A Goal Programming Model for Public Accounting Firms

A Goal Programming Model for Public Accounting Firms

Uday Kumar K N

Department of Mathematics,

Reva Institute of Technology and Management, Yelahanka, Bangalore, Karnataka, India.

Harish Babu G A

Department of Mathematics,

Reva Institute of Technology and Management, Yelahanka, Bangalore, Karnataka, India.

E Keshava Reddy Department of Mathematics, JNTU Anantapur, Anantapur, Andhra Pradesh, India.

Abstract:- The purpose of this paper is to indicate the usefulness of a management science tool to the problem of planning in public accounting firms. Specifically, an attempt will be made to relate goal programming to a planning problem of a public accounting firms.

Key Words:- Public accounting, Goal Programming

INTRODUCTION

Public accountants have, for years, encouraged clients to implement formal planning programs as an aid in the development of the business. However, until the past decade few accountants had implemented formal planning programs for their own practices. Because of this defi- ciency, witnessed the promulgation of written material in the area of planning for public accounting firms by the Institute of Certified Public Accountants and by individual accounting practitioners.[8].Even though most of these publications emphasize the necessity for formal planning by public accounting firms, many firms still have not seriously considered such programs. The professional firm simply cannot continue to ignore planning since it enables a firm to function more effectively and efficiently, to render better services to its clients, and to meet the challenge of a dynamic future [9].Once a firm accepts the concept of planning in future growth deliberations, the footnote-cited publications offer useful guidance to the practitioner concerned with development of an approach to the planning process. For example, Robert Ellyson[9] recommends the following four-step approach to the planning process:

1. Determine the tentative general goals

2. Study the past and present situations and, based on these, project what the future

   will be, assuming the trend continues

3. Define specific goals and tools for implementation and

4. Design a reporting system and updating procedures

   Although the need for formal planning is important to all accounting firms, it is critical in the larger firms. Planning in large accounting firms has become an ex- tremely complex task, just as it has in industrial firms. Company management which public accountants serve

   increasingly have turned to modern management techniques, especially management science tools, as aids in planning and efficiently administering their limited resources. The purpose of this paper is to indicate the use- fulness of a management science tool to the problem of planning in public accounting firms. Specifically, an attempt will be made to relate goal programming to a planning problem of a public accounting firm. Specifically, an attempt will be made to relate goal programming to a problem of a public accounting firm. With this goal in mind, a discussion of the goal programming technique was presented.

   Goal programming, representing a special extension of linear programming, was discovered initially by A. Charnes and W. W. Cooper in their research of linear programming. These authors first introduced goal programming in their highly successful book, Management Models and Industrial Applications of Linear Programming, as a means of considering unsolvable linear programming problems.[4]. Ijiri Y. published a book on the goal programming technique in which he refined and reinforced the general notion of goal programming.[6] As a result of these efforts, goal programming has become an operational mathematical programming model.

   As a practical technique, the goal programming approach first was applied by Charnes and others to advertising media planning.[6] This initial application was followed by those in the areas of manpower planning and aggregate production planning More recently, others have explored the application of goal programming to the areas of portfolio management, municipal planning, and hospital administration[2]. Indeed goal programming is a relatively new technique, and its true potential has yet to be realized. The rather recent development of effective computer programs for the goal programming solution, the lack of which had hindered the technique's application in the past, has opened the avenues for possible application of this quantitative method to the more complicated management problems

   DATA OF THE PROBLEM

   This study was carried out to designing a goal program- ming planning model for a public accounting firm in Hyderabad. The model to be designed is limited to the planning horizon of one year, although once a model for one year is developed, it could subsequently be expanded for a longer planning horizon. In addition to the limited planning horizon, certain other simplifications have been made. For example, the model is concerned only with the firm's audit function, although tax and management services functions could be added; the goals of the firm are not necessarily indicative of the goals any specific public

   accounting firm might have (and are not necessarily in the most desirable order for every firm); and possibly other factors which do not lend themselves easily to quantification, but which must be considered by firms n their planning processes, are absent from the model. Despite these obvious limitations, the model presented here should illustrate how the general goal programming ap- proach may be applied to assist public accounting firms in their planning. Tables 1, 2, and 3 outline the information pertaining to the accounting firm needed for the model design.

   TABLE-1

   AUDIT PERSONNEL, WORKING HOURS, BILLING RATES AND GROSS AUDIT FEES

   Position	Number Employed	Working Total Hr/ Chargeable chargeable Noncharge Noncharge Billing Hr per position Hrs per Hr/Posi- able Hr/ able Hr/ Rates/Hr Individual year Individual tion/Year Individual Position/ Per Year (50 weeks) Per Year /year Year
   Partner	3	2500 7,500 2000 6,000 500	1500	Rs40
   Manager	6	2250 13,500 2000 12,000 250	1500	Rs30
   Senior	12	2250 27,000 2100 25,000 150	1800	Rs20
   Staff	30	2000 60,000 1900 57,000 100	3000	Rs15
   Gross Audit Fees Earned for the Past Year:
   Partner: 6,000 hr @ Rs 40/hr = Rs 2,40,000
   Manager: 12,000 hr @ Rs 30/hr = Rs 3,60,000
   Senior: 25,000 hr @ Rs 20/hr = Rs 5,04,000
   Staff: 57,000 hr @ Rs 15/hr = Rs 8,55,000
   Total Rs 19,59,000

   TABLE-2

   PROJECTED INFORMATION FOR NEXT YEAR BASED ON THE GOALS SET BY THE FIRM

   1. Chargeable Hours (an increase of 5%)

      Partner:	6,000 105% =	6,300
      Manager:	12,000 105% =	12,600
      Senior:	25,200 105% =	26,460
      Staff:	57,000 105% =	59,850

      Total 1,05,210

   2. Total Hours by Position

      Partner	Chargeable	Nonchargeable	Total
      Partner:	6,300	1,500	7,800
      Manager:	12,600	1,500	14,100
      Senior:	26,460	1,800	28,260
      Staff:	59,850	3,000	62,850

      Total Rs1,13,010

   3. Billing Rates/Hour (an increase of 5%) Partner: Rs 40 105% = Rs 42.00

TABLE-3 PROJECTED REVENUES AND EXPENSES

1. Gross Audit Fees

3. Other Expenses

Estimated amount for rent, depreciation, dues Insurance, secretarial salaries,

supplies and other expenses Rs 1, 350,000

Variables:

Let,

GOAL PROGRAMMING MODEL

chargeable hours by 5%, the firm must obtain new clients. A few of the means by which new clients may be obtained are referrals from present clients, speaking engagements by

X1= Number of audit partners required X2= Number of audit managers required X3= Number of audit seniors required X4= Number of audit staff required

Y1= New hourly billing rate for partners Y2= New hourly billing rate for managers Y3= New hourly billing rate for seniors Y4= New hourly billing rate for staff

Z1= Chargeable-hours from clients in the 0-1000 chargeable hour range

Z2= Chargeable-hours from clients in the 1001-5000 chargeable hour range

Z3= Chargeable-hours from clients in the over 5000 chargeable hour range

Z4= Average chargeable-hours from each type Z3 client.

The Goal constraints are developed as follows:

1. Gross Audit Fees and Related goals. A goal set by the firm is to increase gross audit fees by approximately 10% over the past year. The achievement of this goal is dependent on three interrelated subgoals: (1) to increase chargeable hours by 5%; (2) to maintain the present level of total nonchargeable hours per personnel classification; and (3) to increase the hourly billing rates per classification by 5%.

   The partners in charge of the firms planning function have decided that in order to achieve the subgoal of increasing

   partners and other qualified people in the firm, and the publication of articles in accounting and business journals. All of these approaches require non-chargeable time to be spent by the firm's personnel.

   To achieve the subgoal of increasing the hourly billing rates per classification by 5% over the past year, the firm's planning group believes that it is necessary to upgrade their auditing services. The primary means of upgrading services are to conduct professional development courses for the audit personnel and to engage in research aimed toward advancing the firm's auditing techniques. Quality services are also a prerequisite for obtaining new clients.

   The planning group has determined that the present level of nonchargeable hours per position is adequate to provide the time necessary for obtaining the new clients, the upgrading of services, and the administrative work required to realize the projected increase in chargeable hours and billing rates. By maintaining total nonchargeable hours at the present level, the firm's efficiency will be increased. The increase in audit personnel necessitated by the increase in chargeable hours will reduce nonchargeablc hours per employee.

   1. Personnel Requirement

      –

      –

      +

      +

      The constraints for the number of audit personnel required (see Tables 1 and 2), where di represents working hours under the projected requirement and di represents working

      hours in excess of the projected requirement, may be expressed as:

      5

      5

      Y1 d5 d

      Rs42.00

      7

      7

      2500X1 d1 d1 7800

      6

      6

      Y2 d6 d

      Rs31.50

      2250X 2

      • d2

      • d

        14,100

        Y3 d7

      • d

        Rs21.00

        2

        2

        2250X

        d d 28,260

        Y d d Rs15.75

        3 3 3 4 8 8

        2000X 4 d4 d4 62,850

   2. Billing Rates

      i

      i

      The constraints for the new hourly billing rates, where di- represents under-achievement of the projected billing rates (see Table 2) and d + represents over-achievement of the projected billing rates, may be expressed as:

   3. Gross Audit Fees

   i

   i

   i

   i

   The goal of a 10% increase in gross audit fees, where d – represents underachievement of this goal & d + represents overachievement, may be expressed as (see Table 2 & Table 3):

   6300Y1

   12,600Y2

   26460Y3

   59,850Y4

   • d9

     • d9

     Rs2,159,798

     +

     +

2. Management /Staff Ratio. The planning group believes that it is desirable to maintain a ratio of at least one management personnel (partners and managers) to every five staff men (seniors and staff). This constraint, where di- represents over achievement of the desired ratio and di represents underachievement, becomes:

   di = chargeable hours from each classification of clients in excess of the desirable

   +

   +

   distribution

   In addition to these constraints, it is desired that no one client account for more than 20% of the firm's total revenue, which may be expressed in terms of chargeable hours if it is assumed, for purposes of simplification, that

   X 3 X 4

   5X1

   5X 2

   d10

   0

   0

   • d

   • d

   10

   each job requires a constant proportion of hours from each personnel classification. This constraint, which is relevant only for chargeable hours from clients in the over-5000

3. Distribution of Clients. Another firm goal set by the

   planning group is the attainment, of a desirable distribution of clients with respect to size expressed in chargeable

   chargeable-hour range, may be expressed as: 2Z4 Z3 + d – +

   – d

   – d

   = 0

   = 0

   14 14

   14 14

   where d + and d – indicate non achievement and

   i i

   hours. The firm would like to be in a position where:

   1. 10% of their total chargeable hours comes from clients in the 0-1000 chargeable-hour

      range

   2. 50% of their total chargeable hours comes from clients in the 1000-5000 chargeable-

      hour and

   3. 40% of their total chargeable hours comes from clients in the over-5000 chargeable

   hour range.

   These constraints then become:

   achievement of the goal respectively. Z3 is the number of chargeable hours to 5000+ clients which ideally (per earlier constraint) would be 40% of total chargeable hours. Z4, the hours chargeable to the largest desirable client, can be no more than 20% of total. Consequently, 2Z4- Z3 should be less than or equal to zero.

   i

   i

4. Constraint on Seniors and Staff. It is desired that the number of senior and staff accountants not exceed 42 personnel. This constraint, where d – represents the number of

seniors and staff less than 42 and d + represents the number

Z1 0.01T d11 d11 0 i

Z 0.50T d d 0

in excess of 42 becomes:

0

0

2 12 12

• d

• d

Z3 0.40T d13 13

• d

• d

15

15

• d

• d

15

15

X 3 X 4 42

where T= total chargeable hours expressed as (see Table 1):

2000X1 2,000X 2 2100X 3 1900X 4

i

i

d – = chargeable hours from each classification of clients less than the desirable

i

i

i

i

distribution

1. et Income. It is desirable to provide a minimum net income of Rs 1,00,000 in the upcoming year for the growth and enhancement of the firms partners. This constraint, where d – represents under-achievement of the desired net income and d + represents overachievement of the net income goal, may be expressed as:

   6300Y1 12,600Y2

   26460Y3 59,850 y4

   30,000 X1 20,000 X 2

   15,000 X 3 10,000 X 4

   Priority Structure for Firm Goals

   d16

   d16

   1,450,000(1,350,000 100,000)

   1. Increase gross audit fees by 10%(P1)

   2. Increase chargeable hours by 5% (P2)

      The partners in charge of the firm's planning function have set the following priority structure for firm goals:

   3. Increase billing rates by 5% (P3).

   4. (a) Attain a desirable distribution of clients with respect

      to size expressed in chargeable hours (P4).

      (b) Allow no one client to account for more than 20% of the firm's total revenue. This

      preceding ordinal priority structure. The objective function is formulated as follows:

      Min Pd P (d d d d ) P (d d d d )

      goal is considered to be twice as important as Goal

      1 9 2 1 2 3 4

      3 5 6 7 8

      4(a) 2(P4).

      • 2P d

        P (d d d ) P d

      • P d P d

   5. Maintain a ratio of at least one management personnel to every five staff men (P5).

   6. Hold the number of senior and staff accountants to 42

      4 14

      4 11 12 13

      5 10

      6 15

      7 16

      (P6).

   7. Provide a minimum net income of Rs1,00,000 (P7).

      OBJECTIVE FUNCTION

      The objective function in this model is to minimize the deviations from the firm goals established within the

      RESULTS AND DISCUSSION

      The solution will be obtained by using QM for WINDOWS package, which discussed as follows:

      THE FIRST RUN

      1. Goal

         1. Gross audit fee increase Achieved

         2. Chargeable hour increase Not achieved

         3. Billing rate increase Achieved

         4. (a) Client distribution Achieved

            ( b) Revenue distribution Achieved

         5. Management/staff ratio Achieved

         6. Senior and staff ceiling Not achieved

         7. Net income Not achieved

      2. Variables

X1 = 3.12 Y1 = Rs42.00 Z1 = 11,045.86 X2 = 6.27 Y2 = Rs31.50 Z2= 55,229.30

X3 = 12.56 Y3 = Rs21.00 Z3 = 44,183.45 X4 = 34.37 Y4 = Rs15.75 Z1 = 22,091.72

The solution for the first run indicates that the following three goals were not achieved: (1) the chargeable hour in- crease, (2) the senior and staff ceiling, and (3) the desired net income. In order to achieve the optimum solution for all goals, 5897 staff hours in excess of the projected chargeable hour increase were required. A total of 46.93 senior and staff accountants were required in order to achieve the higher order goals. This figure represents an excess of 4.93 over the desired ceiling of 42. Net income of Rs 58,734 was attained, resulting in a Rs 41,266 underachievement of the net income goal of 1 lakh. The goal of a 10% increase in gross audit fees was over-achieved, but only the underachievement of this goal was considered critical.

The client and revenue distributions were achieved in this model, but this probably will not happen very often. For ex- ample, if 51%, rather than 50%, of the firms total chargeable hours came from clients in the 1001-5000 chargeable-hour range, the optimum solution would not be achieved. Nonachievement of this goal would also be the case if one client accounted for 21%, rather than 20%, of the firm's total revenue. Since in neither case would it be rational for the firm to let a client go, the only solution to such a problem would be to change the applicable constraints in the model.

One of the more desirable features of goal programming as an aid in the planning process is that it allows management to review critically their priority structure for goals after an initial solution has been obtained from the planning model. After analyzing the results of the first run, the planning team has decided to modify their hierarchy of goals. This analysis and modification are reflected in the second run.

THE SECOND RUN

1. Modified Priority Structure for Goals

   The firm's planning team has decided to give the net income goal the highest priority. All of the other goals remain in the same order except that this modification lowers each goal one priority level. The firm's modified priority structure for goals is:

   1. Provide a minimum net income of Rs 1,00,000 (P1).

   2. Increase gross audit fees by 10% (P2).

   3. Increase chargeable hours by 5%(P3).

   4. Increase billing rates by 5% (P4).

   5. (a) Attain a desirable distribution of clients with respect to size expressed in

      chargeable hours (P5).

      (b) Allow no one client to account for more than 20% of the firms total revenue.

      This goal is considered to be twice as important as goal 5(a) (2P5).

   6. Maintain a ratio of at least one management personnel to every five staff men (P6).

   7. Hold the number of senior and staff accountants to 42 (P7).

2. Objective Function

   The objective function for the second run then becomes:

   Minimize

   Pd P d P (d d d d ) P (d d d d )

   1 16 2 9 3 1 2 3 4 4 5 6 7 8

   • 2P d

   P (d d d ) P d

   • P d

3. Goals

   5 14

   5 11 12 13

   6 10

   7 15

   1. Net income Achieved

   2. Gross audit fee increase Achieved 3.Chargeable hour increase Not achieved

4.Billing rate increase Not achieved

5.(a) Client distribution Achieved

(b) Revenue distribution Achieved

1. Management/staff ratio Achieved

2. Senior and staff ceiling Not achieved

The solution for the second run indicates that once again the firm failed to achieve three of its seven goals, but a trade-off of scarce resources has been effected in order to achieve a more desirable goal. Two of the goals not achieved in the first run, the chargeable hour increase and the senior and staff ceiling, were also not achieved by identical amounts in this run. The third goal not achieved in the second run was the billing rate increase. In order to achieve the highest goal, a minimum net income of Rs1,00,000, it was necessary to raise the hourly billing rate for staff accountants from the desired rate of Rs15.75/ hour to Rs16.44/hour, which resulted in a deviation of Rs0.69/hour from this goal. Hence, a trade-off of scarce resources has resulted in the achievement of a more de- sirable goal.

CONCLUSIONS

An attempt has been made in this paper to relate the goal programming technique to the planning function in public accounting firms. Although it is recognized that this approach has both desirable features and limitations, its advantages seem to outweigh its limitations. Goal program- ming, as demonstrated by the planning model presented in this paper, can be effectively utilized where the firm has multiple, incompatible, and incommensurable goals. Goal programming does not impose on management a requirement that their goals be compressed into a uni- dimensional decision criterion.

Another advantage of goal programming is that it helps to identify the conflicting nature of firm goals and where trade-offs must occur in order to achieve the most desirable goals under the given constraints. The most desirable feature of goal programming is the opportunity it gives to the planning team to review critically its hierarchy of goals

after an initial solution has been obtained from the planning model. Both the priority structure for goals and constraints can be modified to attain the most desirable set of objectives.

The most apparent limitation of utilizing the goal programming model in the planning process is that it requires the planning team to define, quantify, and establish an ordinal priority structure for the firm's goals. The goal programming model will provide the optimum solution only if there has been correct definition quantification, and ordering of goals. The effect of this limitation is mitigated somewhat when one considers that the efficacy of any type of formal planning model depends on the organized setting of objectives and the evaluation of alternatives. Although the model presented in this paper is not conclusive evidence that goal programming can be applied effectively to the planning process in public accounting firms, it does indicate that potential exists for such an application.

REFERENCES

1. Arisha, A. [2003]: Intelligent Shop Scheduling for Semiconductor Manufacturing. Doctorial dissertation, School of Mechanical and Manufacturing Enginering, Dublin City University, Dublin, Ireland.

2. Baker, R.L., et.al.,[2006]: A Pilot study to evaluate a computerized prototype used to generate hospital staff nurses a patient/shift assignment. Working paper.

3. Bard,J.F., and Purnono, H.W.[2005]: Hospital wide reactive scheduling of nurses with preference considerations. IIE Transactions, 35,589-608.

4. Charnes .A [1968]: Note on an application of a goal programming model for media planning. Management Science, 431-436.

5. Charnes A and Copper WW [1961]: Management models and industrial applications of linear programming. John Wiley and sons, New York, USA.

6. Ijili Y [1965]: Management goals and Accounting for control.

   Amsterdam, North Hollond.

7. Jaaskelainen V [1969]: A Goal Programming model for aggregate

   production planning. Swedich Journal of Economics, 14-29.

8. Robert CE [1968]: Planning the future growth of an accounting practice one approach. The Journal of Accountancy, 46-56

9. Robert EH and Wharton D [1965]: A local CPA firm plans for the future. The journal of Accountancy, 48-58

10. Sevebeck W et al. [1971]: An aggregate budget planning model for hospital administration. Management Science, 104-119