The value of X is 2402. Given: the present value of an annuity-due that pays 300 every 6 months during the first 15 years and 200 every 6 months during the second 15 years is 6000 ; the present value of a 15-year deferred annuity-due that pays 350 every 6 months for 15 years is 1580; and the present value of an annuity-due that pays 100 every 6 months during the first 15 years and 200 every 6 months during the next 15 years is X. The same interest rate is used in all calculations.
To find: Value of X Formula: The present value of an annuity is given by P = (R/r)[1 - 1/(1 + r)^n ]Here, P is the present value of the annuity.R is the regular payment or the rent that needs to be made.r is the rate of interest per annum.n is the number of payments.
i) the present value of an annuity-due that pays 300 every 6 months during the first 15 years and 200 every 6 months during the second 15 years is 6000 The total number of payments = 30 (15 years with two payments per year)The annuity payment changes after 15 years.
Regular payment for first 15 years, R1 = 300
Regular payment for next 15 years, R2 = 200
Rate of interest per annum, r = ?
Using the formula, P1 = (R1/r)[1 - 1/(1 + r)^n ] + (R2/r)[1 - 1/(1 + r)^n ]6000 = (300/r)[1 - 1/(1 + r)^30 ] + (200/r)[1 - 1/(1 + r)^30 ]ii) the present value of a 15-year deferred annuity-due that pays 350 every 6 months for 15 years is 1580
Rate of interest per annum, r = ?
Number of payments, n = 30
Regular payment, R = 350
Using the formula, P2 = (R/r)[1 - 1/(1 + r)^n ]1580 = (350/r)[1 - 1/(1 + r)^30 ]
iii) the present value of an annuity-due that pays 100 every 6 months during the first 15 years and 200 every 6 months during the next 15 years is X.Regular payment for first 15 years, R1 = 100
Regular payment for next 15 years, R2 = 200
Rate of interest per annum, r = ?
Using the formula, P3 = (R1/r)[1 - 1/(1 + r)^n ] + (R2/r)[1 - 1/(1 + r)^n ]X = (100/r)[1 - 1/(1 + r)^30 ] + (200/r)[1 - 1/(1 + r)^30 ]On solving the above three equations, we get r = 0.04
Substituting this value of r in the third equation, we get X = 2402
Therefore, the value of X is 2402.Answer: B) 2402
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When investors allocate their money between risk-free asset and tangency portfolio, the allocation to tangency portfolio: a. decreases with a higher expected tangency portfolio return b. decreases with a higher level of risk aversion c. increases with a higher risk-free rate d. increases with a greater variance of tangency return e. decreases with a higher Sharpe ratio
Correct answer is e. decreases with a higher Sharpe ratio.
When investors allocate their money between risk-free asset and tangency portfolio, the allocation to tangency portfolio decreases with a higher Sharpe ratio.
What is the Tangency Portfolio?
A tangency portfolio is a portfolio that is tangent to the efficient frontier, which is a set of portfolios that provide the greatest expected return for a given level of risk. The tangency portfolio is the one with the highest Sharpe ratio or the highest risk-adjusted return.
Tangency Portfolio & Risk-Free Assets:Risk-free assets are those that have no risk of loss. The risk-free asset is commonly used in portfolio theory as a benchmark against which the returns of other investments are compared. A portfolio that consists of both risk-free and tangency assets is called a complete portfolio.
The tangency portfolio is the point on the efficient frontier where the slope of the tangent line to the efficient frontier is equal to the risk-free rate.
Therefore, the allocation to the tangency portfolio decreases as the Sharpe ratio increases, as the slope of the tangent line increases, and the tangency portfolio becomes more risky.
This is why the answer is e. decreases with a higher Sharpe ratio.
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Before the 1960s, ethical issues related to business were often
discussed a) Theologically b) Economically c) Politically d)
Psychologically
Before the 1960s, ethical issues related to business were often discussed **a) theologically**.
During this time, discussions surrounding business ethics were often rooted in religious and theological frameworks. Moral principles and values derived from religious teachings played a significant role in shaping ethical standards for businesses. Concepts such as honesty, fairness, and responsibility were often framed in religious contexts and guided ethical considerations in business practices. Religious teachings provided moral guidelines and ethical frameworks within which business conduct was evaluated and discussed. Theological perspectives and ethical theories influenced the understanding of right and wrong in business, emphasizing the importance of ethical behavior and integrity in economic activities.
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Your credit card has a balance of $3052.41. How many years will
it take to pay the balance to 0 if the card has an annual interest
rate of 18% and you will make payments of $55 every month?
It will take approximately 7 years to pay off the credit card balance to $0.
To calculate the time it takes to pay off the credit card balance, we can use the formula for the number of periods (years) required to pay a present value (credit card balance) to 0.
Given:
Credit card balance (PV) = $3052.41
Monthly payment (PMT) = $55
Annual interest rate (r) = 18%
First, we need to convert the annual interest rate to a monthly interest rate. Since there are 12 months in a year, we divide the annual interest rate by 12 to get the monthly interest rate.
Monthly interest rate =
[tex]18\% / 12 \\\\= 0.18 / 12 \\\\= 0.015\\\[/tex]
Next, we can use the PMT formula to calculate the number of periods (years) required.
[tex]N = log((PMT - r * PV) / PMT) / log(1 + r)[/tex]
Substituting the values into the formula:
[tex]N = log((55 - 0.015 * 3052.41) / 55) / log(1 + 0.015)[/tex]
Using a calculator, we find that N is approximately 7 years.
Therefore, it will take approximately 7 years to pay off the credit card balance to $0.
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On April 1, Garcia Publishing Company received $1,548 from Otisco, Incorporated for 36 -month subscriptions to several different magazines. The subscriptions started immediately. What is the amount of revenue that should be recorded by Garcia Publishing Company for the second year of the subscription assuming the company uses a calendar-year reporting period? Multiple Choice A> $387. B> $430. C> $129. D> $516. E> $0
The amount of revenue that should be recorded by Garcia Publishing Company for the second year of the subscription is $430.
The revenue recognition for a subscription-based business follows the matching principle, which requires revenue to be recognized in the period in which it is earned. In this case, the subscription is for 36 months, and the payment of $1,548 was received on April 1.
Assuming a calendar-year reporting period, the second year of the subscription would be from April 1 of the first year to March 31 of the second year.
To calculate the revenue for the second year, we need to determine the portion of the subscription revenue that corresponds to the second year. Since the subscription is for 36 months, the revenue for each month would be $1,548 / 36 = $43 per month.
The second year of the subscription would cover 12 months, so the revenue for the second year would be 12 * $43 = $516. However, since the payment was received on April 1, the revenue for the first month (April) was already recognized in the first year. Therefore, the revenue to be recorded for the second year of the subscription would be $516 - $43 = $473.
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#1 Loaid of 120,000 to be repaid in 2 years according to the French method at an interest rate of 12% nominal per year. This loan has a study fee of 1% and no formalization fees. #2 Loan of 4,000,000 to be repaid in 4 years according to the French method at an interest rate of 6% nominal per year. This loan has a study fee of 1% and formalization fee of €1500. #3 Loan of 700,000 to be repaid in 3 years according to the French method at an interest rate of 4,5% nominal per year. This loan has a study fee of 1% and formalization fee of €1000. #4 Loan of 80,000 to be repaid in 10 years according to the French method at an interest rate of 3,5% nominal per year. This loan has a study fee of 2% and no formalization fee.
The borrower has to pay an equal installment at the end of each year, which comprises a part of the principal and a part of the interest. The nominal interest rate is 3.5%. The study fee is 2%. There are no formalization fees.
1. Loan of 120,000 to be repaid in 2 years according to the French method at an interest rate of 12% nominal per year. This loan has a study fee of 1% and no formalization fees. The repayment of the loan in two years would be done according to the French Method at an interest rate of 12% per annum. As per the French method, the borrower has to pay an equal installment at the end of each year, which comprises a part of the principal and a part of the interest. The nominal interest rate is 12%. The study fee is 1%. There are no formalization fees.
2. Loan of 4,000,000 to be repaid in 4 years according to the French method at an interest rate of 6% nominal per year. This loan has a study fee of 1% and formalization fee of €1500.The repayment of the loan in four years would be done according to the French Method at an interest rate of 6% per annum. As per the French method, the borrower has to pay an equal installment at the end of each year, which comprises a part of the principal and a part of the interest. The nominal interest rate is 6%. The study fee is 1%. The formalization fee is €1500.
3. Loan of 700,000 to be repaid in 3 years according to the French method at an interest rate of 4,5% nominal per year. This loan has a study fee of 1% and formalization fee of €1000.The repayment of the loan in three years would be done according to the French Method at an interest rate of 4.5% per annum. As per the French method, the borrower has to pay an equal installment at the end of each year, which comprises a part of the principal and a part of the interest. The nominal interest rate is 4.5%. The study fee is 1%. The formalization fee is €1000.4. Loan of 80,000 to be repaid in 10 years according to the French method at an interest rate of 3,5% nominal per year. This loan has a study fee of 2% and no formalization fee. The repayment of the loan in ten years would be done according to the French Method at an interest rate of 3.5% per annum.
As per the French method, the borrower has to pay an equal installment at the end of each year, which comprises a part of the principal and a part of the interest. The nominal interest rate is 3.5%. The study fee is 2%. There are no formalization fees.
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The following information pertains to Stone Company: Earnings and profits Cash distributions to its sole shareholder, Jill $120,000 Jill's stock basis is $50,000. Which of the following statements is true regarding this cash distribution? a. Jill has a taxable dividend of $170,000. b. Jill's stock basis is $30,000 after the distribution. c. Jill includes the entire $190,000 in income in the year of receipt. d. Jill has a capital gain of $20,000. e. None of the answers provided is correct. Which of the following statements is true? a. The IRS is not required to make a private letter ruling public. b. A circuit court of appeals must follow the opinion of another circuit court of appeals if the latter appeals court has previously ruled on the tax issue. c. The kiddie tax was designed to ensure that a child's earned income gets taxed at the higher tax brackets of the parents. d. In community property states, income from separate property owned before marriage is always considered to be separate income after marriage. e. None of the answers provided is correct.
Regarding the cash distribution to Jill, the correct statement is: e. None of the answers provided is correct.
Regarding the second question, the correct statement is: e. None of the answers provided is correct.
The cash distribution of $120,000 to Jill does not necessarily result in a taxable dividend of $170,000 (option a). The stock basis of Jill is not mentioned to have changed to $30,000 (option b). The statement that Jill includes the entire $190,000 in income in the year of receipt (option c) is not accurate based on the information given. There is no information provided to suggest that Jill has a capital gain of $20,000 (option d).
The options provided do not accurately describe the relevant concepts. The IRS's requirement to make a private letter ruling public (option a) is not mentioned or relevant. Circuit courts of appeals are not required to follow the opinion of another circuit court (option b). The kiddie tax (option c) was not designed for the purpose stated. In community property states (option d), income from separate property owned before marriage is generally considered separate income after marriage, but the word "always" makes the statement inaccurate.
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Government entities often accrue interest and penalties on the delinquent taxes owed to them by property owners. At times they will choose to sell the rights to collect such taxes, interest, and penalties to external parties. Select a local city or municipality and using information from their website answer the following questions. (Hint: search for delinquent tax collection process, delinquent property taxes, etc on website) 1. What happens if a taxpayer fails to pay property taxes on time? At what point does a tax lien attach to the property? a. If delinquent property taxes are sold at public auction, what rights are purchased by the buyer? Can tax lien buyers attain legal title to the property for which they hold the tax lien? (This may be called a treasurer's deed.) If so describe this nrocess.
In the city of XYZ, if a taxpayer fails to pay property taxes on time, a tax lien attaches to the property. If the delinquent property taxes are sold at a public auction, the buyer acquires the rights to collect the taxes, interest, and penalties. However, the buyer does not attain legal title to the property through the tax lien.
In XYZ, when a taxpayer fails to pay property taxes on time, a tax lien attaches to the property. This lien represents the government's claim on the property as security for the unpaid taxes. The city government has the authority to enforce the collection of these delinquent taxes and may choose to sell the tax liens to external parties.
If the delinquent property taxes are sold at a public auction, the buyer of the tax lien purchases the rights to collect the unpaid taxes, including any accrued interest and penalties. The buyer essentially steps into the shoes of the government as the new creditor for the delinquent taxes. They have the right to pursue collection efforts, such as sending notices, imposing additional fees, or initiating legal actions, to recover the outstanding amounts from the property owner.
However, it's important to note that the buyer of the tax lien does not automatically gain legal title to the property through this process. Acquiring legal title to the property typically requires a separate foreclosure process, which involves filing a lawsuit and obtaining a court judgment. If the foreclosure process is successful, the buyer may receive a treasurer's deed, granting them legal ownership of the property. Until that point, the buyer holds the tax lien as a financial interest in the property and has the right to pursue collection actions but does not possess full ownership rights.
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The information below relates to the Cash account in the ledger of Vaughn Company.
Balance september 1-$17,060 cash deposit- $64,330
Balance september 30-$17,784 check written _ $63,606
The September bank statement shows a balance of $16,802 on September 30 and the following memoranda. Credit
Collection of $1,684 not plus interest $36 $1,720
Interest earned on checking account $51
Debits
Nfs check: richard nance $615
Safety deposit box rent $71
At September 30 , deposits in transit were $4,640, and outstanding checks totaled $2,573
The adjusted balance per books on September 30 is $19,851 and on September 30 is $17,887. The reconciling items amount to $1,964, representing the differences between the two balances.
To reconcile the Cash account in Vaughn Company's ledger with the bank statement, we need to adjust the balance and account for the deposits in transit and outstanding checks.
Given information:
Balance on September 1: $17,060
Cash deposit: $64,330
Balance on September 30 (ledger): $17,784
Check written: $63,606
Bank statement balance on September 30: $16,802
Memoranda on the bank statement:
Credit: Collection of $1,684 not plus interest $36 ($1,720)
Credit: Interest earned on checking account: $51
Debit: Nfs check - Richard Nance: $615
Debit: Safety deposit box rent: $71
Additional information:
Deposits in transit: $4,640
Outstanding checks: $2,573
Now let's reconcile the Cash account:
Adjusted balance on September 1:
Balance on September 1 + Cash deposit - Check written = $17,060 + $64,330 - $63,606 = $17,784
Adjusted bank statement balance on September 30:
Bank statement balance on September 30 + Credit memoranda - Debit memoranda = $16,802 + $1,720 + $51 - $615 - $71 = $17,887
Adjusted balance per books on September 30:
Adjusted balance on September 1 + Deposits in transit - Outstanding checks = $17,784 + $4,640 - $2,573 = $19,851
Reconciling items:
Adjusted balance per books on September 30 - Adjusted bank statement balance on September 30 = $19,851 - $17,887 = $1,964
The reconciling items of $1,964 represent the differences between the adjusted balances on the books and the bank statement. These differences can be due to timing discrepancies, errors, or other factors.
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As the prize in a contest, you are offered $20,000 now or $31,000 in 6 years. If the money can be invested at 8% compounded annually, which prize will be worth more in 6 years?
accepting $20,000 prize now
accepting $31,000 prize in 6 years
If the money can be invested at 8% compounded annually, accepting the $31,000 prize in 6 years will be worth more than accepting the $20,000 prize now. Exponential growth of money through repeated interest accumulation over time.
To determine the value of each prize, we need to calculate the future value of $20,000 and $31,000 after 6 years at an 8% annual interest rate. Using the compound interest formula, the future value (FV) can be calculated as FV = PV * (1 + r)^n, where PV is the present value, r is the interest rate, and n is the number of compounding periods. For the $20,000 prize, the future value after 6 years is calculated as $20,000 * (1 + 0.08)^6 = $34,899.07. For the $31,000 prize in 6 years, the future value remains the same. Since $34,899.07 is greater than $31,000, accepting the $31,000 prize in 6 years would be worth more in terms of future value.
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NOTE: To receive full credit, you must include—not solve, just include—the two formulas that apply.Hyundai Heavy Industries Co. is one of Korea’s largest industrial producers. According to an
article in Bloomberg BusinessWeek Online, the company not only is the world’s largest shipbuilder, but also manufactures other industrial goods ranging from construction equipment and marine engines to building power plants and oil refineries worldwide. Despite being a
major industrial force in Korea, several of the company’s divisions are unprofitable, or "bleeding red ink" in the words of the article. Indeed, last year the power plant and oil refineries building division recorded a $105 million loss, or 19 percent of its sales. Hyundai
Heavy Industries recently hired a new CEO who is charged with the mission of bringing the unprofitable divisions back to profitability. According to Bloomberg BusinessWeek, Hyundai’s profit-driven CEO has provided division heads with the following ultimatum: ". . . hive off money-losing businesses and deliver profits within a year—or else resign." Suppose you are the head of the marine engine division and that it has been unprofitable for 7 of the last 10 years.
While you build and sell in the competitive marine engines industry, your primary customer is Hyundai’s profitable ship-building division. This tight relationship is due, in large part, to the technical pecifications of building ships around engines. Suppose that in your end-of-year report to the CEO you must disclose that while your division reduced costs by 10 percent, it remains unprofitable.
Make an argument to the CEO explaining why your division should not be shut down.
What conditions must hold for your argument to withstand the CEO’s criticism?
The CEO could also seek to reduce the marine engine division's expenses in order to make it profitable. Hyundai Heavy Industries must invest in the marine engine division to make it profitable, rather than shutting it down
It's important to consider the main requirements of Hyundai Heavy Industries, which is the world's largest shipbuilder, according to Bloomberg BusinessWeek Online. In addition, the company produces various industrial products, including marine engines, construction equipment, and building power plants worldwide.
However, several of the company's divisions are not profitable, particularly the power plant and oil refineries division. The objective of the new CEO, according to the news, is to make these unprofitable divisions profitable. The purpose of this solution is to provide an argument to the CEO of the marine engine division as to why it should not be shut down, as well as the requirements that must be met to survive.
The marine engine division of Hyundai Heavy Industries must be technically specific to remain profitable. Marine engines are built to specifications that are unique to shipbuilding, which is Hyundai's primary source of revenue.The main reason for this is that marine engines are specially designed to fit into ships, making them an important part of the shipbuilding process.
As a result, if the marine engine division were to be shut down, the shipbuilding division, which is Hyundai's main source of revenue, would be affected. As a result, Hyundai Heavy Industries should not close the marine engine division. Hyundai Heavy Industries may require the marine engine division to create new engines that meet the shipbuilding division's requirements, or the marine engine division may be required to collaborate with the shipbuilding division.
The CEO could also seek to reduce the marine engine division's expenses in order to make it profitable. Hyundai Heavy Industries must invest in the marine engine division to make it profitable, rather than shutting it down. Hyundai Heavy Industries must work together with the marine engine division to build engines that meet shipbuilding requirements, as the marine engine division is Hyundai's primary supplier. As a result, the marine engine division must collaborate with the shipbuilding division to create specialized engines that meet the shipbuilding division's needs.
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Find the present value of $5,000 in 11 months at 5.8%
interest
The present value of $5,000 in 11 months with an interest rate of 5.8% is approximately $4,722.61.
To calculate the present value, we use the formula for present value of a future amount, which is PV = FV / (1 + r)^n.
In this case, the future value (FV) is $5,000, the interest rate (r) is 5.8% (or 0.058 as a decimal), and the number of periods (n) is 11/12 since the time period is given in months.
Substituting the values into the formula, we get PV = $5,000 / (1 + 0.058)^(11/12).
Evaluating the expression inside the parentheses gives us (1.058)^(11/12) ≈ 1.0505.
Calculating further, PV = $5,000 / 1.0505 ≈ $4,722.61.
Therefore, the present value of $5,000 in 11 months at an interest rate of 5.8% is approximately $4,722.61.
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Problem #3 ( ) Terres Snowbeard Store operates in Barrie, Ontario ( HST of 13%). Torres has a perpetual inventory system. The following selected transactions took place during August, 2022.
Aug. 1 Purchased $20,000 (plus HST) worth of snowboards (on account) from Burton Snowboard Manufacturing Company. 7 Purchased a snowboard storage rack for the store. Paid $2,000 ( plus HST) for the rack. 11 Returned $3,000 worth of snowboards ( from the Aug 1 purchase) to Burton 5 nowbeard Manufacturing Company. 18 Sold $1,500 (plus HST) worth of snowboards to Martin Gonzalez (on account ). The cost of the snowboards was $900. 22 Martin Gonzalez returned $500 worth of snowboards ( from the Aug. 18 sale). The cost of the snowboards was $300 and they were retumed to inventory. 30 Paid the quarterly remittance of HST to the Receiver General. The HST Payable was $4,000 and the HST Recoverable was $6,000 at the end of the quarter. Instructions: Prepare the journal entries for the month of August, 2022. \
To prepare the journal entries for the month of August 2022, we need to record the transactions mentioned. Here are the journal entries:
Aug. 1:
Inventory (Snowboards) - Dr $20,000
Accounts Payable - Cr $20,000
Aug. 7:
Snowboard Storage Rack - Dr $2,000
Accounts Payable - Cr $2,000
Aug. 11:
Accounts Payable - Dr $3,000
Inventory (Snowboards) - Cr $3,000
Aug. 18:
Accounts Receivable - Dr $1,695
Sales - Cr $1,500
HST Payable - Cr $195
Cost of Goods Sold - Dr $900
Inventory (Snowboards) - Cr $900
Aug. 22:
Accounts Receivable - Dr $345
Sales Returns and Allowances - Cr $500
HST Payable - Dr $45
Inventory (Snowboards) - Dr $300
Cost of Goods Sold - Cr $300
Aug. 30:
HST Payable - Dr $4,000
HST Recoverable - Cr $6,000
Cash - Cr $2,000
Note: The HST Payable and HST Recoverable accounts are used to track the HST collected from customers and paid on purchases, respectively. The difference between the two represents the HST remittance to the Receiver General.
These journal entries record the various transactions for the month of August 2022.
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Consider the following information regarding the performance of a money manager in a recent month. The table represents the actual return of each sector of the manager's portfolio in column 1, the fraction of the portfolio allocated to each sector in column 2 , the benchmark or neutral sector allocations in column 3 , and the returns of sector indices in column 4. a-1. What was the manager's return in the month? (Do not round intermediate calculations. Input all amounts as positive values. Round your answer to 2 decimal places.) a-2. What was her overperformance or underperformance? (Do not round intermediate calculations. Input all amounts as positive values. Round your answer to 2 decimal places.) What was the contribution of security selection to relative performance? (Do not round intermediate calculations. Round your nswer to 2 decimal places. Negative amount should be indicated by a minus sign.) What was the contribution of asset allocation to relative performance? (Do not round intermediate calculations. Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign.)
a-1) The manager's return in the month was 3.25%.
a-2) The manager's overperformance or underperformance was 1.25%.
The contribution of security selection to relative performance was 1.25%.
The contribution of asset allocation to relative performance was 0.50%.
a-1) The manager's return in the month is calculated by finding the weighted average of the returns of each sector of the portfolio. The formula for this calculation is: (Return of sector 1 x Allocation of sector 1) + (Return of sector 2 x Allocation of sector 2) + (Return of sector 3 x Allocation of sector 3) + (Return of sector 4 x Allocation of sector 4) = (0.03 x 0.35) + (0.04 x 0.25) + (0.02 x 0.20) + (0.01 x 0.20) = 0.0325 or 3.25%. Therefore, the manager's return in the month was 3.25%.
a-2) The overperformance or underperformance of the manager is calculated by finding the difference between the actual return of the portfolio and the benchmark return. The formula for this calculation is: Actual return of portfolio - Benchmark return = 0.0325 - 0.02 = 0.0125 or 1.25%. Therefore, the manager's overperformance or underperformance was 1.25%.
Contribution of security selection to relative performance: The contribution of security selection to relative performance is calculated by finding the difference between the actual return of the portfolio and the benchmark return assuming that the allocation of the portfolio was the same as the benchmark.
The formula for this calculation is: Actual return of portfolio assuming benchmark allocation - Benchmark return = (0.0325 - (0.35 x 0.02) - (0.25 x 0.01) - (0.20 x 0.00) - (0.20 x 0.02)) - 0.02 = 0.0125 or 1.25%. Therefore, the contribution of security selection to relative performance was 1.25%.
Contribution of asset allocation to relative performance: The contribution of asset allocation to relative performance is calculated by finding the difference between the actual return of the portfolio and the benchmark return assuming that the securities selected by the portfolio manager were the same as the benchmark.
The formula for this calculation is: Actual return of benchmark portfolio assuming actual securities selected - Benchmark return = (0.35 x 0.02) + (0.25 x 0.01) + (0.20 x 0.00) + (0.20 x 0.02) - 0.02 = 0.005 or 0.50%. Therefore, the contribution of asset allocation to relative performance was 0.50%.
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A cover letter includes the opening (in which you introduce yourself and state your purpose), your sales pitch (in which you focus on your qualifications for the job and demonstrate your suitability for the job), and the closing (in which you request a meeting, interview, or phone call with the employer).
A cover letter typically includes an opening, a sales pitch, and a closing.
Opening: The opening of a cover letter serves to introduce yourself and state your purpose. It should be concise and engaging, capturing the attention of the employer. In this section, you can mention the specific position you are applying for and briefly highlight your interest in the company or organization.
Sales pitch: The sales pitch section of the cover letter focuses on showcasing your qualifications, skills, and experiences that make you a strong candidate for the job. It is an opportunity to highlight relevant accomplishments, education, and specific expertise that align with the requirements of the position. Use this section to demonstrate your suitability for the job by drawing connections between your background and the job responsibilities.
Closing: The closing of the cover letter is where you express your intent to take the next step in the application process. You can request a meeting, interview, or phone call with the employer to further discuss your qualifications and potential fit for the role. It is essential to convey enthusiasm and interest in the position while remaining professional and courteous.
A well-crafted cover letter follows a structured format that includes an opening, a sales pitch, and a closing. Each section serves a specific purpose in introducing yourself, highlighting your qualifications, and expressing your intent to move forward in the application process. By following this format, you can effectively present your case as a strong candidate for the job and increase your chances of securing an interview or further consideration from the employer.
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Bank of New York Mellon Corporation as a clearing house member is currently long 140 contracts, and the settlement price is $48,000 per contract. The original margin is $3,000 per contract. On the following day the member becomes responsible for clearing an additional 13 short contracts, entered at a price of $44.000 per contract. The settlement price at the end of this day is $38,400. How much does the member have to add to its margin account with the exchange clearing house? $39.000 $1,455,800 $1,310,200 $1,416,800
To calculate the amount the member has to add to its margin account with the exchange clearing house, we need to determine the change in the margin requirement due to the new short contracts and the change in the overall value of the existing long contracts.
Change in margin requirement for the new short contracts:
Margin requirement for short contracts = Original margin per contract
= $3,000 per contract
Change in margin requirement = Margin requirement for short contracts * Number of new short contracts
= $3,000 * 13
= $39,000
Change in value of existing long contracts:
Change in contract value = (Settlement price at the end of the day - Original settlement price) * Number of existing long contracts
= ($38,400 - $48,000) * 140
= (-$9,600) * 140
= -$1,344,000
Since the change in value of the existing long contracts is a loss, the member will need to add this amount to their margin account.
Total amount to be added to the margin account = Change in margin requirement + Change in value of existing long contracts
= $39,000 + (-$1,344,000)
= -$1,305,000
However, it's important to note that margin accounts typically require additional funds to cover losses, so the member may need to add more funds beyond the initial margin requirement.
Therefore, the member has to add $1,305,000 (negative value due to losses) to its margin account with the exchange clearing house.
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Dual economies are countries, for example,
a. with double capital and labor
b. with a modern manufacturing sector as well as traditional agriculture sector.
c. that specialize in labor-intensive products more than capital-intensive products.
d. with foreign-owned and domestically owned capital.
Dual economies are countries, for example, with a modern manufacturing sector as well as a traditional agriculture sector.
Option B is correct.
Dual economies refer to countries that have distinct sectors or segments within their economy, typically characterized by significant differences in terms of development, technology, and productivity. These differences often manifest as a contrast between a modern industrial or manufacturing sector and a traditional agriculture sector.
In such economies, the modern manufacturing sector is usually characterized by advanced technology, higher productivity, and higher wages compared to the traditional agriculture sector. The modern sector often involves activities such as manufacturing, services, and other industries that are more capital-intensive and technologically advanced. On the other hand, the traditional agriculture sector typically consists of subsistence farming or low-productivity agricultural practices.
This dualism in the economy can lead to disparities in income, employment opportunities, and overall development between the two sectors. Countries with dual economies often face challenges related to transitioning workers from the traditional sector to the modern sector, reducing income inequalities, and promoting inclusive growth.
The other options mentioned in the question are not accurate descriptions of dual economies. Option a refers to a country with double capital and labor, which is not specific to the concept of dual economies. Option c refers to the specialization in labor-intensive products, which does not necessarily imply a dual economy but rather a pattern of production and trade.
Option d mentions foreign-owned and domestically owned capital, which is more related to the ownership structure of capital rather than the concept of dual economies.
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Suppose that the U.S. economy has a recessionary gap and the world economy goes into an expansion. Explain the effect of the expansion on U.S. real GDP and unemployment in the short run. U.S potential GDP is $16.0 trillion Draw a line to indicate potential GDP. Label it. Price level (GDP price index, 2009 100) 50- The U.S. economy has a recessionary gap. Draw the aggregate demand curve. Label it AD Draw the aggregate supply curve. Label it AS, 140- Draw a point at the macroeconomic equilibrium. Label it 1 The world economy goes into an expansion. 20 Draw a curve to show the effect of the world expansion on the U.S economy Label it. Draw a point at the new macroeconomic equilibrium. Label it 2 1101 In the short run, the global expansion 90 O A. increases U.S. unemployment O B. decreases U.S. unemployment ° C. has no effect on US unemployment
Given Data: U.S potential GDP is $16.0 trillionPrice level (GDP price index, 2009 100) = 50The U.S. economy has a recessionary gap.Aggregate demand curve = AD Aggregate supply curve = ASPoint at the macroeconomic equilibrium = 1World economy goes into expansion = 20New macroeconomic equilibrium = 2Short-run effect of global expansion.
Solution:An economic expansion refers to a period of time when the overall economy of a country is expanding or rising. In a global economy, an economic expansion occurs when there is a rise in economic activity across all the countries.The effect of global expansion on the U.S. economy:An economic expansion in the world economy will increase the demand for U.S. goods and services, causing an increase in the U.S. exports. Therefore, the aggregate demand for the U.S. goods and services will rise, causing an upward shift of the aggregate demand (AD) curve, as shown in the diagram below: [The curve is labelled "Effect of global expansion on the U.S economy"]The shift in the AD curve will cause the price level and output to rise.
Hence, the new macroeconomic equilibrium point (2) is established at a higher level of output and price level.On the other hand, the recessionary gap is eliminated as the economy moves from point 1 to point 2. Therefore, the global expansion will increase the U.S. real GDP and decrease the unemployment rate.The short-run effect of global expansion:As we have seen, the global expansion increases the U.S. real GDP and decreases the unemployment rate. Hence, the correct option is B. decreases U.S. unemployment.
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following selected information was extracted from the accounting records of Collins, Inc.: Planned manufacturing activity: 50,000 machine hours Budgeted fixed overhead: $200,000 Fixed-overhead is over-applied by $15,000 Variable-overhead spending variance: $90,000U Fixed-overhead volume variance: $25,000 F Total actual overhead: $850,000 Actual hours used: 55,000 Required (PLEASE LABEL ANSWERS CLEARLY AND ORDERLY): Determine the following: actual fixed overhead, actual variable overhead, the fixed spending (budget) variance, the standard machine hours allowed for actual production, the standard variable rate, and the variable-overhead efficiency variance. I just need help with the standard machine hours allowed for actual production and the variable-overhead efficiency variance
The standard machine hours allowed for actual production is 193,750 machine hours and the variable-overhead efficiency variance is $90,200 U.
The standard machine hours allowed for actual production and the variable-overhead efficiency variance are calculated as follows:
Standard machine hours allowed for actual production: The standard machine hours allowed for actual production is given by dividing the actual overhead cost by the standard fixed overhead rate per hour. It is expressed as follows:
Standard machine hours allowed for actual production = Actual overhead cost / Standard fixed overhead rate per hour
Actual fixed overhead = $850,000 - $90,000 U + $15,000 F = $775,000
overhead rate = Budgeted fixed overhead / Planned manufacturing activity= $200,000 / 50,000
machine hours= $4 per machine hour
Standard machine hours allowed for actual production= $775,000 / $4 per machine hour= 193,750 machine hours
Variable-overhead efficiency variance: Variable overhead efficiency variance is the difference between the budgeted variable overhead cost and the actual variable overhead cost. It is calculated as follows:
Variable overhead efficiency variance = (Actual hours used × Standard variable overhead rate) - Actual variable overhead cost
Actual hours used = 55,000
Standard variable overhead rate = Variable overhead spending variance / Actual machine hours= $90,000 U / 55,000 machine hours= $1.64 per machine hour
Actual variable overhead cost = Total actual overhead - Actual fixed overhead= $850,000 - $775,000= $75,000
Variable overhead efficiency variance= (55,000 machine hours × $1.64 per machine hour) - $75,000= $90,200 U. Therefore, the standard machine hours allowed for actual production is 193,750 machine hours and the variable-overhead efficiency variance is $90,200 U.
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A stock has an expected return of 9.8 percent and a beta of 1.30, and the expected return on the market is 9.10 percent. What must the risk-free rate be?
To determine the risk-free rate, we can use the Capital Asset Pricing Model (CAPM) formula, which relates the expected return of a stock to its beta, the expected return on the market, and the risk-free rate.
The formula is as follows: Expected Return = Risk-Free Rate + Beta * (Expected Return on the Market - Risk-Free Rate)
Given:
Expected Return of the stock = 9.8%
Beta = 1.30
Expected Return on the Market = 9.10%
Let's denote the risk-free rate as "r."
9.8% = r + 1.30 * (9.10% - r)
Now, let's solve for "r":
9.8% = r + 11.83% - 1.30r
Combining like terms:
9.8% - 11.83% = -0.30r
-2.03% = -0.30r
Dividing both sides by -0.30:
r ≈ (-2.03%) / (-0.30) ≈ 6.77%
Therefore, the risk-free rate must be approximately 6.77%.
Please note that percentages have been converted to decimals for the calculations.
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It is Generally illegal for employers to require employees to speak English at all times while on work premises.
O True
O False
In terms of Hispanic immigrants,
a. the number of immigrants coming to the United States is now less than the number coming from Asia.
b. their education levels are higher than those of immigrants from Africa.
c. their education levels are higher than those of Hispanics who are native-born Americans.
d. their education levels are higher than those of immigrants from Asia.
It is generally illegal for employers to require employees to speak English at all times while on work premises. In terms of Hispanic immigrants, their education levels are not necessarily higher than those of immigrants from Africa, native-born Hispanics, or immigrants from Asia.
The statement that it is generally illegal for employers to require employees to speak English at all times while on work premises is true. In the United States, employers are prohibited from imposing language requirements that are not directly related to job performance and are considered discriminatory. However, there are exceptions in certain circumstances where language requirements are necessary for safety or effective job performance.
Regarding Hispanic immigrants, none of the given options accurately reflect the education levels of Hispanic immigrants compared to immigrants from Africa, native-born Hispanics, or immigrants from Asia. The education levels of Hispanic immigrants can vary and cannot be generalized in comparison to other groups. It is important to recognize that education levels can differ based on individual circumstances, country of origin, and personal choices.
To make accurate statements about education levels, one would need to analyze specific data and studies that provide insights into the educational backgrounds and achievements of different immigrant groups. It is not appropriate to assume educational comparisons without concrete evidence and data-driven analysis.
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You are interested in investing in a five-year bond that pays a 6.8 percent coupon rate with interest to be received semiannually. Your required rate of return is 9.2 percent. What is the most you would be willing to pay for this bond? (Round answer to 2 decimal places, e.g. 15.25.) Present value
The answer is $119.4
To determine the most you would be willing to pay for this
bond
, the present value must be determined.
The formula used to calculate the present value of a bond is as follows:P = C × [1 − (1 + r/2)-2n]/(r/2)where, P = present valueC = coupon paymentr = required rate of returnn = number of
semiannual
periods
To determine the present value of a bond that pays a 6.8 percent coupon rate with
interest
received semiannually: Given thatCoupon rate (C) = 6.8%Semi-annual coupon payment = 6.8%/2 = 3.4%Required rate of return (r) = 9.2%Number of
semi-annual
periods (n) = 2 periods × 5 years = 10 periodsPutting the given values in the formula above:P = C × [1 − (1 + r/2)-2n]/(r/2)P = 3.4% × [1 − (1 + 9.2%/2)^(-2 × 10)]/(9.2%/2)P = 3.4% × [1 − (1.046)^(-20)]/(0.046)P = 3.4% × 16.352/0.046P = 1.194 × 100P = $119.4
The most you would be willing to pay for this bond is $119.4.
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When preparing a general overhead budget, which category used in
the book would you put a $200 per month gas allowance that the
company pays to a superintendent?
When preparing a general overhead budget, the category that would be used in the book to put a $200 per month gas allowance that the company pays to a superintendent is "Transportation expenses."
An overhead budget is a budget that covers an entire organization's indirect expenses. A general overhead budget would include all costs that are not directly related to manufacturing, such as administrative and selling expenses. It covers all the indirect expenses of an organization.
The amount of money allocated to each expense category in an overhead budget is decided based on the previous year's expenses and changes in the following year's expenses. The costs of indirect expenses are difficult to allocate to a single cost centre or department since they are not directly linked to production.
As a result, the gas allowance that the business pays to a superintendent, which is a transportation expenditure, would be included under the transportation expenditures category in the overhead budget.
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what were the Post-outbreak Assessment of Biosecurity Measures for the Equine Influenza outbreak that occured in Australia in 2007?
what actions could have prevented the outbreak.? Include what further actions you would recommend in the future and what the consequences of the outbreak are for the country, industry, the affected people/enterprise.
The Post-outbreak Assessment of Biosecurity Measures for the Equine Influenza outbreak that occurred in Australia in 2007 primarily involved enhancing and expanding the country's biosecurity procedures to prevent a recurrence. The country's horse industry was estimated to be worth over $6 billion, and the Equine Influenza outbreak resulted in a significant economic loss and social disruption throughout the country.
The following actions could have prevented the outbreak: More stringent biosecurity procedures and monitoring of imported horses. Frequent cleaning and disinfection of horse transport vehicles and equipment to prevent disease transmission. Improving communication and coordination between all stakeholders involved in managing animal diseases. Implementation of risk-based, evidence-based surveillance systems to monitor and respond to animal disease outbreaks. Future actions to prevent the outbreak include: Frequent monitoring of imported animals and people. Implementation of more stringent biosecurity measures and biosecurity education programmes. More efficient and effective communication and coordination between all stakeholders involved in animal disease management. Improved surveillance systems to monitor and respond to animal disease outbreaks. The consequences of the Equine Influenza outbreak were significant, including: Economic losses to the country and industry, including revenue losses, job losses, and business closures. Social disruption caused by movement restrictions and bans on horse racing and events. Limited access to global horse markets due to the loss of the country's Equine Influenza-free status.
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An organization's operating environment is a complex and often difficult to fully describe in the moment. For this week's discussion board, think about a company that misread their environment. 1. What was the outcome/affect on the company? 2. Looking back, what could the company have done differently? Additionally, explain whether or not you think it is important for a company to take steps to mitigate any environmental uncertainty. Do not forget to cite all of your sources and to provide your reasoning when supporting your affirmations.
Example: Blockbuster and the rise of streaming services
Outcome/Effect on the company:
Blockbuster, once a dominant player in the video rental industry, failed to adapt to the changing market dynamics and the emergence of streaming services. The company relied on its traditional brick-and-mortar rental stores while underestimating the potential of digital technologies and shifting consumer preferences. As a result, Blockbuster faced a significant decline in its customer base and revenue. Ultimately, the company filed for bankruptcy in 2010 and closed most of its stores.
What could the company have done differently:
Looking back, there were several steps Blockbuster could have taken to better navigate the changing operating environment:
a. Embrace digital technologies: Blockbuster could have invested in online rental platforms, developing a digital presence and offering streaming services before competitors entered the market.
b. Adapt the business model: Instead of relying solely on physical stores, Blockbuster could have explored new distribution channels, such as kiosks or mail-order rental services, to provide customers with more convenient options.
c. Form strategic partnerships: Blockbuster could have pursued partnerships with emerging streaming services or content providers to leverage their expertise and expand its offerings to meet the changing demands of consumers.
d. Focus on customer experience: Blockbuster could have enhanced its customer experience by personalizing recommendations, providing a seamless online interface, and offering loyalty programs to retain customers.
Importance of mitigating environmental uncertainty:
It is crucial for companies to take steps to mitigate environmental uncertainty as it directly impacts their long-term success and survival. Environmental uncertainty arises from various factors such as technological advancements, changing customer preferences, regulatory changes, and competitive landscape shifts. Ignoring or misreading these changes can lead to missed opportunities and failure to adapt, as seen in the Blockbuster example.
By proactively addressing environmental uncertainty, companies can:
Identify emerging trends and customer needs: By closely monitoring the operating environment, companies can gain insights into emerging trends and customer preferences, enabling them to develop innovative products and services that meet evolving demands.
Seize competitive advantages: Mitigating environmental uncertainty allows companies to stay ahead of competitors by identifying untapped market opportunities, adopting new technologies, and creating unique value propositions.
Enhance risk management: By understanding the operating environment, companies can better anticipate and mitigate risks, reducing the negative impacts of unexpected changes.
Sources:
Digital Disruption: Unleashing the Next Wave of Innovation by James McQuivey
"Blockbuster LLC" - Harvard Business School Case Study by Anita Elberse and Stacie Smith
"Why Blockbuster Failed and Why It Still Matters" - Forbes, 2015 by Larry Downes
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Tattletale News Corporation has been growing at a rate of 20% per year, and you expect this growth rate in earnings and dividends to ontinue for another 3 years. a. If the last dividend paid was $12, what will the next dividend be? Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
The next dividend will be $23.33.Tattletale News Corporation has been growing at a rate of 20% per year, and you expect this growth rate in earnings and dividends to ontinue for another 3 years. a. If the last dividend paid was $12,
To calculate the next dividend, we need to apply the growth rate to the last dividend. Using the formula for calculating future dividends with a constant growth rate, we have:
Next dividend = Last dividend * (1 + growth rate) of periods
Given that the last dividend paid was $12 and the growth rate is 20% (or 0.20), and we want to find the dividend for the next 3 years (or 3 periods), we can substitute these values into the formula:
Next dividend = $12 * (1 + 0.20)³Next dividend = $12 * (1.20)³
Next dividend ≈ $12 * 1.728Next dividend ≈ $20.74
Rounding this answer to 2 decimal places, the next dividend will be approximately $23.33.
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Laura drives a delivery truck for Aubrey’s Antiques. Due to faulty brakes on the delivery truck, Laura is unable to stop the truck and drives right through the front room of the customer's house. The customer sues Laura. Laura files a(n) __________ against Aubrey’s Antiques as she feels that they are to blame for this accident.
A)Counterclaim
B)Cross-claim
C)Affirmative defense
D)
Pendant claim
Laura would file a counterclaim against Aubrey's Antiques, asserting their responsibility for the accident due to the faulty brakes on the delivery truck. Option A.
In this scenario, Laura is an employee of Aubrey's Antiques, driving their delivery truck. Due to faulty brakes, Laura is unable to stop the truck and causes damage to a customer's house. The customer sues Laura for the damages incurred.
A counterclaim is a claim filed by the defendant in response to the plaintiff's original claim. In this case, Laura, as the defendant, believes that Aubrey's Antiques is at fault for the accident due to the faulty brakes on the delivery truck.
Therefore, she would file a counterclaim against her employer, Aubrey's Antiques, seeking to hold them responsible for the damages and potentially seek compensation for any harm caused.
By filing a counterclaim, Laura is asserting her own legal rights and shifting some of the liability onto Aubrey's Antiques. It allows her to present her case and argue that the employer's negligence or failure to maintain the truck's brakes properly contributed to the accident. So Option A is correct.
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An airline ticket office has two ticket agents answering incoming phone calls for flight reservations. In addition, one caller can be put on hold until one of the agents is available to take the call. If all three phone lines (both agent lines and the hold line) are busy, a potential customer gets a busy signal, and it is assumed that the call goes to another ticket office and the business is lost. The calls and attempted calls occur randomly (i.e., according to Poison process) at the mean rate of 15 per hour. The length of a telephone conversation has an exponential distribution with a mean of 4 minutes a) Find the steady - state probability that a caller will get to talk to an agent immediately ( 10 points) (Hint: P 0
=0.3636) The model is (M/M/…):(GD// −
) b) Find the steady - state probability that a caller will be put on hold ( 10 points) c) Find the steady - state probability that a caller will get busy signal ( 10 points)
a. the steady-state probability that a caller will get to talk to an agent immediately is approximately 0.0909.
b. the steady-state probability that a caller will be put on hold is approximately 0.8591.
c. The steady-state probability that a caller will get a busy signal is approximately 0.0500.
To solve the given problem, use the M/M/c queuing model, where:
- Arrivals follow a Poisson process with a rate of λ (given as 15 per hour).
- Service times for each agent follow an exponential distribution with a mean of μ (given as 4 minutes).
a) Steady-state probability that a caller will get to talk to an agent immediately:
In this case, we have two agents (c = 2). Using the formula for the steady-state probability of zero customers in the system (P0), we can find the probability that a caller will get to talk to an agent immediately.
P0 = [1 + (λ/μ)^1 + (λ/μ)^2/2!(c-1)]^(-1)
= [1 + (15/4)^1 + (15/4)^2/2!(2-1)]^(-1)
= [1 + 3.75 + (3.75)^2/2]^-1
= [1 + 3.75 + 7.03125]^-1
= 0.0909 (rounded to four decimal places)
Therefore, the steady-state probability that a caller will get to talk to an agent immediately is approximately 0.0909.
b) Steady-state probability that a caller will be put on hold:
Since there is only one hold line available, the probability of a caller being put on hold is equal to the probability of all agent lines being occupied.
P_hold = P(calls in the system = c)
= (λ/μ)^c * P0/c!
= (15/4)^2 * 0.0909 / 2!
= 0.8591 (rounded to four decimal places)
Therefore, the steady-state probability that a caller will be put on hold is approximately 0.8591.
c) Steady-state probability that a caller will get a busy signal:
If all agent lines and the hold line are busy, a caller gets a busy signal. So the probability of a busy signal is equal to the probability of all lines being occupied.
P_busy = P(calls in the system > c)
= 1 - P0 - P_hold
= 1 - 0.0909 - 0.8591
= 0.0500 (rounded to four decimal places)
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A hotel chain is comparing the results of two locations. Hotel A has a much higher conversion rate than Hotel B. You note that customers at Hotel B tend to abandon the cart after checking Rates and Availability. This could be explained by Hotel B being much smaller or busier than Hotel A.
Question 4 options:
True
False
True. The higher abandonment rate at Hotel B after checking Rates and Availability can be explained by factors such as the smaller size or higher occupancy level of Hotel B compared to Hotel A.
The disparity in the conversion rates between Hotel A and Hotel B can be attributed to the differences in their size or level of busyness. When customers at Hotel B check the Rates and Availability, they may be more likely to abandon the booking process due to factors such as limited room availability or higher occupancy levels.
A smaller hotel may have fewer rooms available, leading to a higher likelihood of customers encountering unavailability after checking the rates and availability. If Hotel B is consistently busier than Hotel A, it could indicate a higher demand for its services, which may result in limited room availability during peak periods.
As a result, customers may abandon the booking process at Hotel B after checking the rates and availability, leading to a lower conversion rate compared to Hotel A.
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Casplan Sea Drinks needs to raise $39.00 million by issuing bonds. It plans to issue a 12.00 year semi-annual pay bond that has a coupon rate of 5.01%. The yieid to maturity on the bond is expected to be 4.78%. How many bonds must Caspian Sea issue? (Note: Your answer may not be a whole number. In reality, a company would not issue part of a bond) ________
Answer format: Number: Round to: 0 decimal places.
Caspian Sea Drinks needs to issue approximately 9,517,167 bonds to raise $39.00 million.
To determine the number of bonds Caspian Sea Drinks must issue, we can use the following formula:
Number of bonds = Amount to raise / Bond face value
First, we calculate the bond face value by dividing the coupon rate by the yield to maturity. Considering the semi-annual payment structure, we divide the coupon rate (5.01%) by 2, resulting in a semi-annual coupon rate of 2.505%. Similarly, we divide the yield to maturity (4.78%) by 2, giving a semi-annual yield to maturity of 2.39%. The bond face value is then computed as:
Bond face value = Semi-annual coupon rate / Semi-annual yield to maturity
Bond face value = [tex]\frac{2.505}{2.39} =1.0460199005[/tex]
Next, we substitute the values into the formula:
Number of bonds = [tex]\frac{39,000,000}{1.0460199005 } = 9,517,166.9425[/tex]
Since it is not possible to issue fractional bonds, we round the number of bonds to the nearest whole number. Therefore, Caspian Sea Drinks needs to issue approximately 9,517,167 bonds in order to raise $39.00 million.
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Firm B is currently producing 1,000 units of output per day. It employs 12 workers, paying each $200 pe day, using 6 machines at a rental rate (r) of $300 per day. The marginal product of labor of the 12 th worker is 40 units of output. a. The firm can acquire a new machine at the same r that will increase production by 50 units of output. Should the firm replace a worker with this machine? Show or briefly explain. b. If your answer is yes, how high would r have to be for the firm to not want the additional K ? If your answer is no, how low would r have to be for the firm to want the additional K ?
a. The firm should replace a worker with a machine that increases production by 50 units of output. b. If the answer is yes, r would have to be $4800 for the firm to not want the additional K. If the answer is no, r would have to be $4,000 for the firm to want the additional K.
a. The firm should replace a worker with a machine that increases production by 50 units of output.
The marginal cost (MC) of the last worker hired is equal to the marginal product (MP) of the last worker hired times the cost of labor (W). Let us find the MC of the 12th worker.
The cost of labor is $200. The marginal product of labor of the 12th worker is 40 units of output. Therefore, the MC of the 12th worker is:MC = MP x W = 40 x 200 = $8,000
The new machine will increase production by 50 units.
Let us find the marginal product of the new machine:
MPl = ∆Q/∆L = (Q1 - Q0)/(L1 - L0) = (1050 - 1000)/(12 - 12) = 50/0 = undefined
Let us find the marginal product of the new machine per dollar of rental rate:
MPl/r = ∆Q/∆L / r = 50/300 = 1/6
The marginal product per dollar of rental rate of the machine is 1/6, which is higher than the marginal product per dollar of wage of the worker, which is 40/200 = 1/5.
Therefore, the firm should replace a worker with this machine.
b. If the answer is yes, r would have to be $8,000/(50/300) = $4800 for the firm to not want the additional K. If the answer is no, r would have to be $8,000/(40/200) = $4,000 for the firm to want the additional K.
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