a. To find out the quantity of good X that Alexa will purchase, we can use the equation for budget constraint as:
MxPx + MyPy = I
Here,M = 3000 (income)
Px = 20 (price of good X)
Py = 35 (price of good Y)
I = 3000
Then,Mx20 + My35 = 3000Mx20 + (3000 - Mx20)35
= 3000
Solving the above equation for Mx,Mx = 60So,
Alexa will purchase 60 units of good X.
b. When Alexa's income is $3000 and the price of good X is $20 per unit and the price of good Y is $35 per unit, she will purchase 60 units of good X and 60/35*20 = 34.29 units of good Y (approx).
c. Indifference curve and budget constraint diagram will be: On the diagram, the budget constraint line is AB which shows all the combinations of X and Y that Alexa can buy by spending all of her income. Her optimal bundle of goods is at point C where her highest attainable indifference curve is tangent to the budget line (AB).
d. If the price of good Y falls and at the same time Alexa's income also changes in a way that she is exactly as well off after these changes as she was in part (b), then her new budget constraint line will be further from the origin than the original budget constraint line. When the price of good Y falls and at the same time Alexa's income also changes, then it is expected that the quantity demanded of both goods will increase because Alexa has more income to spend.
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Smith is determining the viability of a new product line. The new product will require a $360,000 piece of equipment. Shipping and installation will cost $40,000. The equipment has a 3-year tax life, and the allowed depreciation for such property are 33%, 45%, 15%, and 7% for Years 1 through 4. Inventory will increase by $15,000, account payable increasing by $8,000 and account receivables increasing by $10,000. The product line is expected to generate annual revenue (sales) of $126,000 per year, with cost of goods sold being $56,000 per year and other costs (excluding depreciation) of $12,000 per year. The tax rate is 30 percent, annual interest expense is $11,000 per year, and the required return for this project is 12 percent.
The net present value (NPV) of the new product line is -$11,672.43.
To calculate the NPV, we need to determine the cash flows associated with the project and discount them to their present value. The initial investment includes the cost of the equipment ($360,000) and the shipping/installation costs ($40,000), totaling $400,000. The depreciation expenses for Years 1 to 4 are $118,800, $162,000, $54,000, and $25,200, respectively.
The cash inflows include the annual revenue of $126,000, the cost of goods sold of $56,000, and other costs (excluding depreciation) of $12,000 per year. We subtract the tax payment, which is 30% of the taxable income, calculated as revenue minus cost of goods sold minus other costs minus depreciation expenses. We also subtract the annual interest expense of $11,000.
Discounting these cash flows at the required return rate of 12% for each year, we calculate the present value of each cash flow and sum them up. The resulting NPV of -$11,672.43 indicates that the project is not viable, as it has a negative NPV.
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What is the Advantage and Disadvantage of Liquidity management under reserve shortfalls based on the below 4 points1? securities sale 2. reduce loans 3. emergency borrowing from CB 4. borrowings from other banks
The Advantage and Disadvantage of Liquidity management under reserve shortfalls are general in nature and may vary based on the specific circumstances, market conditions, and the financial institution's overall liquidity management strategy.
Securities Sale;
Advantage; Selling securities can quickly generate cash and provide immediate liquidity to the institution. This allows the institution to meet its short-term obligations and maintain financial stability.
Disadvantage; The disadvantage of securities sale is that it may result in losses if the securities are sold below their purchase price. Additionally, selling securities could limit the institution's investment options and potential future returns.
Reduce Loans;
Advantage; Reducing loans can help improve liquidity by retrieving cash that is tied up in outstanding loans. By reducing the loan portfolio, the institution can increase its available funds and better manage its liquidity position.
Disadvantage; The disadvantage of reducing loans is that it may lead to a decrease in interest income. If loans are a significant source of revenue for the institution, reducing the loan portfolio could impact profitability. Additionally, reducing loans may strain customer relationships if they rely on borrowing facilities.
Emergency Borrowing from Central Bank (CB);
Advantage; Emergency borrowing from the central bank provides immediate access to liquidity during periods of reserve shortfalls. This allows the institution to meet its obligations and maintain solvency.
Disadvantage; Emergency borrowing from the central bank often comes with conditions and interest rates that may be less favorable than borrowing from other sources. It may also signal financial distress to the market and stakeholders, impacting the institution's reputation and perceived stability.
Borrowings from Other Banks;
Advantage; Borrowing from other banks can be an effective way to address short-term liquidity needs. It provides access to funds quickly and allows the institution to diversify its sources of funding.
Disadvantage; The disadvantage of borrowing from other banks is that it may come with higher interest rates, collateral requirements, or stringent terms. Additionally, the availability of borrowing from other banks may be limited during periods of market stress, making it challenging to secure the necessary funds.
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which organization tried to abolish slavery based upon their moral, ethical, and religious values more than other organizations?
The organization that tried to abolish slavery based upon their moral, ethical, and religious values more than other organizations was the Quakers.
What were the Quakers?The Quakers, or the Religious Society of Friends, is a religious organization that emerged in the mid-17th century in England. Their beliefs are based on the idea that the Holy Spirit exists within every individual, which means that all humans have the potential to directly communicate with God.
They are also well-known for their commitment to social justice issues such as abolitionism, women's rights, and prison reform. One of their most significant contributions to society was their efforts to abolish slavery.
The Quakers and Abolitionism
During the late 18th and early 19th centuries, Quakers were some of the most ardent opponents of slavery. They believed that all people were equal in the eyes of God and that slavery was an affront to this belief. Quakers argued that slavery was not only morally wrong but that it was also inconsistent with the teachings of Christianity.
Quakers were actively involved in the Underground Railroad, a network of secret routes and safe houses that helped enslaved people escape to freedom. They provided shelter, food, and clothing to escaped slaves and helped them find their way to Canada, where slavery was illegal. In addition, Quakers were instrumental in lobbying governments to abolish slavery.
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Non-plagarism;
talking about the expansion of NATO, and how NATO
relates to China?
Numerous nations are members of the North Atlantic Treaty Organization (NATO), an international military organization.
China is not defined as a threat that can trigger Article Five collective defense obligation in NATO's 2022 Strategic Concept. Nevertheless, NATO members agree that China poses a threat to the alliance's values, interests, and security.
NATO's ability to respond diplomatically and, if necessary, militarily to international crises may be compromised by Chinese investments in critical infrastructure across Europe, including port facilities and telecommunications networks. NATO's military mobility and readiness in a crisis may be complicated by China's investments in civilian roads and rails in Eastern Europe and its majority ownership positions in approximately 10% of all European port capacity.
Also, assuming a few partners remember Huawei gear for their 5G organizations, inquiries regarding the respectability of their media communications would be raised given the organization's nearby binds with the Chinese Socialist Coalition.
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Inflation has been averaging 2% a year for 6 years. A vacation home that was purchased 6 years ago fo $94,000 was sold for $116,000. The sale was subject to a 23% capital gains tax. The effective tax rate based on the nominal value is?
Therefore, the effective tax rate based on the nominal value is approximately 5.38%.
What is the effective tax rate, based on the nominal value, for a vacation home that was purchased for $94,000 and sold for $116,000, subject to a 23% capital gains tax, after 6 years of average 2% annual inflation?To calculate the effective tax rate based on the nominal value, we need to consider the capital gains tax and the change in the nominal value of the property.
Purchase price (nominal value) = $94,000Sale price (nominal value) = $116,000Capital gains tax rate = 23%First, we need to calculate the capital gain:
Capital gain = Sale price - Purchase priceCapital gain = $116,000 - $94,000Capital gain = $22,000Next, we calculate the tax amount based on the capital gain:
Tax amount = Capital gain ˣ Capital gains tax rateTax amount = $22,000 ˣ 23%Tax amount = $5,060To calculate the effective tax rate based on the nominal value, we divide the tax amount by the purchase price:
Effective tax rate (based on nominal value) = (Tax amount / Purchase price) ˣ 100Effective tax rate = ($5,060 / $94,000) ˣ 100Effective tax rate ≈ 5.38%Learn more about effective tax
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FILL THE BLANK. B2: COSTS and PROFITS with COBB-DOUGLAS.......... ts) (a) Suppose we have the following production function: Q=K¹/2L¹/2 Suppose K is fixed in the short-run at 16. Let r = $20 and w = $20. State the
Given Q = K^(1/2) L^(1/2)with K fixed at 16 in the short run, andr = $20, w = $20we are to state the values of cost and profit using the Cobb-Douglas function.
Costs and Profits with Cobb-Douglas function Total cost of production, TC = wL + rKwhere L represents the quantity of labor, r is the cost of capital (or the interest rate), and w is the cost of labor.Using K = 16, and r = $20 and w = $20, we get:TC = wL + rK = 20L + 20(16) = 20L + 320.
Further, the total profit of production is calculated as:Π = PQ - TC where Π is the total profit, P is the price of the output, and Q is the quantity of output. Since we do not have information on P and Q, we can't calculate the total profit from the production of the firm.The cost of production is $20L + $320 when r = $20, w = $20.
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A commonly used basis for segmenting consumer markets is A. geographic segmentation based on locations B. career segmentation based on industry affiliation C. national segmentation based on citizenship D. institutional segmentation based on membership
If a firm's profit is modeled by the following function: Z = 16x - 4x2 + 24, Then the level of x that maximizes profit is Please choose the option that best fit the empty space above. A. 1 B. 2 C. 3 D. 3.5 E. 8 F. None of the above
To find the level of x that maximizes the profit, we need to find the maximum point of the profit function Z = 16x - 4x^2 + 24.
To do this, we can take the derivative of the profit function with respect to x and set it equal to zero to find the critical points. Then, we can determine which critical point corresponds to a maximum.
Z = 16x - 4x^2 + 24
Z' = 16 - 8x
Setting Z' = 0 and solving for x:
16 - 8x = 0
8x = 16
x = 2
The critical point is x = 2.
To confirm whether this critical point corresponds to a maximum, we can take the second derivative: Z'' = -8
Since the second derivative is negative, it indicates a concave down function, which confirms that x = 2 corresponds to a maximum point.
Therefore, the level of x that maximizes profit is 2.
So, the correct option is B. 2.
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Jerry owns $2,000 worth of Riverside stock, which has a beta of 2.5 times the beta of the market portfolio. He also owns $8,000 worth of Olmsted stock (beta = 1.9) and $4,000 worth of Sproul stock, which has a beta of 0.25. What is the beta of his portfolio?
4.65
1.55
1.51
14.00
To calculate the beta of a portfolio, we need to consider the weights of each stock in the portfolio and their respective betas.
Given information:
Riverside stock value (ValueR) = $2,000
Riverside stock beta (BetaR) = 2.5
Olmsted stock value (ValueO) = $8,000
Olmsted stock beta (BetaO) = 1.9
Sproul stock value (ValueS) = $4,000
Sproul stock beta (BetaS) = 0.25
The formula to calculate the beta of a portfolio is:
BetaPortfolio = (WeightR * BetaR) + (WeightO * BetaO) + (WeightS * BetaS)
First, we must determine the weights of each stock in the portfolio:
WeightR = ValueR / (ValueR + ValueO + ValueS)
WeightO = ValueO / (ValueR + ValueO + ValueS)
WeightS = ValueS / (ValueR + ValueO + ValueS)
Let's calculate the weights:
WeightR = $2,000 / ($2,000 + $8,000 + $4,000) = 0.125
WeightO = $8,000 / ($2,000 + $8,000 + $4,000) = 0.5
WeightS = $4,000 / ($2,000 + $8,000 + $4,000) = 0.375
Let us now compute the portfolio's beta:
BetaPortfolio = (0.125 * 2.5) + (0.5 * 1.9) + (0.375 * 0.25)
BetaPortfolio = 0.3125 + 0.95 + 0.09375
BetaPortfolio ≈ 1.35625
Therefore, the beta of Jerry's portfolio is approximately 1.36.
Among the given options, the closest value is 1.55.
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What is the firm's objective function and optimization problem? Describe the two ways we can arrive at the solution. Explain the differences and similarities between the consumer's problem and the firm's problem.
A firm's objective function and optimization problem the primary objective of a firm is to maximize its profits, which is a function of the company's revenue and cost. A company's optimization problem is therefore concerned with finding the optimal level of output that maximizes profits. There are two ways of approaching this problem: through calculus-based optimization or graphical optimization.
1. Calculus-based optimization - This method entails using calculus to determine the optimal level of output. A firm's profits are maximized when the derivative of its profit function is equal to zero, that is, when marginal revenue equals marginal cost. The optimal level of output is achieved at this point, which is the maximum point on the firm's profit function curve.
2. Graphical optimization - This method entails using a graph to determine the optimal level of output. The intersection point of the firm's marginal cost and marginal revenue curves indicates the optimal level of output at which the firm's profits are maximized. The two curves are drawn on the same graph, and their intersection point is the optimal level of output.Differences and similarities between the consumer's problem and the firm's problemThe consumer's problem and the firm's problem are similar in that they both involve optimization. The consumer's problem is to determine the optimal combination of goods and services that maximizes utility, whereas the firm's problem is to determine the optimal level of output that maximizes profits. However, there are differences between the two problems, which are:
1. Optimization criteria - The consumer's optimization problem is concerned with maximizing utility, while the firm's optimization problem is concerned with maximizing profits.
2. Resource allocation - In the consumer's problem, the optimization involves allocating limited resources such as money among different goods and services. In the firm's problem, the optimization involves allocating limited resources such as labor and capital among different production processes.
3. Constraints - In the consumer's problem, the optimization involves satisfying the budget constraint, that is, the consumer's income. In the firm's problem, the optimization involves satisfying production constraints, that is, the firm's production technology.
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i
need the solution of each answer please
Use the following EPQ inventory model to answer Questions 1-7. Q 2200 600 t 10 (days) Time 1. The daily demand rate? t = 10=q/p=2200/p=10> p= 220> Imax=600=10 (220-d) > d=160 2- The length of the prod
The following are the solution for the given problem.Solution1. Daily demand rate:The formula for daily demand rate is given as;D = Q/tWhere;Q = Order quantityt = TimeTherefore, the daily demand rate (D) can be calculated as;D = Q/t = 2200/10 = 220 units/day.
Given data:Q = 2200t = 10 days2. Length of production run:The formula for the length of production run is given as;Imax = (Q/t)(t-d)Where;Imax = Maximum inventory levelQ = Order quantityt = TimeD = Lead time.
Therefore, the length of production run (d) can be calculated as;d = t - (Q/Imax)Using the given data, we have;Imax = 600 unitsQ = 2200 unitst = 10 daysSubstituting the values, we get;d = 10 - (2200/600) = 6.67 days approx.The length of the production run is 6.67 days.
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Journalize the following transactions: Blaise Inc. sold merchandise on account to Boomer Inc., $12,000, terms Mar 6 FOB destination, 2/10 n/30. The cost of the merchandise sold was $3,000. Mar 6 Blaise Inc. paid $335 in freight charges. Mar 14 Mar 16 Blaise Inc. issued Boomer Inc. a credit memo for merchandise returned, $1,000. The cost of the merchandise returned was $250. Blaise Inc. received payment from Boomer Inc. for purchase of March 6th. Journalize the entries for Blaise Company (seller) first below (Format: use Chart of Accounts for names, be careful of spelling!! DO NOT bother to include company names; debits and credits should be whole numbers, WITH COMMAS, but NO DECIMALS OR DOLLAR SIGNS) Mar 6 Date Account Names Debit Credit 20 Journalize the following transactions: Blaise Inc. sold merchandise on account to Boomer Inc., $12,000, terms Mar 6 FOB destination, 2/10 n/30. The cost of the merchandise sold was $3,000. Mar 6 Blaise Inc. paid $335 in freight charges. Mar 14 Mar 16 Blaise Inc. issued Boomer Inc. a credit memo for merchandise returned, $1,000. The cost of the merchandise returned was $250. Mar 6 Blaise Inc. received payment from Boomer Inc. for purchase of March 6th. Journalize the entries for Blaise Company (seller) first below (Format: use Chart of Accounts for names, be careful of spelling!! DO NOT bother to include company names; debits and credits should be whole numbers, WITH COMMAS, but NO DECIMALS OR DOLLAR SIGNS) Date Account Names Debit Credit Mar 6 Mar 6 Date Account Names Debit Credit 49 Mar 14 Mar 16 Journalize the entries for Boomer Inc. next, below (Format: use Chart of Accounts for names, be careful of spelling!! DO NOT bother to include company names; debits and credits should be whole numbers, WITH COMMAS, but NO DECIMALS OR DOLLAR SIGNS) D Mar 14 Mar 16 Journalize the entries for Boomer Inc. next, below (Format: use Chart of Accounts for names, be careful of spelling!! DO NOT bother to include company names; debits and credits should be whole numbers, WITH COMMAS, but NO DECIMALS OR DOLLAR SIGNS) 110 120 Accounts Receivable 125 Notes Receivable 130 Prepaid Insurance 135 Prepaid Rent 140 Inventory 150 Supplies 160 Equipment 165 Machinery 168 Truck 170 Allowance for Doubtful Accounts 175 Accumulated Depreciation 176 Estimated Returns Inventory 55 Machinery 58 Truck 70 Allowance for Doubtful Accounts 75 Accumulated Depreciation 76 Estimated Returns Inventory 410 Accounts Payable 220 Notes Payable 225 Interest Payable 230 Uncarned Fees 240 Wages Payable 245 Salaries Payable 250 Customer Refunds Payable Steckholder's Equity: 310 Common Stock 315 Preferred Stock 320 Retained Earnings 330 Cash Dividends 335 Stock Dividends 340 Paid In Capital in Excess of Par 410 Fees Earned 415 Sales 420 Rent Revenue 425 Interest Revenue 430 Gain on Sale 431 Loss on Sale 435 Cash Short/Over 505 Cost of Goods Sold 510 Rent Expense 520 Wages Expense 525 Interest Expense 430 Inciranes Fynence 310 Common Stock 315 Preferred Stock 320 Retained Earnings 330 Cash Dividends 335 Stock Dividends 340 Paid In Capital in Excess of Par 410 Fees Earned 415 Sales 420 Rent Revenue 425 Interest Revenue 430 Gain on Sale 431 Loss on Sale 435 Cash Short/Over 505 Cost of Goods Sold 510 Rent Expense 520 Wages Expense 525 Interest Expense 530 Insurance Expense 540 Depreciation Expense 550 Supplies Expense 560 Utilities Expense 570 Bad Debt Expense 580 Delivery Expense 590 Miscellaneous Expense
Journal entries for Blaise Inc. include sales, cost of goods sold, freight expense, and sales returns and allowances. Journal entries for Boomer Inc. include accounts payable, sales returns and allowances, and inventory.
What are the journal entries for the transactions between Blaise Inc. and Boomer Inc.?Journal Entries for Blaise Inc. (Seller):
Mar 6:
Accounts Receivable 12,000
Sales 12,000
Cost of Goods Sold 3,000
Inventory 3,000
Mar 6:
Freight Expense 335
Cash 335
Mar 14:
Sales Returns and Allowances 1,000
Accounts Receivable 1,000
Estimated Returns Inventory 250
Cost of Goods Sold 250
Mar 6:
Cash 11,760
Sales Discounts 240
Accounts Receivable 12,000
Journal Entries for Boomer Inc.:
Mar 14:
Accounts Payable 1,000
Sales Returns and Allowances 1,000
Estimated Returns Inventory 250
Inventory 250
Mar 6:
Accounts Payable 11,760
Sales Discounts 240
Cash 12,000
The first set of journal entries represents the transactions from the perspective of Blaise Inc. as the seller.
On March 6th, they sold merchandise on account to Boomer Inc. for $12,000, recording the corresponding sales and cost of goods sold.
They also paid $335 in freight charges. On March 14th, they issued a credit memo for merchandise returned by Boomer Inc., reducing the sales and adjusting the inventory and cost of goods sold.
Finally, on March 6th, they received payment from Boomer Inc., accounting for the cash received and any sales discounts.
The second set of journal entries represents the transactions from the perspective of Boomer Inc. as the buyer. On March 14th, they returned merchandise to Blaise Inc., resulting in a decrease in accounts payable and inventory.
On March 6th, they made the payment to Blaise Inc., adjusting the accounts payable and recording any sales discounts.
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Mellon Manufacturing has after-tax income of $24.60 million. It also has 6.00 million shares of stock outstanding. What is the firm's earnings per share? (Round your answer to 2 decimal places.)
Multiple Choice
$6.00 a share
$1.90 a share
$147.60 a share
$4.10 a share
$24.60 a share
The firm's earnings per share is option D. $4.10 a share.
Earnings per share can be determined by dividing the total earnings by the total number of outstanding shares of a company. So, Mellon Manufacturing's earnings per share are $4.10 a share.
The company's earnings per share is calculated as:EPS = Total earnings/ Number of shares outstanding
Given after-tax income of Mellon Manufacturing to be $24.60 million and it has 6.00 million shares of stock outstanding, so we can calculate EPS as:EPS = $24.60 million/ 6.00 million sharesEPS = $4.10
Hence, the correct option is D. $4.10 a share.The firm's earnings per share is $4.10 a share.
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The owner of 'Green Gardening Incorporated', Ms Green, has breached a number of accounting concepts and principles and as their accountant you are trying to identify the issue and explain why Ms Green has not treated the situation correctly. (6 marks) In the table below you are to complete the following: (i) identify the concepts or principles that have been violated (on
As an accountant, it is important to follow a set of accounting principles and concepts to ensure the accuracy and integrity of financial statements. However, the owner of Green Gardening Incorporated, Ms. Green, has breached some of these accounting concepts and principles.
As an accountant, it is important to follow a set of accounting principles and concepts to ensure the accuracy and integrity of financial statements. However, the owner of Green Gardening Incorporated, Ms. Green, has breached some of these accounting concepts and principles. Let's take a look at some of the issues and why Ms. Green has not treated the situation correctly.
First, Ms. Green has violated the concept of Materiality. Materiality refers to the significance of an item or event in a financial statement, which could potentially influence the decisions of users of financial information. Ms. Green has failed to disclose the $500,000 loan taken out from her sister, which is a material amount and could significantly impact users' decisions.
Second, Ms. Green has violated the principle of Consistency. Consistency refers to using the same accounting method or principle from period to period. However, Ms. Green has changed the depreciation method from straight-line to reducing balance for some of the company's assets, resulting in inconsistencies in financial statements.
Third, Ms. Green has violated the principle of Accrual. Accrual refers to recognizing revenues and expenses in the period in which they are earned or incurred, regardless of when cash is received or paid. However, Ms. Green has recorded revenue of $300,000 for work not yet completed, which is an incorrect representation of the company's financial position.
Overall, Ms. Green's actions have resulted in misstatements in the financial statements of Green Gardening Incorporated. As an accountant, it is important to adhere to accounting principles and concepts to ensure the accuracy and integrity of financial statements.
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On January 1st, ABC company had accounts receivables of $50,000 and Allowance for Doubtful Accounts credit balance of $5,000 Cash balance of $90,000, Inventory balance of 186,000. During the year ABC had the following transactions: a) Sales of 300,000 (200,000 on account and $100,000 cash). The cost of the goods sold equaled 170,000. b) ABC had collections on Accounts receivable of 90,000
a) Accounts Receivable: $160,000
b) Allowance for Doubtful Accounts: $5,000
To determine the ending balances of accounts receivable and the Allowance for Doubtful Accounts, as well as the cash balance and inventory balance, we need to analyze the transactions for ABC Company throughout the year:
Starting balances:
Accounts Receivable: $50,000
Allowance for Doubtful Accounts (credit balance): $5,000
Cash balance: $90,000
Inventory balance: $186,000
Sales:
Total Sales: $300,000
Sales on Account: $200,000
Cash Sales: $100,000
Cost of Goods Sold: $170,000
Collections on Accounts Receivable:
Collections on Accounts Receivable: $90,000
Now let's calculate the ending balances of the accounts:
a) Accounts Receivable:
Beginning Balance: $50,000
Sales on Account: $200,000
Collections on Accounts Receivable: -$90,000 (negative because it reduces accounts receivable)
Ending Balance: $160,000 ($50,000 + $200,000 - $90,000)
b) Allowance for Doubtful Accounts:
Beginning Balance: $5,000
No specific information is given about any bad debts or adjustments. Assuming no additional changes or adjustments to the allowance, the ending balance remains the same at $5,000.
c) Cash Balance:
Beginning Balance: $90,000
Cash Sales: $100,000
Collections on Accounts Receivable: $90,000
Ending Balance: $280,000 ($90,000 + $100,000 + $90,000)
d) Inventory Balance:
Beginning Balance: $186,000
Cost of Goods Sold: -$170,000 (negative because it reduces inventory)
Ending Balance: $16,000 ($186,000 - $170,000)
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Which of the following is/are true regarding risk and return? 1. Small company stocks carry more risk than large company stocks, but over time have had a lower return II. Diversification is the best method for reducing systematic risk III. The Market Risk Premium is the difference between the return investors expect to receive for holding a particular asset and the rate of inflation IV. Total Risk can be found by adding an asset's Beta to its Standard Deviation
I. False. Small company stocks typically carry more risk than large company stocks, but historically they have also provided higher returns over time. This phenomenon is known as the small-cap premium, where investors are rewarded for taking on the additional risk associated with investing in smaller companies. Therefore, small company stocks have had higher returns, not lower returns.
II. True. Diversification is indeed the best method for reducing systematic risk, which is the risk inherent to the overall market or a particular industry. By investing in a diversified portfolio containing a variety of assets from different sectors, geographies, and asset classes, investors can mitigate the impact of adverse events affecting a single investment. Diversification helps to spread the risk across different assets and can potentially reduce the overall volatility of the portfolio.
III. False. The Market Risk Premium (MRP) refers to the excess return that investors demand for taking on the risk of investing in the stock market over a risk-free rate of return, such as the yield on government bonds. It represents the compensation investors expect for bearing the systematic risk associated with equities. The MRP is not directly related to inflation, which is a measure of the general rise in prices over time.
IV. False. Total Risk cannot be found by simply adding an asset's Beta to its Standard Deviation. Beta measures an asset's sensitivity to market movements, representing its systematic risk. Standard Deviation, on the other hand, measures an asset's total volatility or risk, including both systematic and unsystematic (specific to the asset) components. Total Risk can be better estimated by considering both factors and analyzing the covariance between the asset's returns and the market returns.
In conclusion, out of the given statements, only statement II is true. Diversification is indeed an effective method for reducing systematic risk. Statements I, III, and IV are false based on the explanations provided.
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which of the following means that two or more independent variables are highly correlated with each other? multiple choice a.standard error. b.multicollinearity. c.r-squared. d.correlation. e.t-value.
In the following, multicollinearity means that two or more independent variables are strongly correlated with each other.
Option b is correct .
Multicollinearity refers to a high degree of correlation between two or more independent variables in a regression or statistical model. This means that there is a strong linear relationship between the independent variables, making it difficult to determine each variable's individual impact on the dependent variable.
R-squared represents the proportion of the dependent variable's variance explained by the independent variable. There is no specific indicator of correlation between independent variables.
Hence , option b is correct .
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Which of the following is not classified as an intangible asset on the balance sheet? a.Employees b. Copyrights c. Goodwill d. Trademark
Employees is not classified as an intangible asset on the balance sheet. Option A is the correct answer.
Option A is the correct answer. Non-tangible assets utilized in the long run are often considered intangible assets. Intangible property examples that are also intellectual property include:
Patents TrademarksAgreements for franchises or licensingGoodwill Copyrightsa company's reputationIntellectual property is frequently an intangible asset. Because of how intangible assets are managed, it is frequently difficult to value and account for intangible assets properly. The haziness around their potential advantages in the future makes it challenging to assign value. A non-identifiable or identifiable useful life is another option for an intangible asset. The majority of intangible assets have a useful life of more than a year and are considered long-term assets.
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Santana Rey receives the March bank statement for Business Solutions on April 11, 2017. The March 31 bank statement shows an ending cash balance of $67,566. A comparison of the bank statement with the general ledger Cash account, No. 101, reveals the following a. S. Rey notices that the bank erroneously cleared a $500 check against her account in March that she did not issue. The check documentation included with the bank statement shows that this check was actually issued by a company named Business Systems b. On March 25, the bank issued a $50 debit memorandum for the safety deposit box c. On March 26, the bank issued a $102 debit memorandum for printed checks that d. On March 31, the bank issued a credit memorandum for $33 interest earned on e. S. Rey notices that the check she issued for $128 on March 31, 2017, has not yet f. S. Rey verifies that all deposits made in March do appear on the March bank g. The general ledger Cash account, No. 101, shows an ending cash balance per that Business Solutions agreed to rent from the bank beginning March 25 Business Solutions ordered from the bank Business Solutions's checking account for the month of March cleared the bank. statement. books of $68,057 as of March 31 (prior to any reconciliation) Required 1. Prepare a bank reconciliation for Business Solutions for the month ended March 31, 2017 BUSINESS SOLUTIONS Bank March 31, 2017
2. Prepare any necessary adjusting entries. Use miscellaneous for any bank charges. Use interest Revenue for any interest earned on the chekking acount for the month of March. (If no entry is required for a particular transaction, select "No jurnal entry required" In the first accont field.)
On March 26, the bank issued a $102 debit memorandum for printed checks.
Hence, the adjusting entry is made to reflect the same.4. Adjusting Entry Debit Credit Cash (101) 33 Interest Revenue (408) 33 On March 31, the bank issued a credit memorandum for $33 interest earned on the checking account for the month of March. Hence, the adjusting entry is made to reflect the same.
Account Titles and Explanation Debit Credit 1 Miscellaneous Expenses 50 Cash 50 (Adjusting Entry for Safety Deposit Box charges) 2 Miscellaneous Expenses 102 Cash 102 (Adjusting Entry for Printed checks charges) 3 Cash 33 Interest Revenue 33 (Adjusting Entry for Interest earned on Checking account) 4 Accounts Receivable 500 Cash 500 (Adjusting Entry for NSF check)Note: No adjusting entry is required for a check issued on March 31st as it was already included in the Bank Reconciliation Statement.
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Calculate the standard error of the difference in means.
Calculate the number of degrees of freedom.
The standard error of the difference in means (SE) = √[(s1² / n₁) + (s2² / n₂)]
The number of degrees of freedom = n₁ + n₂ - 2
Standard Error of the Difference in Means:The standard error of the difference in means (SE) is calculated using the following formula:
SE = √[(s1² / n₁) + (s2² / n₂)]
where s₁ and s₂ are the sample standard deviations of the two groups, and n₁ and n₂ are the respective sample sizes.
Number of Degrees of Freedom:The number of degrees of freedom (df) depends on the type of analysis or test you are conducting. In the context of comparing means between two groups, the degrees of freedom can be calculated using the following formula:
df = n₁ + n₂ - 2
where n₁ and n₂ are the sample sizes of the two groups.
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1. What is the extent of relative inequality in developing countries, and how is this related to the extent of absolute poverty? 2. Who are the poor, and what are their economic characteristics? 3. What determines the nature of economic growth-that is, who benefits from economic growth, and why? 4. Are rapid economic growth and more equal distributions of income com- patible or conflicting objectives for low-income countries? To put it another way, is rapid growth achievable only at the cost of greater inequalities in the distribution of income, or can a lessening of income disparities con- tribute to higher growth rates? 5. Do the poor benefit from growth, and does this depend on the type of growth a developing country experiences? What might be done to help the poor benefit more? 6. What is so bad about extreme inequality?
1. The extent of relative inequality in developing countries refers to the disparity in income or wealth distribution among different segments of the population. This inequality is closely related to the extent of absolute poverty.
Absolute poverty refers to the condition where individuals or households lack the basic necessities of life, such as food, shelter, and healthcare. In developing countries with high levels of relative inequality, the gap between the rich and the poor is significant, and as a result, the level of absolute poverty tends to be higher.
2. The poor in developing countries are those individuals or households who experience low income levels and struggle to meet their basic needs.
They often lack access to education, healthcare, and productive resources. The economic characteristics of the poor vary but commonly include low wages, limited job opportunities, informal employment, and vulnerability to economic shocks. They may also have limited access to financial services, land, and other productive assets.
3. The nature of economic growth, including who benefits from it, is influenced by various factors. These include government policies, institutions, market structures, and social dynamics. In many cases, economic growth alone does not guarantee equitable distribution of benefits.
Without appropriate policies and institutions in place, the benefits of growth may disproportionately flow to the already wealthy or privileged groups, leading to increased inequality.
However, with effective policies, such as progressive taxation, social safety nets, and inclusive education and healthcare systems, economic growth can benefit a wider section of society and contribute to reducing inequalities.
4. Rapid economic growth and more equal distributions of income can be compatible objectives for low-income countries. While it is possible that rapid growth may initially widen income disparities, with appropriate policies and targeted interventions, income inequalities can be addressed.
In fact, reducing income disparities can contribute to higher growth rates in the long run by creating a more inclusive and stable economic environment. Ensuring that the benefits of growth reach the poor and vulnerable populations through investments in human capital, social protection, and equitable access to resources can help achieve both rapid growth and a more equal distribution of income.
5. The impact of economic growth on the poor depends on the type of growth experienced by a developing country. If growth is inclusive and pro-poor, meaning it generates opportunities for employment, raises wages, and provides access to basic services, the poor can benefit significantly.
However, if growth is concentrated in specific sectors or primarily benefits the already affluent, the poor may not experience substantial improvements in their living conditions. To help the poor benefit more from growth, policies and interventions should focus on promoting equitable access to education, healthcare, infrastructure, and productive resources.
Social safety nets, targeted poverty reduction programs, and inclusive economic policies can also play a crucial role in ensuring that the poor benefit from growth.
6. Extreme inequality can have negative consequences for individuals, societies, and economies. It can lead to social unrest, political instability, and hinder sustainable development. High levels of inequality limit opportunities for upward mobility, perpetuate social divisions, and undermine social cohesion.
Additionally, extreme inequality can result in unequal access to education, healthcare, and other essential services, perpetuating cycles of poverty and hindering overall societal progress. Addressing extreme inequality through equitable policies and measures not only promotes fairness and social justice but also contributes to more sustainable and inclusive economic growth.
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Adding more variables always leads to a lower test MSE. True False
Adding more variables does not always lead to a lower the statement "Adding more variables always leads to a lower test MSE" is is test stands for Mean Squared Error. It is a statistical measure that calculates the average squared differences between the actual and predicted values in a dataset.
It measures the average magnitude of the errors in a set of predictions. Therefore, the lower the MSE, the better the model's predictive performance. The test MSE is the MSE calculated on a dataset that was not used to train the happens when more variables of more variables to a model can have different effects on the model's performance, depending on various factors such as the correlation between variables
, the number of observations, the amount of noise in the data, and the model's complexity. Adding irrelevant variables, or variables that are highly correlated with other variables in the model, can increase the model's complexity and lead to overfitting, which can increase the test MSE. Therefore, it is not always the case that adding more variables leads to a lower test MSE. dataset that was not used to train the happens when more variables of more variables to a model can have different effects on the model's.
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What are the top 5 trading partners for the US (for imports & for exports). Are there any on the list that surprise you? Using the important verbiage of comparative advantage and absolute advantage, why are these countries the ones that made the list? Write a paragraph to summarize your findings and explain why the U.S. wants to trade with those countries. Be sure to apply the concepts of opportunity costs, comparative advantage and absolute advantage. Go online to the US Census site to find international trade statistics
According to the United States Census Bureau, the top five trading partners for the United States (for both imports and exports) are China, Canada, Mexico, Japan, and Germany. These five countries account for the majority of the trade between the United States and other countries.
There are several reasons why these countries are the ones that made the list. One is that they have a comparative advantage in producing certain goods that are in demand in the United States. For example, China is known for producing goods at lower costs than the United States, which is why many companies outsource their production to China. Canada and Mexico are geographically close to the United States, which makes it easier and less expensive to transport goods between the countries. Japan and Germany have strong manufacturing industries that produce high-quality goods that are in demand in the United States.
Based on the concept of opportunity costs, the United States wants to trade with these countries because it allows them to specialize in producing the goods that they are most efficient at producing, while importing the goods that other countries are more efficient at producing. This way, they can maximize their overall production and consumption of goods. For example, if the United States produces cars at a higher cost than Japan, it would make sense for them to import cars from Japan and focus on producing other goods that they are more efficient at producing. By doing this, the United States can lower their opportunity costs and increase their overall standard of living.
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A company has fixed costs per period as follows: Manufacturing $56,000 Non-manufacturing $38,000 Variable costs of the company's single product are $4.20 per unit and the selling price is $7.00 per unit. What sales revenue (to the nearest $'000) is required in a period to make a profit of $6,000? $163,000 $167,000 $241,000 $250,000
The sales revenue required in a period to make a profit of $6,000 is:(71429 × $7) = $499,003 which, when rounded to the nearest $1000, is $499,000.
To find the sales revenue required in a period to make a profit of $6,000,
we have to use the following formula:
Sales revenue = Fixed cost + Variable cost + Profit
Since profit is given, we can substitute the given values and get:
Sales revenue = $56,000 + $38,000 + $6,000 + ($4.20 × n) -----
(1)Selling price of a single product is $7.00
Therefore, the contribution per unit (that is, selling price - variable cost) is $7.00 - $4.20 = $2.80
Thus, sales revenue can be written as:
Sales revenue = (Number of units sold) × ($2.80) -----(2)
From equation (1), we know that Sales revenue = $100,000 + ($4.20 × n)
By substituting this value in equation (2), we get:
(Number of units sold) × ($2.80) = $100,000 + ($4.20 × n)
The above equation can be simplified as follows:
2.8n - 4.2n = 100000n = 100000 / (-1.4) = -71428.57
Since number of units sold can't be negative, we can approximate this value to the nearest whole number to get:71429 units approximately
Therefore, the sales revenue required in a period to make a profit of $6,000 is:(71429 × $7) = $499,003 which, when rounded to the nearest $1000, is $499,000.
Therefore, the correct option is (none of the above) $499,000.
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first movers face: multiple choice demand uncertainty. high entry barriers. cost disadvantages. market rigidities.
The answer to the given question is "high entry barriers."The first movers face high entry barriers.
First movers, particularly those in technical industries, can face enormous costs of R&D, testing, and product development. A significant portion of the cost of producing the first unit is absorbed by the business. Additionally, because first movers typically require several years to develop and test their products, they may encounter severe competition from subsequent movers who may be more efficient, innovative, or agile than the first movers. As a result, early movers must devote significant resources to marketing and advertising to establish brand recognition and retain market share.
In conclusion, the first movers face high entry barriers.
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What does the quantitative evidence tell us about when the Great Divergencehappened? In your answer make reference to the debate between the traditionalists and the revisionists.(Apply knowledge of the global economy)
The quantitative evidence tells us that the Great Divergence started around the late 18th century, but there is a debate among traditionalists and revisionists regarding the exact timing and causes of this divergence.
The Great Divergence refers to the period between the 18th and 20th centuries when some countries, particularly in the West, experienced significant economic growth and prosperity while others, primarily in Asia, remained relatively stagnant. Traditionalists argue that the Great Divergence was caused by Europe's industrial revolution, which led to significant technological advancements and increased productivity. Revisionists, on the other hand, point to factors such as European imperialism and the exploitation of resources from other parts of the world, which they argue allowed for the accumulation of wealth that fueled Europe's economic growth.
Quantitative evidence shows that from the mid-18th century to the mid-19th century, European countries experienced a significant increase in per capita income, while Asian countries saw little to no growth. However, revisionists argue that this growth was not due to any inherent superiority of Western societies but rather was the result of a combination of factors, including imperialism and exploitation.
In conclusion, the quantitative evidence tells us that the Great Divergence started in the late 18th century, but there is a debate among traditionalists and revisionists regarding the exact causes and timing of this divergence. Regardless of the specific causes, it is clear that the Great Divergence had a significant impact on the global economy and contributed to the current distribution of wealth and power around the world.
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A newly issued 10-year maturity, 8% coupon bond making annual coupon payments is sold to the public at a price of $963. What will be an investor’s taxable income from the bond over the coming year? The bond will not be sold at the end of the year. The bond is treated as an original issue discount bond. (Round your answer to 2 decimal places.)
Taxable income?
The investor's taxable income from the bond over the coming year is $117.
To calculate the investor's taxable income from the bond over the coming year, we need to consider the coupon payment and the original issue discount (OID) of the bond.
Given that the bond has a 10-year maturity, an 8% coupon rate, and annual coupon payments, we can calculate the annual coupon payment using the coupon rate and the face value of the bond.
Annual Coupon Payment = Coupon Rate * Face Value
In this case, the annual coupon payment would be 8% * $1,000 = $80.
Next, we need to determine the OID. The OID is the difference between the face value of the bond and the purchase price.
OID = Face Value - Purchase Price
In this case, the purchase price of the bond is $963.
OID = $1,000 - $963 = $37
For an original issue discount bond, the OID represents additional interest income that accrues over the life of the bond. This additional interest income is considered taxable income.
Therefore, the investor's taxable income from the bond over the coming year would be the sum of the annual coupon payment and the OID:
Taxable Income = Annual Coupon Payment + OID
Taxable Income = $80 + $37 = $117
Hence, the investor's taxable income from the bond over the coming year is $117.
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Exercise 6-6 (Algo) Break-Even Analysis (LO6-5] Mauro Products distributes a single product, a woven basket whose selling price is $26 per unit and whose variable expense is $23 per unit. The company'
Given: Selling price per unit= $26 Variable expense per unit= $23Fixed costs= $115,000To find: Break-even point using contribution margin ratio formula, margin of safety in dollars and margin of safety percentage. Contribution Margin Ratio formula is given as.
Contribution Margin Ratio = (Sales - Variable expenses) / Sales Where,Sales = Selling price x Units soldVariable expenses = Variable expense per unit x Units soldUsing the above data, we have: Contribution Margin Ratio = ($26 - $23) / $26 = 11.54%Using the formula for calculating break-even point in dollars : Break-even point (in dollars) = Fixed costs / Contribution Margin Ratio.
The company's break-even point is $996,525.To calculate margin of safety in dollars:Margin of safety (in dollars) = Total sales - Break-even salesTotal sales = Selling price x Units sold = $26 x 60,000 = $1,560,000Break-even sales = Break-even point / Selling price per unit= $996,525 / $26 = 38,328.84Margin of safety (in dollars) = $1,560,000 - $996,525 = $563,475The company's margin of safety is $563,475.To calculate margin of safety percentage.
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QUESTION 2:
Andrea Ltd ("Andrea") is a company with a financial year-end at 30 April 2019.
Andrea's interest on long term loans for the previous 12 months is paid annually on 31 July. For the twelve months to 31 July 2018, the interest on Andrea's long-term loan paid on 31 July 2018 was £12,000. For the twelve months to 31 July 2019, the interest payment to be paid on 31 July 2019 is expected to be £16,000.
REQUIRED:
a) Show calculations for the interest prepayment or accrual as appropriate, and the interest expense. (5 marks)
b) Prepare T accounts, so far as you are able, for each of: 1) cash, 2) interest prepayment or accrual as appropriate, and 3) interest expense. (4 marks)
c) Define and explain the accounting principle underlying your accounting entries in Part b). (4 marks)
d) Explain how accruals and prepayments arise. (7 marks) e) Holly Limited had made a prepayment in respect of insurance as at 31 March 2018 of £600. During the year ended 31 March 2019 payments for insurance of £4,000 were made. This amount included £1,000 in respect of the year to 31 March 2020. Calculate the figure to be included in the statement of profit or loss for the year to 31 March 2019 in respect of insurance.
The figure to be included in the statement of profit or loss for the year to 31 March 2019 in respect of insurance is £3,400.
Calculation for interest prepayment Holly Limited had borrowed a loan of £100,000 from the bank on 1 January 2019 at an interest rate of 10% p.a.
Interest is to be paid on 31 December each year.
Holly Limited made an interest prepayment of £10,000 on 1 January 2019 for the year ended 31 December 2019.
The interest rate of 10% p.a. applies throughout the period.
Use the following formula to calculate the interest prepayment:
Interest prepayment = Principal amount * Rate * Time period
Interest prepayment = £100,000 * 10% * 1
Interest prepayment = £10,000
Calculation for the interest expense:The interest expense can be calculated by deducting the prepayment from the total interest charged by the bank.
Here, the bank charges an interest of £10,000 on 31 December 2019.
Interest expense = Interest charged by the bank – Interest prepayment
Interest expense = £10,000 – £10,000Interest expense = £0
Definition of the accounting principle underlying the accounting entries.
The accounting principle that underlies the accounting entries in part b is the accrual principle.
It requires the recognition of revenue when it is earned and expenses when they are incurred.
Here, the interest expense is not recognized until the bank charges the interest on 31 December 2019, even though Holly Limited made an interest prepayment on 1 January 2019.
This is in line with the accrual principle.
Accruals:Accruals are expenses or revenues that have been incurred or earned but not yet recorded in the financial statements.
They arise due to the time difference between the occurrence of the event and the recording of the event in the books of accounts.
Prepayments:Prepayments are payments made in advance for goods or services that have not yet been received.
They arise when a company makes a payment for a good or service that will be used in the future.
Calculation of the figure to be included in the statement of profit or loss for the year to 31 March 2019 in respect of insurance:
Holly Limited made a prepayment of £600 for insurance as at 31 March 2018.During the year ended 31 March 2019, payments for insurance of £4,000 were made.
This amount included £1,000 in respect of the year to 31 March 2020.
Therefore, insurance expense for the year to 31 March 2019 = Insurance payment – Prepayment
Insurance expense for the year to 31 March 2019 = £4,000 – £600
Insurance expense for the year to 31 March 2019 = £3,400
Therefore, the figure to be included in the statement of profit or loss for the year to 31 March 2019 in respect of insurance is £3,400.
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A. The interest expense for the twelve months to 30 April 2019 is £4,000, and the interest prepayment or accrual is £10,667. B. T-account has cash, interest payment/accrual, and interest expense. C. The actual payment will be made on 31 July 2019.
How did we arrive at these figures?a) To calculate the interest prepayment or accrual and the interest expense, we need to consider the financial year-end and the timing of interest payments.
Since Andrea's financial year-end is 30 April 2019, we need to determine the portion of interest expense for the twelve months to 30 April 2019.
Interest on long-term loans for the twelve months to 31 July 2018 was £12,000. This interest expense is applicable to the period from 1 May 2017 to 30 April 2018. Therefore, we need to adjust this amount for the four months from 1 May 2018 to 31 July 2018, which falls within the financial year-end.
To calculate the interest expense for the twelve months to 30 April 2019:
Interest expense for the twelve months to 30 April 2019 = (£12,000 / 12 months) * 4 months = £4,000
Next, we need to determine the interest prepayment or accrual for the twelve months to 30 April 2019. Since the interest on long-term loans is paid annually on 31 July, we need to account for the remaining eight months from 1 May 2019 to 31 December 2019.
To calculate the interest prepayment or accrual:
Interest prepayment or accrual for the twelve months to 30 April 2019 = (£16,000 / 12 months) * 8 months = £10,667
Therefore, the interest expense for the twelve months to 30 April 2019 is £4,000, and the interest prepayment or accrual is £10,667.
b) T accounts:
1) Cash:
--------------
| |
| Cash |
| |
--------------
2) Interest prepayment or accrual:
-------------------------------
| |
| Interest prepayment/accrual |
| |
-------------------------------
3) Interest expense:
------------------
| |
| Interest expense |
| |
------------------
c) The accounting principle underlying the entries in Part b) is the accrual basis of accounting. This principle states that revenues and expenses should be recognized in the period in which they are earned or incurred, regardless of when the cash is received or paid.
In the case of interest prepayment or accrual, we recognize the expense for the twelve months to 30 April 2019, even though the actual payment will be made on 31 July 2019. This follows the accrual basis, where expenses are recognized when they are incurred, rather than when the cash is paid.
d) Accruals and prepayments arise due to timing differences between when transactions occur and when cash is exchanged.
Accruals occur when expenses or revenues are recognized in the accounting period to which they relate, even though no cash has been exchanged. This means that the expense or revenue is recorded before the associated cash flow occurs. Accruals are used to match expenses and revenues with the period in which they are incurred or earned.
Prepayments occur when cash is paid or received in advance for an expense or revenue that belongs to a future accounting period. This means that cash is exchanged before the related expense or revenue is recognized. Prepayments are recorded as assets or liabilities on the balance sheet until the expense or revenue is recognized in the appropriate accounting period.
e) To calculate the figure to be included in the statement of profit or loss for the year to 31 March 2019 in respect of insurance, we need to consider the prepayment and payments made during the year.
Prepayment as at 31 March 2018 = £600
Payments
for insurance during the year to 31 March 2019 = £4,000
This amount includes £1,000 in respect of the year to 31 March 2020.
To calculate the figure to be included:
Prepayment to be allocated to the year ending 31 March 2019 = Prepayment as at 31 March 2018 - Payments for the year to 31 March 2019
= £600 - £4,000
= -£3,400 (negative value)
Since the prepayment exceeds the payments made during the year, the figure to be included in the statement of profit or loss for the year to 31 March 2019 in respect of insurance is -£3,400. This represents an expense as the prepayment has been allocated to the current year, resulting in a decrease in the prepayment balance.
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Simon recently received a credit card with a 12% nominal interest rate. With the card, he purchased an Apple iPhone 11 for $790. The minimum payment on the card is only $20 per month.
If Simon makes the minimum monthly payment and makes no other charges, how many months will it be before he pays off the card? Do not round intermediate calculations. Round your answer to the nearest whole number.
month(s)
If Simon makes monthly payments of $65, how many months will it be before he pays off the debt? Do not round intermediate calculations. Round your answer to the nearest whole number.
month(s)
How much more in total payments will Simon make under the $20-a-month plan than under the $65-a-month plan? Do not round intermediate calculations. Round your answer to the nearest cent.
Simon will make approximately $1,515 more in total payments under the $20-a-month plan compared to the $65-a-month plan.
How to solve for the amount to be madeTo calculate the number of months it will take for Simon to pay off the credit card, we can use the formula for the number of months to pay off a loan:
Number of months = - (log(1 - r * P / A) / log(1 + r))
Where:
r = monthly interest rate (12% nominal interest rate / 12 months = 1% or 0.01)
P = principal amount ($790)
A = monthly payment
1) Minimum monthly payment of $20:
Number of months = - (log(1 - 0.01 * 790 / 20) / log(1 + 0.01))
Number of months ≈ 118 months
Therefore, it will take Simon approximately 118 months to pay off the credit card by making the minimum monthly payment of $20.
2) Monthly payment of $65:
Number of months = - (log(1 - 0.01 * 790 / 65) / log(1 + 0.01))
Number of months ≈ 13 months
Therefore, it will take Simon approximately 13 months to pay off the debt by making monthly payments of $65.
3) Total payments under the $20-a-month plan:
Total payments = Number of months * Monthly payment
Total payments = 118 * $20
Total payments = $2,360
Total payments under the $65-a-month plan:
Total payments = Number of months * Monthly payment
Total payments = 13 * $65
Total payments = $845
Difference in total payments = Total payments under the $20-a-month plan - Total payments under the $65-a-month plan
Difference in total payments = $2,360 - $845
Difference in total payments ≈ $1,515
Therefore, Simon will make approximately $1,515 more in total payments under the $20-a-month plan compared to the $65-a-month plan.
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