Mazoo's Learning Blog: February 2005 Archives

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February 28, 2005

Income statement - base lines and ratios

Total Revenue or Total Sales - total dollar payment from delivering or producing goods, rendering services or other activities that constitute the entity's ongoing major or central operations.

Cost of Goods Sold (COGS) - is the expense a company incurred in order to manufacture, create, or sell a product. It includes the purchase price of the raw material and the expenses of turning it into a product. Also referred to as "cost of sales".

Gross Profit = Total Revenue - Cost of Goods Sold

Gross Profit Margin = Gross Profit/Total Revenue

Operating Expense - consists of salaries paid to employees, research and development costs, selling and administrative expenses, depreciation and amortization expenses and other misc. charges that must be subtracted from the company's income.

Operating Income = Gross Profit - Operating Expense,
Operating Income = EBIT - the same things, where EBIT is Earnings Before Interest and Taxes.

Operating Margin = Operating Income/Total Revenue

Net Income from Continuing Operations = Operating Income(EBIT) - Interest Expense - Income Tax Expense

Net Income = Net Income from Continuing Operations +- Discontinued +- Extraordinary +- Accounting Changes

Net Profit Margin = Net Income/Total Revenue

Posted by mazoo at 7:40 PM

February 27, 2005

The Multiplier Effect

In the previous post "Keynesian Cross" we have received the expression for equilibrium level of income:
Y* = (C₀ + I₀)/(1-c), where c is marginal propensity to consume, 0 < c < 1, C₀ is autonomous consumption - the consumption expenditures that are unrelated to income and would occur even if household disposable income was zero. We assume that investment is a constant I = I₀

a) Closed private economy: AD(Y) = C₀ + I₀ + cY,
Y* = (1/(1-c)) *(C₀ + I₀), hence change (positive or negative) in C₀ or I₀ by x, result in a multiplied change in equilibrium level of income. Y* will change by (1/(1-c))*x.
(1/(1-c)) is multiplier.
For example, if c=0.8 and autonomous consumption C₀ increases by $10, the increase in equilibrium level of income is $50 {$10*1/(1-0.8)}.

b) Closed economy with government: AD(Y) = C₀ + I₀ + G₀+ c(Y - Tax), where G₀ - government spending, Tax - value of taxes (we consider only Lump-Sum tax that has to be paid regardless of the income level). Solve this equation with respect to Y:

Hence, the tax multiplier is (-c/(1-c)). Change in taxes affect the economy through change in consumption and the tax multiplier is differ from the regular multiplier.

When change in government spending G₀ occurs then we use the standard multiplier.

c) The balanced budget multiplier. The government can stimulate the economy without changing the budget deficit by increase in government spending and taxes by the same amount, i. e.

Hence,

Hence, the balanced budget multiplier is equal 1.

P.S.
GDP (gross domestic product) is the total market value of all goods and services produced within the political boundaries of an economy during a given period of time, usually one year. The aggregate expenditures approach to measurement of GDP reflects in the Basic Keynesian Equation GDP = C + I + G + NE, where C- consumption, I - gross investment, NE - net exports and G - government spending. I. e. we can consider the GDP in the conclusions above and the Y* is the equilibrium GDP that equalize aggregate supply (AS) and aggregate demand (AD).

Posted by mazoo at 6:37 PM | Comments (2)

Keynesian Cross

1. Let's consider closed private economy without government spending and international trade. Hence, according to Keynesian theory, the aggregate demand is the sum of consumption and investment AD = C + I.

Keynes supposed that consumption is the function of disposable income Y: C(Y) = C₀ + cY, where c is marginal propensity to consume, 0 < c < 1, C₀ is autonomous consumption - the consumption expenditures that are unrelated to income and would occur even if household disposable income was zero. Next we assume that investment is a constant I = I₀. Hence

AD(Y) = C₀ + I₀ + cY.

Let us denote C₀ + I₀ = A₀.

2. Let equilibrium level of income Y* is the income at which the economy creates just enough spending to purchase the output produced. In other words, equilibrium occurs when aggregate demand (aggregate expenditures) AD(Y) is equal aggregate supply (aggregate domestic output) AS=Y:
Y* = AD (Y*), hence
Y* = A₀/(1-c)

We can see this equilibrium on the upper graph called Keynesian cross.

3. Marginal propensity to consume is c - the proportion of each additional dollar of income that is used for consumption expenditures. The rest of income goes on savings S = Y - C. Hence,
S(Y) = -C₀ + (1 - c)Y , and for equilibrium level of income:
S(Y*) = -C₀ + (1 - c)A₀/(1-c) = I₀,
i. e. equilibrium occurs in the point where aggregate savings equal aggregate investment.

We can see this conclusion on the lower graph.

We'll consider the multiplier effect in the next post.

Posted by mazoo at 5:11 PM | Comments (4)

February 24, 2005

Equation of a learning curve

Learning curves reflect the increased rate at which people perform task as they gain experience. Ordinarily, the curve is expressed as percentage of reduced time to complete a task for each doubling of cumulative production.

Common assumption is that the cumulative average time per unit is reduced by a certain percentage each time production doubles.

Let's consider 75% learning curve:

Cumulative number of tasks	Cumulative average time per unit	Total time
80	56	4 480
160	42 (56*0,75)	6 720
320	31,5 (42*0,75)	10 080
640	23,625 (31,5*0,75)	15 120

If the average time for 80 units is 56 hours per unit, the total time is 4 480. At an average time of 42 hours for 160 units, the total time is 6 720 hours. Hence the additional 80 units (from 81 to 160) required only 2 240 hours, or 2 240/80 = 28 hours per unit.

From the table above we are able to get learning curve formula. It shows how total time depends on total output:

F(x) = 0.75^( ln(x/80) /ln (2) ) * 56 * x, where

0,75 - learning curve percentage rate divided by 100;
80 - the first lot of units;
x/80 - the number of lots;
ln(x/80) /ln (2) - logarithm of (x/80) to base 2;
56 - the average time for the first 80 units.

The alternative assumption is that incremental unit time (time to produce the last unit) is reduced when production doubled. But it occurs more rarely than the common assumption in the test prep questions.

Posted by mazoo at 3:46 PM | Comments (5)

Example of using simplex algorithm

Let's consider a simple example of solving linear programming problem by using the simplex method.

Let A company manufactures small and large garden benches in two departments, the Machining Department and the Polishing Department. Small bench requires 2 hours in the Machining Department and 3 hours in the Polishing Department. It takes 4 hours to machine large bench and 3 hours to polish. The available time for processing the two models is 100 hours a week in the Machining Department and 90 hours a week in the Polishing Department. The contribution margin expected is $5 for small bench and $7 for large bench. Let's find the optimal mix of products A company should produce to maximize total contribution margin.

Let X is quantity of small benches and Y is quantity of large benches. Let's find such X, Y that:

5X + 7Y - > max - objective function;
2X + 4Y < = 100 - constraints
3X + 3Y < = 90
X , Y > = 0

Let S1, S2 >= 0 are slack variables and then constraint transforms from inequality expressions to equality form. And linear programming problem may be restated as follows:

5X + 7Y +0S1 + 0S2 - > max
2X + 4Y +1S1 + 0S2 = 100
3X + 3Y +0S1 + 1S2 = 90,
X , Y, S1, S2 > = 0

Now we can construct the initial simplex tableau:

1. The Cj row consists of the coefficients from the objective function. 1 and 2 rows consist of the coefficients from the constraint equalities. The values 100 and 90 in the right-hand side (RHS) column come from the right-hand side of the constraint equations. Those variables that form an identity matrix are basic variables. S1 and S2 are the basic variables in this case.

2. The CB column consists of payoff coefficients of the basic variables in profit-maximization problem (objective function), i.e. 0 for S1 (row 1) and 0 for S2 (row 2).

3. The first element of the Zj row (in X column) is the sum of the products of multiplying each element in the CB column by each element in the X column. 0 (row 1, column CB) * 2 (row 1,column X) + 0 (row 2, column CB) * 3 (row 2,column X) . The subsequent elements of the Zj row (columns Y, S1, S2, RHS) are obtained in a similar way.

4. Row 4 (Cj - Zj) is obtained by subtracting each element in the Zj row from each element in the Cj (top) row.

5. Find in row (Cj-Zj) LARGEST STRICTLY POSITIVE element. Corresponding column is leading column. From row 4 we choose element 7 and the
leading column is Y (rows 1, 2) in our case.

6. Find in the leading column MINIMAL POSITIVE element from the elements are obtained from the formula RHS/leading column. This element gives us leading row. Intersection the leading row and the leading column give us leading element. In our case we choose between 100/4=25 and 90/3=30 and the leading row is row 1. Hence the leading element is 4.

7. The rows 5 is obtained by dividing leading row by leading element and row 6 is obtained by subtracting 3*(row 5) from row 2. Hence we have received an identity leading column. Hence the new basic variables are Y and S2. Go to step 2.

Repeat iterations until there are no strictly positive elements in the (Cj-Zj) row (if the optimal solution exists).

If the optimal solution exist then the element in row Zj (row 11) column RHS is objective function value in the optimal solution point. And (20, 10) from rows 9, 10 column RHS is optimal mix of products.

Hence, maximum profit margin is 190 and A company should produce 10 small benches and 20 large benches.

We have considered the solution of standard maximization problem with non-negative right-hand side of the constraints using the simplex method. The more general case of linear programming (LP) problem with the orbitrary right-hand side of the constraints we consider in the example #2.

Posted by mazoo at 1:34 PM | Comments (5) | TrackBack

February 19, 2005

Substitution and Output effects

Let resources are substitutes and the price of one resource (input 1) has changed. How will demand change for second resource (input 2)?

There is only a resulting table in my Gleim book:

Price of input1(Price of substitute)	SE v OE	Demand for input2
increase	SE > OE	increase
increase	SE < OE	decrease
decrease	SE > OE	decrease
decrease	SE < OE	increase

where SE is substitution effect, OE is output effect.

Let's show the given conclusions graphically.

Isocost curves 1 and 3 represent all combinations of factors of production (input 1 and input 2) which in a sum cost C1 and C2 (not depicted on the graph) respectively. Isoquant curves 2 and 4 depict technological limits of the firm - all combinations of input 1 and input 2 that give equal total output Y1 and Y2 (not depicted on the graph) respectively.

An increase in the price of input 1 shifts isocost 1 into isocost 3. The dotted isocost is parallel to isocost 3 and tangent to the isoquant 2. There is new resource allocation and substitution effect in this case equals SE, where "substitution" is movement along isoquant 2 from the point (I1_1,I2_1) to the point x. Output effect OE depends on tangency point of new isoquant 4 to isocost 3. Thus in the upper graph (img 1) we can se that if OE > SE then demand for input 2 decreases from I2_1 to I2_2. Similarly if OE < SE (img 2) then demand for input 2 increases.

Posted by mazoo at 2:27 PM | Comments (1)

February 18, 2005

MC intersects ATC and AVC at their minimums

Let's consider a simple fact.

Let y - firm's output, TC(y) - total cost, ATC(y)= TC(y)/y - average total cost. Given TC = VC+FC - the sum of fixed and variable cost. And, it must be borne in mind - the short run differs from the long run by the presence of the fixed cost, because all inputs are variable in the long run.

MC(y) = dTC(y)/dy .

The reason that MC intersects ATC and AVC in their minimums is that whatever MC curve below ATC and AVC curves, the latter will decrease (because MC - T additional cost and if MC is less then prior average cost so AC decrease), and vice versa, as long as MC curve exceeds ATC and AVC, the latter will increase.

Formal derivation:
MC(y) = dTC(y)/dy, ATC(y) = TC(y)/y - let's find a minimum point. We equate the derivative to zero.

(ATC(y))' = d(ATC(y))/dy = d(TC(y)/y)/dy = (y* MC(y) - TC(y) )/y^2 = 0

y^2 > 0, hence, y* MC(y) - TC(y) = 0, therefore
MC(y) = ATC(y) in the ATC minimum point (minimum, because in this point (ATC)' < 0 under the condition MC < ATC, and under MC > ATC (ATC)' > 0).

The case with AVC is similar, because d(TC(y)-FC)/dy = MC(y) too.

Posted by mazoo at 6:53 PM | Comments (1)

About

I'm preparing for the CMA/CFM certification examinations. I need to complete four examination parts to become Certified Management Accountant (CMA) and one more part for Certified Financial Manager (CFM). I use Gleim's study materials in my learning. But Gleim's cma/cfm review (like all reviews) does not cover deeply some questions and subjects. Some of these questions are not obvious from the review and require more attention for clear understanding. So I have a need to keep some moments for myself.

This blog is not another theoretical study guide. The purpose of this blog is practical use of knowledge for successful passing the CMA/CFM exams. The publications may consist of definitions of terms for memorization, explanations for understanding of concepts and interpretation of data, examples for comprehension of theory and practical application of concepts to solve problems. .

This site has the Russian-language version. Unfortunately, I don't receive enough responses and opinions in Russian. It can be related both to contents, and with that fact, that Russia doesn't have enough Internet-audience, interested in the given theme.

I read in English without effort but the writing in English represents significant difficulties. And one of the purposes of this blog is to improve this skill because fourth examination CMA "Business Applications" will be in form of essay.

I shall be very grateful if you tell me about errors both in a statement of the facts, and in English language.

Posted by mazoo at 3:28 PM

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