CHAPTER 3: APPLICATION OF MATHEMATICS MODELS IN SHORT-
3.2. Apply the Inventory Management Model and Credit and Receivable
3.2.1. The Economic Order Quantity Model
3.2.1.1. The guideline to apply the Economic Order Quantity model
The economic order quantity (EOQ) model is the best-known approach for explicitly establishing an optimal inventory level, which minimizes the total inventory cost.
This model is using to determine what optimal order size the firm should use when it restocks its inventory, depends on data below:
- T: Total unit sales per year
- F: Fixed cost per order, every time we place an order, there are fixed costs associated with that order such as: procedure cost, checking cost.
- CC: Carrying costs per unit, such as storage cost, insurance cost, the opportunity cost of capital on the invested amount.
- Q*: the economic order quantity
Q* = CC
F x 2T
3.2.1.2. Apply the Economic Order Quantity model in determining the optimal size of inventory orders
Apply the economic order quantity (EOQ) model in determining the optimal size of inventory orders of Tuong An Vegetable Oil Joint Stock Company
- T: Total unit sales per year;
- F: Fixed cost per order;
- CC: Carrying costs per unit;
Q* = CC
F x 2T
Table 3.7: The economic order quantity (EOQ) of Tuong An Vegetable Oil Joint Stock Company per year form 2005 - 2007.
Year T (liter) F(VND)/order CC(VND)/liter Q* (liter) 2005 59,113,913.62 204,625,085.59 1,620.00 3,864,397.42 2006 75,825,815.12 214,856,339.87 1,701.00 4,376,686.82 2007 85,412,048.66 225,599,156.86 1,786.05 4,645,115.28
Which the total units sales per year from 2005 – 2007, apply the equation Q* =
CC F x 2T
We can calculate the optimal order size to establish an optimal inventory level.
Total carrying costs = Average inventory x Carrying costs per unit = (Q*/2) x CC
Total restocking cost = Fixed cost per order x Number of orders = F x (T/Q*)
Total costs = Carrying costs + Restocking costs = (Q*/2) x CC + F x (T/Q*)
Table 3.8: The total cost of Tuong An Vegetable Oil Joint Stock Company per year form 2005 - 2007.
Unit: VND Year Total carrying cost Total restocking cost Total cost
2005 3,130,161,913.20 3,130,161,913.20 6,260,323,826.39 2006 3,722,372,142.58 3,722,372,142.58 7,444,744,285.17 2007 4,148,204,077.28 4,148,204,077.28 8,296,408,154.55
The total cost it means the optimal total cost per year.
Conclusion:
Compare the total cost of using EOQ model to determine the economic order quantity with the total cost of the order quantity not apply this model, we can see the total cost of applying EOQ model is smaller than the total cost not apply this model.
Case 1: Determine the economic order quantity base on EOQ model.
Case 2: Determine the order quantity base on experiences and the inventory in the beginning of that year.
Table 3.9: Comparison of the total cost of holding inventory in the case of using EOQ model and in the case of basing on experiences
Case 1 (EOQ model) Case 2
Year Order quantity Total cost Order quantity Total cost 2005 3,864,397.42 6,260,323,826.39 4,303,244.30 6,296,574,412.9 2006 4,376,686.82 7,444,744,285.17 6,315,631.29 7,951,021,392.7 5 2007 4,645,115.28 8,296,408,154.55 7,092,214.65 9,050,431,783.4 7
9 3.2.2. Credit and receivables management models
3.2.2.1. The guideline to apply the Credit and Receivables Management Models All Credit and Receivables Management Models were written in chapter 2 which are used to help Chief Financial Management (CFO) to determine credit policies of company.
The credit policies of company include:
i. Credit standard policy ii. Credit term policy iii. Cash discount policy
In order to making decision about credit and receivable management, CFO need to collect data, input data in the model and process the data. However, the processing data and making decision relate to credit and receivable management is complexity so the mathematic model is complex to apply. Therefore, Van Horn and Machowicz (2001) set up the model to analyze and make decision base on effective of policy on two aspects:
- If the purpose of the policy is increasing profits then considers in increase profits equal or more increase costs.
- If the purpose of the policy is decreasing costs then considers in save costs compensate the decreasing in profits.
i. Credit standard policy
Credit standards are the criteria a company uses to screen credit applicants in order to determine which of its customers should be offered credit and how much. The credit standards policy includes liberal credit policy and illiberal credit policy. To determine which policy company should apply, CFO can do the process of analysis follow one in two model hereafter:
Figure 3.1: Liberal credit policy model Increase Receivables
Liberal credit policy
Increase cost in Receivables
Increase profit equal or more increase Costs
Increase Profit Making Decision
Increase Sales
Figure 3.2: Illiberal credit policy model
This model can apply in manufacture and distribution companies. To apply this model, we can do steps follow:
First, set up a credit standard.
Second, forecast the changing in sales when using either liberal or illiberal credit policy.
Third, forecast the changing in costs when using either liberal or illiberal credit policy.
Fourth, compare between profits and costs to make decision.
Fifth, keep track of effect of liberal or illiberal credit policy on sales and costs to change the policy on time.
ii. Credit term policy
The credit term is the maximum period company allow customer buy product but not pay. Excess this period the debt that customer has not paid is the bad debt. A changing in credit period can be lengthen the credit period or shorten the credit period.
Decrease Receivables
Illiberal credit policy
Safe cost in Receivables
Safe Costs equal or more Decrease profit
Decrease Profit Making Decision
Decrease Sales
Figure 3.3: Lengthen the credit period model
Figure 3.4.: Shorten the credit period model
To apply this model, CFO need to cooperate with Business Manager, Sales Manager to estimate data input:
- Estimate the changing in sales ratio when the credit period changing.
- Estimate the changing in average collection period when the credit period changing.
- Estimate the changing in account receivables affect by changing in sales and average collection period.
Decrease Receivables
Shorten the credit period
Safe cost in Receivables
Safe Costs equal or more Decrease profit
Decrease Profit Making Decision
Decrease average collection period
Decrease Sales
Increase Receivables
Lengthen the credit period
Increase cost in Receivables
Increase profit equal or more increase Costs
Increase Profit Making Decision
Increase average collection period
Increase Sales
- Estimate opportunity of account receivables.
Base on the estimated data, CFO can calculate changing in profits and costs.
Compare between profits and costs to make decision which policy can apply in company.
iii. Cash discount policy
A cash discount is a discount offered on the condition that the customer will repay the credit extended within a specified period of time. A cash discount is normally expressed as a percentage discount on the net amount of the cost of goods purchased (usually excluding freight and taxes). Cash discounts are offered (or increased) to speed up the collection of accounts receivable and, by extension, reduce a company‘s level of receivables investment and associated costs. We have two model of cash discount policy
Figure 3.5: Increase Cash discount policy model Decrease Receivables
Increase Cash discount
Safe cost in Receivables
Safe Costs equal or more Decrease profit
Decrease Profit Making Decision
Decrease average collection period
Decrease Sales
Figure 3.6: Decrease Cash discount policy model
To apply this model, CFO need to cooperate with Business Manager, Sales Manager to estimate data input:
- Estimate the changing in average collection period when the cash discount ratio changing.
- Estimate opportunity of account receivables.
Base on the estimated data, CFO can calculate changing in profits and costs.
Compare between profits and costs to make decision which policy can apply in company.
3.2.2.2. Apply the Credit and receivables management model
Apply the Credit and receivables management model to determine credit policies of Tuong An Vegetable Oil Joint Stock Company per year.
i. Credit standard policy
Liberal credit policy Hypothesis:
- Additional sales: 341,648,194,647 VND when
- Additional investment in inventory: 1,246,264,620VND
- Variable production, administrative, and marketing cost: 70% of total sales.
Increase Receivables
Decrease Cash discount
Increase cost in Receivables
Increase profit equal or more increase Costs
Increase Profit Making Decision
Increase average collection period
Increase Sales
- Profit contribution ratio per dollar of sales is: 30%
- The company‘s required pretax rate of return: 25%
- Average collection period: 60 days - Bad debt loss ratio: 7%
Table 3.10: Tuong An Vegetable Oil Joint Stock Company’s Analysis of the Decision to relax Credit Standard by Extending Full Credit to customers.
Step A: Additional sales 341,648,194,647
Marginal profitability of additional sales 102,494,458,394.2
= Profit contribution ratio x Additional sales
Step B: Additional investment in
receivables 56,161,347,065.33
= Additional average daily sales x average collection period
=Additional annual sales/365*60 Cost of the additional investment in
receivables 14,040,336,766.3
= Additional investment in receivables x Required pretax rate of return
Step C: Additional bad-debt loss 23,915,373,625.3
= Bad-debt loss ratio x Additional sales Step D: Additional investment in
inventory 1,246,264,620
Cost of the additional investment in inventory
=Additional investment in inventory x
Required pretax rate of return 311,566,154.9
Step E: Net change in pretax profits 64,227,181,847.64
= Marginal returns - Marginal costs
= A - (B + C + D)
Conclusion: Tuong An Vegetable Oil Joint Stock Company can use Liberal credit policy with the above hypothesis. With relaxing the Credit Standard the Net change in pretax profits of Net change in pretax profits is 64,227,181,847.64VND.
ii. Credit term policy
Lengthen the credit period Hypothesis:
- Present sales: 1,708,240,973,237 VND - Expect sales increase: 20%
- Expect average collection period to increase: from 35 day to 65 days - The bad debt loss ratio: 7%
- Additional investment in inventory: 1,246,264,620 VND
- Variable production, administrative, and marketing cost: 70% of total sales.
- Profit contribution ratio per dollar of sales is: 30%
- The company‘s required pretax rate of return: 25%
Table 3.11: Tuong An Vegetable Oil Joint Stock Company’s Analysis of the Decision to change its credit term from “net 30” to ” net 60”.
Step A: Additional sales 341,648,194,647
= Percent increase X Present sales = 0.2 x 1,708,240,973,237
Marginal profitability of additional
sales 102,494,458,394.22
= Profit contribution ratio x Additional sales
= 0.3 x 341,648,194,647
Step B: Additional investment in
receivables 201,244,826,984.09
= New average balance - Present average balance
Cost of the additional investment in
receivables 50,311,206,746.02
= Additional investment in
receivables x Required pretax rate of return
Step C: Additional bad-debt loss 23,915,373,625.32
= Bad-debt loss ratio X Additional sales
Step D: Additional investment in
inventory 1,246,264,620 Cost of the additional investment in
inventory 311,566,154.93
= Additional investment in
inventory x Required pretax rate of return
Step E: Net change in pretax
profits 27,956,311,867.95
= Marginal returns - Marginal costs
= A - (B + C + D)
Conclusion: Tuong An Vegetable Oil Joint Stock Company can Lengthen the credit period with the above hypothesis. With changing its credit term from ―net 30‖ to ‖
net 60‖ the net change in pretax profits of Tuong An Vegetable Oil Joint Stock Company is 27,956,311,867.95 VND.
iii. Cash discount policy
Increase Cash discount policy Hypothesis
- Present credit term: ―net 30‖
- Offer ―1/10, net 30‖
- Present Average collection period: 50 days.
- New Average collection period: 28 days.
- 40% of the company‘s customers will take the advantage of the new cash discount.
- Annual credit sales: 1,708,240,973,237 VND.
- The company‘s required pretax rate of return: 25%
Table 3.12: Tuong An Vegetable Oil Joint Stock Company’s Analysis of the Decision to offer a 1 percent cash discount
Step A: Decrease in average
receivables balance 102,962,469,619.76
= Present average balance - New average balance
Earnings on the funds released by the
decrease in receivables 25,740,617,404.94
=Decrease in receivables x Required pretax rate of return
Step B: Cost of cash discount 6,832,963,892.95
= annual sales x Percentage taking discount x Percentage discount
= 1,708,240,973,237 x 0.4 x 0.1
Step C: Net change in pretax profits 18,907,653,511.99
= Marginal returns - Marginal costs
= A - B
Conclusion: Tuong An Vegetable Oil Joint Stock Company can to offer a 1 percent cash discount with the above hypothesis. With offering a 1 percent cash discount the net change in pretax profits of Tuong An Vegetable Oil Joint Stock Company is 18,907,653,511.99 VND.
REFERENCES
1. Brigham, E. F., (1992), Fundamentals of Financial Management, 6 th Edition, The Dryden Press.
2. Van Horne, J.C., and Wachowicz, J.M., (2001), Fundamentals of Financial Management, 11th Edition, Prentice Hall.
3. Higgins R . C, ( 2001), A n a l y s i s f o r Financial Management, 6 th Edition , McGraw-Hill/Irwin.
4. Bonini, Hausman, Bierman, (1997), Quantitative Analysis for Management (9 th Edition), McGraw-Hill/ Irwin.
5. Brealey, R.A., and Myers, S.C., (2003), Principles of Corporate Finance, 6 th Edition, McGraw-Hill/Irwin.
6. David Whitehurst, (2003), Fundamentals of Corporate Finance, 6 th Edition, McGraw-Hill/Irwin.
7. Beverley Jackling and et al, (2003), Accounting – A framework for decision making, McGraw-Hill/Irwin.
8. Leopold A. Bernstein, (1993), Financial Statement Analysis, 3 rd Edition, McGraw-Hill/Irwin
9. Citi bank, (1994), Basic of corporate Finance, Latin America Training and Development center.
10. Financial Statement of Sonadezi Long Thanh and Tuong An Vegetable Oil Joint Stock Company.
11. Sonadezi Long Thanh and Tuong An Vegetable Oil Joint Stock Company annual report.
12. www.sonadezi.com.vn 13. www.tuongan.com.vn 14. www.ssi.com.vn 15. www.vietstock.com.vn 16. www.vcbs.com.vn 17. www.gso.gov.vn
APPENDIX
APPENDIX A: THE DEVELOPMENT OF VIETNAMESE BUSINESSES Depend on the statistical censuses and surveys of General Statistics Office of Vietnam the development of Vietnamese businesses in recent year like this: the increasing about the number of acting enterprises, number of employees in enterprises, annual average capital of enterprises, and net turnover from business of enterprises. This development contributed in growth rate of economics such as GDP 2 quarter of 2007 were estimated in increasing 7.87% against same period in 2005 and 2006. Three economic sectors had growth rates: The agriculture, forestry and fishery sector increased by 2.67%; the industry and construction increased by 9.88%; the service rose by 8.41%. For 7.87% GDP, the agriculture, forestry and fishery contributed 0.53 points percents; the industry and construction shared by 3.94 points percents; the service shared by 3.4 points percents. 15
1. Acting enterprises
a. Number of total acting enterprises increase very quickly, annual average was increasing by 22% against previous year, concretely:
15 Source: Press release: socio-economic statistical data, 2 Quarter in 2007 General Statistics Office of Vietnam.
42288
51680
62908
72012
91755
112952
0 20000 40000 60000 80000 100000 120000
2000 2001 2002 2003 2004 2005
Figure 1: Number of acting enterprises in Vietnam from 2001 - 2005 (Source: General Statistics Office of Vietnam)
b. Number of acting enterprises classifying by type of enterprise
5759 35004
1525
5355 44314
2011
5363 55237 2308
4845 64526
2641
4596 84003
3156
4086 105169 3697
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
2000 2001 2002 2003 2004 2005
State owned enterprise Non-state enterprise Foreign investment enterprise
Figure 2: Number of acting enterprises classifying by type of enterprise in Vietnam from 2001 – 2005.
(Source: General Statistics Office of Vietnam)
2. Employees in enterprises
a. Number of employees in total enterprises increase very quickly, annual average was increasing by 12% against previous year, concretely:
3536998 3933226
4657803
5175092
5770201
6240595
0 1000000 2000000 3000000 4000000 5000000 6000000 7000000
2000 2001 2002 2003 2004 2005
Figure 3: Number of employees in enterprises in Vietnam from 2000-2005 (Source: General Statistics Office of Vietnam)
b. Number of employees in enterprises classifying by type of enterprise: from 2000 to 2005 the employees move from state owned enterprise to Non – state enterprise and foreign investment enterprise. Figure 2.4 can prove that information.
2088531 1040902 407565
2114324 1329615 489287
2259858 1706857 691088
2264942 2049891 860259
2249902 2475448 1044851
2040859 2979120 1220616
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
2000 2001 2002 2003 2004 2005
State owned enterprise Non-state enterprise Foreign investment enterprise
Figure 4: Number of employees in enterprises classifying by type of enterprise in Vietnam from 2001 - 2005
(Source: General Statistics Office of Vietnam) 3. Annual average capital of enterprises
a. Annual average capital of total enterprise increase year by year, annual average capital was increasing by 20% against previous year, concretely:
998423
1186014 1352076
1567179
1966165
2435048
0 500000 1000000 1500000 2000000 2500000
B il li on d ong s
2000 2001 2002 2003 2004 2005
Year
Figure 5: Annual average capital of enterprise from 2000 -2005 (Source: General Statistics Office of Vietnam)
b. Annual average capital of enterprises classifying by type of enterprise, the figure 2.6 shows that the capital in state owned enterprise is the largest from 2000 – 2005 but the ratio is decrease compare with non state enterprise and foreign investment enterprise.
670234 98348 229841
781705 142202 262107
858560 202396 291120
932942 289625 344611
1128483 422892 414789
1338255 607271 489521
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
2000 2001 2002 2003 2004 2005
State owned enterprise Non-state enterprise Foreign investment enterprise
Figure 6: Annual average capital of enterprises classifying by type of enterprise (Source: General Statistics Office of Vietnam)
4. Net turnover from business of enterprises.
a. Net turnover from business of total enterprises increase year by year, annual average capital was increasing by 21.8% against previous year, concretely:
809786 897856
1194902
1436151
1719401
2157802
0 500000 1000000 1500000 2000000 2500000
b il li o n d o n g s
2000 2001 2002 2003 2004 2005
year
Figure 7: Net turnover from business of total enterprises (Source: General Statistics Office of Vietnam)
b. Net turnover from business of enterprises classifying by type of enterprise.
The figure 2.8 show that the net turnover of non-state enterprise and foreign investment enterprise increase year by year in which the net turn over of state owned enterprise decrease year by year. That mean two types of enterprise is stronger than state owned enterprise. It is suitable with the policy of government.
444673 203156 161957
460029 260565 177262
611167 362657 221078
666022 482181 287948
708045 637371 373985
838396 851003 468404
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
2000 2001 2002 2003 2004 2005
State owned enterprise Non-state enterprise Foreign investment enterprise
Figure 8: Net turnover from business of enterprises classifying by type of enterprise.
(Source: General Statistics Office of Vietnam)
APPENDIX B: THE FACT OF USING MATHEMATICS MODELS IN SHORT – TERM INVESTMENT DECISIONS
The managers often make financial decision base on their intuition. With senior managers, this method can successful but to complicate situations this method maybe failure. Besides, the scale of business larger more complicated so hard to make decision base on intuition to expend the business operation.
Therefore, the manager more and more interested in using financial models to find out the optimal solution. However, the applying financial models are needed complicate calculation so the manager often gives to other department. When having the result they can not know it is right or wrong because they don‘t follow the process from the beginning. This thing makes decrease the applying of model and affect the decision of manager, contribute the doubt about the real value of models.
To understand more clearly about the fact of applying the mathematical model in financial decision making especially in investment decision in current assets such as cash management decisions, inventory management decisions, credit decisions, I already done the survey to find out how the manager of others company use these models to make decision.
1. Description of survey
The survey had done by questionnaire send to 30 companies in Dongnai, Vungtau, Ho Chi Minh city by email and the result is having 27 companies replied,… with two company‘s primary business activity are manufacturing and trading company in there has three Type of Ownership are Private enterprise, Limited Liability company and Shareholding company.
The structure of companies are classifying by company‘s primary business activity and Type of Ownership.
Table 1.1: The structure of companies are surveying by company’s primary business activity and Type of Ownership.
Quantity Ratio Company’s primary
business activity Manufacturing company 19 70.37%
Trading company 8 29.63%
Total 27 100%
Type of Ownership Private enterprise 7 25.93%
Limited Liability company 8 29.63%
Shareholding company 12 44.44%
Total 27 100%
Table 1.2: The characteristic of Companies in the survey
Quantity Ratio
The operation time < 2 years 2 7.41%
2 – 5 years 6 22.22%
6 – 10 years 8 29.63%
> 10 years 11 40.74%
Total 27 100.00%
Sales < 15 billions 5 18.52%
15 – 30 billions 2 7.41%
31 – 50 billions 4 14.81%
> 50 billions 16 59.26%
Total 27 100.00%
Total Assets < 15 billions 5 18.52%
15 – 50 billions 8 29.63%
> 50 billions 14 51.85%
Total 27 100.00%
2. The result of survey
Training, knowing and using financial models
Almost the person who answered the questionnaire was chief accountant, accounted 51.85%, accountant, accounted 29.63%, and Board of Management, accounted 18.52%. The ratio 81.48% the person who answered the questionnaire worked in financial field can assure that the information collected could be trusted.
The ratio of attending in training courses that update the financial management method is not high. That means the condition to apply the advanced financial management method still limit. There was 62.96% the person who answered the questionnaire just attend in financial management course 1 – 2 times, in which 94%
is accountant and chief accountant. About 25.93% the person who answered the questionnaire attend in financial management course 3 – 4 times, 2 persons attend usually and 1 person never attending.
The practice of cash management
The result of the survey show that 33.33% in 27 companies in the survey answer that they usually set the cash plan, in which just have 3.7 % answer that they are never set the cash plan. On the others side, 51.85% companies in the survey answer that that set the cash plan per month, 22.22% per week and 7.41% never interested in setting the periodic time for cash plan (Table 2.1).
Table 2.1: The practicing of setting cash plan
Quantity Ratio
The periodic time
of cash plan Never 1 3.70%
Rarely 2 7.41%
Occasionally 4 14.81%
Often 11 40.74%
Usually 9 33.33%
Total 27 100.00%
Periodic period of
cash plan Never 2 7.41%
Every Week 6 22.22%
Every Month 14 51.85%
Every quarter 1 3.70%
Every 6 months 2 7.41%
Every year 2 7.41%
Total 27 100.00%
The determining the target cash balance, the table 2.2 show that having 18.52 % businesses in the survey often or usually determining the target cash balance, in which about 33.33 % businesses in the survey never or rarely determining the target cash balance. So the general trend is that businesses rarely interested in setting up the target cash balance policy. Almost businesses in the survey think that the cash balance is the different between the cash in and cash out but they don‘t have any cash management policy. Besides, the table 2.2 still show that 62.96 % businesses in the survey setting up the target cash balance base on experience of the manager.
The ratio of business apply the cash management theory in setting up the target cash balance is very minimum; just have one company equal to 3.7 %. That means the cash management theories haven‘t applied popularly in practicing in Vietnam.