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Question #1
a)
Break-even analysis is important to assess the current state of the enterprise and its dynamics, as well as for the development strategy of the company.
For the definition of concepts such as break-even point and financial headroom is necessary, first of all, to define the fixed and variable costs. These concepts are used in the solution of almost all kinds of administrative tasks in the system "costs - production volume - profit."
Fixed costs do not depend on the quantity produced.
Example: The company leases land. For this land has to pay a rent of $ 100. This cost is formed regardless of the volume of production of the enterprise. This is the fixed costs.
These costs include depreciation, rent, salaries of administrative employees and other expenses that must be paid even if the company does not produce anything. List of fixed costs for each firm its.
Variable costs depend on the quantity produced and production of this volume change is directly proportional to the rise of the variable costs.
Break-even point for a product called presented in natural units or units of its minimum amount that must be sold to cover all the costs attributable to this product. In other words, the breakeven point - is the level of physical volume of sales over a period of time (month, quarter, year), due to which the company covers the costs.
b)
Break-even analysis is one of the most important pieces of information used to assess the effectiveness of projects. Investor (initiator) of the project is necessary to know at what volume of production it breaks even, i.e. should establish a critical point below which the company is losing revenue and above - gets them.
Break-even point (the threshold of profitability) - a value of revenues, in which the company has no losses, but has received no profit, i.e. it is the result of the sale of goods after compensating variable costs. In this case, the marginal revenue is sufficient to cover fixed costs, and the profit is zero.
Breakeven output (physical units) =
= Total fixed costs / Price per unit -
- The value of the variable costs.
Example. Total fixed costs (SI) - 6000 thousand dollars; Unit price - 12 thousand dollars; Variable costs in the price of goods - 8 thousand dollars. Then:
Breakeven output is (6000)/(12-8)=1500
If the demand for manufactured products is lower than the volume of the product, providing break-even, the production is not self-sustaining. Break-even analysis is to compare the use of production capacity in which receipts from sales of production costs are identical.
Proceeds from the sale of goods at breakeven cost express nonprofit sales and unit price of the product in this situation serves as a break-even selling price. If production program includes a variety of products, for any break-even sales volume will be different pricing options for non-profit products, but not a single break-even price.
1) The cost of production and marketing are a function of production or sales;
2) The output is identical to the volume of sales, i.e., there is no carryover of unsold goods;
3) Constant current costs are the same for any volume of production in this provides relevant period;
4) Variable costs vary in proportion to the volume of production, so similar range and full (general) costs;
5) The sales prices of the product (or group of products) for all release levels are stable over time. Therefore, the total value of sales depends on the level of sales prices and quantities of goods sold ;
6) The amount of the sales price per unit, fixed and variable costs remain unchanged, ie, the price elasticity of demand for inputs is zero ;
7) The amount determined by the break-even for one product, in the case of the diversity of its product line structure should remain constant. It should be noted that the above restrictions are not always respected in practice.
Break-even point is the subject of sensitivity analysis for different values of the fixed and variable costs and selling prices.
Classification of costs into fixed and variable has practical significance only in relation to a given volume of production (sales) in a particularly relevant period.
1. The company will make a profit if the commodity market to sell products more critical number, which is reflected in the x-axis.
2. Point of intersection of revenues and direct general costs called breakeven point (breakpoint), passing the entity will become profitable. The lower left triangle zone characterizes losses, and the upper right - the profit zone.
3. A straight line parallel to the x-axis characterizes the fixed costs, and a line parallel to the line of the general costs - variable costs. Break-even analysis is relevant to the position of the future development of the enterprise.
c)
The trend is not always easy to determine "the eye." Here to help traders come auxiliary tools - trend line. Trend line - it lines connecting consecutive points minima or maxima on the price chart. Trend line and clearly shows the direction in which the market is moving. Apply line on the price chart allow all popular trading platforms, with color and line thickness can be chosen independently.
Spend on the price chart a straight line so that it touches at least two consecutive price highs (to determine a downtrend) or two or more price lows (uptrend to determine), and then look at what angle the line passes.
A trend line is a straight line that connects two important minimum or maximum point in the chart. Within the main trend can occur any number of secondary and small trends. The duration of each of them varies within wide limits. It is worth remembering that the trend line should not interfere with other prices between these two points. A trend line is a corridor of support or resistance where price changes within the band.
Prices can break through the ascending and descending trend line just as support and resistance levels when the expectations of investors.
Trend lines are classified in the following way:
- Downtrend - characterized by the consistent lowering of maximum prices. It can be considered a descending level of resistance: the tone is set bears, pushing prices down.
- Uptrend - characterized by increases in the minimum price. It can be viewed as a bottom support level: Bulls set the tone, pushing prices up.
- Sideways Trend - the price is almost not moving.
d)
For example, we have some data set about average price of some good by years:
Put this data in Excel and make a scatterplot. Then right click on any point and pick “Add a trend line”. The result is:
The obtained equation (look at the graph above) is a trend line equation. We can make further forecasts based on this equation.
Question #2
a)
The law of the random variable gives detailed information about the random variable. However, sometimes it can be described clearly enough random variable with just one or more numbers. For example, you can specify the law of rainfall falling in the area for a given month, but simpler and clearer to specify the average rainfall in a given month.
Numbers, purpose of which is to compress the main features characterize the distributions of random variables, called numeric characteristics. Depending on the distribution of random variable, these measures can be calculated using well-known formulas.
b)
Assume, we have the following discrete distribution of random variable:
We do a histogram of frequencies in Excel and have the following:
Now, the frequency curve is a curve which connects all tops of the bars of the histogram:
The obtained curve could be combined with some well-known distribution curves to understand the character of distribution. This curve is close to the bell-curve of normal distribution. So, we can assume that the distribution of our variable is approximately normal.
Sources
Yates, Daniel S.; Moore, David S; Starnes, Daren S. (2003). The Practice of Statistics (2nd ed.). New York: Freeman. ISBN 978-0-7167-4773-4.
Steigerwald, Douglas G. "Economics 245A – Introduction to Measure Theory". University of California, Santa Barbara. Retrieved April 26, 2013.
Emanuel, Parzen (1962). Stochastic Processes. SIAM. p. 8. ISBN 9780898714418.
L. Castañeda, V. Arunachalam, and S. Dharmaraja (2012). Introduction to Probability and Stochastic Processes with Applications. Wiley. p. 67.
