a. The total profits from triangular arbitrage would be $24,000.
Profits from triangular arbitrage can be calculated by taking the difference between the buying and selling rates. In this case, the difference between buying and selling dollars for euros is 0.008 euros.
The difference between buying and selling Australian Dollars for US Dollars is 0.02 US Dollars and the difference between buying and selling Australian Dollars for Euros is 0.02 Euros. The total profits from triangular arbitrage would be the sum of these differences multiplied by the amount of money invested (3 million). Therefore, the total profits from triangular arbitrage would be $24,000.
b. While triangular arbitrage can be a profitable strategy, it is not without risk. The exchange rates can change quickly and if the company is not able to capitalize on the arbitrage opportunity, it could result in losses. Additionally, there are transaction costs associated with these transactions that could reduce the overall profits.
Therefore, the company should ensure that it has a system in place to monitor the exchange rates and execute transactions quickly to ensure that it can capitalize on any arbitrage opportunities and minimize the risks associated with this strategy.
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On her 18th birthday, Riley deposits $9,000 per year into a retirement account with an estimated 9.5% rate of return. She will stop making deposits after her 61st birthday (i.e., she will make her final deposit on her 61st birthday), and her investment will continue to grow until she retires at age 75. Assuming her deposits occur at the beginning of each year, how much money will Riley have in her retirement account on her 75th birthday?
Riley will have approximately $3,086,367.19 in her retirement account on her 75th birthday.
Based on the given information, Riley will make 44 deposits into her retirement account, starting on her 18th birthday and ending on her 61st birthday. Each deposit is $9,000, so the total amount of money she will deposit into her account is:
44 deposits x $9,000 per deposit = $396,000
Assuming an estimated 9.5% rate of return, her investment will grow each year. To calculate how much money she will have in her retirement account on her 75th birthday, we need to use the formula for the future value of an annuity:
FV = Pmt x (((1 + r)^n - 1) / r)
Where:
- FV is the future value of the annuity
- Pmt is the amount of the regular payments (in this case, $9,000 per year)
- r is the annual interest rate (9.5%)
- n is the number of periods (in this case, 57, since she will make her final deposit on her 61st birthday and retire at age 75)
Plugging in the numbers:
FV = $9,000 x (((1 + 0.095)^57 - 1) / 0.095) = $3,086,367.19
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A portfolio consists of the following two investments:
a bond with face value of $100.00 paying annual coupons of 9% maturing in 5 years
an annuity with payments of $40.00 at the end of each year for 5 years
The portfolio is comprised of 46% bonds and 54% annuities.
The term structure is flat and the current yield is 12% pa effective.
Calculate the duration (D) of the portfolio. Give your answer to 2 decimal places.
D = ______ years
The duration of the portfolio is 3.57 years.
To calculate the duration of the portfolio, we can use the following formula:
D = w1D1 + w2D2
where w1 and w2 are the weights of the bond and annuity in the portfolio, and D1 and D2 are the durations of the bond and annuity, respectively.
First, let's calculate the duration of the bond. Since the term structure is flat, the yield to maturity is equal to the current yield of 12%. Using the formula for the duration of a bond, we get:
D1 = (1 + y) * [ (1 - (1 + y)) / y ] - n * [ (1 + y) ]
where y is the annual yield to maturity, n is the number of years to maturity, and D1 is the duration of the bond.
Plugging in the values, we get:
D1 = (1 + 0.12) * [ (1 - (1 + 0.12) / 0.12 ] - 5 * [ (1 + 0.12) ]
= 3.87 years (rounded to 2 decimal places)
Next, let's calculate the duration of the annuity. Since the payments are made at the end of each year, we can use the formula for the duration of an annuity due and subtract 1 to get the duration of the annuity:
D2 = [ (1 + r) * (1 - (1 + r)) / r ] - 1
where r is the discount rate, n is the number of years, and D2 is the duration of the annuity.
Plugging in the values, we get:
D2 = [ (1 + 0.12) * (1 - (1 + 0.12)^(-5)) / 0.12 ] - 1
= 3.37 years (rounded to 2 decimal places)
Finally, we can calculate the duration of the portfolio by weighting the durations of the bond and annuity by their respective weights:
D = 0.46 * 3.87 + 0.54 * 3.37
= 3.57 years (rounded to 2 decimal places)
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the cost of a firm’s internal common equity is generally higher than the costs of a firm’s external common equity due to issuance costs. (True or False)
True. The cost of a firm's internal common equity is generally higher than the cost of a firm's external common equity due to the issuance costs associated with internal equity, such as the costs of stock option plans, stock purchase plans, and other incentives.
External equity, on the other hand, involves fewer issuance costs since it is generally acquired through public offerings or private placements. The statement is generally true. The cost of a firm's internal common equity, which is the return required by the firm's shareholders on the equity they have invested in the company, is generally higher than the cost of external common equity, which is the return required by new investors in the company's stock. This is because the cost of internal common equity includes not only the cost of the equity capital itself, but also the opportunity cost of retaining earnings rather than distributing them as dividends to shareholders. Additionally, internal common equity may be subject to higher taxes than external equity, further increasing the cost of internal equity financing. On the other hand, external common equity may be subject to issuance costs such as underwriting fees, legal and accounting expenses, and listing fees. However, the magnitude of these costs may vary depending on the size and type of the company and the nature of the external financing used.
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Mr. and Mrs. Norton purchased a ski-chalet for $34,500. (This must have been in 1930!) They paid $3,860 down and agreed to make equal payments at the end of every three months for 15 years. Interest is 7.43% compounded quarterly. Do not include the dollar sign, $, in your answers. Do not include the comma usually used to denote thousands. All dollar figures must be exactly 2 decimals. Although the Cash Flow Concept puts a negative sign, "-", in front of many numbers, do not include the negative sign when you put these numbers into Moodle. (a.) What is the size of the payment? Hint: Make sure your calculator is set to 2 decimal places before using AMORT. (b.) What is the balance after the first payment? (C.) How much of the principal is paid in the first payment? (d.) How much interest is paid in the first payment? (e.) What is the balance after the second payment? (f.) How much of the principal is paid in the second payment? (9.) How much interest is paid in the second payment? (h.) How much will they have paid in total after the 15 years? Total paid in payment = Plus the downpayment = (1.) How much interest will they pay in total? Total paid in payments - Original Mortgage =
(a) Using the PMT function in Excel, with a loan amount of $30,640 ($34,500 - $3,860) and a 15-year term with quarterly payments at 7.43% quarterly interest rate, the size of the payment is $552.23.
(b) After the first payment, the balance is the present value of the remaining payments, which can be calculated using the PV function in Excel. With a rate of 7.43%/4, 14*4 = 56 periods remaining, and a payment of $552.23, the balance is $29,428.05.
(c) The amount of principal paid in the first payment can be calculated by subtracting the interest paid from the total payment. The interest paid can be calculated as the balance multiplied by the quarterly interest rate of 7.43%/4. Therefore, the principal paid is $552.23 - ($29,428.05 x 7.43%/4) = $159.16.
(d) The interest paid in the first payment is $552.23 - $159.16 = $393.07.
(e) After the second payment, the remaining balance is the present value of the remaining payments, which can be calculated using the PV function in Excel. With a rate of 7.43%/4, 13*4 = 52 periods remaining, and a payment of $552.23, the balance is $28,198.54.
(f) The amount of principal paid in the second payment can be calculated by subtracting the interest paid from the total payment. The interest paid can be calculated as the balance multiplied by the quarterly interest rate of 7.43%/4. Therefore, the principal paid is $552.23 - ($28,198.54 x 7.43%/4) = $163.79.
(g) The interest paid in the second payment is $552.23 - $163.79 = $388.44.
(h) The total amount paid after 15 years can be calculated as the total number of payments (154) multiplied by the payment amount, plus the down payment of $3,860. Therefore, the total paid is (154)*$552.23 + $3,860 = $105,791.40.
(i) The total interest paid can be calculated as the total amount paid minus the original mortgage amount of $30,640. Therefore, the total interest paid is $105,791.40 - $30,640 = $75,151.40.
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some economists argue that regional free trade agreements will provide global benefits only if
Some economists argue that regional free trade agreements will provide global benefits only if trade creation exceeds trade diversion.
Free trade agreements (FTAs) are agreements reached between two or more countries on a range of topics, such as investor protections, intellectual property rights, and responsibilities influencing trade in goods and services. It could require keeping more records to be able to receive FTA benefits for your product, but it could provide it a competitive edge against products from other countries.
Each FTA has unique features, but they all generally have the same goal of lowering trade barriers and promoting more secure and open business and investment environments. Free trade agreements (FTAs) make it possible for American exporters and manufacturers to gain greater access to other markets. Tariffs are decreased or eliminated, trade barriers are removed through bilateral and global agreements, and economic growth is promoted.
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boards of directors have responded to financial crises, corporate scandals, regulator obligations, and investor requests for structural changes. in the 2011 harvard business review study of the changes in configuration of boards since 1987, which change has been brought about by government legislation? group of answer choices percentage of boards that have an average age of 64 or older has increased. average pay for directors has increased. percentage of boards with 12 or fewer members has increased. percentage of the directors that are independent has increased.
According to the 2011 Harvard Business Review study, the change in configuration of boards that has been brought about by government legislation is the increase in the percentage of directors that are independent.
What's the change in configuration of boardsThe change was likely a response to financial crises and corporate scandals, as regulators and investors called for greater transparency and accountability in corporate governance.
Independent directors are those who do not have any affiliations or relationships with the company or its executives, and are therefore more likely to provide unbiased oversight and hold management accountable.
The increase in independent directors on boards is a positive development for corporate governance, as it helps to ensure that boards are able to effectively oversee the company's strategy, risk management, and financial performance.
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Paola has little choice in how to accomplish her work tasks—her company employs strict process control.
-Skill variety
-Task Significance
-Task Identity
-Feedback
-Autonomy
Paola's work situation involves strict process control, which means her autonomy is limited. This can affect her skill variety, as she may not have the opportunity to use a diverse range of skills.
Autonomy refers to the degree to which an employee has control over how they perform their work tasks. If Paola's company employs strict process control, she likely has little choice in how to accomplish her work tasks, which suggests a low level of autonomy.Skill variety refers to the degree to which a job requires a variety of different skills and abilities. Task significance refers to the degree to which a job has a meaningful impact on the lives or work of others. Task identity refers to the degree to which a job involves completing a whole, identifiable piece of work. Feedback refers to the degree to which employees receive clear and direct feedback on the effectiveness of their performance.Based on the information provided, it is not clear whether Paola's job involves high or low levels of skill variety, task significance, task identity, or feedback.
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the arrival rate at a parking lot is 6 veh/min. vehicles start arriving at 6:00 p.m., and when the queue reaches 36 vehicles, service begins. if company policy is that total vehicle delay should be equal to 500 veh-min, what is the departure rate?
The departure rate in context to the given question is 6.75 veh/min.
the arrival rate is already given in the question, now we need to find the departure rate
Given,
Arrival rate = 6 veh/min
Total vehicle delay = 5000 veh/min
therefore, we need to implement the formula
Total vehicle delay = total number of vehicles in the line x time spend in the line
adding the given values in the given formula
restructuring the formula concerning the departure rate
500 = 36x (1/departure rate - 1/ arrival rate)
500/36 = 1/departure rate - 1/6
departure rate = 36/500 - 1/6
departure rate = 6.75 veh/min
The departure rate in context to the given question is 6.75 veh/min.
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gatorade is a well-known drink brand that almost every active person is familiar with, whether you are a professional athlete, hiker, or regular at the gym. the best distribution strategy for this product would be multiple choice intensive. specialized. selective. multichannel. exclusive.
The best distribution strategy for Gatorade would be a multichannel approach to reach a wide range of customers.
The target market for Gatorade comprises physically active people who need energy and hydration while exercising. The ideal strategy for this brand would be a multichannel distribution plan. Reaching as many clients as possible entails using a variety of distribution channels, including supermarkets, convenience shops, vending machines, internet merchants, and direct selling.
Gatorade can easily access its product by employing a multichannel strategy, which is crucial for a company that caters to consumers who need to keep hydrated and energised while on the road.
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the process of moving strawberries, blackberries, and raspberries from portland fresh and ready farms to the farmer's market where customers will purchase them, is a marketing activity called
The process of moving strawberries, blackberries, and raspberries from Portland Fresh and Ready Farms to the farmer's market where customers will purchase them is a marketing activity called "distribution."
Distribution is a critical marketing activity that involves moving products from the manufacturer or producer to the end customer. In this case, the strawberries, blackberries, and raspberries are being transported from the farm to the farmer's market, where they will be sold directly to customers.
Effective distribution is important because it ensures that products are available in the right place at the right time, and in the right quantities. This can help to maximize sales and customer satisfaction while minimizing waste and inefficiency.
In the case of fresh produce like strawberries, blackberries, and raspberries, efficient and timely distribution is particularly important to ensure that the products arrive at their destination in good condition and are available for customers to purchase when they want them.
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the opportunity cost of a purchase is: a. always equal to the selling price of what you purchased. b. the lowest possible price. c. the alternative good or service that one sacrifices because a different good was purchased. d. zero if the item is what you want most. e. always greater for people who are out of work than for people who are working.
The opportunity cost of a purchase is: c. the alternative good or service that one sacrifices because a different good was purchased. This term represents the value of the best alternative option that was not chosen when making a decision.
The opportunity cost of a purchase is the alternative good or service that one sacrifices because a different good was purchased. It is the value of the best alternative foregone. It is important to consider opportunity cost when making a decision as it helps to weigh the benefits and drawbacks of different options. It is not always equal to the selling price of what you purchased, the lowest possible price, zero if the item is what you want most, or always greater for people who are out of work than for people who are working.
Option c is correct.
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the loanable funds market in an economy is in equilibrium. draw a correctly labeled graph of the loanable funds market, labeling the equilibrium real interest rate and the equilibrium quantity. show the impact of a decrease in the money supply for this economy in your graph from part (a). will the result be a shortage or surplus in the loanable funds market at the original equilibrium? will lenders of existing fixed-rate loans be better or worse off as a result of the change in the real interest rate? how will investment spending on facilities and equipment in this economy be impacted? explain.
The loanable funds market is where savers provide funds for borrowers to use for investment purposes.
What's loanable fundsIn equilibrium, the quantity of loanable funds supplied equals the quantity demanded. This is represented by a graph with the real interest rate on the y-axis and the quantity of loanable funds on the x-axis. The supply and demand curves intersect at the equilibrium real interest rate and equilibrium quantity.
A decrease in the money supply shifts the supply curve for loanable funds to the left, as there are fewer funds available for lending. This leads to a higher real interest rate and a lower quantity of loanable funds at the new equilibrium point.
At the original equilibrium, there is now a shortage of loanable funds, as the quantity demanded exceeds the quantity supplied. Lenders of existing fixed-rate loans are worse off, as the real interest rate increases, reducing the value of their existing loans.
Investment spending on facilities and equipment is negatively impacted, as the higher real interest rate discourages borrowing and investment due to increased borrowing costs. This may lead to reduced economic growth in the long run.
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Your client wants to prepay $15 million in notes, which bear interest at a fixed rate of 7.5% per annum, payable quarterly. The notes do not provide for any payments of principal other than at maturity and there are 27 months until maturity. The Note Purchase Agreement provides for the payment of a "Make-Whole Amount" in the vent of prepayment of principal. This is an amount, not less than zero, which is the amount by which (i) the present value of all remaining payments of principal and interest that would be due with regard to the amount of principal that is be prepaid, discounted to the present date by a "Reinvestment Yield," exceeds (ii) the amount of principal that is being prepaid. The "Reinvestment Yield" is equal to the sum of (a) 75 basis points plus (y) the yield to maturity implied by the U.S. Treasury yields for the remaining contractual term of the principal being paid. The current implied US Treasury yield for obligations with 27 months remaining in their term is 2.45%.What is the applicable Make-Whole Amount that is due in connection with the prepayment? Show the Excel formula you used to compute the answer.
The applicable Make-Whole Amount that is due in connection with the prepayment is $1,316,485.95.
The Excel formula used to compute this is: =max(0, (PV((0.075/4), 274, -15000000)(0.0245+0.0075/4+1)-15000000))
To calculate the Make-Whole Amount, we need to find the present value of all remaining payments of principal and interest that would be due with regard to the amount of principal that is to be prepaid, discounted to the present date by a "Reinvestment Yield," and then subtract the amount of principal being prepaid.
First, we calculate the Reinvestment Yield, which is equal to the sum of (a) 75 basis points plus (b) the yield to maturity implied by the U.S. Treasury yields for the remaining contractual term of the principal being paid.
So, the Reinvestment Yield is:
= 0.0245 + 0.0075/4
= 0.026875
Next, we calculate the present value of all remaining payments of principal and interest using the PV function in Excel:
PV((0.075/4), 274, -15000000) = $15,869,334
Finally, we calculate the Make-Whole Amount by multiplying the present value by the Reinvestment Yield plus 1, and then subtracting the amount of principal being prepaid:
= 15,869,334 (0.026875 + 1) - 15,000,000
= $1,316,485.95
Since the Make-Whole Amount cannot be less than zero, the final formula used in Excel is =max(0, (PV((0.075/4), 274, -15000000)(0.0245+0.0075/4+1)-15000000)).
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a client is taking tolcapone for parkinson's disease. what blood test will the nurse perform often on this client?
The nurse will likely perform regular liver function tests on the client taking tolcapone for Parkinson's disease.
These tests measure the levels of certain enzymes and proteins in the blood that indicate how well the liver is working. Elevated levels of these enzymes and proteins can indicate liver damage. It is important to monitor these levels as tolcapone has been known to cause liver damage in some people.
The nurse may also test for creatine kinase levels, which can also be elevated due to tolcapone use. Other tests such as complete blood count, blood urea nitrogen, and creatinine levels may also be performed to monitor for any abnormal changes in the blood that may be caused by tolcapone. Regular monitoring of these tests is necessary to ensure the safety of the client taking tolcapone for Parkinson's disease.
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You are given information for a delta-hedged portfolio for European options that you have written. For each scenario, compute the number of shares to buy or sell (indicate which action to take) on day 1 to maintain the delta-hedge for a portfolio of one option.
Stock Price Call premium Call delta (A)
Day 0 55 6.50 0.4
Day 1 60 9.50 0.6
Stock Price Put premium Put Elasticity()
Day 0 50 1.00 -5
Day 1 49 0.91 -7
To maintain the delta-hedge for a portfolio of one European call option, you should buy 0.6 shares on Day 1.
The call delta on Day 0 is 0.4, and on Day 1 it's 0.6. The change in delta (∆delta) is 0.6 - 0.4 = 0.2. Since you have written one option, you need to buy 1 × 0.2 = 0.2 shares to maintain the delta-hedge.
However, since the question asks for maintaining the hedge for a portfolio of one option, it means you need to consider the initial 0.4 delta as well. Thus, you should buy 0.4 + 0.2 = 0.6 shares on Day 1.
To maintain the delta-hedge for a portfolio of one European put option, you should sell 7 shares on Day 1.
The put elasticity on Day 0 is -5, and on Day 1 it's -7. The change in elasticity (∆elasticity) is -7 - (-5) = -2. Since you have written one option, you need to sell 1 × 2 = 2 shares to maintain the delta-hedge.
However, since the question asks for maintaining the hedge for a portfolio of one option, it means you need to consider the initial -5 elasticity as well. Thus, you should sell -5 + (-2) = -7 shares on Day 1.
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g any system of performance compensation: a. should motivate desired actions b. may encourage unethical behavior c. needs compensating accounting controls to detect and prevent fraud d. all of the above answers are correct e. none of the above answers is correct
The correct answer is (d) all of the above answers are correct. A system of performance compensation should motivate desired actions, but it may also have unintended consequences, such as encouraging unethical behavior.
Therefore, compensating accounting controls are necessary to ensure that the system operates with integrity and does not incentivize unethical behavior.
Compensating accounting controls are necessary to detect and prevent fraud, ensuring that the system operates with integrity and does not incentivize unethical behavior. These controls may include regular audits, internal controls, and performance monitoring, among others.
However, such a system may also encourage unethical behavior, as individuals may resort to fraudulent or unethical practices to achieve their targets.
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suppose that the workers were paid 19 dollars per hour for work during the time period 9 am to 5 pm and were paid 28.5 dollars per hour for work during the rest of the day. what would the total personnel costs of the clean up have been under these conditions? total cost
The total personnel costs of the clean up under these conditions would be:
$152/day + $114/day = $266/day
To calculate the total personnel costs of the clean up, we need to know the number of hours worked during each period. Let's assume that the clean up took place for 8 hours per day, from 9 am to 5 pm, and for 4 hours per day, from 5 pm to 9 pm.
For the 8 hours worked from 9 am to 5 pm, the cost per hour is $19, so the total cost for this period is:
8 hours/day x $19/hour = $152/day
For the 4 hours worked from 5 pm to 9 pm, the cost per hour is $28.5, so the total cost for this period is:
4 hours/day x $28.5/hour = $114/day
Therefore, the total personnel costs of the clean up under these conditions would be:
$152/day + $114/day = $266/day
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carol fisher wants to sell the stock of hathaway international at the next available price after the prices reaches $50 per share. what type of transaction is carol making?
Carol Fisher is making a sell limit order transaction for the stock of Hathaway International once the price reaches $50 per share.
A sell limit order is a type of order to sell a security at a specified or better price, meaning that the order will only be executed if the stock reaches a particular price or higher.
Sell limit orders are a common way for investors to set a target price for selling their stocks. This type of order allows investors to control the price at which they sell their shares, ensuring that they receive a minimum price for their investment.
Once the stock price reaches the specified price or higher, the broker will execute the order and sell the stock at the next available price.Carol Fisher is making a "stop order" or "stop-loss order" transaction.
In this case, she wants to sell her Hathaway International stock when the price reaches $50 per share. A stop order is an instruction to sell the stock at the next available price after it reaches the specified price threshold, which helps protect profits or limit losses.
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A retailer received a written firm offer signed by a supplier. The offer committed the supplier to providing the retailer with up to 10,000 tubes of toothpaste over the next 45 days at $1 a tube. Thirty days later, the supplier informed the retailer that the price per tube of toothpaste would be $1.10. The next day the retailer ordered 6,000 tubes of toothpaste from the supplier, which the supplier promptly shipped. Sixty days after the receipt of the offer, the retailer ordered another 4,000 tubes of toothpaste, which the supplier also promptly shipped.
What price is the supplier permitted to charge the retailer for the toothpaste?
The supplier is permitted to charge the retailer $1 per tube of toothpaste for all 10,000 tubes that were ordered by the retailer within the 45-day time frame of the original offer.
The supplier is permitted to charge the retailer $1 per tube of toothpaste for the first 10,000 tubes. This is because the offer committed the supplier to providing the retailer with up to 10,000 tubes of toothpaste over the next 45 days at $1 a tube, and the retailer ordered a total of 10,000 tubes within that time frame.
However, the supplier is not permitted to charge the retailer $1.10 per tube of toothpaste, as they informed the retailer of this price increase after the retailer had already placed an order for 6,000 tubes at the original price of $1 per tube. Therefore, the supplier must honor the original price of $1 per tube for the remaining 4,000 tubes that the retailer ordered.
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big board makes high-end custom surfboards and gets new clients primarily by word of mouth. the small company has a few sample surfboards in stock, but it mostly customizes its products to customer specifications. the best supply chain strategy for big board is the strategy, which enables businesses to .
Based on the information provided, the best supply chain strategy for Big Board would be a flexible supply chain strategy that enables the company to quickly respond to the changing demands of its customers.
Since Big Board primarily customizes its surfboards to meet customer specifications, a flexible supply chain strategy would enable the company to quickly and efficiently adapt to changes in customer demand. This could involve maintaining close relationships with suppliers who can provide the necessary materials and components for custom surfboards, as well as utilizing a streamlined production process that can easily incorporate new designs and specifications.
Furthermore, since Big Board relies heavily on word-of-mouth referrals to attract new customers, a flexible supply chain strategy can also help the company maintain a positive reputation by consistently delivering high-quality, custom surfboards that meet the unique needs and preferences of its customers.
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in how many ways can seven different jobs be assigned to four different employees so that each employee is as- signed at least one job and the most difficult job is as- signed to the best employee?
There are 540 ways to assign the seven different jobs to four different employees, ensuring each employee gets at least one job and the most difficult job is assigned to the best employee.
To find the number of ways seven different jobs can be assigned to four different employees, ensuring that each employee gets at least one job and the most difficult job is assigned to the best employee, we can use combinatorics.
First, let's assign the most difficult job to the best employee, which leaves six jobs for the other three employees. Since each employee must be assigned at least one job, we can use the Principle of Inclusion-Exclusion to find the number of ways to distribute the remaining six jobs.
There are [tex]3^{6}[/tex] ways to distribute the six jobs among the three employees without restrictions. However, this includes cases where one or more employees do not receive any jobs. To correct for this, we need to subtract the number of ways in which one or more employees do not get any jobs.
There are 3 ways to exclude one employee and [tex]2^{6}[/tex] ways to distribute the jobs among the remaining two employees. We've counted cases where two employees are excluded twice, so we need to add back the number of ways all six jobs are assigned to one employee (3 ways).
Using the Principle of Inclusion-Exclusion, the number of ways to distribute the remaining six jobs to the three employees is:
[tex]3^{6} -3*(2^{6} )+3[/tex] =
729 - 192 + 3 = 540
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abc bank offers to lend you $50,000 for one year at a quoted annual rate of 8.31% with each payment at the end of each month. def bank also offers to lend you the same amount at a quoted annual rate of 8.63%, with each payment at the end of each quarter. what is the difference in the effective annual rates charged by the two banks? group of answer choices 0.22% 0.24% 0.26% 0.30% 0.28%
The difference in the effective annual rates charged by the two banks is 0.30%.
How to determine the effective annual rate (EAR)To calculate the effective annual rate (EAR) for each bank, we need to consider the compounding frequency.
For ABC Bank, the compounding period is monthly, so we use the formula (1 + r/n)^n - 1, where r is the quoted annual rate and n is the number of compounding periods.
Plugging in the numbers, we get an EAR of 8.573%.
For DEF Bank, the compounding period is quarterly, so we use the same formula with n = 4.
Plugging in the numbers, we get an EAR of 8.870%.
To find the difference in the effective annual rates, we subtract the EAR of ABC Bank from the EAR of DEF Bank:
8.870% - 8.573% = 0.297% or 0.30% (rounded to the nearest hundredth)
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You find PBB Corp's 2.9% bonds at a price quote of ($)97.3 on the finra.org website. The bond pays semiannually and matures 6 months from now. How many the bond's YTM is _____%.
The bond's Yield To Maturity (YTM) is 3.91%.
To calculate the bond's YTM, we can use the bond pricing formula, which is:
[tex]PV = C / (1+r)^{(1/2)} + C / (1+r)^{(2/2)} + ... + C / (1+r)^{(n-1/2)} + FV / (1+r)^{(n/2)}[/tex]
where PV is the present value, r is the yield to maturity, n is the number of periods to maturity, C is the coupon payment, and FV is the face value of the bond.
Substituting the given values, we get:
[tex]97.3 = 2.9 / (1+r/2)^{(1/2)} + 2.9 / (1+r/2)^{(1)} + 100 / (1+r/2)^{(1)[/tex]
Simplifying the equation, we get:
[tex]0.029 / (1+r/2)^{(1/2)} + 0.029 / (1+r/2) + 100 / (1+r/2) = 97.3[/tex]
Using a financial calculator or a spreadsheet, we can find that the bond's YTM is 3.91%.
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Fred invests 1200 at a nominal rate of 4.8% compounded monthly. After one year, his balance is X. Jane invests 1200 at a nominal rate of 4.8% compounded annually. After one year, her balance is Y. Sam invests 1200 at a continuous force of interest of 4.8%. After one year, his balance is Z. Which of the following is true?
a. X < Y < Z
b. Z < X < Y
c. Z < Y < X
d. Y < X < Z
e. Y < Z < X
Compound interest is the interest earned on both the principal amount and any previously accumulated interest on a sum of money.
The correct answer is option e. Y < Z < X. The formula for compound interest is:A = P(1 + r/n)^(nt)
Where:
A = final amount
P = principal amount
r = nominal annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = time (in years)
For Fred:
P = $1200
r = 4.8% = 0.048
n = 12 (monthly compounding)
t = 1
Using the formula, we get:
X = 1200(1 + 0.048/12)^(12*1)
X = $1270.06
For Jane:
P = $1200
r = 4.8% = 0.048
n = 1 (annual compounding)
t = 1
Using the formula, we get:
Y = 1200(1 + 0.048/1)^(1*1)
Y = $1257.60
For Sam:
P = $1200
r = 4.8% = 0.048
n = continuous compounding
t = 1
Using the formula, we get:
Z = 1200e^(0.048*1)
Z = $1258.96
Therefore, the order of balances from lowest to highest is:
Y < Z < X
So the correct answer is option e. Y < Z < X.
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a/an __________ are motivated by a desire to acquire something, for example food riots. (35)
An acquisitive mob is motivated by a desire to acquire something that is perceived as scarce or in short supply.
These mobs can form when individuals or groups feel that their access to basic necessities such as food, water, or shelter is being threatened or limited. Food riots, for example, are a common type of acquisitive mob that typically occurs in response to food shortages or rising prices. During such riots, people may take to the streets and engage in looting or other forms of violence to secure food or other essential items.
Acquisitive mobs can also form in response to perceived social or economic inequalities. In these cases, individuals may feel that they are being unfairly denied access to resources or opportunities, and may resort to violent or disruptive behavior to express their grievances. Acquisitive mobs can be difficult to control and can pose a significant threat to public safety and social stability.
Effective responses to such mobs require a combination of short-term measures, such as police intervention, and longer-term efforts to address underlying social and economic factors that contribute to mob formation.
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A/an incentive is motivated by a desire to acquire something, for example, food riots.
A motivator or catalyst is something that urges someone to act. Due to a lack of resources, people are driven to buy food in the case of food riots, which gives them the incentive to take action through protests or riots. Positive or negative incentives are possible, as well as financial or non-financial ones. They may also be explicit or implicit, direct or indirect, etc. In economics, incentives are essential in determining how people, businesses, and governments behave. Designing efficient institutions and policies that advance social welfare and economic prosperity requires a thorough understanding of incentives and how they operate.
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You purchased a stock for $175 and sold it for $250 one yearlater. Additionally, you received a dividend payment of $30. Whatwas your total return (yield) on this investment?
The total return (yield) on an investment which involve purchasing a stock for $175 and selling it for $250 as well as a dividend payment of $30 is 60%.
To calculate the total return (yield) on your investment, we will consider the initial stock purchase price, the selling price, and the dividend payment.
In order to calculate the total return, follow these steps:
1. Calculate the capital gain:
Selling price - Purchase price = $250 - $175 = $75.
2. Add the dividend payment:
Capital gain + Dividend = $75 + $30 = $105.
3. Calculate the total return (yield):
(Total gain / Purchase price) x 100 = ($105 / $175) x 100 = 60%.
So, your total return (yield) on this investment was 60%.
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Problem 21-1 (LG 21-2) Jane Doe earns $30,000 per year and has applied for an $80,000, 30-year mortgage at 8 percent interest, paid monthly. Property taxes on the house are expected to be $1,200 per y ear. if her bank requires a gross debt service ratio of no more than 30%, will Jane be able to obtain the mortgage?
Jane's GDS ratio is below the bank's requirement of 30%, she should be able to obtain the $80,000 mortgage at 8% interest, paid monthly.
To determine if Jane Doe can obtain the mortgage, we first need to calculate her monthly gross income and monthly housing expenses.
Jane's monthly gross income can be calculated as follows:
$30,000 / 12 months = $2,500 per month
Next, we need to calculate her monthly housing expenses. This includes the monthly mortgage payment and property taxes. The monthly mortgage payment can be calculated using the following formula:
[tex]M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1][/tex]
where M is the monthly mortgage payment, P is the principal amount of the mortgage, i is the monthly interest rate, and n is the number of months in the mortgage term.
For Jane's mortgage, we have:
P = $80,000
i = 8% / 12 = 0.0067
n = 30 years * 12 months per year = 360 months
Plugging in these values, we get:
[tex]M = $80,000 [ 0.0067(1 + 0.0067)^{360 }] / [ (1 + 0.0067)^{360 - 1 ][/tex]= $587.82 per month
Adding the property taxes, we have:
$587.82 + ($1,200 / 12) = $687.82 per month
Finally, we can calculate Jane's gross debt service ratio (GDS) by dividing her monthly housing expenses by her monthly gross income and multiplying by 100%:
GDS = ($687.82 / $2,500) x 100% = 27.51%
Since Jane's GDS ratio is below the bank's requirement of 30%, she should be able to obtain the $80,000 mortgage at 8% interest, paid monthly.
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Consider historical data showing that the average annual rate of return on the S&P 500 portfolio over the past 85 years has averaged roughly 8% more than the Treasury bill return and that the S&P 500 standard deviation has been about 28% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 6%.
Calculate the expected return and variance of portfolios invested in T-bills and the S&P 500 index with weights as follows:
WBills Windex Expected Return Variance 0.6 0.4 0.092 0.0125 Example
0.8 0.2 0.4 0.6 1 0 0 1 0.2 0.8
Using the given historical data and weights, the expected return and variance of the T-bills and S&P 500 index portfolios are:
Expected return: 9.2% for the 0.6 T-bill/0.4 S&P 500 portfolio and 8.4% for the 0.8 T-bill/0.2 S&P 500 portfolio.
Variance: 1.25% for the 0.6 T-bill/0.4 S&P 500 portfolio and 0.36% for the 0.8 T-bill/0.2 S&P 500 portfolio.
To calculate the expected return of each portfolio, we multiply the weight of each asset (T-bills and S&P 500) by its expected return and sum the results. For example, the expected return of the 0.6 T-bill/0.4 S&P 500 portfolio is:
(0.6 x 6%) + (0.4 x (6% + 8%)) = 9.2%
To calculate the variance of each portfolio, we use the formula:
Variance = (w1^2 x σ1^2) + (w2^2 x σ2^2) + 2(w1 x w2 x σ1 x σ2 x ρ)
where w1 and w2 are the weights of the two assets, σ1 and σ2 are their standard deviations, and ρ is the correlation between them (which we assume to be 0 since they are uncorrelated). For example, the variance of the 0.6 T-bill/0.4 S&P 500 portfolio is:
(0.6^2 x 0) + (0.4^2 x 0.28^2) = 0.0125 or 1.25%
The variance of the 0.8 T-bill/0.2 S&P 500 portfolio is:
(0.8^2 x 0) + (0.2^2 x 0.28^2) = 0.0036 or 0.36%
These calculations can help investors make informed decisions about how to allocate their assets between T-bills and the S&P 500 index.
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The total market value of the common stock of the Okefenokee Real Estate Company is $13.5 million, and the total value of its debt is $8.5 million. The treasurer estimates that the beta of the stock is currently 1.8 and that the expected risk premium on the market is 9%. The Treasury bill rate is 4%. Assume for simplicity that Okefenokee debt is risk-free and the company does not pay tax.
a. What is the required return on Okefenokee stock? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)
Required return %
b. Estimate the company cost of capital. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)
Cost of capital %
c. What is the discount rate for an expansion of the company's present business? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)
Discount rate %
d. Suppose the company wants to diversify into the manufacture of rose-colored spectacles. The beta of unleveraged optical manufacturers is 1.15. Estimate the required return on Okefenokee's new venture. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)
Required return %
The Capital Asset Pricing Model (CAPM) can be used to determine the needed return on Okefenokee capital assets pricing model shares. The CAPM formula is: Required Return = Market Risk Premium x Beta x Risk-Free Rate.
Here, the beta is 1.5, the market risk premium is 6%, and the risk-free rate (Treasury bill rate) is 4%.
Required Return is 4% plus 1.5 x 6%, or 4% plus 9%, or 13%.
b. We must apply the weighted average cost of capital (WACC) methodology to get the firm's cost of capital:
WACC is equal to (e) + (D/VxRdx(1-Tc))
The equation changes because Okefenokee doesn't pay taxes to:
(EN x Re) + (D/W x Rd) = WACC
E is the market value of the company's stock in its whole ($6 million), D is the market value of the company's debt, and WACC = ($6,000,000/$10,000,000 x 13%) + ($4,000,000/$10,000,000 x 4%).
WACC is calculated as (0.6 x 13%) + (0.4 x 4%) = 7.8% + 1.6% = 9.4%
C. The company's cost of capital, which is 9.4%, would be the discount rate for an expansion of the current firm.
d. Using the updated beta of unleveraged optical producers (1.2), we once more apply the CAPM formula to calculate the needed return on Okefenokee's new business.
Required Return = Market Risk Premium x Beta x Risk-Free Rate
Required Return is equal to 4% + 1.2 x 6%, or 4% + 7.2%, or 11.2%.
Okefenokee's new business requires a return of 11.2%.
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distinguish between common-law liability and statutory liability for auditors. what is the basis for the difference in liability?
A Liability is defined as a unborn loss of profitable benefits that an reality is needed to give to another reality as a result of once deals or other once events.
Common law liability arises from the legal opinions of judges in deciding a case, a precedent that serves as a companion for other judges to decide future analogous cases and is used in civil action.
On the other hand, legal liability reflects laws legislated at the state or civil position and prescribes certain procedures.
May involve civil or felonious liability. Liability is an obligation or liability to another that's extinguished by the unborn transfer or use of goods, the provision of services or any other profitable sale at a specific or determinable time, upon the circumstance of a specific event or on demand.
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