Forecasting techniques

Transcription

1 2 Forecastig techiques this chapter covers... I this chapter we will examie some useful forecastig techiques that ca be applied whe budgetig. We start by lookig at the way that samplig ca be used to collect data. This is ofte used for market research, which is a useful tool for collectig data about our products ad services that ca be used to build budgets. We the go o to study time series aalysis the use of umerical data that occurs over time. This ca be used to help forecast the future if it is believed that it will follow historical treds. We iclude here a study of seasoal variatios ad their impact o data. Next we review the use of percetage calculatios i forecastig, ad illustrate how to modify existig assumptios about icreases or decreases. Fially we lear how idex umbers ca help with forecastig. We will examie the rage of idices available, ad lear how to calculate data usig them.

2 f o r e c a s t i g t e c h i q u e s 3 7 f o r e c a s t i g t e c H i Q U e s Forecastig is ofte carried out at the start of the budgetig cycle, as we will discuss further i the ext chapter. Forecastig is cocered with usig data to estimate what will happe i the future. Budgetig ivolves committig to plas that are based o actios that will be take. These plas will take ito accout the iformatio from the forecasts. A aalogy sometimes used is that a weather forecast will predict (for example) whether it will rai or ot. Our pla (or budget) will be based o what we ited to do to i respose to the forecast for example will we take a umbrella? The techiques described below ca be used to help make forecasts. I this chapter we will look at the techiques i outlie form. The specific applicatios will be examied i later chapters. The techiques ivolve the collectio ad the aalysis of data to provide useful iformatio. p r i m a r y a d s e c o d a r y d a t a Where data is collected specifically for aalysis udertake at that time by a orgaisatio, the the data is kow as primary data. Where the data has bee collected ad provided by aother orgaisatio the it is kow as secodary data. For example, if a busiess aalyses its sales figures, that is primary data; if it uses iflatio figures provided by the Govermet s statistical services, that is secodary data. c e s u s o r s a m p l e? If we wat to collect data about a populatio (ot just a populatio of people, but ay large group of items or data) there are two approaches that we could use. A cesus could be used to collect data about every item i the populatio. Oe example of this techique is the Govermet s 10 yearly cesus of all the people i the UK. This provides iformatio which ca be used by the Govermet to pla services. A cesus provides a complete picture of the populatio, but is expesive, ad will ofte be impractical. Samplig is a commoly used techique for collectig data from a small umber withi a populatio, to estimate iformatio regardig the whole populatio. Market research questioaires are a example of samplig. Samplig is cheaper to carry out tha a full cesus, but it must be carried out carefully if the results are to be used with cofidece.

3 3 8 p r e p a r i g a d u s i g b u d g e t s t u t o r i a l s a M P L i g The critical issue to cosider whe examiig samplig techiques is that the sample must be as free from bias as practical. If you wated to estimate the faults i the whole productio output of a factory it would ot make sese to oly sample the output of a machie maed by a traiee o his first day at work! Some commo uses of samplig are to estimate: customer satisfactio levels quality of productio output the views of prospective customers (market research) There are various approaches to samplig. The approach take will deped o the type of populatio ad the resources available. The approach will ifluece the reliability of the estimates produced. r a d o m s a m p l i g This is the approach that will provide the best estimate. It is based o the rule that every item i the populatio has a equal chace of beig selected. I order for this to happe the exact size of the populatio must be kow, ad a samplig frame created by umberig every item. From this frame the sample ca be selected usig radom umbers. This approach could be used (for example) as a way of samplig curret customers to fid out their views o our products. This is assumig the whole populatio (the umber of curret customers) would be kow from the outset. It could ot be used to ascertai the views of bald me i Bradford because there is o way of accurately kowig how may there are ad who they are. q u a s i - r a d o m s a m p l i g This approach cotais a umber of techiques that ca provide a good approximatio to radom samplig. Although they are ot quite as accurate as radom samplig, they ca produce similar outcomes, ofte usig fewer resources. The techiques are: Systematic Samplig Choosig every th item after a radom start. For example selectig customers by startig at customer umber 63, ad the obtaiig the views of every 17th customer from there. Stratified Samplig Dividig the populatio ito groups ( strata meas layers ), ad the choosig a sample from each of the strata based o its size. For example customers could be grouped accordig to their locatio. If there were

4 f o r e c a s t i g t e c h i q u e s 3 9 more customers i Lodo tha i Devo the the sample for Lodo would be larger. Each group would be sampled idepedetly i this way i proportio to its size. Multistage Samplig Dividig the populatio ito groups, ad the radomly selectig several groups as a iitial sample. These selected groups are the subdivided ad sub groups radomly chose (the procedure may be repeated several times). For example customers could be divided ito groups based o their locatio, ad the groups of Yorkshire, Sussex ad Corwall radomly selected. Withi each group tows could the be chose at radom (for example Halifax, Brighto ad Truro), ad the customer sample selected from withi these areas. o - r a d o m s a m p l i g This approach must be used whe a samplig frame caot be established (for example because the size of the populatio is ot kow). The results geerated by this approach will typically be less reliable tha radom or quasi-radom approaches, but are evertheless useful. These techiques are ofte used for market research. Quota Samplig Restrictig the sample to a fixed umber per strata. For example iterviewig people i the street withi certai categories (for example age groups, geder etc) util a predetermied umber have bee iterviewed. Cluster Samplig Selectig oe subsectio of the populatio as represetative, ad just samplig that. For example iterviewig dog owers who live i Cardiff as beig represetative of dog owers throughout the UK. t i M e s e r i e s a a LY s i s Time series aalysis ivolves aalysig umerical treds over a time period. It is ofte used to examie past ad preset treds so that future treds ca be forecast. The term tred aalysis is used to describe the techique that we will ow examie. At its simplest the cocept is based o the assumptio that data will cotiue to move i the same directio i the future as it has i the past. Usig the sales of a shoe shop as a example we will ow look a rage of techiques of dealig with treds.

5 4 0 p r e p a r i g a d u s i g b u d g e t s t u t o r i a l a i d e t i c a l a u a l c h a g e A shoe shop Comfy Feet has sold the followig umbers of pairs of shoes aually over the last few years: , , , , , , ,000 It does ot require a great deal of arithmetic to calculate that if the tred cotiues at the previous rate a icrease of 1,000 pairs a year the shoe sales could be forecast at 17,000 pairs i 20-8 ad 18,000 pairs i Of course this is a very simple example, ad life is rarely this straightforward. For example, for how log ca this rate of icrease be sustaied? a v e r a g e a u a l c h a g e A slightly more complex techique could have bee used to arrive at the same aswer for the shoe shop. If we compare the umber of sales i 20-7 with the umber i 20-1, we ca see that it has rise by 6,000 pairs. By dividig that figure by the umber of times the year chaged i our data we ca arrive at a average chage per year. The umber of times that the year chages is 6, which is the same as the umber of spaces betwee the years (or alteratively the total umber of years mius 1). Show as a equatio this becomes: Average Aual Sales Chage = (Sales i Last Year Sales i First Year) (16,000 10,000) (Number of Years 1) = (7 1) = + 1,000, which is what we would expect. The + 1,000 would the be added to the sales data i 20-7 of 16,000 (the last actual data) to arrive at a forecast of 17,000. This techique is useful whe all the icreases are ot quite idetical, yet we wat to use the average icrease to forecast the tred. A egative aswer would show that the average chage is a reductio, ot a icrease. We will use this techique whe estimatig the tred movemet i more complicated situatios. This is ot the oly way that we ca estimate the directio that data is movig over time, ad it does deped o the data (icludig especially the first ad last poits) fallig roughly ito a straight lie. We will ote alterative methods that ca be used later i this sectio.

6 f o r e c a s t i g t e c h i q u e s 4 1 c o s t r u c t i g a g r a p h The same result ca be produced graphically. Usig the same shoe shop example we ca exted the graph based o the actual data to form a forecast lie. comfy feet: sales of shoes forecast data If i aother situatio the actual data does ot produce exactly equal icreases, the graph will produce the same aswer as the average aual chage provided the straight lie rus through the first ad last year s data poits. u s i g a f o r m u l a The data i the example could have bee expressed i the followig formula: y = mx + c where y is the forecast amout m is 1,000 (the amout by which the data icreases each year) x is the umber of years sice the start year (20-1) c is 10,000 (which is the sales figure i the start year of 20-1) If we wated a forecast for the year 20-9, we could calculate it as: Forecast = (1,000 x umber of years sice 20-1) + 10,000 y (the forecast) = (1,000 x 8) + 10,000 = 18,000, which is what we would expect.

7 4 2 p r e p a r i g a d u s i g b u d g e t s t u t o r i a l This formula works because the formula is based o the equatio of a straight lie. l i e a r r e g r e s s i o I the last sectio o time series aalysis we saw that whe some historical data moves i a cosistet ad regular way over time we ca use it to help estimate the future tred of that data. We also saw that i these circumstaces the data ca be represeted by: a straight lie o a graph, ad / or a equatio of the lie i the form y = mx + c to help us develop the tred. Liear regressio is the term used for the techiques that ca be used to determie the lie that best replicates that give data. You should be aware of the techiques i geeral terms, ad be able to appreciate their usefuless. I a assessmet you may be give historical data or the equatio of a lie ad asked to use it to geerate a forecast. Where data exactly matches a straight lie (as with the Comfy Feet data) there is o eed to use ay special techiques. I other situatios the followig could be used: Average aual chage. This method was described earlier, ad is useful if we are cofidet that the first ad last poits (take chroologically sice we are lookig at data over time) are both represetative. It will smooth out ay mior fluctuatios of the data i betwee. We will see this method used i the Seasoal Compay case study later i this chapter. Lie of best fit. Where the data falls oly roughly ito a straight lie, but the first ad last poits do ot appear to be very represetative the average aual chage method would give a distorted solutio. Here a lie of best fit ca be draw oto the data poits o a graph that will form a better estimate of the movemet of the data. The followig graph illustrates a situatio where the lie of best fit would provide a better solutio tha the average aual chage method. liear regressio techiques uits lie of best fit lie usig average aual chage method time

8 f o r e c a s t i g t e c h i q u e s 4 3 Least squares method. This is a mathematical techique for developig the equatio of the most appropriate lie. It is more accurate tha drawig a lie of best fit oto a graph by eye, but the calculatios ivolved are outside the scope of the learig area covered i this book. All liear regressio techiques assume that a straight lie is a appropriate represetatio of the data. Whe lookig at time series this meas that we are assumig that the chages i the data that we are cosiderig (kow as the depedet variable) are i proportio to the movemet of time (the idepedet variable). This would mea that we are expectig (for example) the sales level to cotiually rise over time. Whe we use time series aalysis later i the book we must remember that sometimes data does ot travel forever i a straight lie, eve though they may do so for a short time. For example share prices o the stock market do ot cotiue to go up (or dow) steadily, but ofte move i a more erratic way. The ideas behid regressio aalysis apply ot oly to time series aalysis, but ca be used i may other situatios, for example, earlier i this chapter, examiig the behaviour of semi-variable costs at differet activity levels. The high-low method was used to split costs betwee their fixed ad variable compoets. This method uses a idetical priciple to the average aual chage method described above. The data that is used for aalysis i various situatios may be the result of usig samplig techiques (as outlied earlier i this chapter). I that case the reliace that ca be placed o the outcomes of our aalysis will the deped ot oly o the regressio aalysis, but also o the validity of the samplig techiques used. t i M e s e r i e s a a LY s i s a D s e a s o a L Va r i at i o s There are four mai factors that ca ifluece data which is geerated over a period of time: The uderlyig tred This is the way that the data is geerally movig i the log term. For example the volume of traffic o our roads is geerally icreasig as time goes o. Log term cycles These are slow movig variatios that may be caused by ecoomic cycles or social treds. For example, whe ecoomic prosperity geerally icreases this may icrease the volume of traffic as more people ow cars

9 4 4 p r e p a r i g a d u s i g b u d g e t s t u t o r i a l ad fewer use buses. I times of ecoomic depressio there may be a decrease i car use as people caot afford to travel as much or may ot have employmet which requires them to travel. Seasoal variatios This term refers to regular, predictable cycles i the data. The cycles may or may ot be seasoal i the ormal use of the term (eg Sprig, Summer etc). For example traffic volumes are always higher i the daytime, especially o weekdays, ad lower at weekeds ad at ight. Radom variatios All data will be affected by iflueces that are upredictable. For example floodig of some roads may reduce traffic volume alog that route, but icrease it o alterative routes. Similarly the traffic volume may be iflueced by heavy sowfall. The type of umerical problems that you are most likely to face i assessmets will ted to igore the effects of log-term cycles (which will effectively be cosidered as a part of the tred) ad radom variatios (which are impossible to forecast). We are therefore left with aalysig data ito uderlyig treds ad seasoal variatios, i order to create forecasts. The techique that we will use follows the process i this diagram: icorporatig seasoal variatios ito the tred historical actual data forecast of future data seasoal variatios historical tred forecast future tred The process is as follows: 1 The historical actual data is aalysed ito the historical tred ad the seasoal variatios. 2 The historical tred is used to forecast the future tred, usig the techiques examied i the last sectio.

10 f o r e c a s t i g t e c h i q u e s The seasoal variatios are icorporated with the forecast future tred to provide a forecast of where the actual data will be i the future. a a l y s i g h i s t o r i c a l a c t u a l d a t a I a task the aalysis may have bee carried out already, or you may be asked to carry out the aalysis by usig movig averages. If you are usig movig averages it is importat that: your workigs are laid out accurately the umber of pieces of data that are averaged correspods with the umber of seasos i a cycle where there is a eve umber of seasos i a cycle a further averagig of each pair of averages takes place h o w d o m o v i g a v e r a g e s w o r k? A movig average is the term used for a series of averages calculated from a stream of data so that: every average is based o the same umber of pieces of data, (eg four pieces of data i a four-poit movig average ), ad each subsequet average moves alog that data stream by oe piece of data so that compared to the previous average it uses oe ew piece of data ad abados oe old piece of data This is easier to calculate tha it souds! For example, suppose we had a list of six pieces of data relatig to the factory output over two days where a three-shift patter was worked as follows: Day 1 Morig Shift 14 uits Afteroo Shift Night Shift 20 uits 14 uits Day 2 Morig Shift 26 uits Afteroo Shift 32 uits Night Shift 26 uits If we thought that the shift beig worked might ifluece the output, we could calculate a three-poit movig average, the workigs would be as follows:

11 4 6 p r e p a r i g a d u s i g b u d g e t s t u t o r i a l First movig average: ( ) 3 = 16 Secod movig average: ( ) 3 = 20 Third movig average: ( ) 3 = 24 Fourth movig average ( ) 3 = 28 Notice how we move alog the list of data. I this simple example with six pieces of data we ca t work out ay more three-poit averages sice we have arrived at the ed of the umbers after oly four calculatios. Here we chose the umber of pieces of data to average each time so that it correspoded with the umber of poits i a full cycle. By choosig a threepoit movig average that correspoded with the umber of shifts we always had oe example of the output of every type of shift i our average. This meas that ay ifluece o the average by icludig a ight shift (for example) is cacelled out by also icludig data from a morig shift ad a afteroo shift. We must be careful to always work out movig averages so that exactly oe complete cycle is icluded i every average. The umber of poits is chose to suit the data. Whe determiig a tred lie, each average relates to the data from its mid poit, as the followig layout of the figures just calculated demostrates. Output Day 1 Morig Shift 14 uits Tred (Movig Average) Afteroo Shift 20 uits 16 uits Night Shift 14 uits 20 uits Day 2 Morig Shift 26 uits 24 uits Afteroo Shift 32 uits 28 uits Night Shift 26 uits This meas that the first average that we calculated (16 uits) ca be used as the tred poit of the afteroo shift o day 1, with the secod poit (20 uits) formig the tred poit of the ight shift o day 1. The result is that we: kow exactly where the tred lie is for each period of time, ad have a basis from which we ca calculate seasoal variatios

12 f o r e c a s t i g t e c h i q u e s 4 7 Eve usig our limited data i this example we ca see how seasoal variatios ca be calculated. A seasoal variatio is simply the differece betwee the actual data at a poit ad the tred at the same poit. This gives us the seasoal variatios show i the followig table, usig the figures already calculated. Output Tred Seasoal Variatio Day 1 Morig Shift 14 uits Afteroo Shift 20 uits 16 uits + 4 uits Night Shift 14 uits 20 uits - 6 uits Day 2 Morig Shift 26 uits 24 uits + 2 uits Afteroo Shift 32 uits 28 uits + 4 uits Night Shift 26 uits The seasoal variatio for the afteroo shift, calculated o day 1, is based o the actual output beig 4 uits greater tha the tred at the same poit (i.e. 20 mius 16 uits). d e a l i g w i t h a e v e u m b e r o f s e a s o s I the last example the tred could be calculated just by usig the three-poit movig average. This was because usig three poits provides a average cetred at its middle figure the secod poit. If there are four seasos we eed to use a four-poit movig average, but the problem is that the the average relates to the middle of the four pieces of data, ad that meas that it falls i betwee the two middle figures. The effect of this is that the fourpoit movig average caot be used directly as a tred sice its poits are ot located at actual periods of time. This problem ca be overcome by a further averagig of each pair of movig averages. This gives figures that ca be used as a tred sice they are based o a equal umber of represetatives of each seaso, ad are aturally aliged with actual periods of time. This calculatio of additioal averages (called cetred movig averages) eeds to be performed wheever there is a eve umber of seasos i each complete cycle (for example whe usig the four quarters of a year, or usig data from a six workig day week). I the Case Study that follows the full process (icludig further averagig) is used to determie the tred ad seasoal variatios, ad these are the used to create a forecast.

13 4 8 p r e p a r i g a d u s i g b u d g e t s t u t o r i a l Case Study T h e S e a S o a l C o m pa y: m o v i g av e r a g e S a d f o r e C a S T T r e d S The Seasoal Compay sells various products, icludig Welligto Boots for use i wet weather. The quarterly maagemet accouts for recet quarters have revealed that the followig umbers of these boots were sold. Quarter 1 Quarter 2 Quarter 3 Quarter ,000 1,600 2,200 4, ,400 2,000 2,500 5, ,800 2,400 3,100 5, ,200 2,800 3,400 6,000 r e q u i r e d 1 Use movig averages to aalyse the historical data ito the tred ad the seasoal variatios. 2 Use the data from (1) to forecast the sales for each quarter of s o l u t i o 1 calculatig the tred ad seasoal variatios step 1 The first thig to do is to rearrage the historical data ito a sigle colum with spaces i betwee each of the figures this is to the right of the date colum: step 1 step 2 step 3 step 4 Year Quarter Historical 4-poit Movig averaged seasoal sales Data average Pairs (tred) Variatio , , ,200 3,150 3,200 1, ,800 3,250 3,300 +1, ,400 3,350 3, , ,000 3,425 3,475 1, ,500 3,525 3,575 1, ,200 3,625 3,675 +1, ,800 3,725 3,800 +1, ,400 3,875 3,925 1, ,100 3,975 4, ,600 4,075 4,125 +1, ,200 4,175 4, ,800 4,250 4,300 1, ,400 4, ,000

14 f o r e c a s t i g t e c h i q u e s 4 9 step 2 Calculate the 4-poit movig averages. This is the average of each group of four figures, startig with 20-0 quarters 1 to 4, followed by 20-0 quarter 2 to 20-1 quarter 1, ad so o. place each movig average i the appropriate colum, alogside the cetre poit of the figures from which it was calculated. We are usig a 4-poit average because there are 4 quarters i our data. This also meas that the average will fall alogside gaps betwee our origial data. ote that the shaded lies ad arrows are draw here for illustratio oly to show where the figures come from. step 3 step 4 Calculate the average of each adjacet pair of movig averages. These are also kow as cetred movig averages. This is carried out so that these figures ca be placed alogside the cetre of each pair, ad will therefore fall i lie with the origial quarterly data (see shaded arrow). if there was a odd umber of seasos i a cycle (for example 13 fourweekly periods) the this stage would ot be required. We have ow calculated the tred figures. otice that the first tred calculated is i quarter 3 of the first year, ad the last oe is i quarter 2 of the last year. This is ievitable whe calculatig a tred from quarterly data usig movig averages. Calculate the seasoal variatios, ad isert them ito the last colum. These are the amouts by which the actual figures (left had colum) are greater or smaller tha the tred figures. Be careful to use the correct + or sig. The shaded arrows show the figures that are used. 2 forecast the sales for each quarter of 20-4 i order to use the data that we have calculated for a forecast we will eed to work out some average figures. This is because i this Case Study you will otice that: the tred is ot icreasig by exactly the same amout every quarter the seasoal variatios are similar, but ot quite idetical for each of the same quarters We ca use the techique for calculatig the average icrease i the tred that we looked at earlier: Average Tred Chage = (Last kow tred First kow tred) (4,300 3,200) = = (Number of Quarterly treds 1) 11 We ca also average the seasoal variatios by groupig them together i quarters: Quarter 1 Quarter 2 Quarter 3 Quarter , , , ,475 1, , ,000 1, , ,500 Totals + 3,000 4,500 3, ,500 averages + 1,000 1,500 1, ,500

15 5 0 p r e p a r i g a d u s i g b u d g e t s t u t o r i a l at this stage we should check that the average seasoal variatios total zero. here they do, but if they do ot the mior adjustmets will eed to be made to the figures. We ca ow use the average tred movemets ad the average seasoal variatios to create a forecast. We start with the tred at the last poit whe it was calculated, ad work out where it will be at future poits by usig the average movemets. for example quarter 1 of 20-4 is 3 quarters past quarter 2 of 20-3, which is whe we last kew the tred. We the icorporate the average seasoal variatios to complete the forecast. forecast Workigs: forecast tred seasoal forecast Variatios 20-4 Qtr 1 4,300 + (3 x 100) = 4, ,000 5,600 Qtr 2 4,300 + (4 x 100) = 4,700 1,500 3,200 Qtr 3 4,300 + (5 x 100) = 4,800 1,000 3,800 Qtr 4 4,300 + (6 x 100) = 4, ,500 6,400 all the data ad the solutio to this Case Study ca be show o a graph, as follows: sales of boots: sales forecast forecast data

16 f o r e c a s t i g t e c h i q u e s 5 1 a b s o l u t e o r p e r c e t a g e s e a s o a l v a r i a t i o s? The examples that we have used so far have used the idea of absolute (or additive ) seasoal variatios oes that are expressed i the same uits as the actual data that is beig aalysed. Sometimes a more accurate forecast ca be obtaied whe the seasoal variatios are expressed as a percetage of the tred. This would make sese whe the variatios aturally become greater as the tred icreases. This could occur, for example, if we were aalysig the cost of domestic heatig over a umber of years: as the tred icreased (due to cost iflatio) the differeces betwee the summer ad witer heatig costs would also icrease at about the same rate. Case Study U K i C e C r e a m C o S U m p T i o a ivestigatio ito the quarterly amout a average UK household speds o ice cream has revealed a uderlyig tred ad percetage variatios as follows. each quarter the tred icreased by 1, ad by quarter 4 of 20-2 it had reached 50 per quarter. The seasoal variatios, based o percetages of the tred i that quarter were calculated as: Quarter 1 70% Quarter % Quarter % Quarter 4 30% r e q u i r e d forecast the average quarterly sped o ice cream per household i each quarter of s o l u t i o The calculatio here is straightforward. ote that quarter 1 of 20-5 is 9 quarters later tha the quarter that we already kow the tred for, ie quarter 4 of forecast tred seasoal forecast Variatios 20-5 Qtr (9 x 1) = 59 70% Qtr (10 x 1) = % Qtr (11 x 1) = % Qtr (12 x 1) = 62 30% 43.40

17 5 2 p r e p a r i g a d u s i g b u d g e t s t u t o r i a l P e r c e ta g e c a L c U L at i o s practical example Percetages are used i various calculatios for budgetig, ad although they are fairly straightforward it is still worth makig sure that we ca deal with them. The most basic percetage calculatio required is whe a amout that is expressed as a percetage eeds to be added to (or deducted from) a origial figure. The labour cost this year is 2,150,000. The budget for this cost ext year eeds to allow for a 4% icrease. 4% of 2,150,000 is calculated as 4/100 x 2,150,000 = 86,000. The 86,000 is the added to the 2,150,000 to give 2,236,000. alteratively, we could calculate it as 2,150,000 x 104/100 = 2,236,000. The sort of calculatio that ca cause problems is whe we are workig back to chage a earlier percetage calculatio. Here we eed to be careful. practical example The labour cost budget has bee calculated as 2,236,000 based o a 4% icrease (as i the last example). The origial figure is ot provided. ow we are asked to calculate alterative budget figures, based o (a) o 4% icrease, ad (b) a 2.5% icrease istead of the 4% icrease solutio (a) To carry out the calculatio we must remember that the 2,236,000 is 104% of the origial figure. We therefore eed to reduce our figure by 4/104. 4/104 x 2,236,000 = 86,000 2,236,000 86,000 = 2,150,000 (b) Usig the origial figure of 2,150,000 that we have just calculated, it is ow a simple matter to add 2.5% of 2,150,000 to it. 2.5/100 x 2,150,000 = 53,750 53, ,150,000 = 2,203,750. ote that we caot arrive at the correct aswer by simply deductig 4% for part (a), or deductig 1.5% for part (b).

18 f o r e c a s t i g t e c h i q u e s 5 3 practical example The same logic applies to percetage reductios, but they ca be a little trickier. The material budget for ext year was provisioally set at 1,843,000, after allowig for a 3% reductio. The reductio is ow thought to be oly 2.2%. The ew budget figure be calculated as follows: Calculate the origial figure: 1,843,000 x 100/97 = 1,900,000 (or calculate 3/97 ad add this o to 1,843,000) Calculate the ew reductio: 2.2/100 x 1,900,000 = 41,800 The 41,800 is the deducted from the 1,900,000 to give 1,858,200 practical example Some calculatios with percetages ivolve both volumes ad costs. Here the overall cost will be foud by multiplyig the uit cost by the volume. Ay percetage chages will similarly be calculated by multiplyig the percetages together. Suppose materials curretly cost 15 per uit, ad the quatity curretly purchased is 200,000 uits. The curret cost would be 200,000 x 15 = 3,000,000. if the cost is to rise 3%, ad the quatity is to reduce by 1%, the the revised total cost could be calculated as: 3,000,000 x 103/100 x 99/100 = 3,059,100 We ca cofirm that this is the same result as calculatig a revised uit cost of 15 x 103/100 = 15.45, ad multiplyig it by a revised quatity of 200,000 x 99/100 = 198,000, givig x 198,000 = 3,059,100. This meas that we ca use this techique, eve if we do t kow the volumes ad uit costs. We ca also icorporate the earlier techique for workig back to make chages to assumptios.

19 5 4 p r e p a r i g a d u s i g b u d g e t s t u t o r i a l practical example Suppose the sales budget was calculated based o a 10% icrease i volume from last year, together with a 2% price rise. This budget amouted to 2,805,000. ow a revised budget eeds to be calculated based o icreased volume from last year of 8%, ad icreased prices of 1.5%. first we ca calculate what last year s sales were: 2,805,000 x 100/110 x 100/102 = 2,500,000 The we ca icrease this figure i lie with the ew assumptios: 2,500,000 x 108% x 101.5% = 2,740,500 i D e X U M B e r s Idex umbers are used to assist i the compariso of umerical data over time. The most commoly used idices are perhaps the Retail Price Idex (RPI) ad the Cosumer Price Idex (CPI), that give a idicatio of iflatio by comparig the cost of a group of expeses typically icurred by households i the UK from year-to-year. There are may other types of idex umbers that have bee created for specific purposes, for example: the average wage rate for a particular job, or for all employmet the average house price either by regio or throughout the UK the market price of shares (eg the FTSE 100 idex) the quatities of specific items that are sold or used (eg litres of uleaded petrol) the quatities of a group of items that are sold or used (eg litres of all motor fuel) the maufactured cost of specific items or a rage of items (sometimes called factory gate prices) May govermet idices ad other idicators are available at If you have the opportuity, have a look at the eormous rage of data that ca either be dowloaded free, or ca be purchased i govermet publicatios. Whe usig published statistics it is importat to make sure that they are specific eough to be useful for your purpose. For example, data o the growth i the populatio of the West of Eglad will be of limited use if you are tryig to forecast the sales i a bookshop i Tauto. Of far more use

20 f o r e c a s t i g t e c h i q u e s 5 5 would be details of proposed housig developmets withi the immediate area, icludig the umbers of ew homes ad the type of households that form the developers target market. l e a d i g a d l a g g i g i d i c a t o r s Some idicators ca be classified as leadig idicators, whilst others are kow as laggig idicators. This meas that some idicators aturally give advace warig of chages that may take place later i other idicators. For example a idex that moitors the prices of maufactured goods ( factory gate prices) will react to chages before they have filtered through to retail price idices. The idex of factory gate prices ca therefore be cosidered to be a leadig idicator of retail prices, ad give early warig of implicatios of idustrial situatios. I a similar way, a idex recordig the volume of maufactured output from factories will lag behid a idex measurig the volume of purchases of raw materials made by idustrial buyig departmets. w e i g h t i g s o f i d i c e s Those idices that are based o iformatio from more tha oe item will use some form of weightig to make the results meaigful. For example while a idex measurig the retail price of premium grade uleaded petrol is based o a sigle product ad therefore eeds o weightig, this would ot be true for a price idex for all vehicle fuel. I this case it will require a decisio about how much weight (or importace) is to be placed o each compoet of the idex. Here the relative quatities sold of types of fuel (for example uleaded petrol ad diesel) would be a logical way to weight the idex. This would esure that if petrol sales were double those for diesel, ay price chages i petrol would have twice the impact o the idex tha a price chage i diesel. As the purchasig habits of cosumers chage, the the weightig ad compositio of complicated idices like the Retail Price Idex are ofte chaged to reflect this. This will iclude chages to the weightig of certai items, for example due to the icrease i the proportio of household expediture o holidays. It ca also ivolve the additio or deletio of certai items etirely (for example the iclusio of certai fast foods). You may have see ews items from time to time about the revisio of items cotaied withi the RPI or CPI as cosumers tastes chage. c a l c u l a t i o s u s i g i d e x u m b e r s Whatever type of idex we eed to use, the priciple is the same. The idex umbers represet a coveiet way of comparig figures.

21 5 6 p r e p a r i g a d u s i g b u d g e t s t u t o r i a l For example, the RPI was i Jauary 1988, ad i Jauary This meas that average household costs had more tha doubled i the 25 years betwee. We could also calculate that if somethig that cost 5.00 i Jauary 1988 had rise exactly i lie with iflatio, it would have cost i Jauary This calculatio is carried out by: historical price x idex of time covertig to idex of time covertig from ie 5.00 x ( ) = You may be told that the base year for a particular idex is a certai poit i time. This is whe the particular idex was 100. For example the curret RPI idex was 100 i Jauary Idex umbers referrig to costs or prices are the most commoly used oes referred to i the uits studied i this book. If we wat to use cost idex umbers to moitor past costs or forecast future oes, the it is best to use as specific a idex as possible. This will the provide greater accuracy tha a more geeral idex. For example, if we were operatig i the food idustry, ad wated to compare our coffee cost movemets with the average that the idustry had experieced, we should use a idex that aalyses coffee costs i the food idustry. This would be much more accurate tha the RPI, ad also better tha a geeral cost idex for the food idustry.

22 f o r e c a s t i g t e c h i q u e s 5 7 Chapter Summary various techiques to help prepare forecasts ca be applied whe budgetig. forecasts are estimatios of future evets that budgets are the created to take accout of. Samplig ca be used to collect data. This is ofte used for market research, which is a useful tool for collectig data about our products ad services that ca be used to build budgets. Time series aalysis is the examiatio of umerical data that occurs over time. This ca be used to help forecast the future if it is believed that it will follow historical treds. it icludes the study of seasoal variatios ad their impact o data. percetage calculatios ad idex umbers ca also be used i forecastig. There is a rage of idices available ad their use will deped o our requiremets. Key Terms samplig time series aalysis tred seasoal variatios liear regressio idex umbers samplig is a commoly used techique for usig data about a small umber of items withi a populatio, to estimate iformatio regardig the whole populatio the examiatio of historical data that occurs over time, ofte with the itetio of usig the data to forecast future data the uderlyig movemet i the data, oce seasoal, cyclical ad radom movemets have bee stripped away regular variatios i data that occur i a repeatig patter. Seasoal variatios ca be expressed i the same umerical form as the tred (absolute or additive form), or as percetages of the tred usig a mathematical formula to demostrate the movemet of data over time. This techique is sometimes used to help forecast the movemet of the tred a sequece of umbers used to compare data, usually over a time period

23 5 8 p r e p a r i g a d u s i g b u d g e t s t u t o r i a l Activities 2.1 The Supashop that is ope 5 days per week has the followig cash sales over a period. tues Wed thurs fri sat Week 1 1,830 1,920 2,080 2,160 2,160 Week 2 1,880 1,970 2,130 2,210 2,210 Week 3 1,930 2,020 2,180 2,260 2,260 required (a) Usig movig averages, aalyse this data ito the tred ad seasoal variatios. (b) Use the data from (a) to forecast the cash sales for each day of week a computer program has used liear regressio to aalyse the sales data of pegasus limited, a garde oramet maufacturer. Usig quarter umbers (quarter 30 is the first quarter of year 2000) the sales tred has bee determied as: Sales Tred (i ) = (Quarter umber x 1,200) + 83,000. The Seasoal variatios have bee determied as the followig percetages of the tred. Quarter 1 10% Quarter % Quarter 3 +15% Quarter 4 85% required (a) (b) Use the above data to calculate the forecast of sales for pegasus limited i for each quarter of Commet o ay drawbacks of producig sales reveue forecasts directly i moey amouts.

24 f o r e c a s t i g t e c h i q u e s The followig historical data relates to sales i uits of the eigma Compay. Quarter 1 Quarter 2 Quarter 3 Quarter 4 year year year year required (a) Usig movig averages, aalyse this data ito the tred ad additive seasoal variatios. (b) Use the data to forecast the uit sales for each quarter of year from the followig data, revise the icome forecast. ext year icome is forecast at 3,675,000. This assumes a 5% icrease i sellig price. i the light of icreasig competitio the marketig maager has decided ot to make the icrease. The forecast should be revised to Select from: 3,491,250 3,500,000 3,675,000 3,858, from the followig data, revise the forecast for eergy costs. ext year, eergy costs are forecast at 686,400. This assumes a 4% icrease i eergy cosumptio ad a 5% icrease i gas ad electricity tariffs. however, eergy savig measures are beig proposed. istead of icreasig, cosumptio should be reduced by 10%. The eergy budget should be Select from: 534, , , ,000