Samir's effective annual return is 9.36%.
The correct answer to the given question is option B.
Here is how we can find the effective annual return:At the beginning of the investment, Samir paid $85 for each share. Over the course of 5 years, he received $2.50 as a dividend every year. He used this dividend to purchase more shares each year. The total amount of shares he owned after 5 years is calculated as follows:Shares owned = original shares + shares purchased with reinvested dividends.
We can find the number of shares purchased with reinvested dividends using the following formula:Shares purchased with reinvested dividends = total dividends received ÷ dividend per share. Substitute the given values in the above formula.Total dividends received = $2.50 × 5 years = $12.50. Dividend per share = $2.50Total shares purchased with reinvested dividends = $12.50 ÷ $2.50 = 5 shares.
Therefore, the total shares owned by Samir after 5 years is:Total shares owned = original shares + shares purchased with reinvested dividends= 14 + 5 = 19 shares. The total amount Samir received after selling all 19 shares is calculated as follows:Total amount received = price per share × total shares= $92 × 19 = $1,748Samir paid $85 for each share initially.
Therefore, the total amount he invested is:Total amount invested = price per share × total shares= $85 × 14 = $1,190Samir's profit is calculated as the difference between the total amount received and the total amount invested:Profit = total amount received - total amount invested= $1,748 - $1,190 = $558Samir held the investment for 5 years.
Therefore, his average annual profit is:Average annual profit = profit ÷ number of years= $558 ÷ 5 = $111.6Samir's effective annual return is calculated as the average annual profit divided by the total amount invested, expressed as a percentage.Effective annual return = (average annual profit ÷ total amount invested) × 100%= ($111.6 ÷ $1,190) × 100%= 0.0936 × 100%= 9.36%Therefore, Samir's effective annual return is 9.36%. Therefore, the correct answer is: B 3.41%.
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How far do most developers push their databases in normalization?
O to the first normal form
O to the second normal form
O to the third normal form
O to the fourth normal form
Answer:
c
Explanation:
The following table lists the Income statement and Balance sheet for First American Furniture Company Income Statement 2017 2018 Balance Sheet 2017 2018 Revenue $516 $630 Current assets $350 $420 30 35 Prop, plant, & Equip 500 520 400 480 Depreciation Other operating costs Income before taxes Taxes Total assets $850 $940 86 115 Current liabilities 130 150 30 40 Long-term debt 50 80 Net income 56 75 Total liabilities $180 $230 20 26 $490 $480 $0.56 $0.95 Dividends Earnings per share Dividend per share # of Common shares Shareholders' equity Total L and equity Capital expenditures $850 $940 $0.20 $0.26 45 50 100 100 You are a financial analyst at RBC. Using the data above, you want to determine the value of First American Bank's stock using the Free Cash Flow to Equity (FCFE) model. You believe that the company's FCFE will grow at 30% for three years and 10% thereafter. Capital expenditures, depreciation, working capital and net debt are all expected to increase proportionately with FCFE. The required rate of return on equity is 15% Calculate the amount of FCFE per share for the year 2018 Calculate Projected 2021 terminal value based on constant growth of 10% Calculate the current value of a share of the stock based on the two-stage FCFE model.
The amount of FCFE per share for the year 2018 is $2.40.
What is the FCFE per share for the year 2018?To calculate the FCFE per share for the year 2018, we need to determine the free cash flow to equity (FCFE) and divide it by the number of common shares outstanding. FCFE represents the cash flow available to the company's equity shareholders after deducting capital expenditures, depreciation, working capital changes, and net debt.
First, we calculate the FCFE for 2018 by taking net income ($75) and adjusting for non-cash expenses (depreciation: $35), changes in working capital ($10 increase in current assets - $5 increase in current liabilities), and net debt ($80 increase in long-term debt). This results in an FCFE of $115.Next, we divide the FCFE by the number of common shares outstanding (50) to obtain the FCFE per share for 2018, which is $2.40.
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For a present sum of $750,000, determine the annual worth (in then-current dollars) in years 1 through 8 if the market interest rate is 7% per year and the inflation rate is 3% per year. The annual worth is $
Taking into account a given interest rate and inflation rate, the annual value in then-dollars for years 1 through 8 would be:
Year 1 : $65,333, Year 2: $62,891, Year 3: $60,560, Year 4: $58,331, Year 5: $56,197, Year 6: $54,150, Year 7: $52,184, Year 8: $50,292.
To determine his 8-year annual value of the current amount of $750,000 in current dollars, we can use the present value concept, considering a market interest rate of 7%/year and an inflation rate of 3% per year . about the pension system. The formula is:
Annual Value = Present Value * (Interest Rate / (1 - (1 + Interest Rate)^(-n))) * (1 + Inflation Rate)^n
where:
The current value is the initial amount ($750,000 in this case).
The interest rate will be the market rate (7% or 0.07).
Inflation is the rate of inflation (3% or 0.03).
n is the number of years (1-8).
Let's calculate the annual value for each year.
For the first year:
Annual Value = $750,000 * (0.07 / (1 - (1 + 0.07)(⁻¹))) * (1 + 0.03)¹
For the second year:
Annual Value = $750,000 * (0.07 / (1 - (1 + 0.07)⁻²)) * (1 + 0.03)²
Continue this calculation for years 3 through 8, adjusting the exponent of (1 + 0.03) accordingly.
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"Explain why the concept of an enterprise as an iceberg is
important". I need to write a 3500-word paper on this
topic, please do not post the same answer as before.
The concept of an enterprise as an iceberg is important as it implies that what we can see is only a small part of the whole, and there is a much larger and complex structure hidden below the surface.
This hidden structure represents the fundamental components of an enterprise such as its culture, values, beliefs, processes, and systems that are not immediately visible to the external stakeholders.
The iceberg model is important in business management as it helps leaders to understand the complexities of their organization and the interdependencies of its various parts. By taking into consideration the hidden structure, they can identify the root causes of the problems, develop more effective solutions, and make better decisions.
Additionally, the iceberg concept can be applied to different areas of an enterprise such as customer service, supply chain management, and employee engagement, to gain a deeper understanding of the underlying issues and opportunities.
Overall, the concept of an enterprise as an iceberg is a valuable tool for business leaders to gain insight into their organization and take strategic action.
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construction cost 130.000 $ X $
annual expenses 12.000 $ 14.000 $
salvage value 18.000 $ 20.000 $
physical life 30 years 32 years
If you consider uniform annual cost values, what is the maximum value of X to make the Project B cheaper.
The maximum value of X to make Project B cheaper is $41,651.75.
Project A :Construction cost = $130,000 Annual expenses = $12,000 Physical life = 30 years Salvage value = $18,000 Project B: Construction cost = $X Annual expenses = $14,000 Physical life = 32 years Salvage value = $20,000. We need to find the maximum value of X to make Project B cheaper. We know that the annual cost of owning and operating an asset for n years is given by the following formula: Annual cost = (construction cost - salvage value + present value of annual expenses) / present value of an annuity of $1 for n years.
Using the above formula, we can calculate the annual cost of Project A and Project B.
Annual cost of Project A: Annual cost = ($130,000 - $18,000 + $12,000 x 21.192) / 21.192= $10,818.18
Annual cost of Project B:Annual cost = ($X - $20,000 + $14,000 x 19.268) / 19.268= (X - $20,000 + $269,752) / 19.268
To make Project B cheaper than Project A, we need to have the annual cost of Project B less than $10,818.18. Therefore, we can write the following inequality: (X - $20,000 + $269,752) / 19.268 < $10,818.18. Multiplying both sides of the inequality by 19.268, we get: X - $20,000 + $269,752 < $208,100.25X < $20,000 + $208,100.25 - $269,752X < -$41,651.75. Therefore, the maximum value of X to make Project B cheaper is $41,651.75.
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cruz company uses lifo for inventory costing and reports the following financial data. it also recomputed inventory and cost of goods sold using fifo for comparison purposes. year 2 year 1 lifo inventory $ 160 $ 110 lifo cost of goods sold 740 680 fifo inventory 240 110 fifo cost of goods sold 660 645 current assets (using lifo) 220 180 current assets (using fifo) 300 180 current liabilities 200 170 1. compute its current ratio, inventory turnover, and days' sales in inventory for year 2 using (a) lifo numbers and (b) fifo numbers.
The Cruz Company's contemporary ratio is higher whilst using FIFO (1.5) compared to LIFO (1.1), indicating higher quick-time period liquidity.
Inventory turnover is better using FIFO (6) than LIFO (4.63), suggesting quicker stock sales. Days' sales in inventory are shorter using FIFO (60.83 days) than LIFO (78.90 four days), indicating faster inventory turnover and capability performance development.
To compute the current ratio, stock turnover, and days' income in stock for Year 2 the usage of LIFO and FIFO numbers, we can use the subsequent formulation:
Current Ratio:
Current Ratio = Current Assets / Current Liabilities
(a) LIFO:
Current Ratio (LIFO) = $220 / $200 = 1.1
(b) FIFO:
Current Ratio (FIFO) = $300 / $200 = 1.5
Inventory Turnover:
Inventory Turnover = Cost of Goods Sold / Average Inventory
(a) LIFO:
Inventory Turnover (LIFO) = $740 / (($160 + $240) / 2) = 4.63
(b) FIFO:
Inventory Turnover (FIFO) = $660 / (($110+ $110) / 2) = 6
Days Sales in Inventory:
Days Sales in Inventory = three hundred and 65 days / Inventory Turnover
(a) LIFO:
Days Sales in Inventory (LIFO) = 365 days / 4.63 = 78.94 days (approx.)
(b) FIFO:
Days Sales in Inventory (FIFO) = 12 months / 6 = 60.83 days (approx.)
Please be aware that the calculations are primarily based at the given financial records.
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What would be worth more at the end of one year? Receiving $10,800 today or receiving $12,050 one year from now? Your Financial Advisor points out today you could invest the $10,800 in the bank at 12% for one year. O It is better to take the $10,800 today Both would equal the same amount in one year so it does not matter which one you choose O It is better to take the $12,050 one year from now O Neither choice is good and it would be better to borrow funds using debt equity
Therefore, it is better to take the $10,800 today rather than receiving $12,050 one year from now.
To determine which option would be worth more at the end of one year, we need to compare the present value of the two amounts.
Option 1: Receiving $10,800 today.
Option 2: Receiving $12,050 one year from now.
Since we are given that the bank offers an interest rate of 12%, we can calculate the present value of Option 2 by discounting it back to today's value.
Using the formula for calculating present value, we have:
PV = FV / (1 + r)^n
Where PV is the present value, FV is the future value, r is the interest rate, and n is the number of periods.
For Option 1: PV1 = $10,800
For Option 2: PV2 = $12,050 / (1 + 0.12)^1 = $10,767.86
Comparing the two present values, we find that PV1 > PV2.
Therefore, it is better to take the $10,800 today rather than receiving $12,050 one year from now.
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15. The fundamental difference between internal and external auditing is that a. internal auditors represent the interests of the organization and external auditors represent outsiders b. internal aud
The fundamental difference between internal and external auditing is that Internal and external auditors are different from each other in their methods and approach. The Correct option is A
What is internal auditing?Internal auditing is the process of assessing and monitoring a company's risk management and control processes. Internal auditors provide an objective assessment of a company's performance, risk management strategies, and the effectiveness of its internal controls. Internal auditors are hired and employed by the company they audit, and they primarily serve the interests of the organization and its management. Their goal is to ensure that the company's internal controls and risk management processes are functioning as intended. The Correct option is A
External auditing, on the other hand, is an independent assessment of a company's financial statements and internal controls. External auditors are not affiliated with the company being audited and represent the interests of outside stakeholders, such as shareholders, regulatory agencies, and the public. External auditors examine the accuracy of a company's financial statements and assess whether they adhere to generally accepted accounting principles (GAAP). They also evaluate the effectiveness of a company's internal controls and risk management processes to identify any significant risks or control deficiencies. The Correct option is A
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3. Suppose Acme Inc. announces that it had profits of $50
million in the previous quarter, and its stock suddenly drops by
$2. How does this make sense?
It makes sense that Acme Inc.'s stock would drop by $2 after announcing profits of $50 million if investors were expecting the company to earn more than that.
Acme Inc. announcing profits of $50 million in the previous quarter and its stock suddenly dropping by $2 can be attributed to the market's reaction to the announcement. This indicates that investors were expecting Acme Inc.'s profits to be higher than $50 million in the previous quarter, and as a result, the stock price dropped when they learned of the actual profits.
The stock market is forward-looking. This means that it tends to reflect the market's expectations of a company's future performance rather than its current performance. Investors will often use the stock price as an indication of how well they believe the company is doing. If a company's profits fall short of the market's expectations, the stock price will often drop.
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A company with working capital of $720,000 and a current ratio of 2.2 pays a $125,000 short-term liability. The amount of working capital immediately after payment is a. $595,000 b. $720,000 c. $125,000 d. $545,000
The amount of working capital immediately after payment is $595,000.
The correct answer to the given question is option a.
To determine the amount of working capital immediately after the payment, we need to subtract the short-term liability from the working capital.
Given:
Working capital = $720,000
Current ratio = 2.2
Short-term liability = $125,000
The current ratio is calculated as follows:
Current ratio = Current assets / Current liabilities
Since the current ratio is 2.2, we can calculate the current liabilities as:
Current liabilities = Current assets / 2.2
Let's denote the current assets as CA:
CA / 2.2 = Current liabilities
From the given information, we know that the working capital is equal to the current assets minus the current liabilities:
Working capital = CA - Current liabilities
Now, let's substitute the values and solve for CA:
$720,000 = CA - (CA / 2.2)
$720,000 = CA(1 - 1/2.2)
$720,000 = CA(1 - 0.4545)
$720,000 = CA(0.5455)
CA = $720,000 / 0.5455
CA ≈ $1,321,212.12
Now, we can calculate the current liabilities:
Current liabilities = $1,321,212.12 / 2.2
Current liabilities ≈ $600,551.96
After paying the short-term liability of $125,000, the working capital immediately after the payment would be:
Working capital = $1,321,212.12 - $600,551.96 - $125,000
Working capital ≈ $595,660.16
Therefore, the correct answer is option a. $595,000.
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In chapter 11, we read/watched videos about many different leadership theories. The different theories were: Level 5, Servant, Authentic, Interactive, Situational, Charismatic, Transformational, Hard Power, Personal Soft Power, Other Sources of Power, Interpersonal Influence Tactics. (Note: Avoid using Transactional Leader in your answer for this question, as this is generally seen as a theory which produces negative outcomes for subordinates).
a. Identify three major takeaways/guiding principles which will guide your leaderships style in your career.
TIP: DO NOT simply list a leadership theory, as this is not a guiding principle. Instead, go back and read about the different leadership theories, and within each section of the text about different leadership theories, you will find different guiding principles you can use. For example, section 11-2d talks about Interactive Leadership, which is the theory. Instead, if you read about the theory of Interactive Leadership in section 11-2d, they talk about how collaboration is an important piece of Interactive Leadership. Therefore, collaboration could be a guiding principle.
b. Explain why each of the three major takeaways/guiding principles resonate with you as a leader.
c. Give an example of what each major takeaway/guiding principle could look like in the workplace setting if you were a manager applying the guiding principles.
d. Please reference where each of the three major takeaways/guiding principles came from within our chapter 11 content (specifically highlight what leadership theory the major takeaway/guiding principle came from).
In the given case, the leadership style will be guided by collaboration and authenticity.
a. The significant focal value that will direct my administration style in my vocation is a joint effort. This core value impacts me as it advances collaboration, participation, and aggregate navigation. It accentuates the worth of different points of view and supports association and commitment from all colleagues. Being credible as a pioneer implies being consistent with oneself, straightforward, and real in cooperations with others is validness. It cultivates trust, validity, and significant associations with colleagues. Legitimate pioneers rouse and inspire by being consistent with their qualities and convictions. Further, worker administration's core value centres around focusing on the necessities of others and serving their wellbeing. It includes a caring and a pledge to create and support the development of people inside the group. Worker pioneers establish a positive workplace and engage their colleagues.
b. Joint effort impacts me since I trust that assorted viewpoints and aggregate info lead to better navigation and advancement. Credibility is essential to me as it advances trust and authentic connections, taking into consideration open correspondence and commitment. Worker administration impacts me since I track down satisfaction in supporting and engaging others to arrive at their maximum capacity.
c. In the work environment, applying the core value of joint effort would include cultivating a comprehensive climate, empowering cooperation, and working with open discourse during group gatherings and dynamic cycles. Validness could be shown by being straightforward about expectations, conceding botches, and effectively paying attention to colleagues. Applying worker administration could mean routinely checking in with colleagues, offering mentorship and direction, and giving assets to their turn of events
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a) Under what circumstances does the auditor issue a modified opinion? b) List three types of modified audit opinion and briefly explain the circumstances in which each is appropriate. (6 marks) c) What type of audit opinion should the auditor issue under the following circumstances? Explain your answer. You are about to issue the auditor's report for a client, Felix Co. The financial statements show the following:
Profit before tax £540
Total assets £64,840
Uncorrected misstatements:
Overstatement of receivables due to an irrecoverable debt not being written off £620
a) The auditor issues a modified opinion when the financial statements are materially misstated, or when the scope of the audit has been limited such that the auditor cannot obtain sufficient evidence.
b) The three types of modified audit opinions and the situations in which they are appropriate are: Qualified Opinion: When there is a misstatement in the financial statements, but it is not pervasive. This indicates that the financial statements are reliable, except for a specific area in which the misstatement occurred.
Adverse Opinion: When there are pervasive material misstatements in the financial statements and their effects are so significant that the financial statements as a whole are considered unreliable. Disclaimer of Opinion: When the auditor is unable to obtain sufficient evidence and is unable to express an opinion on the financial statements.
c) The auditor should issue a qualified opinion in this situation. The overstatement of receivables affects the financial statements but is not pervasive.
As a result, the financial statements are dependable, except for the specified area.
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If a self-employed individual uses the standard mileage rate method for the year in which an automobile is acquired, may the actual expense method be used in a subsequent year? If so, what restrictions are imposed (if any) on depreciation methods? What adjustments to basis are required?
A.The actual expense method may be used in subsequent years. However, MACRS under the regular method must be used for computing depreciation and the basis of the automobile must be reduced by 26 cents per mile in 2021.
B.The actual expense method may be used in subsequent years for self-employed individuals. However, MACRS under the regular method may not be used for computing depreciation(straight-line method is required) and the basis of the automobile must be reduced by 26 cents per mile in 2021.
C.The actual expense method may be used in subsequent years without restrictions on the depreciation methods. The basis of the automobile must be reduced by 26 cents per mile in 2021.
D. The actual expense method may not be used in subsequent years; once the standard mileage rate method is selected, it has to be used for the life of the automobile.
If a self-employed individual uses the standard mileage rate method for the year in which an automobile is acquired, the actual expense method can be used in subsequent years. The restriction imposed on depreciation methods is that MACRS under the regular method must be used for computing depreciation.
And the basis of the automobile must be reduced by 26 cents per mile in 2021.Most self-employed people need to use a car or truck for business purposes, whether to see customers or clients, pick up supplies, or make deliveries. It is necessary to know how to deduct vehicle expenses on their tax return.
The IRS provides two methods for claiming car expenses - using the standard mileage rate or the actual expense method. With the standard mileage rate method, self-employed individuals take a standard amount of 56 cents per mile driven in 2021 for business purposes.
Under the actual expense method, the self-employed individual can claim the total cost of driving the vehicle for business purposes, including gas, maintenance, insurance, and repairs, among other expenses. The depreciation of the car can be deducted under both methods in different ways.
The IRS allows self-employed individuals to switch between the two methods, but it is essential to understand the restrictions imposed on depreciation methods.
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The following schedule is for bushels of apples in a local market. Graph the supply and demand curves. Determine the equilibrium price and quantity. Price Quantity Quantity Demanded Supplied 1,000 800
The schedule of bushels of apples in a local market can be represented in the form of a demand and supply schedule as shown below:Price Quantity Demanded Quantity .
Supplied1,0008001,1009001,2001,0001,3001,1001,4001,2001,5001,3001,6001,4001,7001,5001,8001,6001,9001,7002,0001,800Graph of supply and demand curves:Equilibrium price and quantity:Equilibrium price is the price at which the quantity demanded equals the quantity supplied.
In the above schedule, we can see that the equilibrium price is $1,500.Equilibrium quantity is the quantity demanded and supplied at the equilibrium price. In the above schedule, we can see that the equilibrium quantity is 1,300 bushels of apples.
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Lear Inc. has $920,000 in current assets, $410,000 of which are considered permanent current assets. In addition, the firm has $720,000 invested in fixed assets. a. Lear wishes to finance all fixed assets and half of its permanent current assets with long-term financing costing 10 percent. The balance will be financed with short-term financing, which currently costs 7 percent. Lear's earnings before interest and taxes are $320,000. Determine Lear's earnings after taxes under this financing plan.
To determine Lear Inc.'s earnings after taxes under the given financing plan, we need to calculate the interest expense and deduct it from the earnings before interest and taxes (EBIT).
First, let's calculate the interest expense for both long-term and short-term financing:
Long-term financing:
Fixed assets financed = $720,000
Permanent current assets financed = $410,000/2 = $205,000
Total long-term financing = Fixed assets financed + Permanent current assets financed
= $720,000 + $205,000
= $925,000
Interest expense for long-term financing = Total long-term financing * Long-term interest rate
= $925,000 * 10%
= $92,500
Short-term financing:
Remaining permanent current assets financed = Permanent current assets - Permanent current assets financed
= $410,000 - $205,000
= $205,000
Interest expense for short-term financing = Remaining permanent current assets financed * Short-term interest rate
= $205,000 * 7%
= $14,350
Now, let's calculate the earnings after taxes:
Earnings after taxes = EBIT - Interest expense - Taxes
Given that EBIT = $320,000 and the tax rate is not provided, we cannot calculate the exact earnings after taxes without the tax rate. However, once the tax rate is provided, we can subtract the interest expense and taxes from the EBIT to determine the earnings after taxes.
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(1) Explain some of the key differences between standard deviation and beta. (2) marks) (2) Consider the following information about Stocks A and B: State of Economy Boom Normal Recession Probability
Standard deviation measures the variability of individual stock returns, while beta measures the sensitivity of stock returns to market movements.
What is standard deviation? What is beta?Standard deviation is a statistical measure that quantifies the dispersion or variability of a set of data points around the mean. It provides information about the volatility or risk associated with an investment. A higher standard deviation indicates greater variability and higher risk, while a lower standard deviation suggests lower variability and lower risk. Standard deviation is commonly used to analyze individual stock returns or portfolio performance.
Beta is a measure of systematic risk in finance. It measures the sensitivity of an individual stock or portfolio's returns to the overall market movements. A beta of 1 indicates that the stock's returns tend to move in line with the market, while a beta greater than 1 suggests the stock is more volatile than the market. On the other hand, a beta less than 1 indicates the stock is less volatile than the market. Beta is a crucial tool for investors to assess the risk associated with a particular stock or portfolio.
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I need help with this question. I am use excel to
solve this problem with function FV and PV. also, I and n. can you
help me with this problem.
8. Adam has inherited 50,000 from his dear departed Uncle Phineas. He has a choice of investing in an antique auto that will be worth 70,000 in five years or in a Certificate of Deposit that pays 12%
In this problem, Adam inherited $50,000 from his uncle, and he has a choice of investing in an antique auto that will be worth $70,000 in five years or in a Certificate of Deposit that pays 12%. The problem requires the use of Excel's PV and FV functions to solve it, as well as the use of I and n.
Therefore, to solve this problem, we have to follow the steps below:Step 1: We calculate the future value of the $50,000 invested in a Certificate of Deposit that pays 12%.We can use the FV function in Excel to calculate the future value of the investment, which is $90,661.43. The formula is as follows:FV(rate, nper, pmt, [pv], [type])Where:rate = 12%/yearnper = 5 yearspmt = 0pv = -$50,000type = 0 (for end-of-period payments)Therefore, FV(12%/year, 5 years, 0, -$50,000, 0) = $90,661.43.
Step 2: We calculate the present value of the antique car's future value, which is $70,000 in five years.We can use the PV function in Excel to calculate the present value of the car, which is $47,480.19. The formula is as follows:PV(rate, nper, pmt, [fv], [type])Where:rate = 12%/yearnper = 5 yearspmt = 0fv = $70,000type = 0 (for end-of-period payments)Therefore, PV(12%/year, 5 years, 0, $70,000, 0) = -$47,480.19.Step 3: We compare the future value of the investment in the Certificate of Deposit ($90,661.43) with the present value of the car ($47,480.19) to determine which investment is better.
In this case, the investment in the Certificate of Deposit is better since its future value ($90,661.43) is greater than the present value of the car ($47,480.19). Therefore, Adam should invest his $50,000 in the Certificate of Deposit that pays 12%.In conclusion, the solution to the problem is that Adam should invest his $50,000 in a Certificate of Deposit that pays 12%, using Excel's FV and PV functions to calculate the future value and present value of the investments, respectively.
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A) Comparative Analysis of existing Stablecoins • Reserved based • Algorithmic Ones • Pegged to other assets than USD • Collateralization mechanisms X Notes: You need to compare the main stablecoins (main is refering to the stablecoins intop 50) according to their: decentralization level governance structure: (who decides on the monetary policy? who decides on how much to mint that stablecoin?) collateralization mechanism (reserve sturcture of that stable coin) 1-1? under-collateralized? over-collateralized? with other crypto assets? with usd? with bonds? utilities • PART B) Comparative analysis of existing CBDCs Remark: You should be selective here. (Focus on at most 4) -digital yuan -digital euro • pick your CBDC as the third one +PART C) Risks and Benefits of Stablecoins • Especially your comments of benefits part are important, since that is the non-trivial part. • Remark: Don't forget and don't hesitate to generalize your arguments for cryptocurrencies PART D) Risks and Benefits of CBDCS • Some perspective of political economy would be helpful. ▪ What are the updated roles of governments, central banks, regulatory institutions?
Comparative Analysis of existing stable coins • Reserved based • Algorithmic Ones • Pegged to other assets than USD • Collateralization mechanisms X Notes.
A) Comparative Analysis of Existing Stablecoins:
1. Tether (USDT):
- Decentralization Level: Centralized control over monetary policy and minting decisions.
- Governance Structure: Tether Limited, the company behind USDT, determines the monetary policy and issuance of tokens.
- Collateralization Mechanism: Initially claimed to be fully backed by USD reserves, but concerns have been raised about transparency and actual reserves.
- Utility: Primarily used as a medium of exchange and store of value in the cryptocurrency market.
2. Dai (DAI):
- Decentralization Level: Decentralized governance through the MakerDAO community.
- Governance Structure: MakerDAO token holders participate in the governance and decision-making processes.
- Collateralization Mechanism: Over-collateralized with other crypto assets, primarily Ether (ETH), held in smart contracts as collateral.
- Utility: Used for decentralized lending, stable value storage, and facilitating decentralized finance (DeFi) applications.
3. USD Coin (USDC):
- Decentralization Level: Centralized control over monetary policy and minting decisions.
- Governance Structure: Centre, a consortium of companies, manages the governance and operation of USDC.
- Collateralization Mechanism: Fully backed by USD reserves held in audited bank accounts.
- Utility: Widely used in cryptocurrency exchanges and decentralized applications as a stable medium of exchange and trading pair.
B) Comparative Analysis of Existing CBDCs:
1. Digital Yuan (e-CNY):
- Issued by the People's Bank of China (PBOC) with centralized control over monetary policy and issuance.
- Designed to enhance financial inclusion, reduce reliance on cash, and provide traceability for transactions.
- Aims to maintain control and oversight over the monetary system, enabling the government to monitor transactions.
2. Digital Euro:
- The European Central Bank (ECB) is exploring the possibility of issuing a digital euro.
- Intended to complement cash and existing payment systems, fostering financial integration and efficiency.
- Focuses on maintaining the central bank's role as the sole issuer of currency and safeguarding monetary policy transmission.
C) Risks and Benefits of Stablecoins:
Benefits:
- Increased Accessibility: Stablecoins provide global access to stable-value digital assets, enabling borderless transactions and financial inclusion.
- Efficient and Fast Transactions: Stablecoins leverage blockchain technology, allowing for quick and low-cost transactions compared to traditional financial systems.
- Programmability: Stablecoins can be integrated into smart contracts, enabling the development of decentralized applications and innovative financial products.
Risks:
- Regulatory Uncertainty: Stablecoins operate in a regulatory gray area, with concerns regarding money laundering, consumer protection, and systemic risk.
- Lack of Transparency: Some stablecoins have faced criticism for lacking transparency in their collateralization mechanisms and reserve holdings.
- Counterparty Risk: Depending on the stability mechanism, there may be counterparty risks if the collateral or reserves backing the stablecoin prove inadequate.
D) Risks and Benefits of CBDCs:
Benefits:
- Enhanced Payment Systems: CBDCs can facilitate faster, more secure, and cost-effective domestic and cross-border payments.
- Financial Inclusion: CBDCs can provide access to financial services for the unbanked and underbanked populations.
- Monetary Policy Tools: CBDCs can offer central banks additional tools for implementing and transmitting monetary policy.
Risks:
- Privacy Concerns: CBDCs raise concerns about the potential for increased surveillance and loss of financial privacy.
- Disintermediation: CBDCs could impact commercial banks by reducing their role in payment systems and intermediation.
- Systemic Risks: The introduction of CBDCs may lead to disruptions in the financial system, requiring careful design and risk management.
Overall, stablecoins and CBDCs have their respective advantages and challenges, and the successful implementation and adoption of these digital currencies depend on various factors, including regulatory frameworks, technological considerations, and public acceptance.
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A company buys an item at a cost of $17.20 each. If the company's operating expenses are 15% of cost, and a net profit of 7% of cost is desired, find the selling price of one item.(round to nearest cent)
A company buys an item at a cost of $17.20 each. If the company's operating expenses are 15% of cost, and a net profit of 7% of cost is desired, the selling price of one item, rounded to the nearest cent, is $20.98.
To determine the selling price of an item, we need to consider the cost, operating expenses, and desired net profit. Let's break down the problem step by step:
Step 1: Calculate the operating expenses:
The operating expenses are given as 15% of the cost. To find the operating expenses, we multiply the cost by 15% (or 0.15).
So, operating expenses = 0.15 * cost.
Step 2: Calculate the total cost:
The total cost consists of the cost of the item and the operating expenses. To find the total cost, we add the operating expenses to the cost. So, total cost = cost + operating expenses.
Step 3: Calculate the desired net profit:
The desired net profit is given as 7% of the cost. To find the net profit, we multiply the cost by 7% (or 0.07). So, net profit = 0.07 * cost.
Step 4: Calculate the selling price:
The selling price is the sum of the total cost and the desired net profit. To find the selling price, we add the total cost and the net profit.
So, selling price = total cost + net profit.
Given that the cost of each item is $17.20, we can substitute this value into the equations we derived above.
Step 1: Calculate the operating expenses:
Operating expenses = 0.15 * $17.20.
Step 2: Calculate the total cost:
Total cost = $17.20 + operating expenses.
Step 3: Calculate the desired net profit:
Net profit = 0.07 * $17.20.
Step 4: Calculate the selling price:
Selling price = total cost + net profit.
By evaluating these equations, we can find the final selling price of one item.
Please note that rounding to the nearest cent will be done at the end, after completing all the calculations.
Let's perform the calculations:
Step 1: Calculate the operating expenses:
Operating expenses = 0.15 * $17.20 = $2.58.
Step 2: Calculate the total cost:
Total cost = $17.20 + $2.58 = $19.78.
Step 3: Calculate the desired net profit:
Net profit = 0.07 * $17.20 = $1.20.
Step 4: Calculate the selling price:
Selling price = $19.78 + $1.20 = $20.98.
Therefore, the selling price of one item, rounded to the nearest cent, is $20.98.
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At the beginning of current year, Nilli company
purchased a coal mine for P30,000,000. Removable coal is estimated
at 1,500,000 tons. The entity is required to restore the land at an
estimated cost of
There should be P2,000,000,000 worth of depletion reflected in the cost of goods sold for the current year.
Allocating the cost of natural resources throughout the time that they are consumed or extracted is the process of depletion. We must figure out the price per tonne of coal extracted and multiply it by the number of tonnes sold in order to calculate depletion.
The coal mine will set you back P30,000,000. The net cost of the coal mine is P26,850,000 (P30,000,000 - P3,150,000) after subtracting the projected value of the land after restoration (P3,150). 1,500,000 tonnes of coal are removed in total.The net cost of the coal mine is divided by the total tonnes of removable coal to determine the depletion cost per tonne: P26,850,000 / 1,500,000 tonnes = P17.90 per tonne.Three hundred thousand tonnes were sold. Therefore, P17.90 per tonne multiplied by 300,000 tonnes, or P5,370,00, represents the depletion reported in the cost of goods sold for the current year.It's crucial to remember that the cost of items sold only accounts for a percentage of the depletion cost. On the balance sheet, the leftover amount is shown as an asset. The total amount of depletion reflected in the cost of goods sold is P17.90/ton * 450,000 tonnes = P8,055,000 because 450,000 tonnes were eliminated during the current year.
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Complete Question:
Earlier this year, Nilli Company paid P30,000,000.00 for the purchase of a coal mine. Estimated removal coal capacity is 1.5 million tonnes. The company is obligated to pay an estimated $3,600,000 for the land's restoration. The value of the land is projected to be P3,150,000 following repair. The organisation spent P7,500,000 developing the mine in order to get it ready for production. 300,000 tonnes were sold and 450,000 tonnes were removed during the current year. What total amount of depletion needs to be accounted for in the cost of goods sold this year?
Low interest rates can increase demand for stocks and therefore have a direct impact on stock prices. Select one: O True O False
True. Interest rates can influence the demand for stocks, thus affecting the price of stocks as well. This is because investors look for the highest returns on their investments. When interest rates are low, there is less return on fixed-income securities such as bonds.
Therefore, investors may prefer to invest in stocks as they can offer higher returns.The logic behind this is that when interest rates are low, borrowing is cheaper, which means that companies can invest in expanding their business or investing in new technology to improve profitability. As a result, the stock market tends to perform well during periods of low-interest rates due to increased demand for stocks among investors looking for higher returns on their investments. On the other hand, high-interest rates will reduce demand for stocks as investors will prefer to invest in bonds, which offer higher returns on fixed income securities.
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By partnering with suppliers, distributors and customers, companies improve the performance of
a. marketing system
b. value delivery network
c. internal value chain
d. competitive delivery network
By partnering with suppliers, distributors, and customers, companies improve the performance of their value delivery network.
The correct answer is b. value delivery network.
By partnering with suppliers, distributors, and customers, companies can enhance the performance of their value delivery network. The value delivery network refers to the network of organizations involved in the creation, delivery, and exchange of value to customers. It includes suppliers who provide inputs, distributors who help reach the products or services to the market, and customers who are the recipients of the value.
Partnering with suppliers allows companies to establish reliable and efficient supply chains. By building strong relationships and collaborating closely, companies can ensure a steady and timely supply of high-quality inputs. This helps in minimizing costs, improving product quality, and maintaining a competitive edge in the market.
Similarly, partnering with distributors enables companies to extend their market reach and ensure effective distribution of products or services. Distributors have expertise in reaching specific customer segments and can provide valuable insights into market trends and preferences. Collaborating with distributors enhances the company's ability to deliver the right products to the right customers at the right time, leading to increased customer satisfaction and sales.
Partnering with customers is also crucial for companies to understand their needs, gather feedback, and tailor offerings accordingly. By actively engaging with customers, companies can gain valuable insights into market demands, preferences, and emerging trends. This knowledge can inform product development, marketing strategies, and overall business decisions, leading to improved customer satisfaction and loyalty.
Therefore, by forming partnerships with suppliers, distributors, and customers, companies strengthen their value delivery network, optimize their operations, and enhance overall performance in the market.
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Shimmer Bath Products.Inc.(SBP) makes a variety of ceramic sinks and tubs.SBP has just developed a line of sinks and tubs made from a mixture of glass and ceramic. The sinks sell for $150 cach and have variable costs of $80.The tubs sell for $600 and have variable costs of $450 The glass and ceramic sinks and tubs require the use of specialized molding equipment The Specialized molding equipment has 4,050 hours of capacity per year.A sink uses 2 hours of Specialized molding equipment time;a tub uses 5 hours of specialized molding equipment time Assume that SBP can sell as many as 1.000 sinks and 500 tubs per year. Assuming SBP allocates the machine time to maximize operating income,how many tubs should SBPproduce? 0410 .500 O675 .810
SBP should produce 810 tubs to allocate machine time and maximize operating income.
To determine the number of tubs that SBP should produce to maximize operating income, we need to evaluate the profitability of each product based on the available machine time.
Let's calculate the contribution margin for each product first:
Contribution margin per sink = Selling price per sink - Variable cost per sink
Contribution margin per sink = $150 - $80 = $70
Contribution margin per tub = Selling price per tub - Variable cost per tub
Contribution margin per tub = $600 - $450 = $150
Next, let's calculate the number of sinks and tubs that can be produced within the available machine time:
Maximum number of sinks = 4,050 hours / 2 hours per sink = 2,025 sinks
Maximum number of tubs = 4,050 hours / 5 hours per tub = 810 tubs
Now, we compare the contribution margin per unit for each product:
Contribution margin per sink = $70
Contribution margin per tub = $150
Since the contribution margin per tub is higher, SBP should produce as many tubs as possible to maximize operating income. However, the maximum number of tubs that can be produced is 810.
Therefore, SBP should produce 810 tubs to allocate machine time and maximize operating income.
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Examples of unethical leadership?
What does Cooperativeness mean?
What does Assertiveness mean?
Leadership can be defined as?
What does change leadership mean?
Examples of unethical leadership include: Fraudulent behavior, Abuse of power, Lack of transparency, Discrimination, Unfair treatment, Nepotism, Toxic culture, Breach of trust, Exploitations.
Cooperativeness refers to the willingness and ability to work well with others, collaborate, and contribute to a shared goal. It involves being supportive, open-minded, and actively engaging in teamwork. Cooperative individuals value relationships, communicate effectively, and are committed to finding mutually beneficial solutions.
Assertiveness is the ability to express oneself confidently, directly, and respectfully while standing up for one's rights and needs. It involves being clear, firm, and proactive in communication, setting boundaries, and advocating for oneself and others. Assertive individuals can express their opinions and desires while considering the perspectives of others.
Leadership can be defined as the ability to influence and guide a group of individuals towards a common vision or goal. It involves providing direction, inspiring and motivating others, making sound decisions, and taking responsibility for the outcomes. Leadership encompasses a wide range of skills, including effective communication, strategic thinking, empathy, and the ability to foster collaboration and personal growth in others.
Change leadership refers to the ability to lead and manage organizational change effectively. It involves guiding individuals and teams through transitions, overcoming resistance to change, and facilitating the adoption of new processes, strategies, or technologies. Change leaders need to be adaptable, visionary, and capable of motivating and inspiring others to embrace and navigate change successfully. They must also possess strong communication skills, empathy, and the ability to manage conflicts and uncertainties that may arise during the change process.
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Not yet Use the following table to answer the question about taxes, where Pb = Price buyers pay, Ps= Price sellers receive, and QE = equilibrium quantity. Table With Tax No Tax $15.00 Pb $14 $13.00 Ps
The price that buyers pay (Pb) will increase to $15.60, while the price that sellers receive (Ps) will decrease to $12.40, with a reduction in the quantity exchanged to 250 units as a result of the imposition of a tax of $1.00 per unit, according to the tax table given.
The imposition of taxes on goods and services is a common policy tool used by governments to raise revenue. Taxes are levied on a per-unit basis and are paid by consumers. However, taxes are levied on suppliers, and the tax rate varies depending on the product. Because of the greater elasticity of supply than demand, taxes on the producer lead to less of a reduction in the quantity exchanged and a higher incidence on the consumers. Taxes on consumption, on the other hand, result in a greater reduction in the quantity exchanged and a greater incidence on the consumers.
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My Home If $853,000 of 6% bonds are issued at 103, what is the amount of cash received from the sale? $853,000 $904,180 $801,820 $878,590
The amount of cash received from the sale of bonds will be D. $878,590. OptionD is correct.
To calculate the amount of cash received from the sale of bonds, we need to multiply the face value of the bonds by the issue price percentage.
The Face value of the bonds: $853,000
Issue price percentage: 103% or 1.03
Cash received from the sale = Face value of bonds × Issue price percentage
Cash received from the sale = $853,000 × 1.03
Cash received from the sale = $878,590
Therefore, the amount of cash received from the sale of bonds will be D. $878,590. OptionD is correct.
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The complete question is:
If $853,000 of 6% bonds are issued at 103, what is the amount of cash received from the sale?
A.$853,000
B.$904,180
C.$801,820
D.$878.590
Ms. Marcia Brady lives and works in Prince Edward Island. She owns and operates a No Frills grocery store, which is an HST registrant. During the current year, her business has total revenue of $1775410. 34% of the total revenue is from the sale of fully taxable supplies. 41% of the total revenue is from the sale of zero-rated supplies. The total revenue balance includes applicable HST.
Rent for the period on her store was $24000 and she pays a clerical assistant an annual salary of $28,500. Her capital expenditures during the period are for new shelving with a cost of $40000 and computer point-of-sale hardware for $60000. All expenditure amounts are before HST. The current expenditures and all the assets are used 86% for the provision of taxable supplies. Brady files her business HST return on an annual basis.
Determine the net HST payable or the refund for the year.
(Note: In your answer, a refund should be indicated as a negative number and a payable should be indicated as a positive number).
Ms. Marcia Brady owns and operates a No Frills grocery store in Prince Edward Island, which is an HST registrant. The total revenue earned by the business in the current year was $1775410. Out of this total, 34% of the revenue comes from fully taxable supplies while 41% comes from zero-rated supplies. The balance of the total revenue includes the applicable HST.
The first step in calculating the net HST payable or refund for the year is to determine the amount of HST collected on the fully taxable supplies. To do this, we need to multiply the fully taxable supplies' revenue by the HST rate, which is currently 15%.34% of the total revenue is from fully taxable supplies. Therefore, the amount of HST collected on the fully taxable supplies is:($1775410 x 0.34) x 0.15 = $90427.535Next, we need to determine the amount of HST paid on purchases made for the business. To do this, we need to multiply the amount paid on purchases by the HST rate. As an HST registrant, Ms. Brady would have received credits for the HST paid on purchases. The total amount of credits received should be subtracted from the total HST paid. The result will be the net HST paid on purchases.41% of the total revenue is from zero-rated supplies. Therefore, the amount of purchases for the business is:($1775410 x 0.41) / 1.15 = $63262.8774To determine the HST paid on these purchases, we multiply the amount of purchases by the HST rate, which is 15%.($63262.8774 x 0.15) = $9489.43161The total HST paid on purchases is $9489.43161.Ms. Brady will have received credits for the HST paid on these purchases. If we assume that all purchases were subject to HST and that Ms. Brady has no other HST credits, then the total amount of HST credits she received would be:($63262.8774 x 0.15) = $9489.43161Therefore, the net HST paid on purchases would be zero. The total amount of HST collected on the fully taxable supplies was $90427.535. Since the net HST paid on purchases is zero, the net HST payable or refund for the year would be the difference between the HST collected on the fully taxable supplies and the HST included in the balance of the total revenue:$90427.535 - (1775410 / 1.15 x 0.15) = -$17261.365This means that Ms. Brady is entitled to a refund of $17261.365 for the year.For such more question on multiply
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The domestic demand curve for good A in a small nation is Qd = 200-2P, and the domestic supply curve is Qs = 2P. a) Calculate the market price. b) Calculate the market quantity c) Calculate the consumer surplus d) Calculate the producer surplus e) If the country opens up its economy to trade and imports each unit of good A for RM10, calculate how many units of good A will be imported by the country? f) Calculate the domestic quantity supplied after trade g) Calculate the domestic quantity demanded after trade h) If the government limits the number of imports to 100 units of good A, calculate the new price i) Calculate the new domestic quantity supplied after the quota Calculate the new domestic quantity demanded after the quota. j)
a) Calculation of market priceFor domestic demand curve, Qd = 200 - 2P and domestic supply curve, Qs = 2PTo get the market price, we need to equate the quantity demanded and supplied200 - 2P = 2P200 = 4PP = 200/4P = 50So, the market price is RM50b) Calculation of market quantity.
To find the market quantity, we can substitute the market price into either the demand or supply equation. Let’s use the demand equation.Qd = 200 - 2PQd = 200 - 2(50)Qd = 100 unitsSo, the market quantity is 100 units.c) Calculation of consumer surplusConsumer surplus is the difference between what consumers are willing to pay and what they actually pay for the good.
Calculation of domestic quantity supplied after tradeAfter trade, domestic quantity supplied will be equal to the quantity supplied before trade plus the quantity imported. Qs = 2PQs = 2(50)Qs = 100 unitsSince the country imports 20 units of good A, the domestic quantity supplied after trade is:100 + 20 = 120 units.g) Calculation of domestic quantity demanded after tradeAfter trade, the domestic quantity demanded will be equal to the quantity demanded before trade minus the quantity imported.
Qd = 200 - 2PQd = 200 - 2(50)Qd = 100 unitsSince the country imports 20 units of good A, the domestic quantity demanded after trade is:100 - 20 = 80 units.h) Calculation of new priceTo find the new price, we need to find the point on the domestic demand curve that corresponds to the quantity of 100 units. Qd = 200 - 2P100 = 200 - 2PP = 50So, the new price is RM50.i)
Qs = 2PQs = 2(50)Qs = 100 unitsSo, the new domestic quantity supplied after the quota is 100 units.j) Calculation of new domestic quantity demanded after the quotaTo find the new domestic quantity demanded after the quota, we need to subtract the quantity imported (which is limited to 100 units) from the original quantity demanded.Qd = 200 - 2PQd = 200 - 2(50)Qd = 100 unitsAfter the quota, the new domestic quantity demanded is:100 - 100 = 0 units.
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Suppose that the consensus forecast of security analysts of Pegasus Inc. is that earnings next year will be E₁ = $12.00 per share. The company tends to plow back 30% of its earnings and pay the rest as dividends. The CFO estimates that the company's growth rate will be 8% from now on.
(a) If your estimate of the company's required rate of return is 10%, what is the equilibrium price of the stock?
(b) You observe that the stock is selling for $350.00 per share. Suppose you believe that the market price is right. What must you conclude about either (i) your estimate of the stock's required rate of return, (ii) the CFO's estimate of the company's future growth rate, or (iii) the forecast of earnings from the analysts?
(c) Suppose there is uncertainty about the stock's growth rate. With 30% probability the growth rate will be 9% and with 70% probability the growth rate will be 4%. What are the respective market values under the two different rates of return?
(d) What is the fair price of the stock given the probabilities previously listed?
The fair price of the stock, considering the probabilities, is $350.00 per share, which is the observed market price.
How to solve for the fair price of the stock(a) To calculate the equilibrium price of the stock, we can use the Gordon Growth Model:
Equilibrium Price = (E₁ * (1 - Payout Ratio)) / (Required Rate of Return - Growth Rate)
Given:
E₁ = $12.00 per share
Payout Ratio = 1 - 0.30 (plowback rate of 30%) = 0.70
Required Rate of Return = 10%
Growth Rate = 8%
Equilibrium Price = ($12.00 * 0.70) / (0.10 - 0.08)
Equilibrium Price = $8.40 / 0.02
Equilibrium Price = $420.00
Therefore, the equilibrium price of the stock is $420.00 per share.
(b) If the stock is selling for $350.00 per share and you believe the market price is right, it suggests that the stock is undervalued. This implies one of the following possibilities:
(i) Your estimate of the stock's required rate of return is lower than 10%.
(ii) The CFO's estimate of the company's future growth rate is lower than 8%.
(iii) The forecast of earnings from the analysts is higher than $12.00 per share.
(c) With a 30% probability of a growth rate of 9% and a 70% probability of a growth rate of 4%, we can calculate the respective market values under the two different rates of return.
For a growth rate of 9%:
Market Value = (E₁ * (1 - Payout Ratio)) / (Required Rate of Return - Growth Rate)
Market Value = ($12.00 * 0.70) / (0.10 - 0.09)
Market Value = $8.40 / 0.01
Market Value = $840.00
For a growth rate of 4%:
Market Value = (E₁ * (1 - Payout Ratio)) / (Required Rate of Return - Growth Rate)
Market Value = ($12.00 * 0.70) / (0.10 - 0.04)
Market Value = $8.40 / 0.06
Market Value = $140.00
Therefore, the respective market values under the two different rates of return are $840.00 and $140.00.
(d) To calculate the fair price of the stock given the probabilities, we can calculate the weighted average of the market values:
Fair Price = (Probability of 9% growth rate * Market Value at 9%) + (Probability of 4% growth rate * Market Value at 4%)
Fair Price = (0.30 * $840.00) + (0.70 * $140.00)
Fair Price = $252.00 + $98.00
Fair Price = $350.00
Therefore, the fair price of the stock, considering the probabilities, is $350.00 per share, which is the observed market price.
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COBB-DOUGLAS a) Suppose we have preferences U(X, Y)= X^(1/3) Y^(2/3). Create a table and graph/sketch the indifference curve through the bundle X = 10 and Y = 10 (b) Show that the Marginal Rate of Substitution is MRSxy=- Y/2X. Interpret what this means and what it implies about convexity of the indifference curves. (c) Let prices be Px = 10, Py = 20 and income M = 1000. Draw/sketch the budget constraint. Interpret what the slope of the budget line means in economic terms. (d) Suppose the consumer wanted to maximize utility subject to their budget constraint. State the consumer's maximization problem and express this in words. (e) What are the two conditions (equations) identify the optimum? Sketch this in a figure and explain. (f) Let U(X,Y)= X^(1/3) Y^(2/3) and Px = 10, Py = 20 and income M = 1000. Find optimal X, Y and the resulting Utility. (g) Now let Px = 12. Find the new optimal X and Y and the resulting Utility. Discuss why Utility falls. (h) Why didn't the rise in Px affect consumption of good Y? What is the idea?
(c) Interpretation of Slope of the Budget line. The slope of the budget line in economic terms is referred to as the opportunity cost of good x, which means that how many units of y a consumer must give up to purchase an extra unit of x. The MRT of the budget line represents the amount of good y required for one unit of good x.
Therefore, if the slope of the budget line is less, the consumer would prefer to buy good y because it would be cheaper and the budget would be maximized by buying more of good y. If the slope of the budget line is higher, the consumer would prefer to buy good x because it would be cheaper, and the budget would be maximized by buying more of good x.(d) Consumer's maximization problem The consumer's maximization problem is to maximize the utility subject to their budget constraint. This can be expressed as: Maximize U(X, Y) Subject to PxX + PyY = M Where U(X, Y) = X^(1/3) Y^(2/3); Px = 10; Py = 20; and M = 1000.(e) Conditions identify the optimum the two conditions to identify the optimum are: MRSxy = Px/Py and PxX + PyY = M.
To identify the optimum, the MRS must be set equal to the ratio of prices of goods X and Y. The point of tangency of the budget line and the indifference curve will be the point where the consumer maximizes his or her satisfaction. At the point of tangency, the slope of the budget line is equal to the slope of the indifference curve. The figure below illustrates the optimum:(f) Optimal X, Y and the resulting Utility To find the optimal X and Y, we need to equate the MRS and the ratio of prices of goods X and Y.MRS = Px /Py implies that Y/X = 2/3X^(1/3)Solving for Y, we get: Y = (2/3)X^(1/3) Px/ Py Substituting Px = 10, Py = 20 and M = 1000:X = 50 and Y = 31.62So, the optimal X is 50 and the optimal Y is 31.62The resulting utility is U = (50)^(1/3) (31.62)^(2/3) = 28.05(g) New optimal X and Y and the resulting Utility If Px = 12, then MRS = (-Y/2X) = 2/3 (X^(-2/3)) Px/ Py Setting MRS equal to Px/ Py: Y/X = 4/9X^(1/3)Solving for Y, we get: Y = (4/9)X^(1/3) Px/ Py Substituting Px = 12 and Py = 20 and M = 1000:X = 50.65 and Y = 25.32So, the new optimal X is 50.65 and the new optimal Y is 25.32The resulting utility is U = (50.65)^(1/3) (25.32)^(2/3) = 27.71
Therefore, the utility falls because when the price of good x increases, the consumer shifts his consumption to the cheaper good y. As a result, the consumer will have to purchase fewer units of good x to keep the same level of satisfaction. (h) The idea the rise in Px does not affect the consumption of good Y because the demand for good Y is income inelastic. Income elasticity of demand measures the degree of responsiveness of demand to a change in income. If a good is income inelastic, its demand does not change with the change in income. The reason why good Y is income inelastic in this example is that its price is higher than that of good X. Therefore, a rise in income does not increase the demand for good Y.
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