Application of mathematics models in short - term investment decisions

Apply the Inventory Management Model and Credit and Receivable Management Model in decision making in Tuong An Vegetable Oil Joint Stock Company .... NECESSITY OF THE THESIS In fact, Bo

VIETNAM NATIONAL UNIVERSITY, HANOI

VIETNAM NATIONAL UNIVERSITY, HANOI

TABLE OF CONTENTS

ACKNOWLEDGEMENTS i

ABSTRACT ii

TÓM TẮT iii

TABLE OF CONTENTS iv

LIST OF TABLES viii

LIST OF FIGURES x

INTRODUCTION 1

1 NECESSITY OF THE THESIS 1

2 OBJECTIVE OF THE RESEARCH 1

3 KEY RESEARCH AREA 1

4 METHODOLOGY 2

5 CONTRIBUTIONS OF THE THESIS 2

6 THESIS STRUCTURE 2

CHAPTER 1: LITERATURE REVIEW 3

1.1.Overview of financial decision making 3

1.1.1.Investment decision 3

1.1.2.Financing decision 4

1.1.3.Dividend decision 5

1.1.4.Other decisions 5

1.2.Overview about the model building 5

1.2.1.Definition of Models 5

1.2.2.Classification of Models 6

1.2.3.Basic Modeling Concepts 7

1.2.4.The method to set up a model and apply in the financial decision making 9

1.3.Models using in investment decisions in current assets 9

1.3.1.Determining the target cash balance 9

1.3.1.1.The BAT model 11

1.3.1.2.The Miller – Orr Model: A more general Approach 16

1.3.1.3.Implications of the BAT and Miller-Orr Models 18

1.3.1.4.Other Factors Influencing the Target Cash Balance 19

1.3.2 Inventory management decisions 20

1.3.3 Accounts receivable management 26

1.3.3.1 Credit Standards 27

1.3.3.2 Credit terms 32

1.3.3.3 Collection Effort 40

CHAPTER 2: ANALYZING BUSINESS ACTIVITIES OF SONADEZI LONG THANH SHAREHOLDING COMPANY AND TUONG AN VEGETABLE OIL JOINT STOCK COMPANY 42

2.1 Sonadezi Longthanh Shareholding Company 42

2.1.1 The introduction of Sonadezi Longthanh Shareholding Company 42

2.1.2 The Operating results of Sonadezi Long Thanh Shareholding Company 47

2.1.2.1 The operating results in 2005, 2006 and 9 months 2007 47

2.1.2.2 Some ratios assess the financial stability and business activities results 48

2.1.3 Characteristic of cash in Sonadezi Long Thanh Shareholding Company and relating decisions 49

2.1.3.1 Characteristic of cash in Sonadezi Long Thanh Shareholding Company 49

2.1.3.2 Decision making relate to cash in Sonadezi Long Thanh 51

2.2 Tuong An Vegetable Oil Joint Stock Company (TAC) 52

2.2.1 The introduction of Tuong An Vegetable Oil Joint Stock Company 52

2.2.2 The Operating result of Tuong An Vegetable Oil Joint Stock Company 56

2.2.2.1 The operating result in 2005, 2006 and 9 months 2007 56

2.2.2.2 Some ratios show the financial situation and business activities results 58

2.2.3 Characteristic of current assets in Tuong An Vegetable Oil Joint Stock Company and relating decisions 60

2.2.3.1 Characteristic of Inventory in Tuong An Vegetable Oil Joint Stock

Company 60

2.2.3.2 Decision making relate to inventory in Tuong An Vegetable Oil Joint Stock Company 62

2.2.4 Characteristic of Account Receivables in Tuong An Vegetable Oil Joint Stock Company and relating decisions 63

2.2.4.1 Characteristic of Account Receivables in Tuong An Vegetable Oil Joint Stock Company 63

2.2.4.2 Decision making relate to Account Receivables in Tuong An Vegetable Oil Joint Stock Company 65

2.3 Conclusion 65

CHAPTER 3: APPLICATION OF MATHEMATICS MODELS IN SHORT-TERM INVESTMENT DECISIONS IN SONADEZI LONGTHANH SHAREHOLDING COMPANY AND TUONG AN VEGETABLE OIL JOINT STOCK COMPANY 66

3.1 Apply the cash management model in decision making in Sonadezi LongThanh Shareholding Company 66

3.1.1 The BAT (Baumol) model 66

3.1.1.1 The guideline to apply the BAT (Baumol) model 66

3.1.1.2 Apply the BAT model in determining the target cash balance 67

3.1.2 The Miller – Orr Model 70

3.1.2.1 The guideline to apply the Miller – Orr model 70

3.1.2.2 Apply the Miller – Orr model in determining the target cash balance 71

3.2 Apply the Inventory Management Model and Credit and Receivable Management Model in decision making in Tuong An Vegetable Oil Joint Stock Company 73

3.2.1 The Economic Order Quantity Model 73

3.2.1.1 The guideline to apply the Economic Order Quantity model 73

3.2.1.2 Apply the Economic Order Quantity model in determining the optimal size

of inventory orders 73

3.2.2 Credit and receivables management models 75

3.2.2.1 The guideline to apply the Credit and Receivables Management Models 75

3.2.2.2 Apply the Credit and receivables management model 80

REFERENCES 86

APPENDICES 88

Appendix A: The development of Vietnamese businesses 88

Appendix B: The fact of using mathematics models in short – term investment decisions 95

Appendix C: Number of acting enterprises as of Annual 31 Dec by type of enterprise 106

Appendix D: Number of employees in enterprises as of Annual 31 Dec by type of enterprise 107

Appendix E: Annual average capital of enterprises by type of enterprise 108

Appendix F: Net turnover of enterprises by type of enterprise 109

LIST OF TABLES

Table 1.1: Classification of models 7

Table 1.2: Credit Evaluation Data Compiled by Bassett Furniture Industries 28

Table 1.3: Bassett Furniture Industry’s Analysis of the Decision to Relax Credit Standards by Extending Full Credit to Customers in Credit Risk Group 4 31

Table 1.4: Nike’s Analysis of the Decision to Change Its Credit Terms from “Net 30” to “Net 60” 34

Table 1.5: CBS Record Company’s Analysis of the Decision to Offer a 1 Percent Cash Discount 38

Table 2.1: Capital structure of Sonadezi Long Thanh 45

Table 2.2: Operating results in 2005, 2006 and 9 months 2007 47

Table 2.3: Financial stability and business activities results of SZL 48

Table 2.4: Cash account of Sonadezi Long thanh 50

Table 2.5: Liquidity ratios of Sonadezi Long thanh 50

Table 2.6: Capital structure of Tuong An Vegetable Oil Joint Stock Company 55

Table 2.7: Operating result in 2005, 2006 and 9 months 2007 of TAC 57

Table 2.8: Structure of sales and expenses in 2006 57

Table 2.9: Financial stability and business activities results of TAC 58

Table 2.10: Liabilities structure of TAC 59

Table 2.11: Inventory structure of TAC 60

Table 2.12: Inventory turnover of TAC 61

Table 2.13: Comparison inventory turnover of Tuong An oils and Marvella oils 61

Table 2.14: Comparison inventory turnover between Tuong An oils and Marvella oils 63

Table 2.15: Account receivable turnover of TAC 64

Table 2.16: Comparison account receivable turnover between Tuong An Oils and Marvella Oils 64

Table 3.1: The optimal cash balance of Sonadezi Longthanh from January to June,

2007 68 Table 3.2: Total cost of the optimal cash balance from January to June in 2007 68 Table 3.3: The total cost in optimal cash balance compare with others cash balance

in January 69 Table 3.4: Comparison of the total cost of holding cash in the case of using Baumol model and in the case of basing on experiences 70 Table 3.5: The optimal cash balance of Sonadezi Longthanh from January to June,

2007 72 Table 3.6: The average cash balance of Sonadezi Longthanh from January to June,

2007 72 Table 3.7: The economic order quantity (EOQ) of Tuong An Vegetable Oil Joint Stock Company per year form 2005 - 2007 74 Table 3.8: The total cost of Tuong An Vegetable Oil Joint Stock Company per year form 2005 - 2007 74 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 75 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 81 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” 82 Table 3.12: Tuong An Vegetable Oil Joint Stock Company’s Analysis of the Decision to offer a 1 percent cash discount 84

LIST OF FIGURES

Figure 1.1: The various categories of variables are related 8

Figure 1.2: Cost of holding cash 10

Figure 1.3: Cash Balance for the Company A 11

Figure 1.4: The Miller – Orr Mode 16

Figure 1.5: Costs of holding inventory 23

Figure 1.7: Liberal credit policy model 32

Figure 1.8: Illiberal credit policy model 32

Figure 1.9: Lengthen the credit period model 36

Figure 1.10: Shorten the credit period model 36

Figure 1.11: Increase Cash discount policy model 39

Figure 1.12: Decrease Cash discount policy model 40

Figure 1.13: Credit and receivables management model 41

Figure 2.1: Sonadezi Corporation Structure 44

Figure 2.2: Capital structure of Sonadezi Long Thanh 46

Figure 2.3: Company Organizing Structure of Sonadezi Long Thanh 46

Figure 2.4: Operating results in 2005, 2006 and 9 months 2007 48

Figure 2.5: Tuong An Vegetable Oil Joint Stock Company Ownership 55

Figure 2.6: Company Organizing Structure 56

Figure 2.7: Operating result in 2005, 2006 and 9 months 2007 of TAC 58

Figure 3.1: Liberal credit policy model 76

Figure 3.2: Illiberal credit policy model 77

Figure 3.3: Lengthen the credit period model 78

Figure 3.4: Shorten the credit period model 78

Figure 3.5: Increase Cash discount policy model 79

Figure 3.6: Decrease Cash discount policy model 80

INTRODUCTION

1 NECESSITY OF THE THESIS

In fact, Board of Director and Chief Financial Officer often face with decisions making relate to financial issue, such as how to choose the target cash management, how to manage the inventory, how to management the accounts receivable,…These decisions play an important role, sometime it impact directly on company ‗s success

or failure

From observation the financial management method in some companies, talking with some directors, studying the management experiences in some countries and through the time I work in Sonadezi Longthanh I think we can apply some mathematical models in financial decision making Its gives managers with the analyzing and making decision tool base on scientific and quantitative

So I decide to choose the topic: ―Application of mathematics models in short - term investment decisions‖

2 OBJECTIVE OF THE RESEARCH

The focus of this thesis will be on the researching some mathematical models and how those models can apply in making decision of Director or Chief Financial Officer This thesis has two aims The first aim is to research the way to apply financial models to resolve the issues and find out the best solution for each decision The second aim is to guide to manager apply the models in making decision

3 KEY RESEARCH AREA

Thesis only concentrates on how to use the model in making decision in investment decision in current assets such as: the target cash balance, inventory management, and accounts receivable management These models will be applied in Sonadezi Longthanh Shareholding Company and in Tuong An Vegetable Oil Joint Stock Company

4 METHODOLOGY

Thesis is used methodology of researching the secondary data, primary data, logic reason combination materialistic history, methods in raising the issues, interpretation, analysis and giving the conclusion

Thesis is also used statistic, formula illustration, interpreting the issues means and quantitative method

5 CONTRIBUTIONS OF THE THESIS

The research of this thesis has the important meaning both the science and reality About the science, this thesis chose and improves some theory models appropriate

to conditions and management level of Vietnam

About the reality, this thesis provide for managers the effective tools in analyzing and making decision base on quantitative method and apply mathematical model

6 THESIS STRUCTURE

Topic: ―Application of mathematics models in short - term investment decisions‖ PREFACE

INTRODUCTION

CHAPTER 1: LITERATURE REVIEW

CHAPTER 2: ANALYZING BUSINESS ACTIVITIES OF SONADEZI LONG THANH SHAREHOLDING COMPANY AND TUONG AN VEGETABLE OIL JOINT STOCK COMPANY

CHAPTER 3: APPLICATION OF MATHEMATICS MODELS IN SHORT – TERM INVESTMENT DECISIONS IN SONADEZI LONGTHANH SHAREHOLDING COMPANY AND TUONG AN VEGETABLE OIL JOINT STOCK COMPANY

REFERENCES

APPENDIXES

CHAPTER 1: LITERATURE REVIEW

1.1 Overview of financial decision making

Financial decision making is talked so much in corporate financial management Van Horne and Wachowics (2001) state that financial management interested in buying and selling, financing and asset management follow the general objective The studies by McMahon encompass this thesis that financial management interested in finding the capital to buy the asset and operating the company, analyzing the limited capital for different purposes, guaranteeing the capital is used effectively to get the target

Other researchers such as Brealey and Myers (2003), Ross and other authors (2003) are believed that financial management interesting in investment, financing, asset management to get the target Through the definitions above, we can see the financial decision making have 3 kinds: investment, financing and dividend decisions Besides, there are a lot of decisions relate to company operation but in the field of research, the thesis just study some decisions can quantitative analysis and use the model to make decisions There are some main financial decisions making

1.1.1 Investment decision

Investment decisions are decisions relate to (1) total asset values and the values of each assets (current assets and fixed assets) and (2) the balance between these assets We are used to with the balance sheet in accounting Investment decisions are related to the left hand sight of the balance sheet Concretely as follows:

- Investment decisions in current assets, include:

o Cash management decisions

o Inventory management decisions

o Credit decisions

- Investment decisions in fix assets, include:

o Financing new fixed assets decisions

o Replacing old fixed assets decisions

o Investing in project decisions

o Long – term financial decisions

- The relationship between investing in current assets and investing in fixed assets decisions, include:

o Using operating leverage decisions

o Break – even point decisions

Investment decision is considered the most important decision in financial decision making because it creates the value of firm (Hawawini & Vialiet, 2002) The right investment decision will contribute to increase the value of firm; and the shareholder wealth will increase too Vice versa, the wrong investment decision will decrease the value of firm, so the shareholder wealth decreases

1.1.2 Financing decision

If the investment decisions relate to the left hand sight of the balance sheet then financing decisions relate to the right hand sight of the balance sheet Its relate to chose which source of capital finance to purchase the assets, use owner‘s equity or debt, short term or long term capital In addition, financing decision also consider the relationship between retained earnings and payout earnings by dividend After choosing one kind in those, the second step the manager should make decision how can mobilize that source of capital Concretely as follows:

- Short term financial decisions, include:

o Short term debt or trade credit decisions

o Short term borrowing or commercial paper decisions

- Long term financial decisions, include:

o Long term borrowing: bank loans or bond decisions

o Common Equity or long term debt decisions

o Common equity or preferred equity decisions

- The ratio of total debt to total assets decisions (Financial Leverage)

- Borrowing to buy the assets or leasing decisions

Those above relate to financing decisions in operating of company If manager lack the knowledge of analysis tools before making decision, in order to make the right decision is a big challenge

1.1.3 Dividend decision

The third decision in financial decision making is the disposition of profits or dividend policy In this decision the Chief financial officer (CFO) must be choose between retained earnings or payout earnings by dividend In addition, CFO must

be deciding to use what dividend policy and what effect of dividend policy on the value of firm or stock‘s value on the market

1.1.4 Other decisions

Besides 3 kinds of decisions in financial decision making, there is a lot of other decisions relate to the operations of the business But focus of this thesis will be on the decisions that the model can be applied to make decisions

1.2 Overview about the model building 1

1.2.1 Definition of Models

A model is a simplified representation of an empirical situation Ideally, it strips a natural phenomenon of its bewildering complexity and duplicated the essential behavior of the natural phenomenon with a few variables that are simply related The simpler the model, the better for the decision maker, provided the model serves

as a reasonably reliable counterpart of the empirical problem The advantages of a simple model are:

- It is economical of time and thought

1Bonini, Hausman, Bierman,(1997), Quantitative Analysis for Management (9th Edition), McGraw

- It can be understood readily by the decision maker

- If necessary, the model can be modified quickly and effectively

The object of the decision maker is not to construct a model that is close as possible to reality in every respect Such a model would require an excessive length of time to construct, and then it might be beyond human comprehension Rather, the decision maker wants the simplest model that predicts outcomes reasonably well and is consistent with effective action

 A case or scenario model

 Decision analysis models

Table 1.1: Classification of models

Decision problem

is:

Major variables in a decision problem are

Certain Uncertain Simple Case models Decision analysis

(decision trees) Complex Case models

Linear and integer programming

Simulation

Dynamic Inventory models

PERT or Critical path models

Simulation Inventory models Queuing models

( Sources: Bonini, Hausman, Bierman 1997 Quantitative analysis for management 9 th

Edition New York: McGraw – Hill/ Irwin)

1.2.3 Basic Modeling Concepts

A model is a simplification of a business decision problem The simplification is accomplished by including only important elements and omitting the nonessential consideration Because it is simplified, it is highly useful The factors or variables that the decision maker considers important, includes:

a Decision Variables: the decision variables are those under the control of the decision maker They represent alternative choices for managers These are the major choices, these are the decision variables

b Exogenous variables: exogenous or external variables are those that are important to the decision problem but are controlled by factors outside the purview of the decision maker Generally, economic conditions, actions of competitors, prices of raw materials and similar factors are exogenous variables

c Policies and constraints: A decision maker often operates within constraints imposed by company policy, legal restraints or physical limitations For example, there may be limited capacity available in the plant, and this may restrict the sales that can be made

d Performance measures: In making a decision, managers have goals or objectives that they are trying to achieve Criteria or performance measures are quantitative expression of these objectives

e Intermediate variables: A number of other variables are usually needed to include all the important factors in the decision problem Often these are accounting variables that relate to cost or revenue factors They are used to relate the decision variables and exogenous variables to the performance measures They are thus intermediate variables in the sense that they are between the other variables

Figure 1.1 show how the various categories of variables are related Decision variables, exogenous variablea and policies and constraints are input to the model, and performance measures are outputs The model itself represents the set of all relationships among the variables

Figure 1.1: The various categories of variables are related

Model set of relationships

Exogenous variables

Decision variables

Policies and constraints

Performance measures

1.2.4 The method to set up a model and apply in the financial decision making

Depend on the simple or complex problems and the aim of decision maker, the model can be a simple models, complex models or very complex models These steps to set up a model:

Step 1: define the aim or the nature of decision

Step 2: define the variables affect decision

Step 3: define the relationship among the variables and the aim of decision (Set up the model)

Step 4: input the data of variables into the model, check the result

Step 5: change the data of variables and check again effect on the result

1.3 Models using in investment decisions in current assets

In the field of research, the thesis just study some model using in investment decisions in current assets, include:

- Cash management decisions

- Inventory management decisions

- Credit decisions

1.3.1 Determining the target cash balance 2

Target cash balance: involves a trade-off between the opportunity costs of holding too much cash (the carrying costs) and the costs of holding too little (the shortage costs, also called adjustment costs) The nature of these costs depends on the firm‘s working capital policy

If the firm has a flexible working capital policy, then it will probably maintain a marketable securities portfolio In this case the adjustment, or shortage, costs will be the trading costs associated with buying and selling securities If the firm has a restrictive working capital policy, it will probably borrow in the short term to meet

th

cash shortages The costs in this case will be the interest and other expenses associated with arranging a loan

Figure 1.2 presents the cash management problem for our flexible firm If a firm tries to keep its cash holdings too low, it will find itself running out of cash more often than is desirable, and thus selling marketable securities (and perhaps later buying marketable securities to replace these sold) more frequently than would be the cash balance were higher Thus, trading costs will be high when the cash balance is small These costs will fall as the cash balance becomes larger

Figure 1.2: Cost of holding cash

In contrast, the opportunity costs of holdings cash are very low if the firm holds very little cash These costs increase as the cash holdings rise because the firm is giving up more and more interest that could have been earned

Figure 1.2, the sum of the costs is given by the total cost curve As show, the

minimum total cost occurs where the two individual cost curves cross at point C*

At this point, the opportunity costs and the trading costs are equal This point represents the target cash balance, and it is the point the firm should try to find

Cost of holding cash

1.3.1.1 The BAT model

The Baumol – Allais – Tobin (BAT) model is a classic means of analyzing our cash management problem This model can be used to actually build the target cash balance It is a straightforward model and very useful for illustrating the factors in cash management and, more generally, current asset management

To develop the BAT model, suppose Company A starts off at week 0 with a cash balance of C = $1.2 million Each week, outflows exceed inflows by $600,000 As

a result, the cash balance will drop to zero at the end of week 2 The average cash balance will be the beginning balance ($1.2 million) plus the ending balance ($0) divided by 2, or ($1.2 million + 0)/2 = $600,000, over the two – week period At the end of week 2, Company A replenishes its cash by depositing another $1.2 million

As we have described, the cash management strategy for Company A is very simple and boils down to depositing $1.2 million every two weeks This policy is shown in Figure 1.3 Notice how the cash balance declines by $600,000 per week Because the company brings the account up to $1.2 million, the balance hits zero every two weeks This result in the saw tooth pattern displayed in Figure 1.3

Figure 1.3: Cash Balance for the Company A

Implicitly, we assume that the net cash outflow is the same every day and that it is known with certainty These two assumptions make the model easy to handle We will indicate what happens when they do not hold

If C were set higher, say, at $2.4 million, cash would last four weeks before the firm would have to sell marketable securities, but the firm‘s average cash balance would

in- crease to $1.2 million (from $600,000) If C were set at $600,000, cash would

run out in one week, and the firm would have to replenish cash more frequently, but the average cash balance would fall from $600,000 to $300,000

Because transactions costs (for example, the brokerage costs of selling marketable securities) must be incurred whenever cash is replenished, establishing large initial balances will lower the trading costs connected with cash management However, the larger the average cash balance, the greater is the opportunity cost (the return that could have been earned on marketable securities)

To determine the optimal strategy, Company A needs to know the following three things:

F The fixed cost of making a securities trade to replenish cash

T The total amount of new cash needed for transactions purposes over the

relevant planning period, say, one year

R The opportunity cost of holding cash This is the interest rate on marketable

securities

a The Opportunity Costs

To determine the opportunity costs of holding cash, we have to find out how much interest is forgone Company A has, on average, C/2 in cash This amount could be earning interest at rate R So the total dollar opportunity costs of cash balances are equal to the average cash balance multiplied by the interest rate:

Opportunity costs = (C/2) x R

For example, the opportunity costs of various alternatives are given here assuming that the interest rate is 10 percent:

Initial Cash Balance Average Cash Balance Opportunity Cost

the opportunity costs increase as the initial (and average) cash balance rises

b The Trading Costs

To determine the total trading costs for the year, we need to know how many times Company A will have to sell marketable securities during the year First of all, the total amount of cash disbursed during the year is $600,000 per week, so T =

$600,000 x 52 weeks = $31.2 million If the initial cash balance is set at C = $1.2 million, then Company A will sell $1.2 million in marketable securities T/C =

$31.2 million/1.2 million = 26 times per year It costs F dollars each time, so trading costs are given by:

Total Amount of

Disbursements

during Relevant Period

Initial Cash Balance

Trading Costs (F = $1,000)

c The Total Cost

Now that we have the opportunity costs and the trading costs, we can calculate the total cost by adding them together:

Total cost = Opportunity costs + Trading costs

300,000 15,000 104,000 119,000

Notice how the total cost starts out at almost $250,000 and declines to about

$82,000 before starting to rise again

d The Solution

We can see from the preceding schedule that a $600,000 cash balance results in the lowest total cost of the possibilities presented $82,000 But what about $700,000 or

$500,000 or other possibilities? It appears that the optimum balance is somewhere between $300,000 and $1.2 million With this in mind, we could easily proceed by trial and error to find the optimum balance It is not difficult to find it directly, however, so we do this next

Take a look back at Figure 1.2 As the figure is drawn, the optimal size of the cash balance, C*, occurs right where the two lines cross At this point, the opportunity costs and the trading costs are exactly equal So, at C*, we must have that:

Opportunity costs = Trading costs

For Company A, we have T = $31.2 million, F = $1,000, and R = 10%

We can now find the optimum cash balance:

C* = (2 x $31,200,000 x 1,000)/.10 = $624 billion = $789,937

We can verify this answer by calculating the various costs at this balance, as well

as a little above and a little below:

Cash Balance Opportunity

Costs

$850,000 $42,500 $36,706 $79,206 800,000 40,000 39,000 79,000

750,000 37,500 41,600 79,100 700,000 35,000 44,571 79,571

The total cost at the optimum cash level is $78,994, and it does appear to increase

as we move in either direction

e Conclusion

The BAT model is possibly the simplest and most stripped-down sensible model for determining the optimal cash position Its chief weakness is that it assumes steady, certain cash outflows

1.3.1.2 The Miller – Orr Model: A more general Approach

Different with Baumol, Merton Miller and Daniel Orr develop the target cash balance model with cash inflows and outflows that fluctuate randomly from day to day With this model, we again concentrate on the cash balance, but, in contrast to the situation with the BAT model, we assume that this balance fluctuates up and down randomly and that the average change is zero

Figure 1.4: The Miller – Orr Mode

U* is the upper control limit L is the lower control limit The target cash balance

is C* As long as cash is between L and U*, no transaction is made

Cash

Cash

L C*

U*

Cash balance

a The Basic Idea

Figure 1.4 shows how the system works It operates in terms of an upper limit to the amount of cash (U*) and a lower limit (L), and a target cash balance (C*) The firm allows its cash balance to walk around between the lower and upper limits As long as the cash balance is somewhere between U* and L, nothing happens

When the cash balance reaches the upper limit (U*), such as it does at Point X, the firm moves U* - C* dollars out of the account and into marketable securities This action moves the cash balance down to C* In the same way, if the cash balance falls

to the lower limit (L), as it does at Point Y, the firm will sell C* - L worth of

securities and deposit the cash in the account This action takes the cash balance up

to C*

b Using the Model

To get started, management sets the lower limit (L) This limit essentially defines a

safety stock; so, where it is set depends on how much risk of a cash shortfall the firm is willing to tolerate Alternatively, the minimum might just equal a required compensating balance

As with the BAT model, the optimal cash balance depends on trading costs and opportunity costs Once again, the cost per transaction of buying and selling

marketable securities, F, is assumed to be fixed Also, the opportunity cost of holding cash is R, the interest rate per period on marketable securities

The only extra piece of information needed is σ2 the variance of the net cash flow per period For our purposes, the period can be anything, a day or a week, for example, as long as the interest rate and the variance are based on the same length

of time

Given L, which is set by the firm, Miller and Orr show that the cash balance target,

C*, and the upper limit, U*, that minimize the total costs of holding cash are:3

U* = 3 x C* - 2 x L

Also, the average cash balance in the Miller-Orr model is:

Average cash balance = (4 x C* - L)/3

The derivation of these expressions is relatively complex, so we will not present it here Fortunately, as we illustrate next, the results are not difficult to use

For example, suppose F = $10, the interest rate is 1 percent per month, and the

standard deviation of the monthly net cash flows is $200 The variance of the monthly net cash flows is:

Finally, the average cash balance will be:

Average cash balance = (4 x C* - L)/3

= (4 x $411 - 100)/3 = $515

1.3.1.3 Implications of the BAT and Miller-Orr Models

Two cash management models differ in complexity, but they have some similar implications In both cases, all other things being equal, we see that:

1 The greater the interest rate, the lower is the target cash balance

2 The greater the order cost, the higher is the target balance

These implications are both fairly obvious The advantage of the Miller-Orr model

is that it improves our understanding of the problem of cash management by considering the effect of uncertainty as measured by the variation in net cash inflows

The Miller-Orr model shows that the greater the uncertainty is (the higher σ 2 is), the greater is the difference between the target balance and the minimum balance Similarly, the greater the uncertainty is, the higher is the upper limit and the higher

is the average cash balance These statements all make intuitive sense For example, the greater the variability is, the greater is the chance that the balance will drop below the minimum We thus keep a higher balance to guard against this happening

1.3.1.4 Other Factors Influencing the Target Cash Balance

First, in our discussion of cash management, we assume that cash is invested in marketable securities such as Treasury bills The firm obtains cash by selling these securities Another alternative is to borrow cash Borrowing introduces additional considerations to cash management:

1 Borrowing is likely to be more expensive than selling marketable securities because the interest rate is likely to be higher

2 The need to borrow will depend on management‘s desire to hold low cash balances

A firm is more likely to have to borrow to cover an unexpected cash outflow the greater its cash flow variability and the lower its investment in marketable securities

Second, for large firms, the trading costs of buying and selling securities are very small when compared to the opportunity costs of holding cash For example, suppose a firm has $1 million in cash that won‘t be needed for 24 hours Should the firm invest the money or leave it sitting?

Suppose the firm can invest the money at an annualized rate of 7.57 percent per year The daily rate in this case is about two basis points (.02 percent or 0002)4 The daily return earned on $1 million is thus 0002 x $1 million = $200 In many cases, the order cost will be much less than this; so a large firm will buy and sell securities very often before it will leave substantial amounts of cash idle

1.3.2 Inventory management decisions 5

Inventories represent a significant investment for many firms For a typical manufacturing operation, inventories will often exceed 15 percent of assets For a retailer, inventories could represent more than 25 percent of assets

Despite the size of a typical firm‘s investment in inventories, the financial manager

of a firm will not normally have primary control over inventory management Instead, other functional areas such as purchasing, production, and marketing will usually share decision-making authority regarding inventory Inventory management has become an increasingly important specialty in its own right, and financial management will often only have input into the decision

a Inventory Types

For a manufacturer, inventory is normally classified into one of three categories

The first category is raw material This is whatever the firm uses as a starting

point in its production process Raw materials might be something as basic as iron ore for a steel manufacturer or something as sophisticated as disk drives for a computer manufacturer

The second type of inventory is work-in-progress, which is just what the name

suggests—unfinished product How big this portion of inventory is depends in large part on the length of the production process For an air-frame manufacturer, for example, work-in-progress can be substantial

4

A basis point is 1 percent of 1 percent Also, the annual interest rate is calculated as (1 - R)365

= 1.0757, implying a daily rate of 02 percent.

5

Ross and et al, (2003), Fundamentals of Corporate Finance, 6

th

Edition, McGraw-Hill/Irwin.

The third and final type of inventory is finished goods, that is, products ready to

ship or sell

There are three things to keep in mind concerning inventory types First, the names for the different types can be a little misleading because one company‘s raw materials can be another‘s finished goods For example, going back to our steel manufacturer, iron ore would be a raw material, and steel would be the final product An auto body panel stamping operation will have steel as its raw material and auto body panels as its finished goods and an automobile assembler will have body panels as raw materials and automobiles as finished products

The second thing to keep in mind is that the various types of inventory can be quite different in terms of their liquidity Raw materials that are commodity-like or relatively standardized can be easy to convert to cash Work-in-progress, on the other hand, can be quite illiquid and have little more than scrap value As always, the liquidity of finished goods depends on the nature of the product

Finally, a very important distinction between finished goods and other types of

inventories is that the demand for an inventory item that becomes a part of another

item is usually termed derived or dependent demand because the firm‘s need for

these inventory types depends on its need for finished items In contrast, the firm‘s demand for finished goods is not derived from demand for other inventory items,

so it is sometimes said to be independent

b Inventory Costs

There are two basic types of costs associated with current assets in general and

with inventory in particular The first of these is carrying costs Here, carrying

costs represent all of the direct and opportunity costs of keeping inventory on hand These include:

1 Storage and tracking costs

2 Insurance and taxes

3 Losses due to obsolescence, deterioration, or theft

4 The opportunity cost of capital on the invested amount

The sum of these costs can be substantial, ranging roughly from 20 to 40 percent of inventory value per year

The other type of costs associated with inventory is shortage costs Shortage costs

are costs associated with having inadequate inventory on hand The two components

of shortage costs are restocking costs and costs related to safety reserves Depending

on the firm‘s business, restocking or order costs are either the costs of placing an order with suppliers or the costs of setting up a production run The costs related to safety reserves are opportunity losses such as lost sales and loss of customer goodwill that result from having inadequate inventory

A basic trade-off exists in inventory management because carrying costs increase with inventory levels, whereas shortage or restocking costs decline with inventory levels The basic goal of inventory management is thus to minimize the sum of these two costs

How important it is to balance carrying costs with shortage costs, consider the case of networking equipment manufacturer Cisco In 2000, Cisco found itself chronically short of key parts, and sales were suffering as a result Cisco began stocking up, agreeing to buy parts as far as six months in advance But, about the time that the parts began to arrive, sales unexpectedly slowed dramatically Suddenly, Cisco had a 12-month plus supply of parts, with no use for much of it The

result? In the spring of 2001, Cisco had to write off $2.25 billion in excess

inventory

c The Economic Order Quantity Model

The economic order quantity (EOQ) model is the best-known approach for explicitly establishing an optimal inventory level The basic idea is illustrated in Figure 1.5, which plots the various costs associated with holding inventory (on the vertical axis) against inventory levels (on the horizontal axis) As shown, inventory carrying costs rise and restocking costs decrease as inventory levels increase With the EOQ

model, we will attempt to specifically locate the minimum total cost point, Q*

Total costs of holding inventory

An important point to keep in mind is that the actual cost of the inventory itself is

not included The reason is that the total amount of inventory the firm needs in a

given year is dictated by sales What we are analyzing here is how much the firm should have on hand at any particular time More precisely, we are trying to determine what order size the firm should use when it restocks its inventory

d Inventory Depletion

To develop the EOQ, we will assume that the firm‘s inventory is sold off at a steady rate until it hits zero At that point, the firm restocks its inventory back to some optimal level For example, suppose the Company A starts out today with 3,600 units of a particular item in inventory Annual sales of this item are 46,800 units, which is about 900 per week If Company A sells off 900 units of inventory each week, then, after four weeks, all the available inventory will be sold, and Company A will restock by ordering (or manufacturing) another 3,600 and start over This selling and restocking process produces a saw-tooth pattern for inventory holdings; this pattern is illustrated in Figure 1.6 As the figure shows, Company A always starts with 3,600 units in inventory and ends up at zero On average, then, inventory is half of 3,600, or 1,800 units

Figure 1.5: Costs of holding inventory

Weeks

Restocking costs are greatest when the firm holds a small quantity of inventory

Carrying costs are greatest when there is a large quantity of inventory on hand

Total costs are the sum of the carrying costs and restocking costs

Figure 1.6: Inventory Holding for the Company A

The Carrying Costs

As Figure 3.6 illustrates, carrying costs are normally assumed to be directly

proportional to inventory levels Suppose we let Q is the quantity of inventory that

Company A orders each time (3,600 units); we will call this the restocking quantity

Average inventory would then just be Q/2, or 1,800 units If we let CC be the

carrying cost per unit per year, Company A‘s total carrying costs will be:

Total carrying costs = Average inventory x Carrying costs per unit

= (Q/2) x CC

In Company A‘s case, if carrying costs were $0.75 per unit per year, then total carrying costs would be the average inventory of 1,800 multiplied by $0.75, or

$1,350 per year

The Shortage Costs

For now, we will focus only on the restocking costs In essence, we will assume that the firm never actually runs short on inventory, so that costs relating to safety reserves are not important We will return to this issue later

Restocking costs are normally assumed to be fixed In other words, every time we place an order, there are fixed costs associated with that order (remember that the

cost of the inventory itself is not considered here) Suppose we let T be the firm‘s total unit sales per year If the firm orders Q units each time, then it will need to place a total of T/Q orders For Company A, annual sales are 46,800, and the order

size is 3,600 Company A thus places a total of 46,800/3,600 = 13 orders per year

If the fixed cost per order is F, the total restocking cost for the year would be:

Total restocking cost = Fixed cost per order x Number of orders

= F x (T/Q)

For Company A, order costs might be $50 per order, so the total restocking cost for

13 orders would be $50 x 13 = $650 per year

The Total Costs

The total costs associated with holding inventory are the sum of the carrying costs and the restocking costs:

Total costs = Carrying costs + Restocking costs

x 2

This reorder quantity, which minimizes the total inventory cost, is called the

economic order quantity (EOQ) For the Company A Corporation, the EOQ is:

Q* =

CC

F

x 2T

=

0.75

50

x 46,800

x 2

= 2,498 units Thus, for Company A, the economic order quantity is 2,498 units At this level, verify that the restocking costs and carrying costs are both $936.75

1.3.3 Accounts receivable management 6

Accounts receivable consist of the credit a business grants its customers when selling goods or services 7 They take the form of either trade credit, which the company extends to other companies, or consumer credit, which the company extends to its ultimate consumers 8 The effectiveness of a company‘s credit policies can have a significant impact on its total performance For example, Monsanto‘s credit manager has estimated that a reduction of only one day in the average collection period for the company‘s receivables increases its cash flow by $10 million and improves pretax profits by $1 million

For a business to grant credit to its customers, it has to do the following:

- Establish credit and collection policies

- Evaluate individual credit applicants

Shareholder Wealth and Optimal Investments in Accounts Receivable

When a company decides to extend credit to customers, it is making an investment decision; namely, an investment in accounts receivable, a current asset A company will maximize shareholder wealth by investing in accounts receivable as long as the expected marginal returns obtained from each additional dollar of receivables investment exceed the associated expected marginal costs of the investment, including the cost of the funds invested

The establishment of an optimal credit extension policy requires the company to examine and attempts to measure the marginal costs and marginal returns (benefits) associated with alternative policies What are the marginal returns and costs associated with a more liberal extension of credit to a company‘s customers? With respect to returns, a more liberal extension presumably stimulates sales and leads to

increased gross profits, assuming that all other factors (such as economic conditions, prices, production costs, and advertising expenses) remain constant Offsetting these increased returns are several types of credit-related marginal costs, including the opportunity costs of the additional capital funds employed to support the higher level

of receivables Checking new credit accounts and collecting the higher level of receivables also results in additional costs And finally, a more liberal credit policy frequently results in increased bad-debt expenses because a certain number of new accounts are likely to fail to repay the credit extended to them

In determining an optimal credit extension policy, a company‘s financial managers must consider a number of major controllable variables that can be used to alter the level of receivables, including the following:

- Credit standards

- Credit terms

- Collection efforts

1.3.3.1 Credit Standards

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 process of setting credit standards allows the firm to exercise a degree of control over the ―quality‖ of accounts accepted 9.The quality of credit extended to customers

is a multidimensional concept involving the following:

1 The time a customer takes to repay the credit obligation, given that it is repaid

2 The probability that a customer will fail to repay the credit extended to it

The average collection period serves as one measure of the promptness with which customers repay their credit obligations It indicates the average number of days a company must wait after making a credit sale before receiving the customer‘s cash payment Obviously, the longer the average collection period, the higher a

9

Complete control over the quality of accounts accepted generally is impossible due to uncertainty about future events (for example, a recession or a strike) that could make it difficult or even

company‘s receivables investment and, by extension, its cost of extending credit to customers

The likelihood that a customer will fail to repay the credit extended to it is sometimes referred to as default risk The bad-debt loss ratio, which is the proportion

of the total receivables volume a company never collects, serves as an overall, or aggregate, measure of this risk A business can estimate its loss ratio by examining losses on credit that has been extended to similar types of customers in the past 10The higher a firm‘s loss ratio, the greater is the cost of extending credit

Table 1.2: Credit Evaluation Data Compiled by Bassett Furniture Industries

Credit risk

group

Credit sales ($)

Average Collection Period (Days)

Bad-debt loss ratio (%)

The first step in making this decision involves an evaluation of the overall creditworthiness of the company‘s existing and potential customers (retailers) using

10

This estimation procedure assumes that the loss ratio does not change significantly over time because of changing economic conditions Otherwise, the loss ratio should be adjusted to take account of expected future economic changes This procedure also assumes that credit extension and repayment information is available on a sufficiently large sample of accounts to provide a company with a reliable estimate of its loss ratio

various sources of information Table 1.2 illustrates the credit sales, average collection period, and loss ratio data for various credit risk groups of the company‘s customers in its northwest region

Under its current credit policy, Bassett extends unlimited credit to all customers in Credit Risk Groups 1, 2, and 3 and no credit to customers in Groups 4 and 5, meaning that the customers in these latter two groups must submit payment along with their orders As a result of this policy, Bassett estimates that it ―loses‖ $300,000 per year in sales from Group 4 customers and $100,000 per year in sales from Group

5 customers 11

Bassett also estimates that its variable production, administrative, and marketing costs (including credit department costs) are approximately 75 percent of total sales; that is, the variable cost ratio is 0.75 12

Thus, the profit contribution ratio per dollar of sales is 1.0 - 0.75 = 0.25 or 25 percent The company‘s required pretax rate of return (that is, the opportunity cost)

on its current assets investment is 20 percent

One alternative Bassett is considering is to relax credit standards by extending full credit to Group 4 customers Bassett estimates that an additional inventory investment (i.e., raw materials, work-in-process, and finished goods) of $120,000 is required to expand sales by $300,000 In evaluating this alternative, the financial manager has to analyze how this policy would affect pretax profits If the marginal returns of this change in credit standards exceed the marginal costs, pretax profits would increase, and the decision to extend full credit to the Group 4 customers would increase shareholder wealth

Table 1.3 contains the results of this analysis In Step A, the marginal profitability of the additional sales, $75,000, is calculated Next, the cost of the additional

Without this information, the financial manager simply has to make an ―educated guess‖ as to the size of the loss ratio

11

Estimates of variables, such as sales, the average collection period, and the bad-debt loss ratio, are used in the analysis of credit policy decisions These estimates are subject to uncertainty Sensitivity analysis can be performed to determine the effect on profitability of different estimates of one (or more) of these variables

12 This analysis assumes that the collection costs for Credit Risk Group 4 customers are the same as for

investment in receivables, $9,863, is calculated in Step B13.In Step C, the additional bad-debt loss, $21,000, is computed Then, the cost of the additional investment in inventory, $24,000, is calculated in Step D Finally, in Step E, the net change in pretax profits is determined by deducting the marginal costs computed in Steps B, C, and D from the marginal returns found in Step A Because this expected net change

is a positive $20,137, the analysis indicates that Bassett should relax its credit standards by extending full credit to the Group 4 customers

This analysis contains a number of explicit and implicit assumptions of which the financial manager must be aware One assumption is that the company has excess capacity and thus could produce the additional output at a constant variable cost ratio

of 0.75 If the company currently is operating at or near full capacity, and additional output could be obtained only by paying more costly overtime rates and/or investing

in new facilities, this analysis would have to be modified to take account of these incremental costs This analysis also assumes that the average collection period of the customers in Groups 1, 2, and 3 would not increase once the company began extending credit to Group 4 customers If it became known that the Group 4 customers had 60 days or more to pay their bills with no penalty involved, the Group

1, 2, and 3 customers, who normally pay their bills promptly, might also start delaying their payments If this occurred, the analysis would have to be modified to account for such shifts It also was assumed that the required rate of return on the investment in receivables and inventories for Group 4 does not change as a result of extending credit to these more risky accounts A case can be made for increasing the required rate of return to compensate for the increased risk of the new accounts Finally, this example assumes that an increase in inventory investment is necessary

as a result of changes in the firm‘s credit policy In summary, for this type of analysis to be valid and to lead to the correct decision, it must include all the marginal costs and benefits that result from the decision

13 Note that we have chosen to use sales value in determining the (opportunity) cost of the additional receivables investment

Table 1.3: Bassett Furniture Industry’s Analysis of the Decision to Relax Credit Standards by Extending Full Credit to Customers in Credit Risk Group 4

Marginal profitability of additional sales

= Profit contribution ratio X Additional sales

Step B: Additional investment in receivables

= Additional average daily sales* X Average collection period

=

365

sales annual Additional

Cost of the additional investment in receivables

= Additional investment in receivables X Required pretax

rate of return

Step C: Additional bad-debt loss

= Bad-debt loss ratio X Additional sales

Cost of the additional investment in inventory

=Additional investment in inventory X Required pretax rate of

return

Step E: Net change in pretax profits

= Marginal returns - Marginal costs

= A - (B + C + D)

= $75,000 - ($9,863 + $21,000 + $24,000) +$20,137

*Standard practice is to assume that there are 365 days per year