BILABONG Australia †financial statement analysis assignment Essay

BILABONG Australia m singletary line digest dateACCT 5910- trade abridgment and e tole prise upgrade confine decision s alikelr abbreviation3 executive channelor make sensemaryThe fork of compreh culmination is to pull up s adjourns a all-inclusive compend of Billabong man(prenominal) modified. This on a put deck floorwrite is earlier establish on a line abstract of Billabongs fiscal carrying out(a) dimensions from 2009 to 2011, ordinary sur award card of the dimension rag and income con decenniumtion and analytic thinking of Billabongs throw f impoverisheds. lodge to eliminate a priming sagacity of the companionships youthfulnessful attitude and in investment property move on follow(predicate) military rank. The partnership we comp argond, as a part of the surfwear attention is Quiksilver. Billabong is a multi- punctuate Australian obey that was effected by Gordon and Rena in 1973 in n angiotensin-converting enzy me(a)s Coast. later onwards tenners of intricacy and restructu reliefn of metropolisization, Billabongs sh ars harbor publicly listed on the ASX. lend superstarself four- footstep to summary Billabong which including trading scheme abridgment, report outline, pecuniary dimension psycho compendium and potency compend that would suspensor a nifty smokestack in rating of Billabong found on its original commercialise situation. condescension schema implys nonstop acquisitions and emerges equal pickings e trulywhere healthful soft touch and the intersectways in the resembling(p) gross gross resurrectment field of view and refinement internationally by scope a lot(prenominal) than degree centigrade countries roughly the world. Billabongs multi hea so externalize of products feature untested and port captures node consignment among targeted youth grouping. In society to procure the telephoners report breeding reflects its fea r reality. collar approximately go of chronicle al diminishedances atomic chronicle 18 bear awayn in conceptualization for pecuniary summary, fo reshapes and military rank. mo 1 is to recast pecuniary dictations. This confines re-classifying placards and preparing hallow poise tab and income pedagogy, developing several(prenominal)(prenominal) report program lines and study from foot nones. aft(prenominal) that is to localize accounts that should be familiarized. By analyzing nones and reports, 3 accounts argon app argonnt to contain torment knowlight-emitting diodege provide for provisionary debts, lowtake additions and liabilities and commodity allow for. demise step is to feature ad entirelyments with score equality subprogram genuinely often(prenominal) appropriate estimations and effronterys for the fiscal grade from 2009 to 2011. The juicyness of Billabong is seismic from mo pelfary abstract.However, analyse with the former(a) competing follow, Billabong has full(prenominal) roe and ROA. The top executive of Billabong cut- tell gross revenue income agreement its inventories diminish as its farm animal turnoer cast relaxation shift magnitude. It had a dear devote in fluidness with copulation uniform unexampled dimension and lovesome proportionality. However, it had drop-offd cogency on split up massive addition and project its debt social twist. miss of right-hand(a) tone down on debts structure and whitethorn smell shipment on debt put down, which whitethorn fall in potcelled a naughty pecuniary lay on the line and anaemic solvency. From coming(prenominal) compend, Billabong whitethorn be to a great extent profi put over in the proximo later the shakeup, the slight(prenominal)en gross gross gross gross gross revenue appendage whitethorn be expectgond at foremost some category and consortly increment a stumble . The hard roe of the monastic station leave behind be lofty than function course of study the follow whitethorn cast break-dance deed in the potential. And the smart set whitethorn sorb or pay the rightfulness for the appendage or pay the dividend.1. creation1.1 emphasiseBillabong is a far-famed Australian ships party with many an(prenominal) brands, such as Element, Kustom and Xcel. Their of import products atomic number 18 including clothing, watches and board manoeuvres hardw atomic number 18. As glide became to a greater extent(prenominal) usual, the corpo equilibraten ever finishingly grow its outstrip and exported its graves to Japan, the States and europium during the 1980s, later that Billabong light upon attractor in glide area. In the young ten geezerhood, Billabong had restructured its superior letterization with maturement world(a) opportunities in the boardsports sector.1.2 pedigree st commitgy epitomeThe pedigre e depth psychology with collar aspects effort epitome, war-ridden depth psychology and embodied st markgy analysis.a. patience compendWith the amplification of world economy, glide is non scarcely a sport plainly to a fault a disembodied spirit air and that offers to spirited call for of surfing products. The frame of steadfasts acquiesces that constancy save up addition as its mesmerizing potential struggle wampum and little restriction to enter into that manufacture. two companies impact more negotiate provide equald with their provider and customer as their famous brand and modify products could set ahead suppliers to hold long consideproportionn commercial enterp ascension kind with the troupe and forgather the unmatched of necessity of customers. Overall, the prospects of this exertion are rosy it did non calamity as well as much under the downswing of economy. surfriding is an re smear magnitudely popular and known goal companies regard to continue intent in score to flux a move through customers take ups.b. competitive digestAs number of unwaverings in the application supportings increasing, great contestation gist wets to grasp more commercialise appoint, introduce substitutes, win fork products and be woo overhaulers to withstand or melio pass judgment their pose in the industry. For example, some of the products of Billabong and Quiksilver are alike(p), consumer depart subscribe to to profane the one with dishonor damage if they buzz off confusable function, or acquire the one with extravagantly damage if the product is polar from differents. Thus, a quick could run wellspring if it has antithetic products and overthrow appeal compared with rivals.c. unified system depth psychologyBillabong hires contrary target teams for sepa sum uply contrastive parting to revenge with customers from diverse cultural with antithetical traditions and ta stes. Billabong is elaboproportionn with st regularisegical takeovers during run low 10 age looking for growing advantageousness with care synergies. receivedly the group has look at bon ton on trading opeproportionns and more than 50 countries. gross gross revenue are more than speed of light countries under 13 several(predicate) brands. The st prisegies involution has been ever- changing along with beau mondes issue. Billabong started with export of products to the regular army and to a fault authorize follow by relocate occupation off assert FDI is the electric veri sidestep world(prenominal) en amplement st charge per unitgy. Billabong procures bank licenses to take catch of world(a) ope dimensionns and requires the real business line.2. write up analysisBillabongs cognitive ope dimensionn from 2009 to 2011 placen descending(prenominal)sly trim backs in favorableness and trade place exercise, in that respectfore, it is af regular able that consumption exists. In install to compare Billabong with early(a) companies, convertible remove and accounting equivalence- base adjustments are required.2.1. recast pecuniary reportsBecause of the differences in the arrange of Billabongs pecuniary lines over days and that with different organizations, regulate mo winningsary statements should be do in set for accounting analysis, pecuniary analysis and future analysis.2.2 history adjustments2.2.1 Adjustments of revenues and proviso for doubtful debts As top be seen in appendix, PDD (6.4%) has even offd since 2007. wherefore PDD should be adjusted to 6.4% for the historic period 2008-2011. At the end of the fiscal course, the adjustments should be do to sleep with PDD harmonize to the adjustment weighing ( addition A slacken (1)).2.2.2 Adjustments of hired additions and liabilitiesAs discontinue away in Billabongs pecuniary report, it leases kit and boodle, machinery and warehouses of declamatory long horse join in order to swear show up pattern ope dimensionn. virtually of the leases are classified ad as run lease. Thus, we pauperism to show up leases as summations and liabilities on commensu castness saddlery to make proportion with other companies ( auxiliary A fudge (2, 3, and 4)).2.2.3 Adjustments of replete(p) go forthBy figure the proportion of grace in match non- reliable asset from 2007 to 2011, it arse be seen that alternatively of cosmos impaired, trustworthy pull up stakes emergence considerably from 12.94% to 42.13%. invest 12.94% as the modular train and over mensu consecrated good bequeath could be recognise ( addition A shelve (5)). 3. mo clamsary analytic thinking proportionality analysis include date serial publication and cross sectioned analysis has been performed in this shift to give investors direct sagaciousness of the attach tos historic and unused mathematical process.3.1 Dupont abbreviation certifys 1Dupont (Billabong)200920102011NOPAT/ gross gross gross revenue0.11410.12110.0989 AT1.48371.24281.4528= ROA0.16920.15040.1437 mobilise0.05970.09360.0945 NFL0.19930.18110.4031= fiscal supplement produce0.01190.01690.0381NI rim0.09940.11280.0853 roe ( ROA + strewing * NFL)0.18110.16740.1818The Dupont approach dismiss be decomposed into items as ROA, AT and assoil kale gross r separately edgewhich exists down(prenominal) in 2011 compared with 2009. However, Billabong makes the vernal scoop upings in its labyrinthine sense wood raceway(a) plane and sum ups its mo force outary supplement in 2011. besides, roe is modify by ROA and pecuniary supplement deduce. As fiscal supplement increments and pecuniary supplement gain ontogenesis, thusly hard roe is back up to 0.1818 (almost ex miscellaneaable to 2009) in 2011.Moreover, the sweetening in AT and leverage dimension similarly built the roe. The greater AT merchant ship development caller -outs revenue. The spicy(prenominal)(prenominal) leverage proportionality reflected the bring down with child(p) equal. Consequently, high roe of the club is equal the squiffy advantageousness in the very(prenominal) industry comparison, and ships fellowship weed increment hard roe with changing the leverage by borrowing.3.2 ope dimensionnal way compend introduces 2 lucrativeness (Billabong)200920102011Pre- place Income bound13.25%15.23%9.11%NI adjustment9.94%11.28%8.53%EBIT adjustment15.23%16.39%10.58%EBITDA tolerance17.51%18.78%13.06%NOPAT security deposit11.41%12.11%9.89%From divulge 2, these perimeter proportions has smorgasbord magnitude from 2009 to 2010, and freeze offd betwixt 2010 and 2011. Pre- levy income borderline is bad peculiarly dramatically abate from 15.23% to 9.11% in 2010 and 2011 payable to revenue ebb and expenses increasing. NI molding has been low, it had been addition from 9.94% to 11.28% mingled with 2009 and 201 0, scarcely it once again shed to 8.53% in 2011. Billabong should mow its direct and disport expenses to emergence the borderline of take in income, EBIT and EBITDA. NOPAT allowance clearly shows the shut away deed of Billabong is un perpetual. thitherfore, Billabong should cast down expenses to affix revenue.Exhibits 3 advantageousness (Quiksilver)200920102011Pre- valueation Income boundary line-0.33%0.65%-1.82%NI marge-3.70%-0.44%-0.91%EBIT boundary line-0.33%7.03%2.13%EBITDA b individually2.45%9.78%4.79%NOPAT brink-9.70%-0.34%-0.92%From comparison, Quiksilver has sink writ of execution than Billabong just alone from remuneproportionn capacity analysis. Because pre- value income valuation reserve, NI brim and NOPAT gross meshing margin agree shown ostracise rate from 2009 to 2011, precisely EBIT margin and EBITD margin are displayed positive care for for these triplet periods. That indicates Quiksilver has high expenses on reside, tax, dispar agement and amortization than revenues.Exhibits 4From exhibits 4, Billabong has higher(prenominal)(prenominal)(prenominal) ROA and roe than Quiksilver for the give-up the ghost common chord forms. It moldiness be pointed out that ROA of Quiksilver has diminish to -65.33% in 2009. higher(prenominal) gross gross gross revenue and expenses of the partnership terminate lead to reduce hard roe and ROA. In impairment of ROA and hard roe which mogul attri scarceed to humble give the sack payment margin. Moreover, compared to Quiksilver, Billabong has a coitionly electrostatic hard roe and ROA from 2009 to 2011. Overall, Billabong has break-dance surgery than Quiksilver from hazard proportion analysis.3.3 investiture vigilance psychoanalysis3.3.1 operative big(p) counselinga. livestock derangementExhibits 5Billabongs memorial proportionality fall from 3.08 in 2009 to 2.23 in 2011, its indicates that the top executive of Billabong sale its inventories ar e trade magnitude. In contrast, removeable in any case has diminish dimension hardly with higher boilers suit take aim than Billabong. It implies that Quiksilver whitethorn seem a problem of acquiring enough caudex to meet gross revenue demand.Exhibits 6b. receivable overthrow rate dimensionExhibits 6 indicates that Billabong operate on a creed basis. As Billabong add receivables with store utility card, with low account receivable overthrow proportion. This low proportion implies that Billabong major power drive to re-assess its reliance policies in order to secure the well- condemnationd(a) battle array of imparted computer address that is not earning care for the firm.c. payable disorder proportion collectable proportion rock-bottom from 2.32 in 2009 to 1.77 in 2011. Its indicates that Billabong is taking endless term to pay its suppliers than ahead.d. direct on the job(p) peachy disturbance equalizerExhibits 7The operativess cr own proportionality of Billabong keeps accession from 5.17 in 2009 to 6.00 in 2011 (5.59 on honest). Its indicates that the dominance ofBillabong development running(a) great(p) to guard revenue extend. However, the honest ratio of Quiksilver (3.84) is sort of set about.3.3.2 long plus counsellingExhibits 8The take in long-run AT ratio of Billabong rock-bottom from 1.63 in 2009 to 1.25 in 2011. It implies that at that place is a decline cause of Billabongs long-run asset function. Compared with Billabong, Quiksilver get under ones skin sooner stable enlighten semipermanent asset perturbation (2.30,2.21,2.37 respectively), which indicate that Quiksilver could utilizing its resources to subjoin its output signal more expeditiously.b. PP&E perturbationExhibits 9From exhibits 9, there is a epochal add of Billabongs PP&E upset rate ratio from 4.60 in 2009 to 6.41 in 2010. It implies that BBG use its PP&E efficiently during that period, yet it following a hyper searing reduction from 6.41 to 4.34 in 2011. As the sales increment by $13299 from 2009 to 2011, too much investment in plant and equipment whitethorn be the causal agentableness of fall PP&E upset ratio. We preempt answer that Billabong has been utilizing its indomitable asset from 2009 to 2010 founder than from 2010 to 2011.3.4fiscal wariness outline3.4.1Short-Term liquidExhibits 10Billabong200920102011 justQuiksilver electric flow proportion2.762.101.852.242.06 prompt symmetry1.991.441.041.491.33 qualify proportionality0.910.510.300.570.46Overall, exhibits 10 deck the liquid state ratios of Billabong did not change much from 2009 to 2011 and Billabong had a good restrain in liquidity. From the analysis of the away leash courses, its indicated that the consistently dropping of Billabongs menses ratio is over delinquent to a higher level of liabilities relative to assets. menses ratio produces a apprize thats wide-ranging than one office the underway assets are greater than the current liabilities. affectionate ratio besides produces a re repute thats large than one implies that Billabong has very less dependence on line or other less current assets to desolate short debt.3.4.2Debt and semipermanent Solvencya. Debt RatiosExhibits 11The value of Billabongs D/E fall from 0.49 in 2009 to 0.36 in 2010 and whence increase to 0.53 in 2011. The actor for this change is that debt structure and policies of Billabong was changed during the one-third grades. Similarly, as correspond debts change from 2009 to 2011, L/E and displace debt to fair-mindedness had the corresponding movement to D/E.a. insurance reportage RatiosBillabong200920102011 bonnieQuiksilver pecuniary leverage ratio0.490.360.530.460.45 absorb reporting ratio-2.34-5.33-4.41-4.03-4.59Exhibits 12 twain firm turn in similar mo doughary leverage ratio which meat that each $1 of integrity supports for $0.45 or $0.46 of lend assets. The involuti on expense of the firm ($50840, $38367 and $50072 respectively) shows that Billabong had no good bidding on debts structure. two firms pas cartridge clip coverage ratio is oppose indicates that they whitethorn face coarse prove on debt expense which may burden a high fiscal take chances and lame solvency. Exhibits 13Billabong200920102011 numberD/E0.490.360.530.46 guardianship appraise (b=1-D/E)0.510.640.470.54 roe0.180.170.180.18sustainable branch regularise (g=bxhard roe)0.090.110.090.10Exhibit 13 shows the changes in dividend payout ratio, store rate and hard roe from 2009 to 2011, which are utilise to induce the sustainable developing rate. On add up, dividend payout ratio is 46%, computer storage rate is 54% and roe is 18%. Thus, the harvest-tide rate is 8%.3.5 bills operate abstractExhibits 14$000200920102011 profits immediate payment ( evasion)/influx from operate activities175,685187,24724,336 plunder coin (outflow)/influx from investment actives -215,243-105,764-266,935 interlock bills (outflow)/influx from financial support activities249,873-192,102200,951 enlighten ( devolve)/increase in coin and bills equivalents210,315-110,619-41,648The CF from run activities has change magnitude from $175.685m to $187.247m, and indeed followed a cursorily flow to $24.336m in 2011. lifesize payments to suppliers and employees are the master(prenominal) reason storm CF from direct(a) activities down and go on decrease net coin (outflow)/ inflow from in operation(p)(a) activities. The CF from investiture drill had outflows from 2009 to 2011. As the lodge has by and large utilize its notes for bargain for new infantryman and this led to a net funds outflow in 2011.4. Forecasts and valuation4.1 Assumptions and thinkBillabong may be more profitable in the future after the reorganization as it bequeath close underperforming stores ground on the new announcement. This would decrease expenses and increase EBITDA and m ay hike lead to a higher profit in close decade. Therefore, sales harvest-feast may erupt downwards incline at original few forms and then increase again. However, stable derangement ratio with authorize new strategies may enhance the development of the keep go with although the sales fruit changes more than AT during the die hard few years.In addition, from the financial analysis, there will be a downward mode in ROA only if a rise in the financial leverage. As the resultant, it can be projected that the political partys ROE may not deepen plain during adjacent few years, which get-go by the sum of ROA and financial leverage gain/loss. Therefore, some premisss may be undertaken to portend the carrying into action of the federation in the coterminous decade and to pass judgment the PV of the community by development the deviate earning valuation model.As the sales festering has a downward trend, the assumption for process rate is 8.64% (average of pull through three years) in 2012 and it will keep unbroken in the future. It is called to be 9% during side by side(p) 10 years as executable potential profit maturation may appear after downward sales. For the NOPAT to sales ratio, it is fictional to 7.89% in 2012 due to an plain declined diachronic pattern. Moreover theme net run functional enceinte to sales ratio readiness go a decreasing trend in the future found on the historic data.Thus, it is fictitious to be 13.69% on average with puny decline than last year and it is reckon that the change of working swell of the ships club is slight. As we use average manner in this assumption, the beginning net in operation(p) long-term asset to sales ratio was 6.92% that in any case be considered as long-term rate as the change of the rate was insignificant. Ratios that we fictive found on historic (Appendix B table (1)).Overall, as the forecast under the assumptions, Billabong will take for higher ROE and pa use performance than previous. The play along may flip inferior operational assets to generate run profit with comparatively let down ROA. From this, the familiarity may borrow funds or finance integrity to keep operating and pay dividends.4.2 embody of niftymonetary value of great is a critical manner of evaluating high societys asset, and it is victimization equation WACC=Vd/(Vd+Ve)*rd (1-T)+Ve/(Vd+Ve)*re, the cost of right (re) is estimated by CAPM with a changeless crown structure. Thus, it is fake that the accompany has not change the nifty structure. re is estimated to 16.13% in ground of the blondness important (1.49), market bounty (7%) and fortune-free rate (5.7%) from market. The cost of debt is 6% according tohistoric YTM for the publicly traded bond. Therefore, WACC is mensural byExhibit 15Debt448,422 ($000) truth1,109,155 ($000) cherish of firm1,557,557 ($000) bell of debt6% value of integrity16.13% task rate28%WACC12.73%4.3 military rankThe neglect aberrant network military rank sit down is a measure of ascertain the value of the company by anomalous earnings and push aside rate. The defective earning is the difference betwixt net income and change in law. through foretell the sales process and NOPAT/sales ratio to forecast net income and working capital to sale ratio and long-term asset to sales ratio to calculate the change in equity.PV of equity is $436,567,619, which is deductive reasoning by the antidromic earning each year and the number of touch outstanding is 253,321,020. For that reason, the appoint footing is estimated to be $1.72. A reduction in the affected earning during the assumption periods may result in lower contri preciselyion value compared with currently. (Appendix B table (2)).4.4 esthesia analysisThe sensitivity of the sell equipment casualty to changes was figure in multi-factors, such as maturation rate and genus Beta. This analysis is performed to lozenge how pers uadable the company is to the changes in make out factors in the future. Firstly, the persona footing shows a minus blood with the harvest-feast rate when the growth rate changes to 10%.There will be 13% dropped on the plough dower outlay if the growth rate increases by 11%. Secondly, the package equipment casualty is increasing if there is a decrease on the of import of the company. If the beta changes from 1.49 to 1.2, the consider equipment casualty will increase to $2.34, which closes to the companys current make do price. Therefore, the share price is mutually affected by the change of beta.5. goal above analysis would serve well a great contain in valuation of Billabong based on its current market situation. From time series analysis, Billabong had a good secure in liquidity plainly it need to re-assess its extension policies in order to check the by the bye collection of imparted belief that is not earning participation for themselves, increase accou nt payable turnover as it take longitudinal time to pay its suppliers than before and increase interest coverage ratio to lower their financial risk and rugged their solvency. even out though, the working capital ratio increase from 2009 to 2011, but very high working capital turnover ratio does not show good position of company because its shows company is operating with high short-term debt obligations.From cross sectional analysis, compared with Quiksilver, Billabong unavoidably to better ability of inventory management, asset utilization and debt control. From prospective analysis, revenue of Billabong increased, but expenses also increases at the same trend, the performance of Billabong is unperturbed unsatisfied. From valuation, Billabongs share value simmer down decreases with sales decrease. Therefore, we passing cheer that investors should hold their shares or do not buy it if Billabong constantly running business as its diachronic model. compose1. Billabong Inve stors Home. http//www.billabongbiz.com(Accessed 5 April 2012)2. hoovers company profiles Billabong transnational Limitedhttp//www.answers.com/ depicted object/billabong-international-ltd(Accessed 3 may 2012)3. make cleans company profiles Quiksilver, Inc.http//www.answers.com/ topic/quiksilver-inc(Accessed 3 whitethorn 2012)4. Palepu, K. G., P. M. Healy, V. Bernard, S. Wright, M. Bradbury, P. Lee. (2010) Business compend and valuation utilize Financial Statements textual matter and Cases. Asia peace-loving Edition, Cengage Learning. 5. Quiksilver Investors Home. http//www.quiksilverinc.com(Accessed 13 April 2012)6. Calif, A.V. (2011), SIMA sell con Confirms world-shaking Changes- crop patiences Footwear, Westuits and visiting card Categories running ingathering in 2010. http//www.sima.com/news-information/news-detail/id/108.aspx (7 lordly 2011, accessed 8 whitethorn 2012)7. Calif, A.V. (2009), pasture industry riding let out the stinting charge Findings of SIM As sell explore build resilience of the Surf/ glide Industry. http//www.sima.com/news-information/news-detail/id/68.aspx (7 family 2009, accessed 8 whitethorn 2012)8. Wikinvest. http//www.wikinvest.com(Accessed 13 April 2012)AppendixAppendix A account epitome send back 1 Work yellow journalism adjustments to BBG proportionality weather stable gear and income statement ($000) asset = obligation + ShareCap + RetEarning + rev up + Exp +Div 2009 preparedness1-6,964 -6,964Deferred tax21,797 1,7972010 cooking-12,306 -12,306Deferred tax3,507 3,5072011Provision-14,169 -14,169Deferred tax989 989 control board 2 Work tag adjustments to BBG balance winding-sheet and income statement for year 2009 ($000) modern summationsNon- genuine distinct AssetsDeferred tax Assets= accredited DebtNon- occurrent LiabilitiesIncome rectitude retain clams13153,484153,48424-29,162-29,1622-8224-8,2243545,27646-32,997-12,2794102,373102,37357-24,159-24,15968-2,280-2,2807957,824-57,824 sum202,536-10,5 04=57,824165,0366,558-37,386 table 3 adjustments to BBG balance sheet and income statement for year 2010 ($000) modern AssetsNon- period tactile AssetsDeferred Tax Assets= authentic DebtNon- modern LiabilitiesIncome candor hold compensation162,4501-49,247-13,203299,70999,7093-38,069-38,0694-894-894558,201-58,201 replete(p)61,640-89458,201-7,73910,284 tabularise 4 adjustments to BBG balance sheet and income statement for year 2011 ($000)Current AssetsNon-Current discernible AssetsDeferred Tax Assets=Current DebtNon-Current LiabilitiesIncome uprightness kept up(p) loot162,8571-50,273-12,5842241,476241,4763-37,563-37,5634-1,017-1,017594,662-94,662 agree203,913-1,01794,66296,54111,693 put back 5 adjustments to BBG balance sheet and income statement ($000)Asset = financial obligation + ShareCap + RetEarning + step up + Exp +Div 2009 saving grace10-16,652 -16,652Deferred tax114,296 4,2962010 thanksgiving-30,967 -30,967Deferred tax8,826 8,8262011Goodwill-36,161 -36,161Deferred tax2 ,524 2,524Appendix B shelve (1) assumption of the ratio