10 months.

Month	Demand
1	31
2	34
3	33
4	35
5	37
6	36
7	38
8	40
9	40
10	41

 

Required

a)         Calculate the simple exponential smoothing forecast for these data using α = 0.30, an initial forecast of 31.

b)         Calculate the exponential smoothing with trend forecast for these data using α = 0.30 and β = 0.30, an initial trend forecast of 1 and an initial exponential smoothing forecast of 30.

c)         Calculate the Mean Absolute Deviation (MAD) for each forecast to identify the best one.

 

Solution: 17

Illustration: 18

PM Computer Services assembles customised personal computers from generic parts. They need a good forecast of demand for their computers so that they will know how many parts to purchase and stock. They have compiled demand data for the last 12 months as given below.

Period	Month	Demand
1	January	37
2	February	40
3	March	41
4	April	37
5	May	45
6	June	50
7	July	43
8	August	47
9	September	56
10	October	52
11	November	55
12	December	54

 

There is an upward trend in the demand. Use Trend-Adjusted Exponential Smoothing Method with smoothing parameter, α = 0.5 and trend parameter, β = 0.3 to compute the demand forecast for January (Period 13).

Solution: 18