Cost accounting: Telephone bill analysis: how to unravel cost behav...

Cost accounting: Telephone bill analysis: how to unravel cost behav...:




"Introduction: intended audience This case relates to a stage two cost behaviour analysis problem: for a first year seminar in cost accounti..."

JOE'S PEANUTS

COST ALLOCATION AND CONTRIBUTION MARGIN

Introduction

This case is an oldie but a goodie; and it has appeared in many books and journals over the years. The authorship of this case seems to have been lost and that is really unfortunate. Who ever invented this case deserves the unending gratitude of at least two generations of cost accounting lecturers.
I have taken the liberty of expressing everything in Pounds even though the case is probably American: I have done this purely because this is a British based site.
This case concerns the restaurater who has the good idea of putting a rack of peanuts at one end of his counter. The idea being that customers would make impulse purchases of these peanuts when they are standing at the counter paying their bill, ordering a drink ... at least, he thought it was a good idea!
In discussing the costs incident to various types of operations the analogy was drawn of the restaurant that adds a rack of peanuts to the counter, intending to pick up a little additional profit in the usual course of business. This analogy was attacked as an oversimplification. However, the accuracy of the analogy is evident when one considers the actual problem faced by the Restaurateur (Joe) as revealed by this Accountant-Efficiency expert.
EFF EX: Joe, you said you put in these peanuts because some people ask for them, but do you realise what this rack of peanuts is costing you?
JOE: It ain't gonna cost. 'sgonna be a profit. Sure, I £25 for a fancy rack to hold bags, but the peanuts cost 6p a bag and I sell 'em for 10p. Figger I sell 50 bags a week to start. It'll take weeks to cover the cost of the rack. After that I gotta clear profit of 4p a bag. The more I sell, the more I make.
EFF EX: That is an antiquated and completely unrealistic approach, Joe. Fortunately, modern accounting procedures permit a more accurate picture which reveals the complexities involved.
JOE: Huh?
EFF EX: To be precise, those peanuts must be integrated into your entire operation and be allocated their appropriate share of business overhead. They must share a proportionate part of your expenditure for rent heat, light, equipment deprecation, decorating, salaries for your waitresses, cook......
JOE: The cook? What's he gotta do wit'a peanuts? He don't even know I got 'em.
EFF EX: Look Joe the cook is in the kitchen, the kitchen prepares the food, the food is what brings people in here, and the people ask to buy peanuts. That's why you must charge a portion of the cook's wages, as well as part of your own salary to peanut sales. This sheet contains a carefully calculated cost analysis which indicates the peanut operation should pay exactly £1,278 per year toward these general overhead costs.
JOE: The peanuts? £1,278 a year for overhead? The nuts?
EFF EX: It's really a little more than that. You also spend money each week to have the windows washed, to have the windows washed, to have the place swept out in the mornings, keep soap in the washroom, and provide free cokes to the police. That raises the total to £1,313 per year.
JOE: [Thoughtfully] But the peanut salesman said I'd make money ..... put 'em on the end of the counter, he said ... and get 4p a bag profit.
EFF EX: [With a sniff] He's not an accountant. Do you actually know what the portion of the counter occupied by the peanut rack is worth to you?
JOE: Ain't worth nothing - no stool there ... Just a dead spot at the end.
EFF EX: The modern cost picture permits no dead spots. Your counter contains 60 square feet and your counter business grosses £15,000 a year. Consequently, the cost of a square foot of space occupied by the peanut rack is £250 per year. Since you have taken that area away the general counter use, you must charge the value of the space to the occupant.
JOE: You mean I gotta add £250 a year more to the peanut?
EFF EX: Right. That raises their share of the general operating costs to a grand total of £1,563 per year. Now then, if you sell 50 bags of peanuts per week, these allocated costs will amount to 60p per bag.
JOE: What?
EFF EX: Obviously, to that must be added your purchase price of 6p per bag, which brings the total to 66p. So you see by selling peanuts at 10p per bag, you are losing 5p on every sale.
JOE: Somethin's crazy!
EFF EX: Not at all! Here are the figures. They prove your peanuts operation cannot stand on its own feet.
JOE: [Brightening] Suppose I sell lotsa peanuts ... thousands bags a week 'stead of fifty.
EFF EX: [Tolerantly] Joe, you don't understand the problem. If the volume of peanuts sales increases, our operating costs will go up... you'll have to handle more bags with more time, more depreciation, more everything. The basic principal of accounting is firm on that subject: "The Bigger the Operation, the More General Overhead Costs That Must be Allocated." No,increasing the volume of sales won't help. JOE Okay, you so smart, you tell me what I gotta do.
EFF EX: [Condescendingly] Well .... you could first reduce operating expenses.
JOE: How?
EFF EX: Move to a building with cheaper rent. Cut salaries. Wash the windows bi weekly. have the floor swept only on Thursday. Remove the soap from the washrooms. Decrease the square-foot value of your counter. For example, if you can cut your expenses 50%, that will reduce the amount allocated to peanut form £1,563 to £781.50 per year, reducing the cost to 36p per bag.
JOE: [Slowly] That's better?
EFF EX: Much, much better. However,even then you would lose 26p per bag if you only charge 10p. Therefore, you must raise your selling price. If you want a net profit of 4p per bag you would have a charge 40p.
JOE: [Flabbergasted] You mean even after I cut operating costs 50% I still gotta charge 40p for a 10p of peanuts? Nobody's that nuts about nuts! who'd buy 'em?
EFF EX: That's a secondary consideration. The point is, at 40p you'd be selling at a price based upon a true and fair evaluation of your then reduced costs.
JOE: [Eagerly] Look! I gotta better idea. Why don't I just throw the nuts out ... put 'em in the dustbin.
EFF EX: Can you afford it?
JOE: Sure. All I got is about 50 bags of peanuts ... cost about three bucks.... so I lose £25 on the rack, but I get outta this nutty business and no so more grief.
EFF EX: [Shaking head] Joe it isn't that simple. You are in peanut business! The minute you throw those peanuts out you are adding £1,563 of annual overhead to the rest of your operation. Joe ... be realistic... can you afford to do that?
JOE: [Completely crushed] It's unbelievable! last week I was making money. Now I'm in trouble ... just because I believe 50 bags of peanuts a week is easy.
EFF EX: [With raised eyebrow] that is the object of modern cost studies, Joe ... to dispel those false illusions.
REQUIRED

1. Is Joe losing 56p on every sale of peanuts? Explain.
2. Do you agree that if the volume of peanut sales is increased, operating losses will increase? Explain.
3. Do you agree with "Efficiency Expert" that, in order to make peanut operation profitable, the operating costs in the restaurant should be decreased and selling price of the peanuts should be increased? Give reasons.
4. Do you think that Joe can afford to get out of the peanut business? Give reasons.
5. Do you think that Joe should eliminate his peanut operations? Why or why not?

Additional Materials
I think this case is so good that I included it in my own book: Williamson Duncan (1996) Cost and Management Accounting Prentice Hall
Joe received the attention of a creative couple of gentlemen in 1992 when they had a go at creating some Joe Specific additional resources. They worked on a solution and on a sequel. Both are worthy of a read and a work through, if you can find copies of them.

Labour Turnover and Labour Stability

Introduction

Labour turnover is a topic, or concept, that's widely discussed in business circles. Labour turnover concerns that rate at which people leave and join an organisation; and is basically concerned with the rate of replacement of employees. Labour stability, on the other hand, is a little known topic that deserves a bit more consideration than it gets. Labour stability is concerned with an organisation's ability to retain its employees.

This page discusses both labour turnover and labour stability.

Labour Turnover

We can define labour turnover by means of formulae: here are three of them.

Let's work through these formulae to see how they work and what they tell us:

	Jan	Feb	35547.02
Total employees at start	400	420	35566.22
Total employees at end	420	415	29982.28
Total leavers	30	28	43162.56
Total leavers replaced	20	28

Solution

	Jan	Feb
Total employees at start	400	420
+ New starters	50	23
	450	443
- Total employees at end	420	415
Total Leavers	30	28
Total leavers replaced	20	28
Turnover ratios
1	4.88%	6.71%
2	7.32%	6.71%
3	19.51%	12.22%

Check the calculations to your own satisfaction!

Since a lot of people know and understand the labour turnover ratio well enough, this paper concentrates on the labour stability measure.

Fiona wrote to me just the other day with a particular question relating to labour turnover so I put together a new page to answer that query: with a bit of an overlap with this page. See the menu on the left for the link.

Labour Stability

I came across labour stability in a paper by the Independent Labour Organisation (ILO) about 15 years ago now; and I haven't seen it anywhere else … apart from my own text book … and here!

The labour stability formula is

where

Ln is the total length of service in months of the employees concerned measured over the past n months.
n is the number of months over which stability is being measured
N is the total number of employees

The formula expresses stability as a percentage of the maximum possible stability.

The significance between labour stability and labour turnover is shown best of all when a high labour turnover rate is due mostly to a small proportion of jobs in the units being filled several times in the time period considered.
(Source: ILO 1984: 7)

Comparison of the Two Methods

For the 6 month period NW plc had an establishment of 75 people. Of the 75 people, there was a total of 15 leavers, all of whom were replaced. More specifically, though, 72 of the 75 people were employed throughout the whole 6 month period, therefore, the 15 leavers represented significant changes in only one or two jobs or positions. The average length of service of the people who had changed jobs during the 6 month period is 2 weeks.

Calculate the labour turnover and labour stability rates for NW plc.

labour turnover:

labour stability:

The turnover rate suggests that NW plc is 80% stable, 20% unstable whereas the stability rate suggests that NW plc is 97.67% stable, only 2.33% unstable.

The Benefit of the Stability Ratio

The benefit of the stability ratio is that it picks out that although a relatively large number of employees have left and been replaced, the majority of employees have remained in post.

Regression Analysis

How good is my regression model?

This page takes us through a question from an old copy of Charles T Horngren's Cost Accounting textbook. The purpose of the exercise is that we are given a set of data from which we are to derive and comment on a regression model that we can use to predict cost values.
What follows is the table of data, a table that takes us step by step through a comparison of the validity of the variables in the data set; and three graphs that give us an insight into the normality or otherwise of the variables.
By the end of the page, we have a much deeper insight into the model, the variables in the model and the usefulness of the model we might finally decide to use.
The data set

Year	Non academic overhead costs	Number of non academic staff	Number of student applications	Number of enrolled students
1	2200	29	1010	342
2	4120	36	1217	496
3	3310	49	927	256
4	4410	53	1050	467
5	4210	54	1563	387
6	5440	58	1127	492
7	5600	88	1892	513
8	4380	72	1362	387
9	5270	83	1623	346
10	7610	73	1646	487
11	8070	101	1870	564
12	10388	103	1253	764

The results of the regression analysis: including the Durbin Watson statistic: we ar dealing here with time series data; and we use the Durbin Watson technique to assess the possibility of autocorrelation being present in our data.

Regression 1
Overhead costs = f(number of non academic staff)
variable	coefficient	standard error
constant	112.04	1119.4
independent variable 1: number of staff	79.68	15.89
r2 =	0.72
standard error of residuals =	1269.2
Durbin Watson =	1.82
Regression 2
Overhead costs = f(number of student applicants)
variable	coefficient	standard error
constant	1147.4	2710
independent variable 2: number of applicants	3.1	1.91
r2 =	0.21
standard error of residuals =	2118.7
Durbin Watson =	0.89
Regression 3
Overhead costs = f(number of enrolled students)
variable	coefficient	standard error
constant	-1382.2	1350.3
independent variable 3: number of students	14.83	2.84
r2 =	0.73
standard error of residuals =	1233
Durbin Watson =	1.09

The table that takes us through the comparison of the variables in the data set

	Regression A	Regression B	Regression C
Criterion	Non academic staff	Student applications	Enrolled students
1 Economic Plausibility	One would expect that there is a relationship between the number of non academic staff and non academic overheads	The relationship between non academic overheads and student applications should be small unless the most significant non academic job is dealing with student applications	Enrolled students must, by definition, be a significant driver of non academic costs
2 Goodness of fit	r2 = 0.72	r2 = 0.21	r2 = 0.73
3 Significance of independent variables	t statistic of non academic staff of 5.02 is significant	t statistic of student applications of 1.62 is insignificant	t statistic of enrolled students of 5.22 is significant
4 Specification analysis
A linearity	Reasonably linear with a relatively high correlation coefficient of 0.72	This data series returns a correlation coefficient of only 0.21 suggesting a poor relationship between student applications and non academic costs	Students enrolled values are reasonably linear
B constant variance of residuals	We only have 12 data points for this exercise so our results are not that reliable. However, the constant variance assumption does not appear valid here … plot non academic costs against the residuals of non academic staff and see for yourself!	The same as with non academic staff!	There is some hope here: the residuals plot doesn’t seem to contradict the constant variance assumption with enrolled students.
C independence of residuals	DW = 1.92 In general for such a sample size, this means that there is no problem of serial correlation (aka autocorrelation)	DW = 0.89 is outside of the range 1.3 – 2.7 thus there is the possibility that we are dealing with data that suffers from autocorrelation	DW = 1.09 is outside of the range 1.3 – 2.7 thus there is the possibility that we are dealing with data that suffers from autocorrelation
D normality of residuals	Using SKEW from Excel this distribution of residuals is slightly skewed	This distribution of residuals is heavily skewed	This distribution of residuals is not skewed

Graphs to accompany the normality analysis section of the table. The graphs show the skewness coefficient derived from the =SKEW() function in Excel together with the plot of the residuals for each variable.

Conclusions

This page has been prepared to help anyone who is carrying out a regression analysis of a time series data set.
The comparison table has been based on the table found in Horngren and Foster on page 780: the contents of the table found here are my own,
Work through your own example and apply the analysis you see here. Let me know if it helps ... or not!
References
Charles T Horngren & George Foster(1987)
Cost Accounting: a managerial emphasis
6th edition
Prentice Hall

Telephone bill analysis: how to unravel cost behaviour

Introduction: intended audience

This case relates to a stage two cost behaviour analysis problem: for a first year seminar in cost accounting by accounting undergraduates; or a second year management accounting class exercise for business or management studies undergraduates.  The case is also suitable as a cost behaviour analysis case for MBA students.

The data that follow are taken from an actual telephone bill or statement in the United Kingdom some time during early 1999.

The purpose of this page is to take us through a first and then second stage analysis of the bill.  That is, we would like to derive a cost function for the telephone expense.

Unscientific analysis

Firstly, have a look at the data that follow and try to estimate the overall behaviour of the data: are they fixed, variable or semi variable?  Once you have done that, you should attempt to estimate the cost function for the data!

                 

Duration	Cost	Duration	Cost	Duration	Cost
(secs)	(£)	(secs)	(£)	(secs)	(£)
181	0.101	3620	1.514	4	0.042
134	0.074	80	0.088	4	0.042
106	0.059	52	0.057	783	8.824
35	0.042	83	0.092	52	0.147
358	0.074	75	0.083	54	0.153
13	0.042	575	0.644	442	1.253
110	0.061	1540	0.224	228	0.646
40	0.042	38	0.042	150	0.425
83	0.046	696	0.411	182	0.516
85	0.047	1254	14.127	1	0.08
108	0.059	16	0.172	133	0.377
165	0.091	595	6.587	585	1.659
326	0.182	317	3.562	40	0.113
1	0.042	653	7.356	248	0.703

Not easy is it?  Let’s sort out how we should do it properly.

Stage one analysis

The first stage is to take the data in their entirety and assess how the cost is behaving: refer to the page on cost behaviour if you are unsure of what this means.

This case represents an excellent example of why the first thing we should do with any attempt to assess the behaviour of a cost is to plot the data on a graph  

Helpful?  Well, possibly.  There is a section of the data that extend from just under £4 to £14; and there’s another one that seems to extend from about 350 seconds to almost 4,000 seconds.  Then there’s another series that seems to start around 150 seconds and rises to 600 seconds at a cost of around 1.8 pounds. Apart from that, it’s difficult, isn’t it?

Just for the sake of argument, let’s carry on and assume that we can apply the method of Ordinary Least Squares (OLS), or regression analysis, to help us to estimate a cost function.  The following graph contains the basic data and the line of best fit as derived from OLS.  The graph also includes the cost function derived from OLS.

   

The function tells us that we can estimate the telephone cost, Y’, by applying the function

Y’ = 0.6492 + 0.0017x

where x is the duration, in seconds, of the call relating to the cost we would like to estimate or predict.

However, we can see from the graph that even if we carry out all of the calculations now available to us, it won’t be much use because, as both the line of best fit and the r² value, 0.1286, tell us, we haven’t found an especially good model. 

Have we failed in our quest?

We haven’t failed yet.  As we saw just a short while ago, there do seem to be some patterns buried in the data: we found suggestions of at least three different sub series of data.  Our quest now, then is to unravel the data and see if we can derive the cost function we are looking for.

Stage two analysis: disaggregate the data

Take a closer look

In a situation such as this, the accountant has to go back to the invoice, the journals, the technical analysis and find out how he might unravel the telephone bill story.

Imagine the accountant has sent his assistant to the files to take a closer look at the telephone bills and she comes back with some additional information.  The assistant finds that telephone calls can be classified according to whether the calls are invoiced as

o        Local

o        Regional and National

o        International

o        Chargecard

That is, local calls are invoiced at one cost per unit/minute; regional and national calls are invoiced at another cost per unit/minute; and so on.  The assistant has found, therefore, that there are at least four different rates that telephone costs are invoiced at. 

So, what do we do now?  The accountant asked the assistant to sort the telephone cost data according to whether they relate to local, regional/national, international and Chargecard calls. The assistant does this and comes up with the data below.  We should see straight away that the assistant accountant has provided some very useful information for us.  Take a look at the costs per minute that have been derived from the newly sub classified data.  Not perfect; but better.

Local				Regional and National
duration	cost	cost/min		duration	cost	cost/min
181	0.101	0.0335		4	0.042	0.63
134	0.074	0.0331		4	0.042	0.63
106	0.059	0.0334		3620	1.514	0.0251
35	0.042	0.072		80	0.088	0.066
358	0.074	0.0124		52	0.057	0.0658
13	0.042	0.1938		83	0.092	0.0665
110	0.061	0.0333		75	0.083	0.0664
40	0.042	0.063		575	0.644	0.0672
83	0.046	0.0333		1540	0.224	0.0087
85	0.047	0.0332		38	0.042	0.0663
108	0.059	0.0328		696	0.411	0.0354
165	0.091	0.0331
326	0.182	0.0335
1	0.042	2.52
International				BT Chargecard
duration	cost	cost/min		duration	cost	cost/min
1254	14.127	0.6759		52	0.147	0.1696
16	0.172	0.645		54	0.153	0.17
595	6.587	0.6642		442	1.253	0.1701
317	3.562	0.6742		228	0.646	0.17
653	7.356	0.6759		150	0.425	0.17
783	8.824	0.6762		182	0.516	0.1701
				1	0.08	4.8
				133	0.377	0.1701
				585	1.659	0.1702
				40	0.113	0.1695
				248	0.703	0.1701

Let’s go back to basics again and put these on a graph: 4 separate graphs this time.  On each graph, we have the actual data and, by use of OLS analysis, what is called “Linear” that is the OLS based cost prediction for the costs of the telephone calls.

In the case of both International and Chargecard calls, we seem to have found a near perfect model because all we can see on each graph is the cost prediction for each call.  The actual costs are there, trust me!, but as we can see from the r² values, the OLS model is so good that cost prediction virtually exactly equals actual costs in every case.

Y'_{international} = -0.02788 + 0.011276X

r² 1.000

Y'_chargecard = 0.015453 + .002791X

r² 0.998

What about the models for the other calls?

What about local and regional and national calls, however?  Why do they have relatively poor r² values and hence why are their models relatively poor?  Have a look at the charts and the statistics and verify that this viewpoint is true.

Y'_local = 0.034781 + 0.000272X

r² 0.588

Y'_{regional and national} = 0.065861 + 0.000372X

r² 0.837