# When Calculating The Eoq Two Costs Are Relevant For Decision Making Accounting Essay

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This assignment is designed to test and apply our knowledge of sensitivity analysis using various Excel models. It allows us to experiment and perform 'what if' analyses under different scenarios and also to evaluate the strengths and weaknesses of the models we have used.

## Section A

Annual holding cost per unit = Storage cost per unit + (Purchase cost per unit x interest rate)

= £25 + (£150 x 6%) = £34

1.2

Economic order quantity = sqrt (2RcD)/Hc

= sqrt [(2 x 400 x £45)/ £34]

= 33 units

1.3

## Order quantity

## Average stock

## Number of orders

## Annual holding costs

## Annual ordering costs

## Total costs

1

0.50

400

17

18,000

18,017

2

1.00

200

34

9,000

9,034

3

1.50

133

51

6,000

6,051

4

2.00

100

68

4,500

4,568

5

2.50

80

85

3,600

3,685

6

3.00

67

102

3,000

3,102

7

3.50

57

119

2,571

2,690

8

4.00

50

136

2,250

2,386

9

4.50

44

153

2,000

2,153

10

5.00

40

170

1,800

1,970

11

5.50

36

187

1,636

1,823

12

6.00

33

204

1,500

1,704

13

6.50

31

221

1,385

1,606

14

7.00

29

238

1,286

1,524

15

7.50

27

255

1,200

1,455

16

8.00

25

272

1,125

1,397

17

8.50

24

289

1,059

1,348

18

9.00

22

306

1,000

1,306

19

9.50

21

323

947

1,270

20

10.00

20

340

900

1,240

21

10.50

19

357

857

1,214

22

11.00

18

374

818

1,192

23

11.50

17

391

783

1,174

24

12.00

17

408

750

1,158

25

12.50

16

425

720

1,145

26

13.00

15

442

692

1,134

27

13.50

15

459

667

1,126

28

14.00

14

476

643

1,119

29

14.50

14

493

621

1,114

30

15.00

13

510

600

1,110

31

15.50

13

527

581

1,108

32

16.00

13

544

563

1,107

33

16.50

12

561

545

1,106

34

17.00

12

578

529

1,107

35

17.50

11

595

514

1,109

36

18.00

11

612

500

1,112

37

18.50

11

629

486

1,115

38

19.00

11

646

474

1,120

39

19.50

10

663

462

1,125

40

20.00

10

680

450

1,130

## Table 1: Inventory Costs

The economic order quantity (EOQ) is the optimum order size which is the order quantity that will result in the total amount of ordering and holding costs being minimized. This is a decision model that calculates the optimum quantity of inventory to order. However, there are a number of assumptions underlying the EOQ model (Atkinson et al, 2007).

One, the same quantity is ordered at each reorder point. Two, demand, ordering costs and carrying costs are known with certainty. The purchase order lead time, which is the time that elapses between placing an order and its delivery is also known with certainty. Three, purchasing cost per unit is unaffected by the quantity ordered. This assumption makes purchasing costs irrelevant to determining the EOQ because purchasing costs of all units acquired will be the same regardless of the order size in which the units are ordered. Four, no stockouts are assumed to occur. The basis for this assumption is that the costs of stockouts are so high that managers maintain adequate inventory to prevent them. Finally, in deciding on the size of a purchase order, managers consider costs of quantity only to the extent that these costs affect ordering or carrying costs.

When calculating the EOQ, two costs are relevant for decision making. They are holding costs and ordering costs (Drury, 2006). Holding costs usually consist of the opportunity cost of investment in stocks, incremental insurance costs, incremental warehouse and storage costs, incremental material handling costs and the cost of obsolescence and deterioration of stocks. The relevant holding costs for use in quantitative models should include only those items that will vary with the levels of stock. Costs that will not be affected by changes in stock levels are not relevant costs. For example, in the case of warehousing and storage only those costs should be included that will vary with changes in the number of units ordered. Salaries of storekeepers, depreciation of equipment and fixed rental of equipment and buildings are often irrelevant because they are unaffected by changes in stock levels.

Ordering costs usually consist of the clerical costs of preparing a purchase order, receiving deliveries and paying invoices (Drury, 2006). Ordering costs that are common to all stock decisions are not relevant, and only the incremental costs of placing an order are used in formulating the quantitative models.

1.4

Annual number of re-orders = Annual demand / EOQ

= 400/33 =12 times

1.5

At the EOQ, total costs are £1, 106. If the order quantity is 2 units less than the EOQ, the total costs are £1, 108, based on the calculations in Table 1. This is a cost penalty of £2. Any deviation will invariably incur cost penalties because the EOQ represents the optimum order size where ordering costs and holding costs are at their lowest. Any order size lower than the EOQ will incur lower holding costs but higher ordering costs. Conversely, any order size higher than the EOQ will incur lower ordering costs but higher holding costs.

## Section B

The EOQ model is very useful in decision making. Based on the sensitivity analysis, it was easy and clear to find out how much costs change based on reorder size. The EOQ can be calculated using a formula, table or graphically. In my opinion, the formula method is the best as it gives us one definitive answer. The graph and table methods are useful for evaluating costs at different levels, though the graph may be sometimes difficult to read, especially when a small scale is used. An EOQ model works best in a relevant range, as figures at the extreme ends are generally inaccurate. However, the EOQ model is not without its weaknesses or limitations and these were uncovered using sensitivity analysis.

One major shortcoming is the assumption that the consumption of material is evenly distributed and can be predicted with exactitude (Atkinson et al, 2007). When this does not occur, the formula is redundant. To overcome this, more complex formulas should be developed to account for wide fluctuations in material usage, assuming that these fluctuations can be predicted also.

Another weakness is that the basic input data is often faulty. EOQ figures are only correct if ordering costs and handling costs are correct. Yet, it is not easy to determine ordering costs. For one, they vary from material to material. In addition, holding costs are dependent on the firm's opportunity cost of capital which can also change from time to time.

A third shortcoming is the potentially high costs of making calculations (Horngren et al, 2000). Estimating costs with precision requires the utmost skills by management accountants, and is a laborious process that can take a long time. Even though the formulas may appear to be simple, collecting input is not. In the end, the costs of collecting the data may outweigh the savings made by the actual calculations, thus rendering it meaningless and an exercise in futility.

Next, management accountants may get blindsided by mathematics instead of using common sense. In fact, all economists and many business executives are often guilty of being so besotted with financial models and figures that they often lose sight of reality. It should always be remembered that a model is a vast simplification of the real world and that the real world is infinitely more complex than even the best model. As variables pile up on variables, a model becomes less and less effective. A model is a useful tool, but it should not be the sole criterion for decision making. Decisions have to be made by considering a host of other factors.

Finally, the EOQ model assumes that demand for each item of material occurs independently of other activities. However, in complex manufacturing environments the demand for material purchases is not independent. It is dependent on the volume of the planned output of components and sub-components which include the raw materials that must be purchased.

In conclusion, the EOQ model is useful, but it must be tempered with sound judgment. Often, EOQ figures may be incongruous with strategic goals and it is top management's responsibility to reconcile these opposing figures to work out a strategy that will benefit the organization the most.

## Question 2

## Section A

## 2.1

## Table 1

## Sample

## Xbar

## R

## R

## Xbar

## USL

## LSL

## USL

## LSL

1

22.2

1.88

4.8601

0.60991

22.8904

21.2056

2

22.69

3.3

4.8601

0.60991

22.8904

21.2056

3

22.25

2.61

4.8601

0.60991

22.8904

21.2056

4

21.97

2.8

4.8601

0.60991

22.8904

21.2056

5

21.19

2.9

4.8601

0.60991

22.8904

21.2056

6

22.29

2.92

4.8601

0.60991

22.8904

21.2056

7

22.24

2.69

4.8601

0.60991

22.8904

21.2056

8

21.42

3.14

4.8601

0.60991

22.8904

21.2056

9

22.52

2.34

4.8601

0.60991

22.8904

21.2056

10

21.71

2.77

4.8601

0.60991

22.8904

21.2056

Mean

22.048

2.735

Xbar and R charts are used in statistical quality control to monitor a variable data. These charts are highly useful when the sample size is relatively small and relatively constant. The Xbar chart is used to monitor the standard deviation of a variable whereas the R chart is used to monitor the process mean. In both cases, the upper and lower safety limits are shown.

Both graphs are drawn based on a number of assumptions. One, the qualitative feature that is monitored is sufficiently modeled by a normally distributed random variable. Two, the mean and standard deviation for the random variable are identical for each unit which is in turn independent of the one before or after it. Three, the inspection process is consistent and identical for each sample.

In this case, the process is in control as it falls within the upper and lower safety limits of both Xbar and R charts. Its range and standard deviation are within the control limits. Ideally, the range variation should be small and consistent over time.

## 2.2

## Table 2.2

## Sample

## Xbar

## R

## R

## Xbar

## USL

## LSL

## USL

## LSL

1

21.78

1.84

5.11421

0.64179

23.9604

22.1876

2

24.12

3.51

5.11421

0.64179

23.9604

22.1876

3

22.33

2.62

5.11421

0.64179

23.9604

22.1876

4

24.55

3.13

5.11421

0.64179

23.9604

22.1876

5

21.86

2.99

5.11421

0.64179

23.9604

22.1876

6

24.82

3.26

5.11421

0.64179

23.9604

22.1876

7

22.24

2.7

5.11421

0.64179

23.9604

22.1876

8

23.65

3.47

5.11421

0.64179

23.9604

22.1876

9

22.53

2.34

5.11421

0.64179

23.9604

22.1876

10

22.86

2.92

5.11421

0.64179

23.9604

22.1876

Mean

23.074

2.878

In this case, the process is not in control because there are instances where its standard deviation fall outside the upper and lower safety limits. This indicates that there are often wide fluctuations in the process. On the other hand, its range is within the control limits.

## 2.3

In the first case, the sample size was larger than in the second case. This might have caused the second sample to appear to be more volatile than the first because when the sample size is smaller, major fluctuations in or two random samples will have a larger influence on the mean and standard deviation than the same number of fluctuations but in a larger sample. Henceforth, it is not entirely fair to conclude that the process in the second set of data is less in control because of the differences in sample size.

## 2.4

An = A0(1 - r)n

100, 000 = 250, 000 (1 - 0.08)n

0.92n = 0.4

n log100.92 = log100.4

n = log100.4/ log100.92

n = 11 years

Depreciation is the part of the original fixed cost that is consumed during its period of use by the business (Wood and Sangster, 2005). It needs to be charged to profit and loss every year. The amount charged in a year to profit and loss for depreciation is based upon an estimate of how much of the overall economic usefulness of a fixed asset has been used up in that accounting period.

There are a number of causes of depreciation. The first is physical deterioration and consists of wear and tear, erosion, rust, rot and decay. Even if an asset is in good physical condition, it is often depreciated because of economic factors that put it out of use such as obsolescence and inadequacy. Then there are fixed assets that depreciate on a time basis. This does not refer to the passage of time that causes an asset to physically deteriorate. Rather, it relates to assets that have a legal life fixed in terms of years such as a lease or a patent. Finally, an asset can be depleted and this accounts for its depreciation. Natural resources such as minerals and oil are finite and tend to be depleted eventually.

There are many ways of calculating for depreciation but the two most popular are the straight line and reducing balance methods. The straight line method assumes that depreciation is the same every year throughout the useful life of the fixed asset (Das and Junaidah, 2007). On the other hand, the reducing balance method means that depreciation is highest in the first year of usage and becomes progressively lower and lower based on a certain percentage.

Based on the formula for the reducing balance method of depreciation, it would take approximately 11 years for the machine to depreciate from 250, 000 to 100, 000 monetary units. This is a reasonable estimate. The purpose of depreciation is to spread the total cost of a fixed asset over the periods in which it is to be used. The method chosen should be that which allocates cost to each product in accordance with the proportion of the overall economic benefit from using the fixed asset that was expanded during that period. Since the main value of the machine is obtained in its earliest years, it is appropriate that the reducing balance method is used since it charges more in the early years.

## Section B

## Depreciation

Using the following financial formula,

An = A0(1 - r)n

We are able to calculate one variable, if all other variables are provided. For example, if the cost, interest rate and time period are given, we can calculate the book value of the fixed asset at a particular point in time. We can manipulate the formula to calculate other things such as the time period for the asset to depreciate to a particular level or the interest rate required.

These are all useful information that can be obtained through sensitivity analysis. For example, if we raise the useful life of an asset, we can see how it will impact the book value of the asset for a particular period. Similarly, we can see how much the net book value of the fixed asset will be if we change the interest rate.

The major drawback of this method is that the depreciation figure tends to be cumulative. For instance, if we input cost of 250, 000, useful life of 11 years and interest rate of 8%, we obtain a book value of approximately 100, 000. This does not tell us how much depreciation has been incurred in each of the 11 years. In the straight line method, this would be easy to calculate since depreciation is the same each year. However, in the reducing balance method, depreciation becomes progressively lower. Therefore, to calculate annual depreciation, we need to apply the formula for year 1 to year 11 and find the difference. This is rather tedious and a major drawback of the formula.

## Xbar and R Charts

Constructing Xbar and R charts involves five steps (Berenson et al, 2009). The first step is to collect the data. The subgroup size must be rationally considered and then selected. The aim here is to minimize the amount of variation within a subgroup so that variations patterns can be discerned more easily. The frequency of the data is also selected, as is the number of subgroups. Next, the control limits are calculated. For each subgroup, the individual sample results are recorded. Then the subgroup average is calculated for each subgroup. This is followed by calculating the subgroup range.

The next stage is plotting the data. If done manually, the scales have to be selected and the coordinates plotted. However, there are numerous computer software today to assist us in producing charts such as Microsoft Excel and Minitab so all one has to do is input the data and follow the relevant software guide.

The third step is to calculate the overall process averages and control limits. This requires calculating the average range and the overall process average before the lines are plotted on the relevant charts.

The fourth step is to interpret both charts for statistical control. Variations must always be considered first. This is because when the R chart is out of control, the control limits on the Xbar chart are not valid since the estimate is wrong. Statistical control tests must be applied on the X bar chart. Tests that are applicable to the R chart are points beyond the limit, length of runs and number of runs.

Finally, the process standard deviation is calculated, if applicable. If the R chart is in statistical control, then the process standard deviation can be calculated. Degrees of freedom are used to calculate the control limits and standard deviation of the control charts.

## Conclusion

There are many mathematical and financial models that we can apply to different business scenarios. Sensitivity analysis is a highly useful tool in decision making. However, its effectiveness depends on the quality of input and the strengths of the models used. If incorrect data is used or if the model is seriously flawed, then they are useless and perhaps even dangerous since they provide us with false information. I have learned a lot of useful things while doing this assignment and the skills I have mastered will serve me well in future.