# Break-even analysis

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**Section A**

a) Calculate the number of rooms occupancy required to break even in each of the six month periods based on original forecasts.

One of the most common tools used in evaluating the economic feasibility of a new enterprise or product is the break-even analysis. The break-even point is the point at which revenue is exactly equal to costs. At this point, no profit is made and no losses are incurred (Holland, 1998). First, we must calculate the fixed costs for the two different periods. Fixed costs are the costs that do not vary in total when the level of output by the business varies. When the sales level within a business increases, fixed costs would not increase (RuralWomen'snetwork, 2006).

April-September:

Fixed cost_{1}=65,000+39,000+75,000+23,600= £202,600

October-March:

Fixed cost_{2}=50,000+30,000+75,000+18,600= £173,600

In order to find the two break even points, we must also calculate the contribution per room per day which is the difference between selling price and variable costs. It is the portion of the selling price that contributes to paying off the fixed cost after covering the variable costs. Variable include things like raw materials that vary in cost and quantity used. Sometimes they are called direct costs because they are directly connected and affected by the volume of the production (Horngren, Datar, & Rajan, 2012). When the total contribution is exactly equal to total fixed costs, sales are at the break-even point. The contribution of each unit sold beyond BEP is the increment of profit and it is calculated as below (The Association of Business Executives, 2008).

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Contribution _{per room per day} = Price – Variable cost = 60-16 = £44

BEQ_{1}^{*} = occupancy in days

BEQ_{2}^{*} = occupancy in days

In order for the hotel to avoid losses, there should be a number of 4,605 rooms occupied during the April to September period and 3,945 during the October to March period. Although there will be no losses for these specific number of occupied rooms, there will be no profits. Profits will be generated from each room occupied above the break even number of rooms occupied calculated above.

b) Calculate, and comment on, the profit for the year based on i) the original forecasts.

In order to find the profit for the whole year, we must calculate the profit of the two seasons and add them together. But first we must calculate the total contribution for the two seasons by multiplying the number of the occupied rooms with the contribution per room.

Total Contribution_{1} = 44 x 6,500 = £286,000

Total Contribution_{2} = 44 x 4,500 = £198,000

The profit will be calculated by deducting the fixed cost from the total contribution of all the occupied rooms for each period as shown below.

Profit_{1} = Total Contribution_{1} – Fixed cost_{1} = 286,000 – 202,600 = £ 83,400

Profit_{2} = Total Contribution_{2} – Fixed cost_{2} = 198,000 – 173,600 = £ 24,400

Total Profit _{for the year} = Profit_{1} + Profit_{2} = 83,400 + 24,400 = £ 107,800

Based on the original forecasts, the total profit for the year will be £ 107,800.

b) Calculate, and comment on, the profit for the year based on ii) option 1.

The new data has a different price room for the second period which affects the number of rooms occupied, the contribution and of course the profit for the season and the total profit for the year. The profit of the first period will remain unchanged as well as the fixed costs in both periods.

Contribution _{per room per day ii} = 55 – 16 = £ 39

Occupancy _{ii} = 4,500 x 10% = 4,950 rooms occupied

Total Contribution _{ii} = 39 x 4,950 = £193,050

Profit _{ii} = Total Contribution _{ii} – Fixed cost =193,050 –173,600= £19,450

Total Profit _{for the year ii} = Profit_{1} + Profit _{ii} = 83,400 + 19,450 = £ 102,850

Based on option 1, the total profit for the year will be £ 102,850 whereas if the hotel follows the original forecasts will be £ 107,800 which means that they will be £4,950 less profits.

b) Calculate, and comment on, the profit for the year based on iii) option 2.

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According to the new data there will be changes in the October to March semester in terms of the number of rooms occupied, general running costs, the fixed cost and the contribution as shown at the calculations that follow.

Occupancy _{iii } : x 4,500 = 3,000 occupancy in days

Maintenance _{iii } : x 30,000 + x 30,000 x 50% = 20,000 + 5,000 = £ 25,000

Reception & office staff _{iii } : x 50,000 = £ 33,333

General running costs _{iii} : x 18,600 + x 18,600 x 50% =12,400 +3,100 =£ 15,500

Total Contribution _{iii} = 44 x 3,000 = £132,000

Fixed cost _{iii } = 33,333 + 25,000 + 75,000 + 15,500 = £148,833

Profit _{iii} = Total Contribution _{iii} – Fixed cost _{iii} = 132,000 - 148,833 = **-** £16,833

Total Profit _{for the year iii} = Profit_{1} + Profit _{iii} =_{ } 83,400 + (-16,833) = £ 66,567

Based on option 1, the total profit for the year will be £ 102,850 based on the original forecasts will be £ 107,800 and based on option 2 will be £66,567 making option 2 the least optimistic alternative so far.

c) Calculate and comment on the income of John Brown and Wendy Brown if option 3 is implemented.

If the third choice is implemented the fixed cost will be affected as well as the variable costs and the reception and office costs as demonstrated below.

Variable cost _{c} = 16 – 10% (16) = £ 14, 4 per occupied room

Reception & office staff _{April-September} = 65,000 – 20% (65,000) = £ 52,000

Reception & office staff _{October-March} = 50,000 – 20% (50,000) = £ 40,000

At the fixed costs of each period we must add the fee of the new manager which is £40,000 annually, so we will add £20,000 at the fixed cost of the semesters.

Fixed cost _{April-September c} = 52,000+39,000+75,000+23,600+20,000= £ 209,600

Fixed cost _{October-March c} =40,000+30,000+75,000+18,600+20,000= £ 183,600

Contribution _{c} = Price – Variable cost _{c} = 60 – 14, 4 = £ 45, 6

Total Contribution _{April-September c} = 45, 6 x 6,500 = £ 296,400

Total Contribution _{October-March c} = 45, 6 x 4,500 = £ 205,200

Profit _{April-September c} = Total Contribution _{April-September c} – Fixed cost _{April-September} = 296,400- 209,600 = £86,800 ** **

Profit _{October-March c} = Total Contribution _{October-March c} – Fixed cost _{October-March} =

205,200 - 183,600 = £21,600 ** **

Total Profit _{for the year c} = Profit _{April-September c +} Profit _{October-March c} = 86,800 + 21,600 =

£108,400 ** **

** **

The total profit for the year will be £ 108,400 making option 3 the most profitable. Wendy’s share is 70% of the profit and John’s share is 30% of the profit. John will have an additional £25,000 annual income for working part time as a landscape gardener. Their incomes in numbers will be:

Wendy’s income = Total Profit _{for the year c } x 70% (Total Profit _{for the year c)} = £ 75,880

John’s income = Total Profit _{for the year c } x 30% (Total Profit _{for the year c)} + 25,000 =

32,520 + 25,000 = £57,520

In the other cases it is known that the shares of the profits would be equal. This means that based on the original forecasts, their share would be £ 107,800 / 2 = £ 53,900, based on option 1, their share would be £ 102,850 / 2 = £ 51, 425 and based on option 2 their share would be £ 33, 3283.5. Therefore, the last scenario is the most profitable for John and Wendy.

**Section B**

Cost-Volume-Profit Analysis, sometimes referred to as break-even analysis, is one of the most powerful tools that managers have. It helps them understand the interrelationship between cost, volume and profit in an organization by focusing on interactions between the prices of the products, the volume of level of the activity, the per unit variable costs, the total fixed costs and the mix of products sold. The break–even point can be defined as the level of sales at which profit is zero. Once the break-even point has been reached, profit will increase by the unit contribution margin for each additional unit sold. In order to calculate the anticipated profit, managers can simply take the number of units to be sold over the break-even point and multiply that number by the unit contribution margin. CVP is a handy and easy tool which does not require knowledge of previous sales or preparation of profit and loss accounts and seeks the most profitable combination of variable costs, fixed costs, selling price and sales volume.

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