THEORETICAL CONSIDERATIONS ON THE CALCULATION OF TURNOVER OF BREAK-EVEN IN INSURANCE COMPANIES

Transcription

1 THEORETICAL CONSIERATIONS ON THE CALCULATION OF TURNOVER OF BREAK-EVEN IN INSURANCE COMPANIES Florin Cătălin OLTEANU, Gavrilă CALEFARIU* *Economic Engineering and Manuacturing Systems epartment, Transilvania University o asov, Romania Abstract: Risk management in the case o insurance companies involves two major aspects. The irst aspect reers to taking over the insurable risks o individuals and companies by signing an insurance contract instead o an insurance premium. The second aspect regards inancial risks that insurance companies ace. In order to evaluate the inancial risks o an insurance company one o the major inluence actors that has to be considered is: turnover o break-even. The paper s aims are to identiy speciic actors o insurance and their inluence on the values o ixed and variable costs, essential parameters in determining the break-even point o any type o activity. Keywords: Risk management, insurances, costs, turnover o break-even 1. INTROUCTION Proitability analysis o insurance companies is as important as with any productive organization. As deined in the literature [1,4,6] proitability threshold (critical point, equilibrium point) is the volume o production to cover all expenses. Under proitability threshold, the company works on loss. Ater overcoming the proitability threshold, the company gets proit again. Proitability threshold can be determined by the algebraic method, or graphical representation o the relationships involved. The algebraic method involves highlighting elements that make up company costs. As well known, ixed costs represent all costs over a period o time that are independent o production volume and variable costs represent costs are all costs dependent on the production volume. To write the relations established notations are used C F - ixed costs; - variable cost; C A - turnover, Q - production volume (in the case o insurance companies, the number o policies cashed), p - average price o a policy, v -variable costs per unit o product (policy), P - earned proits. The relationship between these elements is also known, also as that below: CA = P C F, where: CA = p Q and = v Q. When turnover equals costs proit is zero, and the system is at the proitability threshold (critical point). Production volume corresponding to the critical point is QCR =. (1) p v The graphical method involves representation on the same graphic the variation o turnover and total costs based on production volume. Total costs are given by the relationship: CT = v Q. Abscissa o their intersection point represents Q CR.. The above relations being known, on general level, this paper aims to highlight speciic issues in insurance. 2. SPECIFIC OF COST CALCULATION IN GENERAL INSURANCES General calculation relation [2] or any cost C is : 98

2 HENRI COANA GERMANY GENERAL M.R. STEFANIK AIR FORCE ACAEMY ARME FORCES ACAEMY ROMANIA SLOVAK REPUBLIC INTERNATIONAL CONFERENCE o SCIENTIFIC PAPER AFASES 2011 asov, May 2011 C = Cu Q [um] (2), where: Cu is the unit cost, expressed in adequate measuring units, and Q is the quantity (production volume). Relation (2) is valid also or the insurance ield, so that Q signiies the number o cashed policies. In terms o direct relationship they have with insurance products, the insurance costs may be direct costs and indirect costs. Similarly, in terms o volume dependency to insurance, costs can be ixed costs and variable costs. 2.1 Calculation o direct costs. irect costs [2] include the ollowing two components: material costs or the direct productive sta Costs o materials Acquisition unit cost o materials needed or the materialization o an insurance contract: paper, toner, stickers, etc. will be: C m = nck pk [units/pieces], where: -n ck represents consumption norm or material k; -p k represents unit price o material k. For a total number o policies pro year Q, material costs will be : C An = C Q [um/year] Costs with direct productive sta Total number o policies Q may be provided by three ways: -Q represents the number o insurances concluded during a year by insurance agents. -Q represents the number o insurances concluded during a year by brokerage companies. -Q IA represents the number o insurances concluded during a year by insurance inspectors The commission or agents C represents a percent o the selling price or a policy -p. 99 Yearly costs or commissions o policies concluded by agents: C An = Q ( C p) (4) The commission or brokerage companies C represents procent o the selling price or a policy. Yearly costs or commissions o policies concluded by brokerage companies: C An = Q ( C p), (5) Expenses or the salaries o insurance inspectors: CIA = 12 n IA RIA (6) where:- n IA is the number o insurance inspectors; -R IA is the average expense recorded by an organization (monthly gross salary plus the employer s contribution to the state budget), or an insurance inspector. Costs associated to direct productive sta will be: C PP An = C An C An CIA irect costs pro year: C An = CAn CPPAn C = C Q Q p Q An p 12 nia RIA 2.2 Calculation o indirect costs. Indirect costs [2] include the ollowing components: Expenditure on maintenance and repairs o computer equipment (C IR ) Electricity charges C EE = NT Te pue where: - N T [KW] is the total power used; -T e [ore] is the eective operating time; -p UE [um/kwh] is the unit price o electricity Charges or uel used or heating and hot water C = N N p GM ( GMI GMA ) UG

3 where: -N GMI [m 3 ] is the volume o gas used or heating; -N GMA [m 3 ] is the volume o gas used or hot water; -p UG [um/m 3 ] ist he unit price o gas Fixed assets depreciation expenses C A : q CMFi C A = i= 1 TAi where: - q ist he number o the company s ixed assets; - C MFi [um] is the expense recorded or the asset acquisition, including reight, installation, commissioning, etc.; - T Ai [ani] is the normal service lie o the ixed asset i Taxes and ees expense, C IT [um/year] Rent expenses: C CH = CChi where: C Chi is the yearly rent expense or the location,,i Indirect productive sta costs: managers, accountants, etc., C PIP ; C PIP = 12 npip RPIP where: - n PIP is the number o indirect productive sta; - R PIP is the average expense recorded by the organization (monthly gross salary plus the employer s contribution to the state budget), or a indirect productive employee Annual damage costs (C aune ), represent the total value o compensation paid in a year. Caune = Q R p (7) where: - R loss ratio. Total indirect costs are: C = C C C C C IN An IR EE GM CCH CPIP Caune irect and indirect costs calculation serves to highlight aspects o business eiciency, since only directly productive activities are related to the activity o the company. Indirect activities provide the conditions to achieve directly productive activities. A IT 2.3 Fixed costs. C F ixed costs, represent the total expenditure over a period o time, which are independent o production volume. = CIR CEE CGM C A (8) CIT CCH CPIP CIA 2.4 Variable costs. variable costs, represent the total expenditure increased with increasing production volume. The category o variable insurance costs includes: material costs, annual costs or policies concluded by agents and annual costs or commissions on policies concluded by brokerage companies as well as damage costs. = C An C An C An Caune (9) Yearly damage costs - C aune are considered as variable costs, because they depend on the yearly concluded policies (Q). 2.5 Total costs. Total costs (C T ) represent the sum o ixed costs and variable costs C = C C (10) T F V 3. PROFITABILITY ANALYSIS 3.1 Calculation o ixed costs. In the relation (8) we are noting CIR CEE CGM C A CIT CCH CPIP = C 0, resulting: C F = 0 12 RIA nia (11) 3.2 Calculation o variable costs. In the relation (9), we replace (3), (4), (5), and (7). We obtain: CV = C Q Q R p (12) Q p Q p We note: - share o the number o policies concluded by agents rom the total number o policies and share o the number o policies concluded by the brokerage companies rom the total number o policies. Then: Q = Q and Q = Q, The relation o variable costs calculation (12) becomes: 100

4 HENRI COANA GERMANY GENERAL M.R. STEFANIK AIR FORCE ACAEMY ARME FORCES ACAEMY ROMANIA SLOVAK REPUBLIC INTERNATIONAL CONFERENCE o SCIENTIFIC PAPER AFASES 2011 asov, May 2011 C V = Q [ C p ( p R (13) )] The unitary variable costs are: v = C p R (14) p ) ( The slope o variable costs is: Tg = C p ( R α 1 ) (15) 3.3 etermination o proitability threshold We use the most common method that applies linear model o costs and revenue growth with increases in output Analytical method Replacing (11) and (14) in relation (1) we obtain: 0 12 RIA nia QCR= p 1 R C [ ( ] ) Turnover o the proitability threshold (breakeven) is calculated with relation: CA CR = p Q CR Graphic method Functions chart is plotted Turnover: CA = p Q and o total costs C = C 12 R n [ C p R T p ( FO IA )] Q At the intersection o the two graphs Q CR is obtained. 3.4 ependency o ixed costs to a production level. imum turnover achieved by a number,,n IA o inspectors is: C IA = nia TIA (17) where:- T IA is the target imposed to an insurance inspector, ie. total o insurance premiums cashed during a year. We note IA - weight o turnover achived by insurance inspectors rom the total turnover CA o the insurance company. We have CA CA IA = IA A nia TIA = (18) IA CA = p Q where :Q is the maximum number o policies. From relation (18), we obtain the number o insurance inspectors who could achieve Q IA p Q n IA = 1 (19) IA p Q where; represents the ull part o the respective expression. Replacing relation (19) into the relation o ixed costs (11) we obtain the dependency between ixed costs and Q : (16) IA p Q = O 12 RIA 1 TIA (20) where Q is the maximum number o policies which may be concluded by this level o ixed costs. 3.5 The case o the company turnover growth over CA. We note: n 1IA initial number o insurance inspectors; CA 1 - maximum turnover reached by the company with n 1IA insurance inspectors; Q 1 - maximal number o policies due to this turnover; The due ixed costs are: 1 = 0 12 RIA n1ia (21) The new turnover imposed by the insurance company is CA 2 CA2 = CA1 ΔCA, where - ΔCA represents the turnover growth. The number o policies is: Q 2 = Q 1 ΔQ This turnover growth is achieved only ` 101

5 by employing a certain number o insurance inspectors, namely,, n 2IA calculated by the relation: ΔQ p n 2 IA = 1 ( Q2 Q1 ) p n2 IA = 1 Fixed costs C F2 corresponding to the new situation will be: 2 = 1 12 RIA n2ia (22) By operating the accordingly replaces, we obtain: 2 = O 12 RIA n1ia 12 RIA n2ia (23) Variable costs: For Q= Q 1, variable cost will be: C Q V 1 = 1 [ C p R p ( )], (24) I Q exceeds Q 1 variable costs will be: CV = CV 1 ( C p R ) ΔQ, (25) The new slope o variable costs will be: Tg α 2 = ( C p R ) (26) By comparing relations (26) and (15) we ound the variable costs lowering. In relation (25) we replace: Δ = Q, and (24) obtaining: v Q Q1 C V = Q 1 p ( ( C p R ) Q, (27) Variable costs as per product unit are: [ Q p ( )]/ Q = 1 ) ( C p R ), (28) To obtain analytic proitability threshold (breakeven) we replace (28) and (22) into the relation (1). We obtain: 2 ( ) Q1 QCR = p ( 1 R) C (29) To obtain graphically proitability threshold unction graphs will be plotted Turnover: CA = p Q, and o total costs: CT = 2 Q p ( ) ( C p R) Q, At the intersection o the two graphs we obtain Q CR 4. NUMERICAL RESULTS ata are coming rom the,,x insurance company - Yearly turnover : CA=16,800,000 [RON] ; - Number o ywarly cashed policies: Q AN =12,000 [buc}] ; - Average price o a policy: p=1,400 [RON]; - Number o indirect productive employees: n PIP =42; -Average expenditure or an indirect productive employee R PIP =2,000 [RON/month] ; - Number o insurance inspectors: n IA = 12; - Average expenditure or an insurance inspector: R IA =2,000 [RON/month] ; - Turnover share achieved by the insurance inspectors orm the total turnover: IA =30%=0.3 ; - Commission or agents as percent o the selling price o a policy: C =10%=0.1 ; - Turnover share achieved by the insurance agents rom the total turnover: =40%=0.4 ; Calculation o ixed costs C PIP =1,008,000 [RON /YEAR]; C F0 =3,200,000 [RON/YEAR] C IA =288,000 [RON /YEAR]; C F1 =3,488,000; We consider: C F1 =3,500,000 [RON /YEAR]; Calculation o variable costs = 801 Q [RON] Tgα 1 =801 Proitability threshold will be: Q PR1 =5,850 [policies] Calculation o total costs C T = 3,500, Q (30) CA = 1, 400 Q (31) Equaling the relations (31) and (31) we obtain Q CR =5,850 [policies] 102

6 HENRI COANA GERMANY GENERAL M.R. STEFANIK AIR FORCE ACAEMY ARME FORCES ACAEMY ROMANIA SLOVAK REPUBLIC INTERNATIONAL CONFERENCE o SCIENTIFIC PAPER AFASES 2011 asov, May 2011 imum turnover to be obtained with the n 1IA =12, is CA 1 =16,000,000 [RON]; imum number o policies to be obtained: Q 1 =11,430 [policies] To this production, both the n 1IA =12 inspectors and the agents and brokerage companies are contributing. The company wishes the turnover growth to: CA 2 =24,000,000 [RON]; This growth can be achieved only by increasing the number o inspectors. ΔCA =8,000,000 [RON]; Additional number o inspectors will be: n 2IA =21 inspectors In this situation ixed costs will be: C F2 =4,000,000 [RON]; By operating replacements, relations (21) and (22), become: 1 = 3,500,000 24,000 ([0,00105 Q1 ] 1) 2 = 3,500,000 24,000 ([0,00105 Q1 ] 1) 24,000 ([0,0035 ( Q Q )] 1) 2 Variable costs: For Q Q 1, we have: = 801 Q 1 Total costs: C T = 3,500, Q For Q Q 1, we have: 1 =9,160,000 [RON] = 9,160, ΔQ, By replacing Δ Q = Q Q1, we have: = 1,360, Q The slope or variable costs in the new situation: Tgα 2 =682; The slope o variable costs decreased rom tgα 1 = 801 to tg α 2 = Total costs will be: C T = 5,360, Q (32) The business turnover will be: CA = 1, 400 Q (33) Equaling the relations (33) and (34) we obtain: Q PR =7,465 (policies) Proitability threshold may be determined also analytically, as per relation (29) Q PR = 7,465 (policies). 5. CONCLUSIONS The paper deals with speciic issues in insurance cost calculation o the proitability threshold (breakeven). By determining the computing relations we ound two undamental eatures. The irst concerns the dependence o the threshold unction depending on the ixed costs. The second concerns the change o the straight lines slope that shapes variable costs once with the appearance o ixed costs thresholds. This makes the total cost depending on the number o insurances to be a airly complex unction, so that proitability threshold (breakeven) is diicult to be determined by solving an algebraic equation. Thereore, the graphical representation allows much easier to determine the proitability threshold. REFERENCES 1. BARSAN-PIPU, N., POPESCU, I.. Managementul riscului: concepte, metode, aplicatii. asov: Transilvania University Publishing House (2003). 2.CALEFARIU, G.. Optimizarea sistemelor de abricatie. asov : Transilvania University Publishing House (2002). 3.GHIC, G., GRIGORESCU, C. J.. Analiza economico-inanciara. Repere teoretice si practice Bucuresti: University Publishing House (2009).

7 4. MANU, P., ANTONOAIE, N.. Managementul riscului: curs postuniversitar de masterat. asov: Transilvania University Publishing House (2008). 5. PETCU, M.. Analiza economico - inanciara a intreprinderii. Probleme, abordari, metode, aplicatii. Bucuresti: Economical Publishing House ( 2009). 6. SUMEREA, S.. Management si strategii inanciare. asov: Transilvania University Publishing House (2006). ACKNOWLWGEMENT The scientiic research has been done in the project Burse doctorale pentru dezvoltare durabila POSRU/107/1.5/S/