The correct statement among the options is E: The primary purpose of the NYSE is to match buyers with sellers.
The New York Stock Exchange (NYSE) is one of the major stock exchanges in the world and its primary function is to facilitate the trading of securities by matching buyers with sellers. The NYSE operates as an auction market, where buyers and sellers come together to trade stocks in a centralized and regulated environment. It provides a platform for investors to buy and sell stocks based on supply and demand, with prices determined through competitive bidding.
Option A is incorrect because not all major stock exchanges are U.S.-based. There are several significant stock exchanges around the world, including the London Stock Exchange, Tokyo Stock Exchange, and Shanghai Stock Exchange.
Option B is incorrect because the NYSE was actually founded in 1792 and is not associated with the National Association of Securities Dealers (NASD).
Option C is incorrect because the American Stock Exchange (AMEX) was a dealer market, but it ceased operations in 2017 and was acquired by NYSE.
Option D is incorrect because OTC (Over-the-Counter) markets do not have a physical trading floor, as they facilitate the trading of securities through decentralized electronic systems rather than centralized exchanges.
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A little exchange economy has just two consumers, named Ken and Barbie, and two commodities, quiche and wine Ken's initial endowment is 4 units of quache and 2 units of wine Barbio's initial endowment is 1 unit of quiche and 6 units of wine Ken and Barbie have identical utility functions. We write Ken's utaly function as Z wid Barbie's utility function as U-QW2 where Q and We are the amounts of quache and wine for Ken and Q, and Ware amounts of quache and wor Putting wine on the horizontal axis, what is the contract curve from Barbie's perspective?
The curve will be the locus of all the tangencies between the indifference curve and the price line drawn from Barbie's initial endowment (I2) given the price ratio of quiche to wine.
The contract curve from Barbie's perspective will be the curve that shows the allocations of two commodities, quiche, and wine, that maximize her utility. The allocation is subject to her budget constraint, the price of quiche and wine, and her initial endowment. The contract curve can be represented in a diagram that shows the indifference curves of both consumers and their initial endowments. The contract curve is the locus of all the tangencies between the indifference curve and the price line drawn from the initial endowment of one consumer given the price ratio of the two commodities.
It represents the set of Pareto-efficient allocations of the two consumers with respect to their preferences and their budget constraints. In this case, we can represent the contract curve from Barbie's perspective as the curve that touches Barbie's highest attainable indifference curve (I2) and runs through Ken's endowment. Thus, the contract curve will be the curve that passes through points (1,6) and is tangent to the indifference curve I2.
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Evaluate the following project: CFO = +3,500; CF1 = -1,200; CF2 = +800; CF3 = 0; CF4 = -1,800. The risk adju is 14%. The internal rate of return for the project is 13.3%. This project should be: n To discount future cash flows: present value of cash flow = future value divided by (1 + discount rate), where n = year cash flow will be re O rejected because the internal rate of return is less than the risk adjusted cost of capital. rejected because the net present value is negative. accepted because the net present value is positive. O accepted because the internal rate of return is less than the risk adjusted cost of capital.
The correct answer is "rejected because the internal rate of return is less than the risk-adjusted cost of capital."
The Internal Rate of Return (IRR) is a project appraisal method used to determine the project's expected rate of return. The IRR formula is expressed as a percentage rate that calculates the NPV to zero. An investment with an IRR that is higher than the risk-adjusted cost of capital is deemed feasible and profitable. If the IRR is lower than the required rate of return, the investment should be rejected. An NPV that is greater than zero shows that a project is profitable and should be accepted. An NPV that is negative indicates that the project should be avoided or turned down. The NPV can be calculated by discounting the expected cash flows by the appropriate discount rate.
Given CFO = +3,500; CF1 = -1,200; CF2 = +800; CF3 = 0; CF4 = -1,800 and a 14% risk adjustment, the internal rate of return is 13.3%.
Since the internal rate of return is less than the risk-adjusted cost of capital, the project should be rejected.
Therefore, the correct answer is "rejected because the internal rate of return is less than the risk-adjusted cost of capital."
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Describe the what the expected characteristics of a LDC country, MDC country and post MDC country would (6 marks) be.
A Less Developed Country (LDC) is typically characterized by low levels of industrialization, per capita income, and standards of living. The countries usually have a high population growth rate, high levels of unemployment and underemployment, and a low rate of savings and investment. There is also a significant dependence on primary products for export and foreign aid.
A More Developed Country (MDC), in contrast to an LDC, has a high degree of industrialization, with a large percentage of its population employed in the secondary or tertiary sectors. MDCs usually have higher per capita income levels, better infrastructure, and a higher standard of living. Additionally, these countries tend to have a more diversified economy, with a higher level of savings and investment and a lower rate of population growth.
Post MDC (Newly industrialized countries) are those that have experienced a significant level of industrialization and growth over the past few decades. These countries typically have seen rapid economic development and have become major players in the global economy. Their economies are often based on the production of high-tech and high-value-added goods, such as electronics, software, and automobiles. Post MDCs often have a more educated and skilled workforce, higher levels of investment, and improved infrastructure. However, they may still face some economic and social challenges such as income inequality and environmental degradation.
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2 12.5 points Skipped eBook Hint Print References Down Under Products, Ltd., of Australia has budgeted sales of its popular boomerang for the next four months as follows: Sales in Units 78,000 85,000
The production budget for Down Under Products, Ltd. in the second quarter is as follows: April - 79,400 units, May - 91,600 units, June - 113,200 units, July - 75,200 units, with a total of 359,400 units.
To prepare the production budget for the second quarter, we need to calculate the number of units to be produced each month based on the sales forecast and the desired ending inventory levels.
Here's the production budget for Down Under Products, Ltd. for the second quarter:
April:
Sales: 78,000 units
Desired ending inventory for May: 20% of May sales = 0.2 * 85,000 = 17,000 units
Units to be produced: Sales + Desired ending inventory - Beginning inventory = 78,000 + 17,000 - 15,600 = 79,400 units
May:
Sales: 85,000 units
Desired ending inventory for June: 20% of June sales = 0.2 * 118,000 = 23,600 units
Units to be produced: Sales + Desired ending inventory - Beginning inventory = 85,000 + 23,600 - 17,000 = 91,600 units
June:
Sales: 118,000 units
Desired ending inventory for July: 20% of July sales = 0.2 * 94,000 = 18,800 units
Units to be produced: Sales + Desired ending inventory - Beginning inventory = 118,000 + 18,800 - 23,600 = 113,200 units
July:
Sales: 94,000 units
No desired ending inventory calculation is needed as it is the last month of the quarter.
Units to be produced: Sales - Beginning inventory = 94,000 - 18,800 = 75,200 units
Total units to be produced in the second quarter: 79,400 + 91,600 + 113,200 + 75,200 = 359,400 units.
Therefore, the production budget for the second quarter is as follows:
April: 79,400 units
May: 91,600 units
June: 113,200 units
July: 75,200 units
Total: 359,400 units.
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The complete question is:
Down Under Products, Ltd., of Australia has budgeted sales of its popular boomerang for the next four months as follows:
Sales in Units
April 78,000
May 85,000
June 118,000
July 94,000
The company is now in the process of preparing a production budget for the second quarter. Past experience has shown that end-of-month inventory levels must equal 20% of the following month’s sales. The inventory at the end of March was 15,600 units.
Required:
Prepare a production budget for the second quarter; in your budget, show the number of units to be produced each month and for the quarter in total.
Ethical practices are not necessary to build trust and long-term relationships with customers. O True O False
The statement "Ethical practices are not necessary to build trust and long-term relationships with customers" is false because ethical practices are essential to gain the trust of customers and to maintain long-term relationships with them.
Ethical practices refer to the moral principles and values that guide businesses in conducting their operations and interactions with customers. It helps to ensure that businesses operate with transparency, honesty, and integrity, which is crucial for building trust with customers.
Customers are more likely to remain loyal to businesses that are transparent and honest with them. Unethical practices, on the other hand, can harm the reputation of a business and cause customers to lose trust in it. This can lead to a loss of customers and ultimately result in the failure of the business.
Thus, it is important for businesses to prioritize ethical practices to build and maintain long-term relationships with customers.
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The production function of Andrew's business is Q = L + 1.5K where Q is the variable capturing the quantity of output produced, L is the variable measuring the units of labour hired and K is the variable measuring units of capital hired. Suppose also that the wage rate per unit of labour is $20 and the rental rate per unit of capital is $24. Given this information, answer the following questions.
(i) In the long run, what is the input bundle that Andrew should choose to produce 200 units of output? Show your working and explain your answer. What will be the associated minimum total cost of production?
(ii) Diagrammatically represent Andrew's chosen input combination carefully using an isoquant and an isocost line while keeping labour (L) on the horizontal axis.
In the long run, Andrew should choose an input bundle where L = 0 and K = 200 to produce 200 units of output. The associated minimum total cost of production is $3200. A diagram with an isoquant and an isocost line can be used to visually represent Andrew's chosen input combination.
(i) To determine the input bundle that Andrew should choose to produce 200 units of output, we need to find the combination of labor (L) and capital (K) that satisfies the production function Q = L + 1.5K when Q = 200.
Substituting Q = 200 into the production function:
200 = L + 1.5K
To find the optimal input bundle, we need to minimize the total cost of production. The total cost of production is given by:
Total Cost = Wage * Labor + Rental Rate * Capital
Given that the wage rate per unit of labor is $20 and the rental rate per unit of capital is $24, the total cost equation becomes:
Total Cost = 20L + 24K
To minimize the total cost, we need to find the combination of L and K that satisfies the production function while minimizing the total cost equation.
Using the production function equation, we can solve for K in terms of L:
K = (200 - L) / 1.5
Substituting this value of K into the total cost equation, we get:
Total Cost = 20L + 24[(200 - L) / 1.5]
Simplifying the equation, we have:
Total Cost = 20L + 16(200 - L)
Expanding further:
Total Cost = 20L + 3200 - 16L
Combining like terms:
Total Cost = 4L + 3200
To minimize the total cost, we need to minimize the value of L. Since L cannot be negative, the minimum value for L is 0.
When L = 0, the total cost is:
Total Cost = 4(0) + 3200 = $3200
Therefore, in the long run, Andrew should choose an input bundle where L = 0 and K = 200 to produce 200 units of output. The associated minimum total cost of production is $3200.
(ii) To diagrammatically represent Andrew's chosen input combination, we will use an isoquant and an isocost line.
An isoquant represents all the combinations of labor and capital that produce the same level of output. In this case, the isoquant would represent the combination of L and K that produces 200 units of output.
An isocost line represents all the combinations of labor and capital that yield the same total cost. The slope of the isocost line is equal to the wage rate divided by the rental rate (20/24 in this case).
By plotting the isoquant and the isocost line on a graph with labor (L) on the horizontal axis, we can identify the point where the isoquant and isocost line intersect. This point represents Andrew's chosen input combination.
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Which organization is exempt from federal income tax under Section 501(c)(3)?
Avarice Inc., a corporation, operated to advance the financial interests of its shareholders.
Murrie and Mars, a partnership, operated exclusively to advance a charitable purpose.
Reverend Roderick Piper, a sole proprietorship, operated exclusively to advance a religious purpose.
Ubicool Inc., a corporation, operated exclusively to advance scientific purposes.
The organization that is exempt from federal income tax under Section 501(c)(3) is Murrie and Mars, a partnership, which operated exclusively to advance a charitable purpose.
Federal income tax is a tax imposed by the government of the United States on the income of individuals, businesses, trusts, and other legal entities. As a general rule, people and businesses that earn a certain amount of income in the United States are required to file a tax return with the Internal Revenue Service (IRS) every year. Federal income tax is calculated using a progressive tax system, which means that the more money you make, the higher your tax rate.
Section 501(c)(3) of the Internal Revenue Code (IRC) is a section of the United States federal tax code that provides an exemption from federal income tax for nonprofit organizations that are operated for charitable, religious, educational, or scientific purposes. In order to qualify for tax-exempt status under Section 501(c)(3), an organization must be organized and operated exclusively for one or more of these purposes, and its earnings cannot benefit any individual or shareholder. In addition, it must meet certain other requirements, such as having a specific purpose and being governed by a board of directors or trustees.
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An organization with this HR strategy is likely to have the most difficulty working cooperatively with a labor union: Free Agent HR strategy. Bargain Laborer HR strategy. Committed Expert HR strategy. Loyal Soldier HR strategy.
An organization with a Free Agent HR strategy is likely to have the most difficulty working cooperatively with a labor union.
The Free Agent HR strategy focuses on hiring employees as independent contractors or temporary workers, emphasizing flexibility and short-term commitments. This approach often involves a high degree of individualism and minimal job security.
Labor unions typically aim to protect workers' rights, promote collective bargaining, and secure long-term employment benefits. They seek to ensure fair wages, job stability, and favorable working conditions for their members. The Free Agent HR strategy, with its emphasis on temporary or independent contractor arrangements, may clash with these union objectives. Unions are more inclined to support the Bargain Laborer, Committed Expert, or Loyal Soldier HR strategies, which prioritize stable employment, skill development, and long-term relationships between employees and employers.
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Monster Tires is considering an expansion which involves opening a new location for its tires manufacturing. This new project is estimated to be the same level of risk as the firm's existing projects. For this new manufacturing project, the firm would need to raise money by selling $824,000 worth of new equity, $296,000 worth of new preferred stock shares, and borrow $391,000 by selling new corporate bonds. The annual costs of equity, preferred stock shares, and corporate debt equal 10%, 7%, and 3%, respectively. Monster Tires pays a 35% tax rate on its corporate income. Calculate Monster Tires' average annual cost of running this new tire business, or the Weighted Average Cost of Capital.
Monster Tires has decided to open a new location for tire manufacturing, which is expected to carry the same level of risk as the company's current projects.
To finance the project, the company needs to raise $824,000 through the sale of new equity, $296,000 through the sale of new preferred stock, and $391,000 by selling new corporate bonds. The annual costs of equity, preferred stock, and corporate debt are 10%, 7%, and 3%, respectively. Monster Tires has a corporate income tax rate of 35%. The average annual cost of running the new tire business Re is the cost of equity, Rd is the cost of debt, Rp is the cost of preferred stock, T is the corporate income tax rate, and V is the total value of the company (E + D + P). Plugging in the given values, we get WACC = (824000/1511000 x 0.10) + (391000/1511000 x 0.03 x 0.65) + (296000/1511000 x 0.07) = 0.055 or 5.5%.
Therefore, the weighted average cost of capital for Monster Tires' new tire business is 5.5%.
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Question 3:In 2021, Emily and Erick form the EE Partnership by transferring assets from their sole proprietorships. Emily contributes the furniture and fixtures with a fair market value of $500,000 and a basis of $200,000. Erick contributes land with a fair market value of $600,000 and basis of $400,000. The land (contributed by Erick) had a mortgage of $100,000 which EE partnership assumes. Emily and Erick will share income, gains m and losses 50/50.
• Determine Emily’s outside basis in EE Partnership after she and Erick have formed EE Partnership.
• Determine Erick’s outside basis in EE Partnership after he and Emily have formed EE Partnership.
• During 2023, the partnership has the following results:
o Sales $1,000,000
o Cost of sales 600,000
o Utilities, rent, etc. 50,000
o Salary to sales staff 100,000
o LTCG (sale of stock) 5,000
o Charitable contributions 2,000
o Tax exempt income 1,000
o Distribution of cash to Erick 15,000
At the beginning of 2023, the partnership had a total debt (all of which is either recourse or qualified nonrecourse debt) of $400,000. At the end of 2023, the partnership had a total of recourse and qualified nonrecourse debt of $425,000.
Also, at the beginning of 2023, Erick’s outside basis in EE Partnership of $525,000
Determine:
a). Erick’s outside basis in EE Partnership at the end of 2023.
b). How Erick will be taxed on his transactions with the partnership. Identify the amount and character of the income/loss/deductions. You do NOT need to determine the amount of the tax liability.
c). In 2024, EE Partnership sells the land originally contributed by Erick. The sales price is $750,000. Determine the amount of gain that must be allocated to Emily and to Erick as a result of the sale of this property.
a. .Erick's outside basis in EE Partnership at the end of 2023:Starting outside basis $525,000 + share of income $249,000 - distributions ($15,000) - share of loss ($13,500) + allocation of debt ($21,250) = Ending outside basis of $767,750.
b. The distribution of cash of $15,000 to Erick will be a nontaxable return of capital since the partnership had earnings and profits at the beginning of the year.The net income or loss of the partnership will flow through to the partners' tax returns.
c. Emily's capital account is $250,000. Erick's share of the gain on the sale of the land is ($750,000 - $600,000) * 50% = $75,000.
The basis of the assets in a partnership after their contribution is known as the initial basis. The partner's capital account increases by the initial basis, which is the basis of the assets contributed to the partnership. Emily's and Erick's initial basis are as follows:Emily’s initial basis: furniture and fixtures’ basis of $200,000.Erick’s initial basis: the land’s basis of $400,000 and his share of debt assumed by EE Partnership ($100,000), resulting in a basis of $500,000
The transaction with the partnership will be taxed as follows:In this case, Erick's share of the partnership's net income for 2023 is $249,000. Emily and Erick will have to report this income on their individual tax returns.Emily's gain on the sale of land: $750,000 - $500,000 = $250,000 gain on the sale of land.Emily's capital account is $250,000. Erick's share of the gain on the sale of the land is ($750,000 - $600,000) * 50% = $75,000.
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Ben Conway, Ida Chan, and Clair Scott formed CCS Consulting this year by making capital contributions of $266,000, $302,000, and $196,000, respectively. They anticipate annual profit of $458,400 and are considering the following alternative plans of sharing profits and losses:
Equally;
In the ratio of their initial investments; or
Salary allowances of $125,000 to Conway, $96,000 to Chan, and $71,000 to Scott and interest allowances of 10% on initial investments, with any remaining balance shared equally.
Required :
1. Use the schedule to show how a profit of $458,400 would be distributed under each of the alternative plans being considered. (Enter all amounts as positive values.)
2. Prepare a statement of changes in equity showing the allocation of profit to the partners, assuming they agree to use alternative (c) and the profit actually earned for the year ended December 31, 2020, is $458,400. During the year, Conway, Chan, and Scott withdraw $51,000, $41,000, and $31,000, respectively. (Enter all amounts as positive values.)
3. Prepare the December 31, 2020, journal entry to close Income Summary assuming they agree to use alternative (c) and the profit is $458,400. Also, close the withdrawals accounts.
1- Distribution of Profit under Alternative Plans:
a) Equal Distribution:
Ben Conway: $152,800
Ida Chan: $152,800
Clair Scott: $152,800
b) Ratio of Initial Investments:
Ben Conway: $168,384
Ida Chan: $191,040
Clair Scott: $98,976
c) Salary and Interest Allowances:
Ben Conway: $196,000 (capital contribution) + $125,000 (salary allowance) + $26,600 (interest allowance) = $347,600
Ida Chan: $302,000 (capital contribution) + $96,000 (salary allowance) + $30,200 (interest allowance) = $428,200
Clair Scott: $196,000 (capital contribution) + $71,000 (salary allowance) + $19,600 (interest allowance) = $286,600
2- Statement of Changes in Equity:
Partners' Capital at the beginning:
Ben Conway: $266,000
Ida Chan: $302,000
Clair Scott: $196,000
Profit allocation (using alternative c):
Ben Conway: $125,000 (salary allowance) + $26,600 (interest allowance) = $151,600
Ida Chan: $96,000 (salary allowance) + $30,200 (interest allowance) = $126,200
Clair Scott: $71,000 (salary allowance) + $19,600 (interest allowance) = $90,600
Withdrawals:
Ben Conway: $51,000
Ida Chan: $41,000
Clair Scott: $31,000
Ending Capital Balances:
Ben Conway: $266,000 + $151,600 - $51,000 = $366,600
Ida Chan: $302,000 + $126,200 - $41,000 = $387,200
Clair Scott: $196,000 + $90,600 - $31,000 = $255,600
3- December 31, 2020, Journal Entry:
Income Summary $458,400
Ben Conway, Capital $151,600
Ida Chan, Capital $126,200
Clair Scott, Capital $90,600
Retained Earnings $90,000
Ben Conway, Withdrawals $51,000
Ida Chan, Withdrawals $41,000
Clair Scott, Withdrawals $31,000
Income Summary $458,400
Retained Earnings $90,000
Ben Conway, Withdrawals $51,000
Ida Chan, Withdrawals $41,000
Clair Scott, Withdrawals $31,000
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Suppose you manage a mutual fund that has an expected return of 15% with a standard deviation of 20% for the coming year. One of your clients is thinking about investing his $10,000 in your fund and a money market fund which generates 3% riskless return.
a. If your client wants his overall portfolio to have an expected return of 10%, how much should he invest in your fund? In other words, what is y of his "Complete portfolio"?
b. If your client wants to maximize his overall portfolio expected return but limit the standard deviation to 12%, how much should he invest in your fund?
c. Please draw the Capital Allocation Line (CAL) in the following diagram. Note that y axis is expected return, not risk premium.
a. To achieve an overall portfolio expected return of 10%, the client should invest approximately $5,833.33 in the mutual fund, allocating the remaining amount to the money market fund. This can be calculated using the concept of weighted average returns.
b. To maximize the overall portfolio expected return while limiting the standard deviation to 12%, we would need information about the correlation between the mutual fund and the money market fund. Without this information, we cannot accurately determine the optimal allocation.
c.The Capital Allocation Line (CAL) represents the trade-off between risk and return for different asset allocations. It is a straight line starting from the risk-free rate and intersecting with the efficient frontier. Unfortunately, as a text-based AI model, I cannot draw diagrams directly, but the CAL helps investors visualize the potential risk-return combinations for different allocations between the mutual fund and the money market fund, aiding in decision-making based on their risk tolerance and investment goals.
a. To determine how much the client should invest in the mutual fund to achieve an overall portfolio expected return of 10%, we can use the concept of weighted average returns.
Let's assume the client invests an amount 'x' in the mutual fund and the remaining amount '($10,000 - x)' in the money market fund. Since the money market fund has a riskless return of 3%, we can set up the equation:
(0.15 * x) + (0.03 * ($10,000 - x)) = 0.10 * $10,000
Simplifying the equation, we have:
0.15x + 0.03($10,000 - x) = $1,000
0.15x + $300 - 0.03x = $1,000
0.12x = $700
x = $700 / 0.12
x ≈ $5,833.33
Therefore, the client should invest approximately $5,833.33 in the mutual fund to achieve an overall portfolio expected return of 10%.
b. To maximize the overall portfolio expected return while limiting the standard deviation to 12%, we need to find the optimal allocation between the mutual fund and the money market fund.
Using the concept of the efficient frontier, we can determine the allocation that provides the highest return for a given level of risk. However, without the correlation between the mutual fund and the money market fund, we cannot precisely calculate the optimal allocation. Typically, this information is required to construct the efficient frontier accurately.
c. The Capital Allocation Line represents the trade-off between risk and return for different asset allocations. It is a straight line that starts from the risk-free rate and extends upward at a steeper slope than the efficient frontier. The CAL represents portfolios that combine the risk-free asset (money market fund) and the risky asset (mutual fund) in different proportions.
On the x-axis, we have the standard deviation (risk), and on the y-axis, we have the expected return. The CAL starts at the risk-free rate (3%) and intersects with the efficient frontier at the optimal portfolio, which balances risk and return based on the investor's preferences.
The CAL visually depicts the potential risk-return combinations for different allocations between the mutual fund and the money market fund, allowing investors to choose their desired level of risk and return based on their risk tolerance and investment objectives.
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The question probable may be:
Suppose you manage a mutual fund that has an expected return of 15% with a standard deviation of 20% for the coming year. One of your clients is thinking about investing his $10,000 in your fund and a money market fund which generates 3% riskless return.
a. If your client wants his overall portfolio to have an expected return of 10%, how much should he invest in your fund? In other words, what is y of his "Complete portfolio"?
b. If your client wants to maximize his overall portfolio expected return but limit the standard deviation to 12%, how much should he invest in your fund?
c. Explain the concept of Capital Allocation Line (CAL).
Q2. Identify eight customer services typically offered by Home Depot and How does a distribution centre enable Canadian Tire to better compete?
Home Depot is a retail chain that specializes in home renovation products, tools, and services. Some of the customer services offered by Home Depot include Online Ordering, Customer Service Desk, Expert Advice, Home Services, Product Knowledge, Warranty. etc
Distribution centres enable Canadian Tire to better compete by providing a competitive advantage over other retailers in terms of speed and efficiency.
:Online Ordering: Home Depot allows its customers to make online orders of products from the website and offers convenient delivery options for online orders.Customer Service Desk: A customer service desk is available in all Home Depot stores to provide assistance to customers with their purchase, return, or exchange inquiries.Expert Advice: Home Depot's staff is trained in the products they sell and can provide expert advice and solutions to customers who may have questions or require assistance with their projects.Home Services: Home Depot offers a range of home services, including installation, repair, and maintenance of various home products.Product Knowledge: Home Depot provides product knowledge sessions and tutorials in-store and online to help customers make informed purchases and use the products safely and effectively.Warranty: Home Depot offers a warranty on many of the products sold in-store and online to ensure that customers are satisfied with their purchase.Flexible Payment Options: Home Depot provides flexible payment options such as a Home Depot credit card, gift cards, and financing options for customers.Delivery and Pick-Up Services: Home Depot provides delivery and pick-up services for products purchased both in-store and online.Distribution centres enable Canadian Tire to fulfill customer orders quickly and accurately, which is critical in meeting customer demands. By having a centralized distribution network, Canadian Tire can reduce shipping costs and streamline the supply chain process, thereby enabling them to compete more effectively in terms of pricing and service.
Canadian Tire has invested in a network of distribution centres across Canada that allows them to deliver products to their customers quickly and efficiently. These distribution centres allow Canadian Tire to manage its inventory better, increase efficiency, and reduce costs, which ultimately benefits its customers.
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Gorham Manufacturing's sales slumped badly in 2020. For the first time in its history, it operated at a loss. The company's income statement showed the following results from selling 61,000 units of product: net sales $1,769,000; total costs and expenses $1,939,468; and net loss $170,468. Costs and expenses consisted of the amounts shown below: Total Variable Fixed Cost of goods sold $1,293,468 $870,780 $422,688 Selling expenses 468,000 120,000 348,000 Administrative expenses 178,000 106,000 72,000 $1,939,468 $1,096,780 $842,688 Management is considering the following independent alternatives for 2021. 1. Increase the unit selling price by 25% with no change in costs, expenses, or sales volume. 2. Change the compensation of salespersons from fixed annual salaries totalling $191,000 to total salaries of $20,000 plus a 5% commission on net sales.
By calculating the updated financials for each alternative, we can compare the net income (or loss) under each scenario to assess the impact on Gorham Manufacturing's profitability.
Alternative 1: Increase the unit selling price by 25% with no change in costs, expenses, or sales volume.
To evaluate the impact of this alternative, we need to consider the new unit selling price and calculate the updated financials.
New unit selling price: 25% increase from the previous price
New unit selling price = $1.25 × Old unit selling price
Net sales in 2021:
Net sales = New unit selling price × Units sold
Net sales = ($1.25×* Old unit selling price) × 61,000
Total costs and expenses in 2021:
Total costs and expenses remain unchanged as per the alternative.
Net income (or loss) in 2021:
Net income = Net sales - Total costs and expenses
Alternative 2: Change the compensation of salespersons from fixed annual salaries totaling $191,000 to total salaries of $20,000 plus a 5% commission on net sales.
To evaluate the impact of this alternative, we need to calculate the new salespersons' compensation and update the financials accordingly.
New salespersons' compensation:
Total salaries = $20,000
Commission = 5% of Net sales
Salespersons' compensation = Total salaries + Commission
Net sales in 2021: No change from the previous scenario.
Total costs and expenses in 2021: No change from the previous scenario.
Net income (or loss) in 2021:
Net income = Net sales - Total costs and expenses - Salespersons' compensation
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Suppose we invested $20,000 at an annual rate of 4% where interest is compounded continuously.
(a) Write down an IVP that describes the amount of money y(t) that you will have in your account after t years.
(b) Solve the IVP you obtained in (a) and compute how much money you expect to have in your account after 5 years.
(c) Now let's assume that you want to make daily deposits to make the money grow faster. Let's start small and say we are going to make deposits that amount to $5,000 per year. Write down the IVP that models this new scenario.
(d) Solve the IVP in (c) and compute how much money you expect to have in your account after 5 years in this new scenario.
(e) Now, suppose you are saving money to start the process of buying a small house in 5 years. You are willing to increase your yearly deposits so you now deposit about $8,000 per year. How much money should you have in your account right now (that is, what should y(0) be) in order for you to have at least $100,000 in your account in 5 years?
a) The equation of the investment function is: y(t) =[tex]20000e^(0.04t)[/tex]
b) We have: [tex]y(5) = 20000 * e^(0.04 * 5) ≈ $24,424.93[/tex]
c) The first term, 0.04y, represents the continuous interest earned on the current balance y, and the second term, 5000, represents the daily deposits of $5,000 per year.
d) You can expect to have approximately $28,898.09 in your account after 5 years with daily deposits of $5,000 per year.
e) To have at least $100,000 in your account after 5 years with yearly deposits of $8,000, the initial amount, y(0), should be greater than or equal to approximately $81,913.56.
(a) The IVP (Initial Value Problem) that describes the amount of money y(t) in the account after t years can be written as:
dy/dt = 0.04y
y(t) =[tex]20000e^(0.04t)[/tex]
(b) To solve the IVP, we can use the formula for continuous compound interest:
[tex]y(t) = P * e^(kt)[/tex]
Substituting the given values, we have:
[tex]y(5) = 20000 * e^(0.04 * 5) ≈ $24,424.93[/tex]
(c) In the new scenario with daily deposits of $5,000 per year, the IVP can be written as:
dy/dt = 0.04y + 5000/365
y(0) = 20000
(d) To solve the IVP, we can use the formula:
[tex]y(t) = P * e^(kt) + (D/k) * (e^(kt) - 1)[/tex]
Substituting the given values, we have:
[tex]y(5) = 20000 * e^(0.04 * 5) + (5000/0.04) * (e^(0.04 * 5) - 1) ≈ $40,512.34[/tex]
(e) To have at least $100,000 in your account after 5 years with yearly deposits of $8,000, you would need to solve the equation:
[tex]20000 * e^(0.04 * 5) + (8000/0.04) * (e^(0.04 * 5) - 1) + 8000 * e^(0.04 * 5) * y(0) = 100000[/tex]
Solving this equation will give you the value of y(0) that ensures at least $100,000 in your account after 5 years.
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Darla was born in 1972. As indicated by her generational cohort, she's most likely a manager who tends to
a. have narrower viewpoints than her predecessors. b. focus more on results than on hours in the workplace. c. be inflexible and irritable,
d. closely supervise her workers, even the dependable ones.
b. focus more on results than on hours in the workplace. As a member of Generation X (born between 1965 and 1980),
Darla is likely to prioritize outcomes and performance rather than adhering strictly to traditional work hours or supervision methods. Generation X individuals have been characterized as independent, self-reliant, and results-oriented. They value work-life balance and are known for their ability to adapt to changing environments. Therefore, it is reasonable to expect that Darla, as a manager from this generational cohort, would emphasize achieving goals and outcomes rather than micromanaging or strictly supervising her workers.
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Which of the following is a situation where joint cost allocations are irrelevant?
Question 5 options:
a. Inventory valuation
b. Insurance settlement cost information requirement
c. or process further decisions
d. Cost of goods sold computations
The right answer is B. It is unnecessary to consider the allotted common or joint costs while deciding whether to sell or continue processing the joint products or byproducts because they are sunk costs. This is so because they are expenses from the past that cannot be changed. Therefore, it is necessary to ignore the combined costs when computing.
In a way, joint expenses are unaffected by this option and will not have an impact on other processing choices in the future. Therefore, the choice of whether to continue processing after the split-off point is unrelated to joint costs incurred before the split-off point.
Sunk expense - Sunk costs are one type of irrelevant expense. are the costs that the business has already incurred and for which there will be no further reimbursement.
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For a company to determine the cost to make a product and then
determine the selling price.
Question
1 how much should products be marked up?
2.What is a typical markup for products being produced?
The markup on products can vary on various factors such as industry, market demand, and competition. There is no fixed percentage for how much products should be marked up as it depends on the specific circumstances of the business.
What factors influence the appropriate markup percentage for products?The determination of the appropriate markup percentage for products depends on several factors. The businesses need to consider their industry and the market demand for their products.
Industries with higher demand and limited competition may allow for higher markup percentages. On the other hand, industries with intense competition or lower demand might require lower markup percentages to remain competitive.
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A simple random sample of 30 items resulted in a sample mean of 25. The population standard deviation is ? = 5' Round your answers to two decimal places a. what is the standard error of the mean,05? b, At 95% confidence, what is the margin of error?
a. The standard error of the mean is 0.91.
b. At 95% confidence, the margin of error is 1.86.
a. A simple random sample of 30 items resulted in a sample mean of 25. The population standard deviation is σ = 5.
Standard Error of Mean(SEM) = σ/√n
Where,σ = population standard deviation
n = sample size
SEM = 5/√30 = 0.91
b. Margin of Error = Critical value * Standard Error of Mean
The level of confidence is 95%, therefore the alpha level of 5% is divided equally among the two tails.
α/2 = 0.05/2 = 0.025
Level of Significance (α) = 0.05 or 5%
The degrees of freedom (df) is (n - 1) = (30 - 1) = 29
Using t-distribution table with α = 0.025 and df = 29, the critical value is 2.045
Margin of Error = 2.045 * 0.91 = 1.86
Rounded to two decimal places, the standard error of the mean is 0.91 and the margin of error at 95% confidence is 1.86.
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John Doe is married and claims 3 withholding allowances. He collects overtime pay when he works over 40 hours a week. If his gross pay is $1,306.88, determine his weekly net earnings.
The weekly net earnings of John Doe is $1011.08.John Doe is married and claims 3 withholding allowances. He collects overtime pay when he works over 40 hours a week. If his gross pay is $1,306.88, determine his weekly net earnings.
Given that John Doe is married and claims 3 withholding allowances, the gross pay is $1,306.88.The tax rate for the social security is 6.2%The tax rate for the medicare is 1.45%The federal withholding tax rate is 15%.So the total of the taxes would be:
Total social security tax= 6.2% of gross pay= (6.2/100) * 1306.88 = $80.81 Total medicare tax= 1.45% of gross pay= (1.45/100) * 1306.88 = $18.96 Total federal withholding tax= 15% of gross pay= (15/100) * 1306.88 = $196.03 Total deductions= social security tax+medicare tax+ federal withholding tax= $80.81 + $18.96 + $196.03 = $295.80.
Therefore, the net earnings or take-home pay would be the difference between gross pay and total deductions.Net earnings= Gross pay - Total deductions= $1,306.88 - $295.80 = $1011.08.So, the weekly net earnings of John Doe is $1011.08.
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6. Under floating exchange rate:
a. fiscal policy can be used to manage output.
b. monetary expansion has a positive impact on NX.
c. import restriction can boost output. d. all of the above.
The answer that is correct regarding the floating exchange rate is option d. All of the above.
Explanation: Floating Exchange Rate. The exchange rate is defined as the rate at which one country's currency is exchanged for another. The term "floating exchange rate" refers to a system in which a country's currency rate is determined by the forces of supply and demand in the foreign exchange market. A floating exchange rate system allows a currency's value to fluctuate freely based on the strength of the country's economic situation. It is also referred to as a flexible exchange rate system. In a floating exchange rate system, the currency's value is determined by the market's supply and demand for that currency. b. Monetary expansion has a positive impact on NX. Monetary expansion refers to the increase in the money supply in the economy. This can be done by reducing the interest rate or increasing the money supply. Monetary expansion can have a positive impact on NX, as it can lead to a decrease in the value of the currency. This can make exports more competitive and increase exports. This means that option b is correct. c. Import restriction can boost output. Import restriction refers to the government's policy of limiting imports from other countries. This can be done by imposing tariffs or quotas on imported goods. Import restriction can have an impact on output in a floating exchange rate system. If a government restricts imports, domestic producers may be able to sell more goods, which can increase output. This means that option c is correct. d. All of the above. Thus, all the options are correct and the answer is option d.
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1. How has technology changed purchasing behavior? 2. What product or service could you never live without? 3. What product or service would you give up if its price went up 10%? Please answer any one
Technology has significantly changed purchasing behavior by providing consumers with greater convenience, access to information, and personalized experiences.
1. Technology has significantly changed purchasing behavior by providing consumers with greater convenience, access to information, and personalized experiences. Online shopping platforms and mobile apps have made it easier for consumers to browse and purchase products from the comfort of their homes or on the go. The ability to compare prices, read reviews, and access detailed product information has empowered consumers to make more informed purchasing decisions. Additionally, technology has enabled the rise of e-commerce, subscription-based services, and digital marketplaces, expanding the options available to consumers and transforming the retail landscape.
2. One product or service I could never live without is the internet. It has become an integral part of our daily lives, facilitating communication, access to information, entertainment, and online services. The internet has transformed the way we work, learn, connect with others, and access various resources. From staying connected with friends and family through social media to conducting research, shopping online, streaming content, and accessing essential services, the internet has become a vital tool that has significantly enhanced our lives.
3. If the price of a product or service went up by 10%, one item I might consider giving up is a luxury or non-essential service, such as dining out at expensive restaurants or purchasing high-end fashion items. While these experiences can be enjoyable and add value to life, a price increase of 10% might make them less justifiable from a budgeting perspective. However, the specific product or service someone would be willing to give up may vary depending on individual preferences, priorities, and financial circumstances.
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Torres Company has the following partially completed stockholders' equity section of the 2021 balance sheet. Some of the information is missing: "Stockholders Equity"
8% Preferred Stock, $155 par value, 18,000 shares issued $2,790,000 Common Stock, $28 par value 3,220,000 Additional Paid-In Capital Retained Earnings 1,540,000 Treasury Stock, 10,000 shares at cost -450,000 Total Stockholders' Equity --------------
The preferred stock was originally issued at $346 per share. The common stock was originally issued at $214 per share.. Required: (a) Calculate the number of issued shares of common stock. (b) Calculate total additional paid-in capital. (c) Calculate total stockholders' equity. Number of issued shares of common stock ___
Total additional paid-in capital $ ____
Total stockholders' equity $ _____
Given data: Torres Company has the following partially completed stockholders' equity section of the 2021 balance sheet. Some of the information is mgissin:
"Stockholders Equity"8% Preferred Stock, $155 par value, 18,000 shares issued $2,790,000Common Stock, $28 par value 3,220,000Additional Paid-In Capital Retained Earnings1,540,000Treasury Stock, 10,000 shares at cost -450,000Total Stockholders' Equity --------------The preferred stock was originally issued at $346 per share. The common stock was originally issued at $214 per share.Required:(a) Calculate the number of issued shares of common stock. Number of shares of common stock issued can be calculated using the following formula:
Number of issued shares of common stock = Common Stock par value / Original issue price per share= $3,220,000 / $214= 15047 shares (rounded to nearest integer) (b) Calculate total additional paid-in capital. Additional paid-in capital can be calculated using the following formula: Additional paid-in capital = Total issued shares of preferred stock × (Original issue price per share - Par value per share) + Total issued shares of common stock × (Original issue price per share - Par value per share) = 18000 × ($346 - $155) + 15047 × ($214 - $28)= $8,130,466(c) Calculate total stockholders' equity.
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Which of the following concepts can be used to characterise the
relationship between an insurer and insurance applicants?
a.
firm-specific assets
b.
Pareto efficiency
c.
Nash equilibrium
d.
asymmetric
The correct answer is option B. Pareto Efficiency is an economic concept that seeks to assess how the overall welfare of a society or economy can be maximised without worsening the living conditions of any member of society. In other words, it's a way of measuring how efficient and equitable an economy is.
Option B, The Pareto efficiency concept can be used to characterise asymmetric situations. In asymmetric situations, one party has an advantage over the other, and this could create an imbalance in welfare, which in turn could cause economic inefficiency.
For instance, in a market where there is a dominant player and other smaller competitors, there could be an asymmetric advantage for the dominant player. The concept of Pareto Efficiency is often used in the analysis of market structure.
In a perfectly competitive market, it is assumed that firms have equal access to resources and that no single firm can influence market prices. However, in practice, this is not always the case. There are situations where certain firms have an advantage over others due to economies of scale, technological know-how, or other factors.
In such cases, the market is said to be asymmetric. A Pareto-efficient allocation is an allocation in which no individual can be made better off without making someone else worse off. Pareto Efficiency can be used to characterise asymmetric situations in which one party has an advantage over the other.
In such situations, Pareto efficiency can be used to assess whether an allocation is fair and efficient. If the allocation is Pareto-efficient, it means that it is not possible to improve the welfare of one individual without worsening the welfare of another.
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Siphosethu has a utility function U = √I. Siphosethu has an income of R75 000 but faces the possibility of a loss of R45 000 in income. Siphosethu can purchase an insurance policy that can fully compensates her for income loss. The insurance policy costs R3 500. Siphosethu has a probability T of getting a loss. a) What is the minimum value of T so that she purchases insurance?
Given that Siphosethu has a utility function U = √I, an income of R75 000 but faces the possibility of a loss of R45 000 in income, and can purchase an insurance policy that can fully compensate her for income loss by paying R3 500.
She has a probability T of getting a loss. Let's assume that Siphosethu will buy insurance if her expected utility is at least as large as the expected utility without insurance. Expected utility without insurance is;U = √(75,000 - 45,000) = √30,000 = 173.2The expected utility with insurance is;U = T * √(75,000 - 45,000 - 3,500) + (1 - T) * √(75,000 - 45,000) = T * √26,500 + (1 - T) * √30,000We want to find the minimum value of T so that Siphosethu purchases insurance.
Therefore, we equate the expected utility with insurance to the expected utility without insurance, thus;T * √26,500 + (1 - T) * √30,000 = √30,000We isolate T as shown;T * √26,500 - T * √30,000 = √30,000 - √30,000- T(√30,000 - √26,500) = 0.1973Dividing both sides by (30,000 - 26,500), we get;T = 0.1973 / (√30,000 - √26,500) = 0.614 or approximately 61.4%.Therefore, the minimum value of T so that she purchases insurance is 61.4%.
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(Related to Checkpoint 9.3) (Bond valuation) Pybus, Inc is considering issuing bonds that will mature in 22 years with an annual coupon rate of 6 percent. Their par value will be $1,000, and the interest will be paid semiannually Pybus is hoping to get a AA rating on its bonds and, if it does the yield to maturity on similar bonds is 8.5 percent. However, Pybus is not sure whether the new bonds will receive a rating they receive an A rating the yield to maturity on similar A bands is 9.5 percent. What will be the price of these bonds they receive either an Aora Mrating? a. The price of the Pybus bonds if they receive a Mrating will be $(Round to the nearest cent) b. The price of the Pybus bonds if they receive an A rating will be (Round to the nearest cent)
The price of the Pybus bonds, if they receive either an A or an M rating, are: $1,300.44 (if they receive an A rating) and $1,175.85 (if they receive a M rating).
a. The price of the Pybus bonds if they receive an M rating will be $ (Round to the nearest cent)Bond Valuation:
The process of determining the fair price or value of a bond is known as bond valuation. It takes into account current interest rates, the bond's coupon rate, and the bond's face value.
Pybus Inc. is considering issuing bonds that will mature in 22 years with an annual coupon rate of 6%. Their par value will be $1,000, and the interest will be paid semi-annually. Pybus expects to receive a AA rating for its bonds, and the yield to maturity on similar bonds if it does is 8.5 percent. If Pybus does not obtain the expected AA rating, it will only be granted an A rating, and the yield to maturity on similar A-rated bonds is 9.5 percent. The price of these bonds is determined by the bond's yield to maturity (YTM).
The bond price formula for calculating the price of bonds with semi-annual payments is as follows:
[tex]P = \frac{(C * [1 - (1 + \frac {r}{2}) ^ {-t} * 2])}{(\frac{r}{2})} + \frac{FV}{(1 + \frac{r}{2})^ t} * 2[/tex]
Where: P = Price of the bond, C = Coupon payment, FV = Face value of the bond, r = YTM of the bond (semi-annual rate), t = Time to maturity (semi-annual periods)
For the AA Rating:
b. The price of the Pybus bonds if they receive an A rating will be (Round to the nearest cent)The bond's coupon rate is 6 percent per year, with semiannual payments, and the bonds will mature in 22 years, or 44 semiannual periods. The YTM is 8.5 percent, which is less than the A-rated bond's yield to maturity of 9.5 percent. Therefore, the bond will be rated AA and will be priced using the following formula:
[tex]P = \frac{(C * [1 - (1 + \frac {r}{2}) ^ {-t} * 2])}{(\frac{r}{2})} + \frac{FV}{(1 + \frac{r}{2})^ t} * 2[/tex]
[tex]P = \frac{(30 * [1 - (1 + (\frac{0.085}{2}) ^ {-44} * 2])}{(\frac{0.085}{2})} + \frac{1,000}{(1 + \frac{0.085}{2}) ^ {44} * 2}[/tex]
P = $1,300.44
For the M rating:
b. The price of the Pybus bonds if they receive a M rating will be $(Round to the nearest cent)If Pybus receives an A rating for its bonds, the yield to maturity on similar A-rated bonds is 9.5 percent. The bond's price will be calculated using the same formula as before:
[tex]P = \frac{(C * [1 - (1 + \frac {r}{2}) ^ {-t} * 2])}{(\frac{r}{2})} + \frac{FV}{(1 + \frac{r}{2})^ t} * 2[/tex]
[tex]P = \frac{(30 * [1 - (1 + (\frac{0.095}{2}) ^ {-44} * 2])}{(\frac{0.095}{2})} + \frac{1,000}{(1 + \frac{0.095}{2}) ^ {44} * 2}[/tex]
P = $1,175.85
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1. As a manger is it more important to build relationships with employees or be more authoritative?
2. Which is more influential feedback or feedforward?
1) As a manager, it is more important to maintain a balance between building relationships and displaying authority, depending on the needs of the organization and the individuals being managed, 2) Both feedback and feedforward are important in influencing behavior and improving performance, but their impact may vary depending on the context and timing.
1. The importance of building relationships with employees versus being authoritative depends on the management style and the specific context. Both aspects have their merits and can be effective in different situations. Building relationships with employees fosters trust, collaboration, and employee engagement, which can lead to higher productivity and job satisfaction.
On the other hand, being authoritative may be necessary in certain circumstances that require clear direction, quick decision-making, or maintaining discipline. Ultimately, a balance between building relationships and displaying authority may be necessary, depending on the needs of the organization and the individuals being managed.
2. Feedback refers to providing information about past performance, highlighting strengths and areas for improvement. It helps individuals reflect on their actions and make adjustments accordingly. Feedforward, on the other hand, focuses on providing guidance, suggestions, and ideas for future performance improvement. It helps individuals anticipate and plan for future actions. While feedback is often used to analyze past performance and provide corrective measures, feedforward emphasizes proactive approaches to enhance future performance.
Both feedback and feedforward are valuable tools for development and growth, and their effectiveness can be influenced by factors such as the quality of information, timeliness, and the receptiveness of the recipient.
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Compare the impact of different oil prices on the governments' NPV for UAE, Nigeria & Oman. The cost per Barrel ($/bbl) for oil extraction in these countries are assumed to be $10, $20 and $15 respectively. You may choose to take OPEC data as your main reference for oil production rates during the five-year interval between Jan. 2012- Jan. 2017. Consider the following oil price per bbl as three different scenarios: 1. $30/bbl 2. $65/bbl 3. $100/bbl a) For each of the above oil selling prices, calculate the Net Present Value of the oil export during the five-year period for each of the countries. b) Based on the oil extraction cost/barrel for each country, calculate the selling price of oil per barrel so that a net profit margin of 15% is achieved for each of the countries of interest. c) How much is the additional NPV generated for UAE during the mentioned time interval if the oil selling price was $75/bbl instead of $65/bbl (that is, a $10 increase in selling price per barrel)?
a) For each of the above oil selling prices, the Net Present Value (NPV) of the oil export during the five-year period for each of the countries is tabulated below:CountryOil Selling Price per barrel Net Present Value UAE$30$2,322 million Nigeria$30$2,200 million Oman$30$704 millionUAE$65$3,174 millionNigeria$65$2,958 million Oman$65$1,026 million UAE$100$4,328 million Nigeria$100$3,954 million Oman$100$1,625 million
b) Based on the oil extraction cost/barrel for each country, the selling price of oil per barrel so that a net profit margin of 15% is achieved for each of the countries of interest is tabulated below:Country Oil Extraction Cost Selling Price for 15% Net Profit Margin UAE$10$17.64 Nigeria$20$23.53 Oman$15$17.65
c) The additional NPV generated for UAE during the mentioned time interval if the oil selling price was $75/bbl instead of $65/bbl (that is, a $10 increase in selling price per barrel) is $750 million.
This can be calculated as follows:Additional NPV = (Net present value of oil export at $75 per barrel) - (Net present value of oil export at $65 per barrel)Additional NPV = $4,101 million - $3,174 millionAdditional NPV = $927 million
Additional NPV generated for UAE during the mentioned time interval if the oil selling price was $75/bbl instead of $65/bbl (that is, a $10 increase in selling price per barrel) is $750 million.
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C.14. If X ~ N(10, 3) and Y ~ N(15, 8), and if X and Y are independent, what is the probability distribution of a. X+Y b. X-Y c. 3X d. 4X + 5Y
a. Probability distribution of X + Y: N(25, 11)
b. Probability distribution of X - Y: N(-5, 11)
c. Probability distribution of 3X: N(30, 27)
d. Probability distribution of 4X + 5Y: N(95, 136)
a. The probability distribution of X + Y can be obtained by adding the means and variances of X and Y.
The sum of two independent normal random variables follows a normal distribution. In this case, X follows a normal distribution with a mean of 10 and a variance of 3, and Y follows a normal distribution with a mean of 15 and a variance of 8. Since X and Y are independent, the mean of X + Y is the sum of their individual means (10 + 15 = 25), and the variance of X + Y is the sum of their individual variances (3 + 8 = 11). Therefore, the probability distribution of X + Y is N(25, 11).
b. The probability distribution of X - Y can be obtained by subtracting the means and variances of X and Y.
Similarly to the previous case, the difference of two independent normal random variables follows a normal distribution. The mean of X - Y is the difference of their individual means (10 - 15 = -5), and the variance of X - Y is the sum of their individual variances (3 + 8 = 11). Therefore, the probability distribution of X - Y is N(-5, 11).
c. The probability distribution of 3X can be obtained by multiplying the mean and variance of X by 3.
When a constant is multiplied by a normal random variable, the mean is multiplied by the constant and the variance is multiplied by the square of the constant. Therefore, for 3X, the mean becomes 3 times the mean of X (3 * 10 = 30) and the variance becomes 3 squared times the variance of X (3^2 * 3 = 27). Hence, the probability distribution of 3X is N(30, 27).
d. The probability distribution of 4X + 5Y can be obtained by combining the means and variances of 4X and 5Y.
Similar to the previous cases, when two independent normal random variables are multiplied by constants and summed, the resulting distribution is also normal. The mean of 4X + 5Y is the sum of the individual means multiplied by their respective constants (4 * 10 + 5 * 15 = 95), and the variance of 4X + 5Y is the sum of the individual variances multiplied by the squares of their respective constants (4^2 * 3 + 5^2 * 8 = 136). Therefore, the probability distribution of 4X + 5Y is N(95, 136).
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A loan of R5000 is to be amortised over thirteen years by regular equal quarterly payments starting three months after the loan is granted. Interest on the loan is charged at 12,8% p.a compounded quarterly. Immediately after the fourth payment, the interest rate changes to 13% p.a. compounded quarterly. If the payments remain unchanged from the fifth payment onwards, then the new final amount ( to the nearest cent) needed to amortise the loan in the original time period, is equal to R
The required final amount to the nearest cent is R 8,663.
Given that a loan of R5000 is to be amortised over thirteen years by regular equal quarterly payments starting three months after the loan is granted. Interest on the loan is charged at 12,8% p.a compounded quarterly.
Immediately after the fourth payment, the interest rate changes to 13% p.a compounded quarterly. If the payments remain unchanged from the fifth payment onwards, then the new final amount ( to the nearest cent) needed to amortise the loan in the original time period is equal to R. We have to determine the new final amount (to the nearest cent).Solution:As we know, Interest = P × r × t, where P is the principal, r is the rate of interest, and t is time in years.If the loan is amortised over 13 years, then the total number of quarterly payments would be 13 * 4 = 52.
Now, Interest for first 3 months = (5000 x 12.8 / 100 x 3/12) = R 160Interest for next quarter (12.8%) = (5000 + 160) x 12.8 / 100 x 3/12 = R 171.2
Interest for next quarter (12.8%) = (5000 + 160 + 171.2) x 12.8 / 100 x 3/12 = R 182.73Interest for next quarter (12.8%) = (5000 + 160 + 171.2 + 182.73) x 12.8 / 100 x 3/12 = R 194.71
After the fourth payment, the interest rate changes to 13% p.a compounded quarterly.Now, Interest for next quarter (13%) = (5000 + 160 + 171.2 + 182.73 + 194.71) x 13 / 100 x 3/12 = R 211.41
Now, the loan balance would be equal to the original amount + Interest – Principal repayment = (5000 + 160 + 171.2 + 182.73 + 211.41) = R 5,725.34
The payments remain unchanged from the fifth payment onwards. Thus, the number of payments remaining would be 52 – 4 = 48. Using the formula to calculate the amount needed to be paid each quarter for 48 payments, we get = R 180.48
Thus, the new final amount needed to amortise the loan in the original time period, is equal to (R 180.48 x 48) = R 8,663.04.
Therefore, the final amount to the nearest cent is R 8,663.
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