Notes, summaries, assignments, exams, and problems for Mathematics

Linear Programming

Linear Programming is an optimization technique useful for allocating scarce resources among competing demands.

Examples of LP Applications

• Selecting the product mix in a factory to make the best use of machine and labor hours available while maximizing the firm’s profit.
• Scheduling tellers at banks so that needs are met during each hour of the day while minimizing the total cost of labor.
• Determining food ingredient combinations that satisfy stated nutritional requirements at a minimum cost level.

Basic Concepts

• A single objective function states mathematically what is being maximized or minimized.
• Decision variables represent choices that the decision maker can control.
• Constraints are limitations that restrict the decision variables.

Golden circle:

This relates to the innovation. If a company is able to attract those who share its beliefs, it is also able to connect easier with innovators.

This is a graph made up of three circles, each inside the other. Each circle has a meaning and a way to apply it to our business efficiently.

We can explain the operation of the Golden Circle in such a way that while most companies ask themselves the answers to the question 'what' as their starting point, they are fully aware of the 'how', but very few companies are clear about the 'why'.

The 'what' responds to what we do and what we want to do. The 'how' responds to the processes through which we carry out our actions, and the 'why' would respond to the reason why we develop our business.... Continue reading "The Golden Circle: Driving Innovation and Quality Management" »

Essential Aspects of Corporate Liquidity Analysis

There are two essential aspects in the analysis of the liquidity of a company. On one hand, there is the quality of the coverage of current debts with the most liquid assets; on the other hand, there is the temporal aspect—that is, the agility of current assets to become cash, as well as the agility of current debts to expire.

Evaluating Debt Coverage and Working Capital

In order to analyze the quality of the coverage of current debts, we start by calculating the working capital and its complementary ratios. The positive value of the working capital serves as an indicator (though never definitive evidence) of a good liquidity situation.

Liquidity Ratios: Acid Test and Cash Ratio

Due to the limitations... Continue reading "Analyzing Corporate Liquidity and Financial Health" »

B. Changes in Inventories

The company must make an inventory of the stocks it has, doing a physical count of them and checking the result with the information recorded in the book balance. After verifying this data and correcting any differences, it is necessary to stabilize stock accounts; that is, to correct the accounting balance of these accounts to reflect reality.

C. Verification of Accounting Data

Before determining the result of the accounting fiscal year, the company must verify accounting data by checking, on the one hand, that there are no mistakes in arithmetic or transcription and, on the other, contrasting it with the economic reality. To do this, perform the following inventories and balances:

• Trial Balance: Its purpose is to check

International Accounting Standard No. 10

Events Occurring After the Balance Sheet Date

Objective

The objective of this Standard is to prescribe:

1. when an entity shall adjust its financial statements for events after the balance sheet date and
2. the disclosures that an entity should give about the date on which the financial statements were authorized for issue and about events after the balance sheet date.

The Standard also requires the entity that does not prepare its financial statements under the assumption of going concern, if the events after the balance sheet date indicate that this hypothesis of continuity is not appropriate.

Scope

This Standard is applicable in the accounting and disclosures related to events after the balance sheet date.

The events

Statistical Concepts

Municipal Capital Gains Tax (Plusvalía)

Taxpayers for Capital Gains Tax

This tax applies to two types of contributors:

• The person who transmits or constitutes property rights for consideration.
• The person who acquires property rights free of charge (the acquirer).

Tax Base Calculation

To determine the tax base, three key facts are considered:

1. The cadastral value of the land at the time of accrual, excluding the value of any construction.
2. The period elapsed from acquisition to transmission, rounded down to a maximum of 20 years.
3. The annual percentage increase set by the City (in the tax ordinance), within a state-mandated ceiling.

Usufruct and Life Interest

For usufruct, a distinction is made between temporary usufruct and life interest. A percentage... Continue reading "Municipal Capital Gains and Vehicle Taxes: Key Details" »

Quantitative Variables

1. Discrete: values of x have "gaps" between them (ex: test scores)

2. Continuous: no gaps between x values

Random Variable X

Assigns a number to outcomes of an experiment

Probability Distribution of a Discrete X

A table, graph, or forumla that shows the values of X and P(X) where:

Expected Value of Discrete X

1. The probability distribution of x represents a population (μ,σ^2,σ)

2. Mean of X = expected value of X

(1) Discrete in General

Variance of Discrete X

Standard Deviation of Discrete X

Ex:

(2) Binomial X

• Need n, P and q
• x = # of successes in n
• P(X) use binomial tables (if n < 5) or="" the="">

• mean --> μ = nP   variance --> σ^2 = nPq   standard deviation --> σ = √nPq
• NOTE: Formula gives

Inheritance Tax Base Reductions

We highlight three primary types of base reductions:

Kinship-Based Reductions

The amount of reduction varies depending on the heir's kinship group. There are four standard groups:

• Group I: Descendants under 21 years old.
• Group II: Descendants aged 21 and older, ascendants, and the spouse.
• Group III: Second and third-degree collateral relatives by affinity.
• Group IV: Fourth-degree or more distant collateral relatives, and strangers.

Life Insurance Reductions

If the beneficiary is a spouse, ascendant, or descendant, a 100% reduction applies, up to a maximum limit.

Primary Residence Reductions

If the heir is a spouse, descendant, or ascendant and inherits the primary residence, a 95% reduction applies, up to a specific ceiling.... Continue reading "Understanding Inheritance Tax: Reductions, Rates, and Coefficients" »