These journal entries record the transactions for the given scenarios in October. Please note that the sales revenue is calculated based on the 30% above cost for the shipped jobs.
Here are the journal entries to record the transactions for Polaris Company:
Raw materials purchased on account:
Debit: Raw Materials Inventory.................................$210,000
Credit: Accounts Payable...............................................$210,000
Raw materials used in production:
Debit: Work in Process Inventory (Direct Materials).......$152,000
Debit: Manufacturing Overhead (Indirect Materials)....$38,000
Credit: Raw Materials Inventory......................................$190,000
Accrued direct labor cost:
Debit: Work in Process Inventory (Direct Labor)............$48,000
Credit: Accrued Payroll...................................................$48,000
Accrued indirect labor cost:
Debit: Manufacturing Overhead (Indirect Labor)..........$21,000
Credit: Accrued Payroll...................................................$21,000
Depreciation recorded on factory equipment:
Debit: Manufacturing Overhead......................................$105,000
Credit: Accumulated Depreciation - Factory Equipment...$105,000
Other manufacturing overhead costs accrued:
Debit: Manufacturing Overhead......................................$130,000
Credit: Accounts Payable...............................................$130,000
Application of manufacturing overhead:
Debit: Work in Process Inventory....................................$380,500 ($5 per machine-hour x 76,100 machine hours)
Credit: Manufacturing Overhead.....................................$380,500
Completion of jobs and transfer to Finished Goods:
Debit: Finished Goods Inventory......................................$511,000
Credit: Work in Process Inventory..................................$511,000
Shipment of completed jobs to customers:
Debit: Accounts Receivable.............................................$583,700 ($449,000 + 30% of $449,000)
Credit: Sales Revenue.....................................................$583,700
Debit: Cost of Goods Sold..............................................$449,000
Credit: Finished Goods Inventory..................................$449,000
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1. Explain the difference between financial accounting and managerial accounting. Also, explain the accounting equation.
2. Explain the purposes and use of Ratio analysis in general and Current, Activity, Short-Term and Long-Term Debt Ratios in particular.
(150 words.)
Financial accounting and managerial accounting are two branches of accounting that serve different purposes within an organization.
Financial accounting focuses on preparing financial statements for external stakeholders such as investors, creditors, and regulatory authorities. Its primary objective is to provide accurate and reliable information about the financial performance and position of the company. Financial accounting follows generally accepted accounting principles (GAAP) and reports historical financial data in the form of income statements, balance sheets, and cash flow statements. Managerial accounting, on the other hand, is concerned with providing financial information to internal users, such as managers and decision-makers within the organization. Its main goal is to assist in planning, controlling, and decision-making processes. Managerial accounting provides detailed and timely information that is used for budgeting, cost analysis, performance evaluation, and strategic planning.
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Discuss vertical and horizontal integration in a supply
chain. How does the integration work and why is it so important for
a supply chain? (10 marks)
Vertical integration is the process in which a company expands its supply chain by acquiring companies or building its facilities.
In contrast, horizontal integration occurs when a company expands its operations at the same level of the supply chain, such as adding new products or services. The combination of both forms of integration in a supply chain results in a fully integrated supply chain.Varieties of vertical integrationVertical integration is divided into three categories based on the degree of control that a company has over its production or distribution operations. These three types are backward, forward, and balanced integration.Backward integrationBackward integration occurs when a company begins to manufacture the materials required for production. Raw materials, for example, can be produced by a business that normally purchases them from suppliers.Forward integrationForward integration occurs when a company enters the distribution industry by acquiring or constructing its distribution system. A manufacturer, for example, may sell its products to a wholesaler, who then sells them to retailers, who then sell them to the end customer.Balanced integrationThe term "balanced integration" refers to the ability of a company to balance both forward and backward integration to optimize supply chain performance. This integration approach takes into account the importance of manufacturing quality raw materials and the ability to distribute products to consumers effectively. The balanced integration model considers both forward and backward integration when determining the most efficient method of conducting business.
Benefits of vertical integration in a supply chainVertical integration results in several advantages in a supply chain, including the following:Improved quality controlA vertically integrated company can control every aspect of its production and distribution. As a result, the company can better monitor its goods' quality, ensuring that they meet or exceed customer expectations.Cost savingsA vertically integrated company can reduce costs by producing and distributing its products rather than outsourcing the work to suppliers.
Furthermore, vertical integration improves communication and collaboration between departments, reducing costs related to miscommunication, delays, and product recalls.The importance of horizontal integrationHorizontal integration aids in the development of a more effective supply chain by expanding the company's operations to include new products or services. Horizontal integration results in a better distribution system and a broader customer base. It improves supply chain efficiency and streamlines the production process by enabling companies to combine efforts and resources to expand their reach and produce products that cater to consumers' needs.
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Esfandairi Enterprises is considering a new three-year expansion project that requires an initial fixed asset investment of $2.41 million. The fixed asset will be depreciated straight- line to zero over its three-year tax life, after which time it will be worthless. The project is estimated to generate $1,775,000 in annual sales, with costs of $685,000. The tax rate is 23 percent and the required return on the project is 10 percent. What is the project's NPV? (Do not round intermediate calculations. Enter your answer in dollars, not millions of dollars, and round your answer to 2 decimal places, e.g., 1,234,567.89.) NPV
The project's npv is -$4,000..to calculate the net present value (npv) of the project, we need to discount the cash flows generated by the project to their present value and subtract the initial investment.
here are the steps to calculate the npv:
1. calculate the annual cash flows generated by the project:
annual cash flow = sales - costs
annual cash flow = $1,775,000 - $685,000 = $1,090,000
2. calculate the depreciation expense for each year:
depreciation expense = initial investment / tax life
depreciation expense = $2,410,000 / 3 = $803,333.33 per year
3. calculate the taxable income for each year:
taxable income = annual cash flow - depreciation expense
taxable income = $1,090,000 - $803,333.33 = $286,666.67
4. calculate the annual tax payment:
tax payment = taxable income * tax rate
tax payment = $286,666.67 * 23% = $65,833.33
5. calculate the after-tax cash flows for each year:
after-tax cash flow = annual cash flow - tax payment
after-tax cash flow = $1,090,000 - $65,833.33 = $1,024,166.67
6. calculate the present value factor for each year using the required return:
present value factor = 1 / (1 + required return)^year
present value factor for year 1 = 1 / (1 + 10%)¹ = 0.9091
present value factor for year 2 = 1 / (1 + 10%)² = 0.8264
present value factor for year 3 = 1 / (1 + 10%)³ = 0.7513
7. calculate the present value of the after-tax cash flows for each year:
present value of year 1 cash flow = after-tax cash flow * present value factor for year 1
present value of year 2 cash flow = after-tax cash flow * present value factor for year 2
present value of year 3 cash flow = after-tax cash flow * present value factor for year 3
present value of year 1 cash flow = $1,024,166.67 * 0.9091 = $930,000
present value of year 2 cash flow = $1,024,166.67 * 0.8264 = $846,667
present value of year 3 cash flow = $1,024,166.67 * 0.7513 = $769,333
8. calculate the npv by summing up the present values of the cash flows and subtracting the initial investment:
npv = present value of year 1 cash flow + present value of year 2 cash flow + present value of year 3 cash flow - initial investment
npv = $930,000 + $846,667 + $769,333 - $2,410,000
npv = -$4,000
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Using database Furniture write down the following Queries in MS Access 1. Which product has standard price less than 275? 2. What is the address of Customer named Home Furnishings? 3. What is the aver
To write down the given queries in MS Access for the given database Furniture, follow the below steps:
1. Open MS Access and create a new blank database.
2. Click on the "External Data" tab in the top menu and select the "Access" option.
3. In the "Get External Data - Access Database" wizard, select the "Import tables, queries, forms, reports, macros, and modules into the current database" option.
4. Browse to the location where the Furniture database is saved and select it.
5. In the "Import Objects" window, select the "Queries" option and then click on the "Select All" button to select all the queries in the Furniture database.
6. Click on the "OK" button to import all the queries into the MS Access database.
7. Now, to execute the given queries, go to the "Queries" section in the left navigation pane and select the respective query.
8. Click on the "Run" button in the top menu to execute the query and get the required results.
Now, let's write down the queries for the given requirements:
1. Which product has standard price less than 275?To find the product with standard price less than 275, we need to use the following query:SELECT ProductID, ProductName, StandardPriceFROM ProductsWHERE StandardPrice < 275ORDER BY StandardPrice ASC.
2. What is the address of Customer named Home Furnishings?To find the address of the customer named Home Furnishings, we need to use the following query:SELECT CustomerName, AddressFROM CustomersWHERE CustomerName = "Home Furnishings".
3. What is the average price of products in the Furniture database?To find the average price of products in the Furniture database, we need to use the following query:SELECT AVG(StandardPrice) AS AveragePriceFROM Products;Hence, the required queries for the given database Furniture are written down in MS Access.
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How to solve this?
Prepare a December 31,2020,balance sheet for Long Print Shop from the following:cash,$40,600;accounts payable,$28,600 merchandise inventory,$14,600;Joe Ryan,capital,$47,200;and equipment,$20,600
LONGPRINTSHOP
Balance Sheet
December31,2020
Assets Liabilities
LONGPRINTSHOP Balance Sheet December 31, 2020
Assets:
Cash: $40,600
Stock: $14,600
Equipment: $20,600
Assets $75,800
$28,600 Accounts Payable
Joe Ryan, $47,200 equity,
Equity and Liabilities: $75,800
Explanation: A company's balance sheet shows its current financial situation. It displays firm assets, liabilities, and equity.
Long Print Shop's balance sheet on December 31, 2020, includes:
Assets:
Company cash: $40,600.
Merchandise Inventory: Goods for sale cost $14,600.
Equipment: The company possesses $20,600 in machinery, tools, and other commercial assets.
Liabilities:
Accounts Payable: $28,600 is owed to vendors for products and services.
Equity:
Joe Ryan's initial investment in the business was $47,200.
The accounting equation: Assets = Liabilities + Equity applies to the total assets ($75,800), liabilities ($28,600), and equity ($47,200).
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What is the present value of a $5500 perpetuity discounted back
to the present at 14 percent?
Therefore, the present value of a $5500 perpetuity discounted back to the present at 14 percent is approximately $39,285.71.
To calculate the present value of a perpetuity, we need to discount the cash flow at a given discount rate. In this case, the perpetuity has a cash flow of $5500 and a discount rate of 14%. The present value can be calculated using the formula for the present value of a perpetuity. The formula for the present value of a perpetuity is: PV = Cash Flow / Discount Rate.
In this scenario, the cash flow is $5500 and the discount rate is 14%. Plugging these values into the formula, we can calculate the present value as follows:
PV = $5500 / 0.14
By performing the calculation, we find that the present value of the perpetuity is $39,285.71.
Therefore, the present value of a $5500 perpetuity discounted back to the present at 14 percent is approximately $39,285.71.
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Background Due to the global pandemic, a number of manufacturing organizations in South Africa have been facing problems related to low-out or productivity, leading to customer's dissatisfaction and loss of market shares due to customers' demands not being met, including poor quality of supplied good/products.
As Junior Industrial Engineers working in a team, identify and discuss from an Industrial Engineering point of view, what are the possible problems causing the low productivity and also possible techniques/solutions including recommendations for this Industries.
Manufacturing organizations in South Africa are experiencing low productivity and customer dissatisfaction due to various problems. As Junior Industrial Engineers, we will discuss potential causes of low productivity and propose techniques/solutions to address these issues.
Inefficient Process Design: One possible cause of low productivity could be an inefficient process design. This includes factors such as poor layout, inadequate workflow, inefficient use of resources, and lack of standard operating procedures. To address this, Industrial Engineers can conduct process analysis and redesign, optimize layouts, implement efficient workflow systems, and develop standardized work instructions. By improving process design, organizations can streamline operations, eliminate bottlenecks, and enhance productivity.
Inadequate Workforce Training and Skills: Another factor contributing to low productivity is a lack of proper training and skills among the workforce. Insufficient training can result in employees struggling to meet production targets and deliver quality products. Industrial Engineers can identify skill gaps through training needs assessments and develop comprehensive training programs. These programs should focus on improving technical skills, enhancing problem-solving abilities, and promoting a culture of continuous learning and improvement.
Equipment and Technology Issues: Outdated or malfunctioning equipment, along with inadequate technology adoption, can hamper productivity. Industrial Engineers can conduct equipment and technology assessments to identify areas of improvement. This may involve upgrading machinery, implementing automation and robotics, and utilizing advanced software systems for production planning and control. By investing in modern equipment and technologies, organizations can enhance efficiency, reduce downtime, and improve product quality.
Quality Control and Assurance: Poor quality of supplied goods/products can lead to customer dissatisfaction and loss of market shares. Industrial Engineers can implement robust quality control systems, including statistical process control techniques, quality audits, and continuous monitoring. They can also introduce quality assurance practices throughout the production process to prevent defects and ensure consistent product quality.
In conclusion, as Junior Industrial Engineers, addressing the low productivity issues in South African manufacturing organizations requires a holistic approach. By focusing on process design, workforce training, equipment and technology, and quality control, Industrial Engineers can drive improvements in productivity, customer satisfaction, and market competitiveness. It is essential to analyze the specific challenges faced by each organization and tailor the solutions accordingly to achieve long-term success.
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Current Attempt in Progress
Cost of goods sold $435400
Income tax expense $67600
Operating expenses 352800
Sales 1040000
Gross profit would be:
a. $537000
b. $604600
c. $184200
d. $687200
The gross profit can be calculated by subtracting the cost of goods sold from the sales revenue. Based on the given figures, the gross profit would be $604,600.
Gross profit is a measure of profitability that represents the amount remaining from sales revenue after deducting the cost of goods sold. To calculate the gross profit, we subtract the cost of goods sold from the sales revenue.
Given:
Cost of goods sold = $435,400
Sales = $1,040,000
Gross Profit = Sales - Cost of Goods Sold
Gross Profit = $1,040,000 - $435,400
Gross Profit = $604,600
Therefore, the correct answer is option b. The gross profit would be $604,600.
It's important to note that gross profit does not take into account operating expenses or income tax expenses. It solely focuses on the direct cost of producing or acquiring the goods sold. Gross profit is a key indicator of a company's profitability and helps assess its ability to generate revenue from its core operations.
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What are specific price differentiation tactics you could
implement in regard to this specific discount program? Explain why
each tactic you selected was chosen.
Price differentiation The price difference equation is a term that means when A shopkeeper or seller charges different prices from many customers for the same product.
Price differentiation, also known as price discrimination, refers to a strategy employed by businesses to set different prices for their products or services based on various factors. It involves charging different customers or market segments different prices for essentially the same product or service. The goal of price differentiation is to maximize profits by tailoring prices to capture the maximum value from each customer group.
There are several types of price differentiation strategies. First-degree price differentiation, also known as personalized pricing, involves setting a unique price for each individual customer based on their willingness to pay. Second-degree price differentiation involves offering different pricing tiers or quantity discounts to incentivize customers to purchase more.
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Question 1 The Statement of Financial Position of Wakon, a private company, at 31 December were as follows: 2020 2021 RM'000 RM'000 RM'000 RM'000 Assets Non-current Assets 1,000 1,600 Current Assets I
The Statement of Financial Position of Wakon, a private company, shows an increase in total assets from 2020 to 2021 with a significant increase in non-current assets.
Wakon's non-current assets have increased by 60% from RM 1,000,000 in 2020 to RM 1,600,000 in 2021. This indicates that Wakon has invested in long-term assets that it expects to use for several years and potentially benefit from in the future.
On the other hand, current assets have decreased by 20% over the same period. This may suggest that Wakon has used some of its short-term assets such as cash and cash equivalents, trade receivables or inventories to invest in its non-current assets.
However, it's important to note that without additional information such as the company's cash flow statement, it's difficult to fully understand the reasons for the changes in the current assets. Nonetheless, the overall increase in total assets suggests that the company has been able to invest in its growth and future potential.
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indirect costs are often pooled, and not allocated individually because:
Indirect costs are costs that cannot be easily and accurately traced to a specific product, service, or project. These costs are often incurred for general business activities that benefit multiple products or services.
Indirect costs are typically allocated to products or services using an allocation rate based on some cost driver, such as direct labor hours, machine hours, or square footage. However, in some cases, indirect costs may be pooled and not allocated individually for several reasons:
Difficulties in measurement: Some indirect costs, such as rent, utilities, and insurance, are difficult to measure accurately for each product or service.
Immateriality: Indirect costs may be immaterial or insignificant to the overall cost of a product or service, and therefore not worth allocating separately.
Cost-benefit analysis: The cost of allocating indirect costs individually may outweigh the benefits of more accurate product costing.
Management discretion: In some cases, management may choose to pool indirect costs because they believe it is more appropriate or consistent with their accounting policies and practices.
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José invests $15,000 at 5%, compounded quarterly, for 3 years.
He then takes the total proceeds at maturity, adds $1,000, and
reinvests it at 4%, compounded semi-annually, for an additional 2
years.
To calculate the total proceeds of José's investments, we'll first calculate the value of the initial investment after 3 years, and then calculate the value of the reinvested amount after 2 years.
Step 1: Calculate the value of the initial investment after 3 years.
The formula to calculate compound interest is:
[tex]A = P(1 + r/n)^{nt}[/tex]
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial investment)
r = annual interest rate (in decimal form)
n = number of times that interest is compounded per year
t = number of years
For the initial investment:
P = $15,000
r = 5% or 0.05 (5% expressed as a decimal)
n = 4 (quarterly compounding means 4 times per year)
t = 3 years
[tex]A = 15000(1 + 0.05/4)^{4*3}[/tex]
[tex]A = 15000(1 + 0.0125)^{12}[/tex]
A = 15000(1.0125)^12
A ≈ 15000(1.16075)
A ≈ $17,411.25
So, after 3 years, the initial investment will grow to approximately $17,411.25.
Step 2: Calculate the value of the reinvested amount after 2 years.
Now, José takes the total proceeds at maturity, which is $17,411.25, adds $1,000 to it, and reinvests the total amount.
P = $17,411.25 + $1,000 = $18,411.25
r = 4% or 0.04 (4% expressed as a decimal)
n = 2 (semi-annual compounding means 2 times per year)
t = 2 years
[tex]A = 18411.25(1 + 0.04/2)^{2*2}[/tex]
[tex]A = 18411.25(1 + 0.02)^4[/tex]
[tex]A = 18411.25(1.02)^4[/tex]
A ≈ 18411.25(1.082432)
A ≈ $19,966.11
After 2 years of reinvestment, the total amount will grow to approximately $19,966.11.
Therefore, the total proceeds of José's investments after the reinvestment period would be approximately $19,966.11.
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What is the most effective approach to issues management? O Fighting public opinion Advocating the company position to the public Limiting communication with the public Organizing promotions for public
The most effective approach to issues management is advocating the company position to the public. In advocacy, the company uses effective communication strategies to defend its position on an issue to the public.
This approach is essential as it helps the public understand the company's view on the issues at hand and helps establish a positive image and reputation for the company. However, it's important to note that advocacy should be done in a way that is open, transparent, and honest. The public may hold a negative view of a company's position if they feel that the company is not transparent or is dishonest with them. Therefore, it is important for companies to be honest and transparent when communicating with the public. In advocacy, the company should also take into account public opinion, trends, and concerns. They should address these concerns and trends in their communication to show that they are aware of these issues and are working to address them. This approach helps to build trust between the company and the public.
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The shipping terms are clearly stated in the contract is not a criteria for revenue recognition under ASC Topic 606. The five criteria for revenue recognition under ASC Topic 606 are:
Identify the contract(s) with a customer.
Identify the performance obligations in the contract.
Determine the transaction price.
Allocate the transaction price to the performance obligations in the contract.
Recognize revenue when (or as) the entity satisfies a performance obligation.
Under ASC Topic 606, the shipping terms being clearly stated in the contract is not a criteria for revenue recognition.
The criteria for revenue recognition under ASC Topic 606 are as follows:1. Identify the contract(s) with a customer: The first criterion for revenue recognition requires that the entity identify the contract(s) with its customer(s). It is considered a contract under Topic 606 if it is approved by the parties involved, the rights and obligations are well defined, the payment terms are determined, the contract has commercial substance and collection of consideration is probable.2. Identify the performance obligations in the contract: The second criterion requires that the entity identifies the performance obligations in the contract, or the promises to transfer goods or services to the customer. Performance obligations are distinct goods or services that are separately identifiable from other parts of the contract.3. Determine the transaction price: The third criterion is about determining the transaction price, which is the amount of consideration that the entity expects to receive in exchange for transferring the promised goods or services to the customer.4. Allocate the transaction price to the performance obligations in the contract: The fourth criterion requires that the entity allocate the transaction price to the performance obligations in the contract. This is done by estimating the stand-alone selling price of each distinct performance obligation and allocating the transaction price in proportion to those amounts.5. Recognize revenue when (or as) the entity satisfies a performance obligation: The fifth and final criterion requires that the entity recognize revenue when (or as) it satisfies a performance obligation by transferring control of a promised good or service to the customer.In conclusion, ASC Topic 606 has a set of five criteria that need to be followed for revenue recognition. These criteria are essential and need to be applied in the order they are listed.
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What is the value of a building that is expected to generate fixed annual cash flows of 95,100 dollars every year for a certain amount of time if the first annual cash flow is expected in 3 years from today and the last annual cash flow is expected in 6 years from today and the appropriate discount rate is 13.31 percent?
The value of the building can be calculated using the discounted cash flow (DCF) valuation method. Considering the fixed annual cash flows of $95,100, a discount rate of 13.31%, and a time period of 4 years (from year 3 to year 6), the value of the building can be calculated as follows:
Value = [tex]CF1 / (1 + r)^1 + CF2 / (1 + r)^2 + ... + CFn / (1 + r)^n[/tex]
Where:
CF1 = Cash flow in year 3 = $95,100
CF2 = Cash flow in year 4 = $95,100
CF3 = Cash flow in year 5 = $95,100
CF4 = Cash flow in year 6 = $95,100
r = Discount rate = 13.31%
n = Number of years = 4
Plugging in the values:
Value = [tex]$95,100 / (1 + 0.1331)^1 + $95,100 / (1 + 0.1331)^2 + $95,100 / (1 + 0.1331)^3 + $95,100 / (1 + 0.1331)^4[/tex]
Calculating this equation will give you the present value or the value of the building.
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In Myanmar, five laborers, each making the equivalent of $3.00 per day, can produce 38 units per day. In China, nine laborers, each making the equivalent of $2.00 per day, can produce 45 units. In Billings, Montana, two laborers, each making $57.00 per day, can make 100 units. Shipping cost from Myanmar to Denver, Colorado, the final destination, is $1.50 per unit. Shipping cost from China to Denver is $1.00 per unit, while the shipping cost from Billings, Montana to Denver is $0.30 per unit. Based on total costs (labor and transportation) per unit, the most economical location to produce the item is .......... with a total cost (labor and transportation) per unit of $ ...... (Enter your response rounded to two decimal places.)
The required answer is China with a total cost labor and transportation per unit of $1.40.
In China, nine laborers, each making the equivalent of $2.00 per day, can produce 45 units.In Billings, Montana, two laborers, each making $57.00 per day, can make 100 units.Shipping cost from Myanmar to Denver, Colorado, the final destination, is $1.50 per unit.Shipping cost from China to Denver is $1.00 per unit, while the shipping cost from Billings, Montana to Denver is $0.30 per unit.To find the most economical location to produce the item, we need to find the total cost (labor and transportation) per unit of the item.
Total cost per unit in Myanmar labor cost per unit = (5 × 3)/38 = $0.39Shipping cost per unit = $1.50Total cost per unit = 0.39 + 1.5 = $1.89Total cost per unit in Chinalabor cost per unit = (9 × 2)/45 = $0.40Shipping cost per unit = $1.00Total cost per unit = 0.4 + 1 = $1.40Total cost per unit in Billings, Montanalabor cost per unit = (2 × 57)/100 = $1.14Shipping cost per unit = $0.30Total cost per unit = 1.14 + 0.3 = $1.44Thus, the most economical location to produce the item is China with a total cost (labor and transportation) per unit of $1.40 (rounded to two decimal places).
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Comparative financial statement data of Canfield, Inc. follow: (Click the icon to view the income statement.) (Click the icon to view the balance sheet.) Begin by selecting the formula to compute the debt to equity ratio. Debt to equity ratio = Total liabilities - Total equity Now, compute the debt to equity ratios for 2024 and 2023. (Round your answers to two decimal places, X.XX.) Debt to equity ratio 2024 1.56 2023 1.58 Requirement 1g. Compute the rate of return on common stockholders' equity for 2024 and 2023. Begin by selecting the formula to compute the rate of return on common stockholders' equity. Rate of return on common stockholders' equity (Net income-Preferred dividends) + Average common stockholder's equity Now, compute the rate of return on common stockholders' equity for 2024 and 2023. (Round your answers to one tenth of a percent, X.X. Do not enter Rate of return on common stockholders' equity % 2024 % 2023 % Help me solve this Demodocs example 0-1 D (Click Read the TS for hold ge co d 20 help- ▲ Income Statement Canfield, Inc. Comparative Income Statement Years Ended December 31, 2024 and 2023 2024 2023 $ 466,000 $ 422,000 237,000 218,000 229,000 204,000 137,000 135,000 92,000 69,000 9,000 10,000 83,000 59,000 22,000 24,000 $ 61,000 $ 35,000 Done Net Sales Revenue Cost of Goods Sold Gross Profit Operating Expenses Income From Operations Interest Expense Income Before Income Tax Income Tax Expense Net Income Print - X - kample, Balance Sheet Assets Current Assets: Cash Accounts Receivables, Net Merchandise Inventory Prepaid Expenses Total Current Assets Property, Plant, and Equipment, Net Total Assets Liabilities Total Current Liabilities Long-term Liabilities Tatal Liabilition Get more neip Canfield, Inc. Comparative Balance Sheet December 31, 2024 and 2023 2024 Print $ 2023 2022* 90,000 $ 89,000 111,000 115,000 $103,000 143,000 161,000 211,000 19,000 10,000 363,000 375,000 217,000 179,000 580,000 $ 554,000 $601,000 230,000 $ 240,000 123,000 99,000 252.000 230.000 Done - X 0.2% E Balance Sheet Accounts Receivables, Net Merchandise Inventory Prepaid Expenses Total Current Assets Property, Plant, and Equipment, Net Total Assets Liabilities Total Current Liabilities Long-term Liabilities Total Liabilities Stockholders' Equity Preferred Stock, 5% Common Stockholders' Equity, no par Total Liabilities and Stockholders' Equity * Selected 2022 amounts Print Get more help 111,000 115,000 $ 103,000 143,000 161,000 211,000 19,000 10,000 363,000 375,000 217,000 179,000 580,000 $ 554,000 $601,000 230,000 $ 240,000 123,000 99,000 353,000 339,90 110,000 110,000 117,000 105,000 $ 580,000 $ 554,000 Done $ 89,000 - X 0.2
The rate of return on common stockholders' equity is 14.1% and 11.4% for 2024 and 2023 respectively.
Debt to equity ratio is a financial ratio that is used to evaluate a company's ability to pay off its debts by comparing its total liabilities to shareholders' equity. Here, we will compute the debt-to-equity ratio for 2024 and 2023. The formula to compute the debt to equity ratio is as follows:
Debt to equity ratio = Total liabilities / Shareholders' equity
Thus, the debt to equity ratios for 2024 and 2023 are computed as follows:
Debt to equity ratio for 2024 = Total liabilities / Shareholders' equity
= $353,000 / $226,000
= 1.56
Debt to equity ratio for 2023 = Total liabilities / Shareholders' equity
= $339,900 / $214,900
= 1.58
Rate of return on common stockholders' equity is the return on investment that common stockholders receive on their shares. It is calculated by dividing net income minus preferred dividends by the average common stockholder's equity. The formula to compute the rate of return on common stockholders' equity is as follows:
Rate of return on common stockholders' equity = (Net income - Preferred dividends) / Average common stockholder's equity
Thus, the rate of return on common stockholders' equity for 2024 and 2023 are computed as follows:
Rate of return on common stockholders' equity for 2024 = (Net income - Preferred dividends) / Average common stockholder's equity
= ($61,000 - $9,000) / ($226,000 + $214,900) / 2
= 14.1%
Rate of return on common stockholders' equity for 2023 = (Net income - Preferred dividends) / Average common stockholder's equity
= ($35,000 - $10,000) / ($214,900 + $179,000) / 2
= 11.4%
Thus, the rate of return on common stockholders' equity is 14.1% and 11.4% for 2024 and 2023 respectively.
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11. Loxelle Corporation has set the following standards for production: Direct materials: 20 gallons at $3 per gallon Direct labor: 4 hours at $8.50 per hour Loxelle: . Budgeted fixed costs at $200,00
So, the total cost of each unit is $94 + $20 = $114.
Loxelle Corporation Standards for Production
Direct materials: 20 gallons at $3 per gallon.
Direct labor: 4 hours at $8.50 per hour.
Loxelle: Budgeted fixed costs at $200,000.
Loxelle Corporation has a production standard that is determined by the cost of direct materials, direct labor, and overhead. For example, the cost of direct materials is calculated by multiplying the number of gallons by the cost per gallon. In this case, the cost of direct materials is 20 x $3 = $60.
Direct labor costs are determined by multiplying the number of hours by the hourly rate.
So the direct labor cost for each unit is 4 x $8.50 = $34.
Therefore, the total cost for each unit of production is $60 + $34 = $94.Overhead costs, such as rent and utilities, are budgeted as fixed costs.
Therefore, the budgeted fixed costs for Loxelle are $200,000. This means that the cost of overhead for each unit of production is $200,000 divided by the number of units produced. If Loxelle produces 10,000 units, then the overhead cost per unit is $200,000/10,000 = $20.
So, the total cost of each unit is $94 + $20 = $114.To summarize, Loxelle Corporation has set production standards that include the cost of direct materials, direct labor, and overhead. The total cost of each unit is calculated by adding the cost of direct materials and direct labor to the overhead cost per unit. The overhead cost per unit is determined by dividing the budgeted fixed costs by the number of units produced.
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Which of the following characteristics of a company business
structure is true?
A. Owners have limited liability.
B. Easy to set up.
C. Not a separate legal entity.
D. Owners pay individual tax on com
D. Owners pay individual tax on company profits characteristics of a company business the structure true.
Option D is true because, in a company business structure, such as a partnership or sole proprietorship, the owners are personally liable for paying taxes on the company's profits. This means that the profits are passed through to the owners, and they report and pay taxes on their individual tax returns. In this type of structure, the company itself does not pay taxes as a separate legal entity. Options A, B, and C are not necessarily true for all company business structures. For example, option A (limited liability) is true for a corporation, but not necessarily for a partnership or sole proprietorship. Option B (easy to set up) can vary depending on the specific requirements and regulations of different business structures. Option C (not a separate legal entity) is not true for a corporation, which is considered a separate legal entity from its owners.
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For each of the following state whether each person is employed, unemployed, or not in the labor force if the survey was taken today. Then explain why you answered the way you did.
a. Someone who was laid off 6 months ago, hasn’t worked since, and went on an interview the previous week.
b. A full-time student who is searching for a part-time job
c. A parent who leaves their job to stay home with their children full time.
d. Someone who was laid off 1 year ago, hasn’t worked since, and went on an interview 6 weeks ago.
e. A person who retired 2 years ago, but last week began looking for a new part-time job
a. Someone who was laid off 6 months ago, hasn’t worked since, and went on an interview the previous week - Unemployed Reason: The person is currently looking for a job after being laid off for six months. This person would be classified as unemployed.
b. A full-time student who is searching for a part-time job -
Unemployed Reason: The person is not currently employed, but they are searching for a job. This person would be classified as unemployed.
c. A parent who leaves their job to stay home with their children full time -
Not in the labor forceReason: The person has chosen to leave the labor force and stay home with their children full time. This person is not counted as part of the labor force.
d. Someone who was laid off 1 year ago, hasn’t worked since, and went on an interview 6 weeks ago - UnemployedReason: The person is currently looking for a job after being laid off for a year. This person would be classified as not employed.
e. A person who retired 2 years ago, but last week began looking for a new part-time job -
Employed Reason: The person is currently seeking work and is available for work. This person would be classified as employed.
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A local municipality is considering promoting tourism in the city. It will cost $20.000 to develop a plan. The anticipated annual benefits and costs are as follows: Annual benefits: Increased local income and tax collections Annual support service costs: Parking lot expansion, rest room,patrol car and street repair $112,500 $62,500 If the city uses a discount rate of 12% and a study period of ten years, what is the B/C ratio for this project,is this project justifiable according to the benefit-cost analysis? A) This project is justifiable based on the benefit-cost analysis B) This project is not justifiable based on the benefit-cost analysis C) It is ambiguous. D Answers AB and C are not correct
A local municipality is considering promoting tourism in the city. The B/C ratio for this project is this project justifiable according to the benefit-cost analysis is This project is justifiable based on benefit-cost analysis. The correct option is A.
The cost to develop a plan = $20,000
Annual benefits = Increased local income and tax collections = $112,500
Annual support service costs: Parking lot expansion, restroom, patrol car, and street repair = $62,500
Discount rate = 12%Study period = 10 years
Calculation of B/C ratio:
Net present value (NPV) of the benefits:
NPV = $112,500 {(1-1/(1+0.12)^10)/0.12} = $695,242.75
NPV of the costs :
NPV = $62,500 {(1-1/(1+0.12)^10)/0.12} = $387,143.88
Net Present Value (NPV) of the project:
NPV = -$20,000 + $695,242.75 - $387,143.88 = $288,098.87
Benefit-cost ratio (B/C) = NPV of benefits / NPV of costs = $695,242.75/$387,143.88 = 1.795.
The benefit-cost ratio for this project is 1.795. This project is justifiable based on the benefit-cost analysis since the B/C ratio is greater than 1. Option: A) This project is justifiable based on the benefit-cost analysis.
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a. XYZ company is looking for a 4-months term source of $800,000 to supplement working capital. Which source below should the company choose? The bank A accepts loans at annual nominal rate of interest of 15% a year. The bank B accepts loans at discount interest rate of 14% a year. The bank C accepts a loan with interest rate of 10% per year and deposits rate at 12%.
XYZ company should choose Bank B, which offers loans at a discount interest rate of 14% per year, for the 4-month term source of $800,000 to supplement working capital.
To determine the most suitable source for the 4-month term loan of $800,000, we compare the interest rates offered by three banks: Bank A, Bank B, and Bank C. Bank A offers loans at an annual nominal rate of interest of 15% per year. Bank B accepts loans at a discount interest rate of 14% per year. Bank C offers a loan with an interest rate of 10% per year and deposits rate at 12%.
Since the term required by XYZ company is 4 months, we need to adjust the interest rates to a comparable basis. Assuming a 12-month year, we divide the interest rates by 12 to obtain the monthly rates. Bank A's nominal rate becomes 1.25% per month (15% divided by 12), Bank B's discount rate remains at 1.17% per month (14% divided by 12), and Bank C's interest rate becomes 0.83% per month (10% divided by 12).
Based on the adjusted rates, Bank B offers the lowest interest rate of 1.17% per month, making it the most favorable option for XYZ company. Bank A has a higher rate of 1.25% per month, and Bank C's interest rate of 0.83% per month is lower but comes with a deposits rate of 1% higher than the loan rate. Therefore, Bank B is the best choice for XYZ company as it provides the lowest cost of borrowing for the required term.
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ABC Company had total earnings last year of £5,000,000, but expects total earnings to drop to £4,750,000 this year because of a slump in the housing industry. There are currently 1,000,000 shares of common stock outstanding. The company has £4,000,000 worth of investments to undertake this year. The company finances 40% of its investments with debt and 60% with equity capital. The company paid £3.00 per share in dividends last year.
(i) If the company follows a pure residual dividend policy, how large a dividend will each shareholder receive this year? Discuss the pros and cons of this policy from the perspective of company and shareholders.
(ii) If the company maintains a constant dividend payout ratio each year, how large a dividend will each shareholder receive this year? Discuss the pros and cons of this policy from the perspective of company and shareholders.
(iii) If the company follows a constant dollar dividend policy, how large a dividend will each shareholder receive this year? Discuss the pros and cons of this policy from the perspective of company and shareholders.
b. A corporation decides to cut its dividend from £2 per share to £1.50 per share. Give rationales/theories to explain why this action may cause the stock price to increase.
c. Bella owns 10,000 shares in Cinnamon Spice, which currently has 500,000 shares outstanding. The stock sells for $86 on the open market. Cinnamon Spice's management has decided on a two-for-one split.
(i) Will Bella's financial position change after the split, assuming that the stock's price will fall proportionately? Based on your finding, explain why a firm's management would want to have a stock split.
(ii) Assuming only a 35% decrease in the stock price, what will be Bella's value after the split? Based on your finding, what could have caused such reaction to stock price?
d. An article on stock repurchases in the Los Angeles Times noted "An increasing number of companies are finding that the best investment they can make these days is in themselves." Discuss this view. How is the desirability of repurchase affected by company prospects and the price of its stock?
(i) According to a pure residual dividend policy, the company will distribute dividends only after meeting its investment requirements. In this case, the company plans to invest £4,000,000, financed by 40% debt (£1,600,000) and 60% equity (£2,400,000). As earnings are expected to be £4,750,000, the funds available for dividends are £4,750,000 - £4,000,000 = £750,000. Dividing this amount by the number of outstanding shares (1,000,000), each shareholder would receive a dividend of £0.75 per share.
The pros of a pure residual dividend policy for the company are that it ensures investments are prioritized and adequately funded before distributing dividends. It helps maintain financial stability and the ability to fund growth opportunities. However, shareholders may view this policy negatively as their dividend income can be unpredictable and subject to fluctuations in earnings and investment needs.
(ii) With a constant dividend payout ratio, the company maintains a fixed percentage of earnings as dividends each year. If the company paid £3.00 per share last year, the dividend payout ratio can be calculated as £3.00 / (£5,000,000 / 1,000,000) = 0.60. Applying this ratio to this year's earnings (£4,750,000), the dividend per share would be £0.60 * (£4,750,000 / 1,000,000) = £0.57.
The advantage of a constant dividend payout ratio is that it provides shareholders with a consistent and predictable income stream. It can also signal stability and financial discipline. However, if the company's earnings decline, as in this case, the dividend amount may decrease, which can be viewed negatively by shareholders.
(iii) In a constant dollar dividend policy, the company maintains a fixed dividend amount per share regardless of earnings. If the company paid £3.00 per share last year, it would continue paying the same amount this year, resulting in a dividend of £3.00 per share.
The benefit of a constant dollar dividend policy for shareholders is that they receive a fixed dividend amount, providing stability and predictability. However, from the company's perspective, this policy may not be sustainable if earnings decline, as it can strain financial resources and potentially lead to a dividend that exceeds earnings, impacting the company's financial health.
b. When a corporation decides to cut its dividend, it may cause the stock price to increase due to several rationales/theories. One reason is that a dividend cut can signal financial prudence and a commitment to preserving cash for other important uses like investments or debt reduction. This action may be seen as a positive signal to investors and may increase confidence in the company's financial stability and future prospects, leading to an increase in the stock price.
c. (i) Bella's financial position will not change after the stock split, assuming the stock price falls proportionately. If the stock splits two-for-one, Bella will still own the same proportionate ownership in the company. A stock split does not affect the underlying value of the investment but increases the number of shares held while reducing the price per share. A firm's management may want to have a stock split to make the stock price more affordable to a wider range of investors and potentially increase liquidity in the stock market.
(ii) Assuming a 35% decrease in the stock price after the split, Bella's value after the split would be 10,000 shares * ($86 * 0.65) = $559,000. Such a decrease in stock price after a split could be caused by various factors, including changes in market conditions, investor sentiment, company performance, or other external factors impacting the stock's.
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evelina has a variety of inventory items that have become obsolete. how does she account for this inventory adjustment
Evelina can account for the inventory adjustment of the obsolete inventory items using the process of write-off. When inventory items have become obsolete, the write-off is the best method to remove them from the stock as it reflects the true financial situation of the company. During this process, the value of the obsolete inventory items is adjusted to zero, and they are no longer included in the financial statements.In order to account for the inventory adjustment of the obsolete inventory items using write-off method, the following journal entry should be recorded:
Debit: Loss on write-off of inventory (expense account)
Credit: Inventory (asset account)
The debit will record the expense of writing off the obsolete inventory items, and the credit will reduce the inventory account by the same amount. This method will help to show the true value of inventory in the balance sheet.
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Inventory adjustments are crucial in ensuring that the financial statements accurately reflect the inventory situation of the company.
When the inventory items become obsolete, Evelina should account for this inventory adjustment by using the direct method.
The direct method entails crediting the inventory account with the amount of inventory value and debiting the cost of goods sold account with the same amount. The inventory account should be debited, and the cost of goods sold account should be credited if the obsolete inventory has not yet been sold by the company.
However, if the obsolete inventory has already been sold, the entry will be different. In this case, Evelina should debit the sales account with the proceeds from the sale, credit the inventory account with the amount of obsolete inventory that was sold, and then debit the cost of goods sold account with the cost of the sold obsolete inventory.
Therefore, by using the direct method, Evelina can adjust her inventory to account for the obsolete items.
In general, inventory adjustments are crucial in ensuring that the financial statements accurately reflect the inventory situation of the company. These adjustments, when correctly made, help to improve the quality of information that investors use to make investment decisions.
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A manufacturer has the capability to produce both chairs and tables. Both products use the same materials (wood, nails and paint) and both have a setup cost ($100 for chairs, $200 for tables). The firm earns a profit of $20 per chair and $65 per table and can sell as many of each as it can produce. The daily supply of wood, nails and paint is limited. To manage the decision-making process, an analyst has formulated the following linear programming model: Max 20x1 + 65x2 - 100yı - 20042 s.t. 5x1 + 10x2 < 100 {Constraint 1} 20x1 + 50x2 > 250 {Constraint 2} 1x1 + 1.5x2 > 10 Constraint 3} Myı 2 X1 Constraint 4} My2 + x2 {Constraint 5} 1, if product is produced o, otherwise yi = Which of the constraints limit the amount of raw materials that can be consumed? Multiple Choice Constraint 1 Constraint 4 0 Constraint 5 O Constrain Constraint 1 and 4 only 0 None of these
The linear programming model presented in the question aims to determine the optimal production quantities of chairs and tables that maximize the manufacturer's profit while taking into account limited raw materials and setup costs.
The objective function of the model is:
Max 20x1 + 65x2 - 100y1 - 200y2
where x1 is the quantity of chairs produced, x2 is the quantity of tables produced, y1 is a binary variable that takes a value of 1 if chairs are produced and 0 otherwise, and y2 is a binary variable that takes a value of 1 if tables are produced and 0 otherwise. The objective function represents the total profit earned by the manufacturer, which is the difference between the revenue earned from selling chairs and tables and the setup costs incurred.
The model also includes five constraints that limit the production quantities of chairs and tables based on the availability of raw materials and the setup costs. The first constraint limits the total amount of wood and nails that can be consumed per day to 100 units, while the second constraint sets a minimum production requirement for chairs and tables combined. The third constraint limits the total amount of paint that can be consumed per day to 10 units. The fourth constraint ensures that y1 is equal to or greater than x1, which means that chairs can only be produced if y1 is equal to 1. Similarly, the fifth constraint ensures that y2 is equal to or greater than x2, which means that tables can only be produced if y2 is equal to 1.
Out of these constraints, the first three limit the amount of raw materials that can be consumed by the manufacturer per day. Constraint 1 limits the total amount of wood and nails that can be consumed to 100 units, which means that the total consumption of these materials by chairs and tables cannot exceed 100 units per day. Constraint 3 limits the total amount of paint that can be consumed to 10 units, which means that the total consumption of paint by chairs and tables cannot exceed 10 units per day.
Therefore, the constraints that limit the amount of raw materials that can be consumed are:
Constraint 1: 5x1 + 10x2 < 100
Constraint 3: x1 + 1.5x2 > 10
In summary, the linear programming model presented in the question helps the manufacturer determine the optimal production quantities of chairs and tables that maximize its profit while ensuring that the consumption of raw materials and setup costs are within the available limits. The constraints that limit the amount of raw materials that can be consumed are Constraint 1 and Constraint 3.
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According to Writing (2019), the purchasing department is responsible for procuring raw materials and other resources at the best possible price. In relation to the above, and with the aid of examples, discuss the functions of the purchasing management.
The functions of purchasing management include sourcing suppliers, negotiating contracts, managing supplier relationships, ensuring timely delivery, and controlling costs.
What is the explanation for this ?Purchase management is the management of the company's purchases of products and servicesfrom suppliers and vendors.
For example,purchasing managers may identify reliable suppliers, negotiate favorable terms,and track inventory levels to optimize procurement efficiency.
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The following are all examples of product costs:
A Direct material, direct labor and indirect labor.
B Direct labor, VP of sales salary, and insurance on the factory.
C Depreciation on the factory equipment, depreciation on the office building, and depreciation on the factory building.
D Factory insurance, interest expense, and property taxes on the factory.
E Office supplies, sales commissions, and maintenance costs on office copier.
Product cost is the cost of manufacturing or purchasing a product. Product costs may include direct material, direct labor, and manufacturing overhead. The correct answer is A: Direct material, direct labor, and indirect labor.
There are two primary categories of cost when making a product or offering a service: product costs and period costs. Product costs are expenditures directly related to the manufacturing of a product.
The cost of raw materials, labor, and manufacturing overhead is all part of the total product cost.
Period costs, on the other hand, are costs incurred by the company in running the business.
Office expenses, sales commissions, and maintenance costs are examples of period costs.
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Group that has been given power by Congress to enforce the proper application of financial reporting rules for companies whose securities are publicly traded.
The group that has been given power by Congress to enforce the proper application of financial reporting rules for companies whose securities are publicly traded is the Securities and Exchange Commission .
The Securities and Exchange Commission (SEC) is a regulatory agency established by the U.S. federal government to protect investors, maintain fair and efficient markets, and facilitate capital formation. One of its primary responsibilities is to enforce the proper application of financial reporting rules for companies whose securities are publicly traded.
The SEC has been granted this power by Congress through legislation such as the Securities Exchange Act of 1934 and the Sarbanes-Oxley Act of 2002. These laws require publicly traded companies to adhere to certain financial reporting standards and disclose accurate and timely information to investors.
To enforce these rules, the SEC has the authority to conduct investigations, impose sanctions, and bring legal actions against companies or individuals that violate securities laws. It has the power to review financial statements, audit reports, and other relevant documents to ensure compliance with accounting principles and disclosure requirements.
By overseeing and regulating financial reporting practices, the SEC aims to promote transparency, integrity, and confidence in the financial markets. Its enforcement efforts help protect investors from fraudulent or misleading financial information and contribute to the overall stability and fairness of the securities industry.
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Given the following data, what is this person's net worth? GIVEN DATA Balance on car loan $3,250 Balance on student loans $9,850 Cash in checking account $1,100 Clothing purchases $350 Current value of automobile $10,500 Donations $100 Entertainment $250 Food expenses - monthly $425 Home computer $2,200 $5,500 Household possessions Light, gas water bill $110 O $10,205 O $9,805 O $10,705 $9,505 Loan payment Lunches/parking at work Monthly auto insurance Monthly car note Monthly gross income Monthly rent expense Monthly take-home pay Savings account balance Stereo & video equipment Telephone bill-home & cell VISA balance $230 $115 $120 $320 $4,500 $900 $3,650 $2,100 $3,550 $155 $1,145
To calculate the net worth, we need to sum up all the assets and subtract all the liabilities.
Assets:
Current value of automobile: $10,500
Cash in checking account: $1,100
Savings account balance: $3,650
Home computer: $2,200
Stereo & video equipment: $155
Total Assets = $10,500 + $1,100 + $3,650 + $2,200 + $155 = $17,605
Liabilities:
Balance on car loan: $3,250
Balance on student loans: $9,850
VISA balance: $1,145
Total Liabilities = $3,250 + $9,850 + $1,145 = $14,245
Net Worth = Total Assets - Total Liabilities = $17,605 - $14,245 = $3,360
Therefore, the person's net worth is $3,360.
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QUESTION 74 Given The Following Data, What Is This Person's Net Worth? GIVEN DATA Balance On Car Loan Balance On Student Loans Cash In Checking Account Clothing Purchases Current Value Of Automobile Donations Entertainment Food Expenses - Monthly Home Computer Household Possessions Light, Gas & Water Bill O $9,505 O $10,705 O $10,205 0 $9,805 $3,250 $9,850
LP. Model Minimize Subject to: 7X+11Y266 (C₂) 16X+4Y280 (C₂) X,Y 20 On the graph on right, constraints C, and C, have been drawn. Using the point drawing tool, plot all the comer points for the feasible area. Z= 15X+15Y CO 24 22- 20- 18- 16- 14- 124 10- 8 16 4 2 10 12 14 16 18 20 22 24 GOO Q S
The given problem is a Linear Programming problem. It can be solved using graph method. The constraints are: 7X+11Y≥266 (C1) 16X+4Y≥280 (C2) X,Y≥0 20 (C3)To plot these constraints, we can start with equation of line for each constraint.
For C1: 7X + 11Y = 266 → Y = (-7/11)X + 266/11 For C2: 16X + 4Y = 280 → Y = (-4/16)X + 70 To plot the feasible area, we need to find the intersection points of the lines representing the constraints. This gives the values of X and Y that satisfy both constraints. Then, we need to check if they lie in the feasible region defined by non-negativity constraint and plot them on the graph. Computation of intersection points: (-8.14, 20.36) = Intersection of C1 and C2 (-4, 0) = Intersection of C1 and C3 (20, 0) = Intersection of C2 and C3 (0, 0) = Intersection of all three lines. These intersection points are the vertices of feasible region and can be plotted on the graph as shown: Z = 15X + 15Y CO 24 22 20 | X Y | 18 |0 20| 16 |4 16| 14 |8 12| 12 |12 8| 10 |16 4| 8 |20 0| 6 4 2 2 4 6 8 10 12 14 16 18 20 22 24 GOO Q S
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The feasible area is bounded by the corner points: (0, 24.18), (38, 0), (17.5, 0), (10, 30) and (-22.15, 25.96).
The given LP model is shown below:
Model Minimize Z = 15X + 15Y
Subject to:7X + 11Y ≤ 266 ... (C1)16X + 4Y ≤ 280 ... (C2)X, Y ≥ 0; X, Y ≤ 20
The constraints are:C1 : 7X + 11Y ≤ 266 ⇒ 11Y ≤ -7X + 266
⇒ Y ≤ (-7/11)X + (266/11)C2: 16X + 4Y ≤ 280
⇒ 4Y ≤ -16X + 280 ⇒ Y ≤ (-16/4)X + (280/4)
⇒ Y ≤ -4X + 70
Graphing these constraints, we get:
So, we have to find out all the corner points for the feasible area as follows:
For C1, put X = 0, we get
Y = (266/11) = 24.18 (approx)
For C1, put Y = 0, we get
X = (266/7) = 38
For C2, put X = 0, we get
Y = (280/4) = 70
For C2, put Y = 0, we get
X = (280/16) = 17.5
Now, to get the coordinates of other corner points, solve the equations of the lines containing the boundary constraints.
C1: Y = (-7/11)X + (266/11)
C2: Y = -4X + 70
Intersection of these lines: (-22.15, 25.96) and (10, 30)
Plotting all the corner points, we get:
Therefore, the feasible area is bounded by the corner points: (0, 24.18), (38, 0), (17.5, 0), (10, 30) and (-22.15, 25.96).
The detailed answer is as follows:
To find out all the corner points for the feasible area, we have to solve the pairs of equations of the constraints, as follows:C1: Y = (-7/11)X + (266/11)C2: Y = -4X + 70
Solving these two equations, we get:(-22.15, 25.96) and (10, 30)
Thus, the feasible area is bounded by the corner points: (0, 24.18), (38, 0), (17.5, 0), (10, 30) and (-22.15, 25.96).
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