Cost Volume Profit (CVP) Analysis: Break-Even Point and Profit Calculation, Exams of Business Policy and Regulation

Download Cost Volume Profit (CVP) Analysis: Break-Even Point and Profit Calculation and more Exams Business Policy and Regulation in PDF only on Docsity! Chapter 4 Solutions Question 4.1 A) Explain the following The term marginal cost refers to the additional costs incurred in providing a unit of product or service. The term contribution refers to the amount that a product or service contributes towards covering fixed costs. It is simply sales value less variable costs. A fixed cost is a cost that is unaffected by fluctuations in the level of activity (within a relevant range). B) Marginal format Marginal Statement € € Sales 4,300,000 Variable costs Direct material 1,250,000 Direct labour 760,000 Variable overhead 95,000 Variable sales expenses 75,000 2,180,000 CONTRIBUTION 2,120,000 Fixed costs Fixed overhead 1,165,000 Fixed sales expenses 450,000 Fixed administration 550,000 2,165,000 NET LOSS (45,000) Solution 4.2 a) Profit Statement (showing apportionment of overheads) b) Profit Statement (marginal principles) c) Effect of closing Dept. 2 Overall the company would reduce profit by €198,000 by closing department 2 (€1,004,000 before closure to €806,000). This can be explained by the lost contribution of €248,000 and only savings of €150,000 in overheads. I would advise management not to close department 2. 1. The total revenue curve begins to slope upwards but less steeply, as price reductions become necessary and then slopes downward as the effect of price reductions outweigh the beneficial effect of volume increases, as the business approaches capacity. 2. The total cost curve increases at a slower rate as the effects of economies of scale and quantity discounts show up. However the curve begins a steeper upward trend as the business rises towards full capacity, because the variable cost per unit will normally increase as a result of diminishing returns. The accountants approach argues that it is not intended to provide a precise representation of total revenue and cost functions throughout all levels of activity. The objective of the accountant’s CVP model is to represent an approximation of revenue and cost behaviour over the relevant range in the short term. As the relevant range of activity can be narrow and the short term time period less than 12 months, the linearity assumption is reasonable. Also, the cost of obtaining more accurate cost and revenue functions may outweigh the benefits to be gained from such information. Question 4.5 a) Calculate the profit or loss if the above estimates prove to be correct b) What is the break-even point in units and revenue c) What is the margin of safety in units and revenue d) How many alterations need to be sold to achieve a profit of €30,000 e) How much should be charged for each alteration if a profit of 20 per cent of selling price is required based on existing forecast sales volume Prepare a break-even chart summarising the above CVP relationship showing clearly the break-even point and the margin of safety. d) Prepare a profit volume graph showing clearly the break-even point and the margin of safety, if he achieves his required profit. e) Comment on the viability of the venture At present the venture is not a viable one. To break-even requires 11,845 customers which equates with 228 visitors per week. This is very high and will just achieve break- even. The admission charge however is quire low. If this was increased to €9 including VAT (€7.93 net) then the break-even point would fall to 6573 persons which is 126 per week (see below). This is a more realistic figure. The business should also consider adding in other revenue streams such as souvenir and café shop as well as possibly developing organic farm produce to sell. Selling price excluding VAT = (€9 x 100/112.5) 7.93 Less variance costs 15% 1.19 Contribution 6.74 New break-even point = 44,300/6.74 = 6573 persons Question 4.8 a) The profit or loss at each of the four levels of projected demand In this question the approach to take is to layout a profit statement at the four levels of demand and input the fixed and variable cost information given in the data. From this one can see that the calculation of sales is vital to answering the question. One can calculate sales at each level from using the C/S ratio of 60%. If the C/S = 60% that implies sales = 100% and variable costs = 40%. Thus sales is calculated by dividing the variable costs at each level by 40% and multiplying by 100%. For example sales under the adverse demand level is calculated as €30,000 x 100/40 = €75,000 Profit statement Adverse Average Good Excellent ('000) ('000) ('000) ('000) Sales 75 112.5 150 212.5 Variable costs 30 45.0 60 85.0 Contribution 45 67.5 90 127.5 Fixed costs 46 46.0 46 46.0 Net profit -1 21.5 44 81.5 b) The break-even point in sales value As there is no unit information given in this question the break-even point must be calculated by using the contribution to sales ratio which calculates the break-even point in euro sales. Fixed costs 46,000 = €76,667 C/S ratio 0.60 c) The level of sales required for the business to make a return on an initial investment of 20 per cent As there is no unit information given in this question the sales to make a required profit must be calculated by using the contribution to sales ratio which calculates this in euro sales. The required profit is €100,000 (20% x 500,000). Fixed costs + required profit 46,000 + 100,000 = €243,333 C/S ratio 0.60 d) Briefly comment on the viability of the venture In this new venture according to the projected data the risk of failure seems quite low in the first year. However it does not seem likely that the project will achieve returns of 20%, at least not in its first year. Thus overall the project looks to be a safe one capable of achieving reasonable returns. It must be noted that this opinion is based on the accuracy of the research data which may be flawed. Solution 4.10 a)Calculate, based on variable cost levels of 35 per cent, 40 per cent and 45 per cent, the annual break-even point for the heritage centre, t he number of customers required to give the heritage centre a return on investment of 20 per cent and the margin of safety at this level of profit. Fixed costs are €135,000 Profit for a return on investment of 20% = €62,000 (€310,000 x 20%) Variable costs Variable costs Variable costs 35% 40% 45% Sales price(9/1.125) 8.00 8.00 8.00 Variable Costs 2.80 3.20 3.60 Contribution 5.20 4.80 4.40 i) Break-even point 135,000 / 5.2 = 135,000 / 4.8 = 135,000 / 4.4 25961.54 customers 28125 customers 30681.82 customers ii) RoI (20%x310,000) 135,000+62,000/5.2 135,000+62,000/4.8 135,000+62,000/4.4 37,885 customers 41,042 customers 44,773 customers Margin of safety 11923.08 customers 12916.67 customers 14090.91 customers 31.47% 31.47 31.47% Note: The margin of safety is calculated by subtracting the break-even point calculated in (1) from the number of customers required to achieve the return. This it is assumed is the forecast sales. The margin of safety can also be calculated as a percentage. For example under variable costs at 35% the % margin of safety is calculated as 11,923/ 37885 x 100 b) Based on variable cost levels of 40 per cent, prepare a profit volume chart estimating profit at demand levels of 25,000, 30,000 and 35,000 customers The profit or loss based on demand levels of 25,000, 30,000, and 35,000 customers is calculated below and presented in a profit volume chart Profit at demand levels of 25,000 30,000 35,000 Contribution €4.8 x 25,000 120000 €4.8 x 30,000 144000 €4.8 x 35,000 168000 Less Fixed costs 135000 135000 135000 Profits -15000 9000 33000 c) If the initial study forecasts a demand of between 25,000 and 35,000 customers, comment on the viability of the venture. Based on the forecast figure the project is not feasibly if variable costs are greater than 40%. If variable costs are for example 35% then the project is a viable one however it is still unlikely to achieve the required returns of the investors. Solution 4.11 a) Present a statement showing which of the marketing manager’s proposals provide the greater amount of profit. To answer this question one needs to know the number of packages sold in the current year. To calculate this figure one needs to use the information given on the current yerar. For example current year profit amount to €150,000 after fixed costs of €120,000 are deducted. That implies that current yea contribution is €270,000. If the current year contribution per package is €125 then the number of packages sold in the current year amounts to 2160 (270,000/125). Now one can prepare profit statements based on the marketing managers proposals. Proposal 1 Proposal 2 € € Sales (€250 x 2376) 594,000 €230 X 2700 621,000 Variable costs (€135 x 2376) 320,760 €135 X 2700 364,500 Contribution ( €115 x 2376) 273,240 €95 X 2700 256,500 Fixed costs 144,000 144,000 129,240 112,500 b) Calculate, in respect of each alternative, the break-even point in terms of sales volume and sales value Proposal-1 Proposal 2 Fixed costs 144000 144,000 Contribution per unit 115 95 Break-even point (packages) = 1252 packages 1515 = packages 1252 x €250 1515 x €230 Break-even point (sales value) = €313,043 revenue = €348631 revenue Solution 4.12 Workings Product 1 Product 2 Product 3 Product 4 Total Volume 15,000 5,000 10,000 7,500 37,500 Total sales revenue €37,500 €16,250 €43,000 €13,125 €109,875 Contribution per unit * €1.55 €2.00 €2.30 €1.10 Total contribution €23,250 €10,000 €23,000 €8,250 €64,500 *Contribution per unit is found by dividing sales revenue by volume to get sales price per unit and then deducting variable costs. a) Calculate the total revenue required to break-even based on the current sales mix Fixed cost: 37,500 units x 50p = €18,750 C/S ratio: €64,500 / €109,875 x 100 = 58.7% (average based on mix ratio) Break-even: €18,750 / 0.587 = €31,942 revenue b) Calculate the number of units of each product required to break-even based on the current sales mix Average selling price: €109,875 / 37,500 = €2.93 Total units to break-even: €31,942 / €2.93 = 10,902 units Ratio: 15 : 5 : 10 : 7.5 Product 1: 10,902 / 37.5 x 15 4,361 units Product 2: 10,902 / 37.5 x 5 1,454 units Product 3: 10,902 / 37.5 x 10 2,907 units Product 4: 10,902 / 37.5 x 7.5 2,180 units c) Calculate the margin of safety in revenue €109,875 - €31,942 = €77,933 revenue d) Calculate the break-even point and margin of safety if the business follows a strategy of increasing advertising by €15,000 which is forecast to increase sales by 10 per cent Product 1 Product 2 Product 3 Product 4 Total Volume 15,000 5,000 10,000 7,500 37,500 New volume + 10% 16,500 5,500 11,000 8,250 41,250 Contribution per unit €1.55 €2.00 €2.30 €1.10 New contribution €25,575 €11,000 €25,300 €9,075 €70,950 New sales: €109,875 x 110% = €120,863 C/S ratio: €70,950 / €120,863 x 100 = 58.7% New fixed cost: €18,750 + €15,000 = €33,750 Break-even: €33,750 / 0.587 = €57,493 Margin of safety: €120,863 - €57,493 = €63,370 e) Should the increase in advertising be implemented? Existing profit: €64,500 - €18,750 = €45,750 New profit: €70,950 - €33,750 = €37,200 NO, although the proposal increases volume the proposal should not be implemented as the profit will fall from €45,750 to €37,200 the break-even revenue will increase and the margin of safety decrease. Solution 4.13 a) How much sales revenue must be generated per week from the shop in order to break-even. (You may assume the trading year is 50 weeks) To begin this question the information must be presented in a marginal costing format with costs classified according to whether they are fixed or variable and contribution calculated. Then calculating the average C/S ratio one can calculate the break-even point in sale value Skis Suits Total (168 x 100/120 ) (240x100/120) Selling Price excl vat 140 200 340 Less variable costs per unit Purchases excluding vat 70 120 190 Commissions 28 40 68 98 160 258 Contribution per unit 42 40 82 Fixed Costs Wages & salaries 45,000 Estimated Overheads for the year 14,400 Loan Interest (8% x 50,000) 4,000 Depreciation of fixed assets 10,000 73,400 Weighted Average C/S (82/340) = 0.24 Break-even point Fixed cost 73,400 €305,833 C/S ratio 0.24 b) Calculate the amount of sales revenue to be generated per week if a return on equity of 20 percent is required A return on capital of 20% equates to a net profit figure of €32,000 (160,000 x 20%)