The initial loan amount is $7908 and the outstanding balance right after the 6th payment has been made is $34,845.39.
To find the initial loan amount, and also the outstanding balance right after the 6th payment has been made in a 1-year loan with payments at the end of each month:
First, we need to find the present value of the payments.
Present value of the payments = Payment × Present Value of an Annuity × payments of $1000
= $1000 × 6.5225
= $6522
Final 4 payments of $600 = $600 × 3.4651 = $1386
Next, we need to find the amount of the loan.
First, we need to find the future value of the payments.
Future value of the payments = $6522 + $1386 = $7908
Using the formula for the future value of an annuity and given interest rate = 6/12 = 0.5%
No. of periods = n = 12
Future value = FV = R [{(1 + r) n - 1}/r]
FV = $7908, R = $1000, r = 0.005 and n = 8
Putting the values in the formula:
FV = R [{(1 + r) n - 1}/r] = $7908=$1000× [{(1 + 0.005)8 - 1}/0.005]
On solving, we get the value of R.
FV = R [{(1 + r) n - 1}/r]
R = $922.31
Therefore, the amount of the loan is equal to the present value of all payments added together.
Loan Amount = Present Value of the Payments + Present Value of the Last Payment
= $6522 + $1386
= $7908
Outstanding balance right after the 6th payment has been made = The balance remaining after five payments have been made, which is the present value of the remaining seven payments.
Remaining payments = 7 payments of $1000 and 4 payments of $600.
Remaining payment = $1000 × 5.0404 + $600 × 3.4651 = $7164.24
Outstanding balance right after the 6th payment has been made = Present value of remaining payments
= $7164.24 × Present Value of an Annuity = $7164.24 × 4.8682 = $34,845.39
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Jackie Chiles has decided that he would like to retire in 15 years. In order to maintain his current standard of living, he decides that he will withdraw $90,000 each year (at the end of the year) during retirement. Jackie's financial planner advised him that he should plan to live 25 years in retirement and use an annual return of 9%; Jackie is following that advice. Given these assumptions and the fact that Jackie already has $85,000 saved for retirement; how much does Jackie need to save each year to reach his retirement goals?
With an existing retirement savings of $85,000, Jackie needs to save $9,285.69 each year to reach his retirement goals.
To determine the annual savings needed for Jackie to reach his retirement goals, we can use the concept of present value of an annuity. This calculates the equal annual payments required to accumulate a future value.
In this case, Jackie wants to withdraw $90,000 each year during his 25-year retirement. We need to calculate the annual savings required to accumulate this amount, given an annual return of 9% and a time frame of 15 years until retirement.
The formula to calculate the present value of an annuity is:
Annual Savings = (Desired Future Value / Present Value Factor)
The Present Value Factor is calculatd using the formula:
Present Value Factor = (1 - (1 + r)^-n) / r
where r is the annual return rate and n is the number of years.
Substituting the values into the formulas, we find:
Present Value Factor = (1 - (1 + 0.09)^-15) / 0.09
Present Value Factor ≈ 9.6894
Annual Savings = ($90,000 / 9.6894)
Annual Savings ≈ $9,285.69
Therefore, Jackie needs to save approximately $9,285.69 each year to reach his retirement goals and maintain his desired standard of living.
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Money and Inflation (a) Indicate whether the following statement is true, false, or uncertain and explain your answer using words, graphs and equations as appropriate. (i) If the commercial banking system does not hold any reserves, then it cannot affect the money supply. (ii) If consumption depends positively on the level of real balances and real balances depend negatively on the nominal interest rate in a neoclassical model, then the nominal interest rate rises 1 percent for each 1 percent rise in the money growth rate. (iii) If only unanticipated changes in the money supply affect real GDP, the public has rational expectations, and everyone has the same information about the state of the economy, then a policy of keeping the money supply constant is optimal.
keeping the money supply constant is optimal and will lead to the stability of the economy. (i) If the commercial banking system does not hold any reserves, then it cannot affect the money supply.
False, since even if banks are not holding any reserves, they can still generate money by lending and taking in deposits. The supply of money in circulation in an economy is influenced by many factors such as the amount of money created by the commercial banks through loans, interest rates, monetary policy of the central bank, among others.(ii) If consumption depends positively on the level of real balances and real balances depend negatively on the nominal interest rate in a neoclassical model, then the nominal interest rate rises 1 percent for each 1 percent rise in the money growth rate.Uncertain. Since it is stated that consumption depends positively on the level of real balances and real balances depend negatively on the nominal interest rate. When nominal interest rate rise, the real balance demand will decrease, leading to a fall in the consumption expenditure. Hence, it cannot be concluded with certainty that nominal interest rate rises by 1 percent for each 1 percent rise in the money growth rate.(iii) If only unanticipated changes in the money supply affect real GDP, the public has rational expectations, and everyone has the same information about the state of the economy, then a policy of keeping the money supply constant is optimal.True. If unanticipated changes in the money supply affect real GDP, the public has rational expectations, and everyone has the same information about the state of the economy, then it is optimal to maintain a constant money supply. A sudden change in the supply of money will lead to disequilibrium in the economy.
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King Motors manufactures Engine equipment, and they are planning on introducing a new product which would require an initial investment of $7 million in assets and would produce a net annual revenue of $1.1 million over a service life of 8 years. After the 8 years, the product will likely become obsolete, and the assets would be sold for an estimated $0.6 million. What is the rate of return of this project? And would it be an acceptable project with the MARR = 7%?
Rate of return = 0.0327 or 3.27%. As the MARR (Minimum Acceptable Rate of Return) is 7%, the rate of return of the project is less than the MARR, which means that this project is not an acceptable project. Therefore, this project should not be pursued by King Motors.
The solution for the given problem is as follows: Firstly, the net cash inflow for each year can be calculated as follows:
Year Cash inflow
0 -7,000,0001 1,100,0002 1,100,0003 1,100,0004 1,100,0005 1,100,0006 1,100,0007 1,100,0008 1,100,0009 1,700,000 (1.1 million revenue minus 0.6 million proceeds from the sale of assets).
Next, the total net cash inflow is calculated by adding the net cash inflow for each year:
Total net cash inflow = -7,000,000 + 1,100,000 + 1,100,000 + 1,100,000 + 1,100,000 + 1,100,000 + 1,100,000 + 1,100,000 + 1,700,000
Total net cash inflow = $9,200,000
The rate of return of the project can be calculated using the following formula:
Rate of return = (Total net cash inflow / Initial investment)^(1 / Service life) - 1Rate of return = ($9,200,000 / $7,000,000)^(1 / 8) - 1
Rate of return = 0.0327 or 3.27%
As the MARR (Minimum Acceptable Rate of Return) is 7%, the rate of return of the project is less than the MARR, which means that this project is not an acceptable project. Therefore, this project should not be pursued by King Motors.
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Sky Diving Inc. is a new firm located in Toronto that focuses on training people to skydive in a simulated environment. It has hired 30 professionals to help with the training. The firm has funds to support its plans to become the world's leading skydiving firm, so it wants to focus on high quality. You have been asked to formulate and implement a compensation system for the firm.
2a. Using the 5-stage compensation strategy formulation process, discuss your recommended plan of action.
2b. Describe THREE legislated constraints on the compensation strategy of this firm. [12 marks]
The 5 - stage compensation strategy for coming up with an appropriate compensation system for the firm would be:
Job Analysis Compensation Philosophy Market Analysis Design Compensation Structure:Implementation and ReviewSome of the legislated constraints would be:
Minimum Wage LegislationPay Equity LegislationCanada Labour CodeHow to come up with the compensation strategy ?Conduct a thorough job analysis to understand the roles, responsibilities, and skill requirements of the professionals involved in training people to skydive in a simulated environment.
Define the compensation philosophy and objectives that align with the firm's focus on high quality and its goal of becoming the leading skydiving firm. Conduct a market analysis to understand the prevailing compensation practices and benchmarks in the skydiving industry.
Design a compensation structure that includes both fixed and variable components. Implement the compensation system, ensuring effective communication and understanding among employees.
Sky Diving Inc. must comply with minimum wage legislation, which sets a minimum hourly rate that employees must be paid. In some jurisdictions, pay equity legislation may require employers to provide equal pay for work of equal value.
The Canada Labour Code sets minimum standards for wages and working conditions. Sky Diving Inc. must comply with these standards in setting its compensation system.
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Please determine which countries would be classified as growth miracles or growth disasters. Growth miracles Growth disasters Answer Bank Japan Nigeria Argentina South Korea Which statement regarding economic growth is supported by the histories of the listed countries? Most countries will experience slow and steady economic growth over several decades. Growth is not guaranteed, even when a country has experienced it in the past Only capitalist nations experience rapid growth Once a country begins to develop economic growth, it will continue to do so. DOLL Priser F
There are a few countries that could be classified as growth miracles or growth disasters. In the context of this question, Japan and South Korea would be classified as growth miracles while Nigeria and Argentina would be classified as growth disasters.
In Japan, the economic growth rate accelerated in the 1950s and 1960s, and by the 1970s Japan was one of the world's most powerful economies. Japan’s economic growth is credited to the development of its automobile industry, steel production, and its strong work ethic. Similarly, South Korea has also experienced significant economic growth in recent years. The country has undergone rapid development, with its economy transitioning from an agricultural one to an industrialized one.
On the other hand, Nigeria and Argentina have struggled with economic growth. Nigeria has faced numerous challenges such as corruption, terrorism, and political instability, which have hindered its economic development. In Argentina, economic growth has been hindered by high inflation rates, lack of investment, and political instability.
Therefore, the statement that is supported by the histories of these countries is: Growth is not guaranteed, even when a country has experienced it in the past. While Japan and South Korea have been able to maintain their economic growth, Nigeria and Argentina have struggled, demonstrating that economic growth is not a guaranteed outcome.
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As the time period until receipt increases, the present value A) decreases B) remains the same C) increases D) not enough information to tell
The present value decreases as the time period until receipt increases.
When it comes to calculating present value, the principle of time value of money is applied. The time value of money states that the value of money decreases over time due to factors such as inflation and the opportunity cost of investing funds elsewhere. As the time period until receipt increases, the future cash flows are discounted back to the present at a higher rate, resulting in a lower present value. Therefore, the present value decreases with an increase in the time period until receipt.
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Briefly distinguish between a group and team.
A group refers to a group of individuals or organizations that have a shared identity or interest and can exist without a shared purpose. A team is a group of people who work together to achieve a common goal or objective.
A group is any collection of people that come together and communicate, but don't necessarily work together to achieve anything specific. On the other hand, a team consists of a group of people who come together and work towards a common goal or objective. Teams have specific roles for each team member, and members rely on one another to achieve the team's objectives. Groups and teams have distinct differences, which include:
- Size: A group can be of any size, while a team is usually small enough to maintain effective communication and collaboration.
- Composition: Groups can be homogenous or heterogenous, while teams are usually diverse in terms of skills, experience, and background.
- Purpose: A group has a shared identity or interest, while a team has a shared objective or goal.
- Interdependence: Groups may or may not have interdependence, while a team is characterized by interdependence among members.
In conclusion, groups and teams are different based on their size, composition, purpose, and interdependence. While a group is any collection of people that come together and communicate, a team is a group of people who come together to work towards a common goal or objective. Groups are more about shared interests or identity, while teams are focused on achieving a specific outcome.
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17. Answer all parts of this question. (a) [10 marks] Consider a monopolist that faces a downward sloping market demand. The monopoly has constant marginal cost equal to the average cost. Using a diagram to illustrate your answer explain why a monopoly can obtain supernormal profits. (b) [8 marks] Explain how a monopoly can increase its profits by using price discrimination. (c) [7 marks] Explain the main differences between a monopoly and perfect competition in terms of total welfare (e.g. consumers plus producers surplus). Use a diagram to illustrate your answer.
(a) A circumstance where the seller can make more than usual earnings is known as a supernormal profit. Because the seller has control over the prices to be determined for the product and the entrance of new businesses is thus constrained, a monopoly firm may therefore make a supernormal profit in the long run as well as in the short run.
b) A company that has the ability to charge various prices for various units of an item or service is said to have a price-discriminating monopoly. Airlines, for instance, provide various fares for the same journey. Because there is just one business in a monopoly, its demand curve mirrors the market's.
c) The primary distinction between Perfect Competition and Monopoly is that Perfect Competition involves many vendors competing for many consumers, whereas Monopoly involves only one seller competing for many buyers. In a perfect market, total welfare is maximized along with consumer surplus and producer welfare, but welfare is lost owing to consumer welfare loss, hence total welfare is not maximized.
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Information for an EOQ problem:
Annual sales (in units) 2,000,000
Ordering Costs $100
Inventory Cost of each unit is $50
Inventory Carrying Cost as a percentage is 20% of Inventory Cost
Lead time for new orders to arrive at our plant is 3 weeks.
Our policy is to always keep a safety stock of 1 week supply.
1.What is the EOQ = _____________units
2.What is the Reorder Point___________units (when do we reorder?)
3.What is the Safety stock in units___________units
The EOQ is 6,325 units, the reorder point is (3 weeks * 2,000,000 units / 52 weeks) + 1 week's supply of safety stock, and the safety stock is 1 week's supply of units.
To solve the EOQ (Economic Order Quantity) problem, we need to determine the optimal order quantity, reorder point, and safety stock level.
EOQ (Economic Order Quantity): The EOQ formula is used to calculate the optimal order quantity that minimizes the total cost of inventory. It takes into account the annual demand, ordering cost, and carrying cost per unit. In this case, the annual demand is 2,000,000 units, the ordering cost is $100, and the carrying cost per unit is 20% of $50. By plugging these values into the EOQ formula, we find that the EOQ is approximately 6,325 units.
Reorder Point: The reorder point is the inventory level at which a new order should be placed. It is determined by considering the lead time demand and the safety stock. The lead time is 3 weeks, and the lead time demand is calculated by dividing the annual demand by the number of weeks in a year. Adding the lead time demand to the safety stock (1 week's supply) gives us the reorder point.
Safety Stock: The safety stock is extra inventory maintained to account for unexpected demand fluctuations or supply delays. In this case, the safety stock is set at 1 week's supply of units.
Therefore, the EOQ is 6,325 units, the reorder point is determined by adding the lead time demand and safety stock, and the safety stock level is set at 1 week's supply of units. These calculations help optimize inventory management and ensure timely replenishment while minimizing costs.
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JoyFM Inc. has an investment opportunity, which generates cash flows shown below. The investment opportunity gives an IRR of Year Cash Flow 0 - $13,600 1 6,500 2 7,800 3 4,300 4 3,900 a 26.78% b 27.89% c 29.01% d 29.75% e 31.24%
To calculate the internal rate of return (IRR) of the investment opportunity, we need to find the discount rate that makes the present value of the cash flows equal to zero. We can use trial and error or financial software to calculate the IRR.
Using trial and error, we can try different discount rates until we find the one that results in a present value close to zero. Let's calculate the present value of the cash flows at different discount rates:
At a discount rate of 26%:
PV = -13,600 + 6,500/(1+0.26)^1 + 7,800/(1+0.26)^2 + 4,300/(1+0.26)^3 + 3,900/(1+0.26)^4
PV ≈ -13,600 + 5,158.73 + 5,236.86 + 2,589.15 + 2,008.08
PV ≈ 1,392.82
At a discount rate of 27%:
PV = -13,600 + 6,500/(1+0.27)^1 + 7,800/(1+0.27)^2 + 4,300/(1+0.27)^3 + 3,900/(1+0.27)^4
PV ≈ -13,600 + 5,118.11 + 5,187.61 + 2,549.47 + 1,974.24
PV ≈ 1,228.43
At a discount rate of 28%:
PV = -13,600 + 6,500/(1+0.28)^1 + 7,800/(1+0.28)^2 + 4,300/(1+0.28)^3 + 3,900/(1+0.28)^4
PV ≈ -13,600 + 5,079.37 + 5,139.28 + 2,511.40 + 1,941.61
PV ≈ 1,071.06
At a discount rate of 29%:
PV = -13,600 + 6,500/(1+0.29)^1 + 7,800/(1+0.29)^2 + 4,300/(1+0.29)^3 + 3,900/(1+0.29)^4
PV ≈ -13,600 + 5,042.29 + 5,092.15 + 2,474.42 + 1,910.03
PV ≈ 917.29
At a discount rate of 30%:
PV = -13,600 + 6,500/(1+0.30)^1 + 7,800/(1+0.30)^2 + 4,300/(1+0.30)^3 + 3,900/(1+0.30)^4
PV ≈ -13,600 + 5,006.71 + 5,045.49 + 2,438.97 + 1,879.12
PV ≈ 773.29
Based on these calculations, we can see that the present value is closest to zero when the discount rate is around 29%. Therefore, the internal rate of return (IRR) for the investment opportunity is approximately 29.01%.
Therefore, the correct answer is option c) 29.01%.
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As part of an EHR system selection, due diligence should be done:
a. After installing an EHR to test for acceptance
b. Before contracting for an EHR product
c. During system build to check interface quality
d. Prior to any user authorization for access to data
b. Before contracting for an EHR product. Due diligence should be performed before contracting for an Electronic Health Record (EHR) product.
This is a critical step in the EHR system selection process to ensure that the chosen EHR meets the organization's requirements and is capable of supporting its workflows and needs.
Performing due diligence before contracting involves conducting a thorough evaluation of the EHR vendor and their product. This includes assessing the vendor's financial stability, reputation, experience in the healthcare industry, customer references, and compliance with regulatory requirements such as HIPAA. It also involves evaluating the EHR system's functionalities, features, usability, interoperability, data security measures, and scalability.
By conducting due diligence before contracting, organizations can mitigate risks and make informed decisions. It allows them to select an EHR system that aligns with their specific needs, budget, and long-term goals. This step ensures that the organization enters into a contract with a reliable vendor and minimizes the chances of facing issues and challenges during implementation and use of the EHR system.
Therefore, option b. Before contracting for an EHR product, is the correct answer.
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In May, one of the processing departments at Messerli Corporation had beginning work in process inventory of $22,000 and ending work in process inventory of $43,000. During the month, $156,000 of costs were added to production and the cost of units transferred out from the department was $135,000. The company uses the FIFO method in its process costing system. In the department's cost reconciliation report for May, the total cost to be accounted for would be:
Process costing system is a costing system in which the cost per unit of product is obtained by dividing the total production cost of a process by the number of units produced. In this system, costs are accumulated for a period of time and then divided by the number of units produced in that period to determine the cost per unit.
The FIFO method is one of the methods of process costing. In the FIFO method, the cost of the oldest work in process inventory is used first to determine the cost of units transferred out and the cost of ending work in process inventory. In the given problem, the beginning work in process inventory was $22,000, costs added during the month were $156,000, and cost of units transferred out was $135,000. Therefore, the total cost to be accounted for would be:$22,000 (beginning work in process inventory)+$156,000 (costs added during the month)= $178,000Then, to determine the cost of ending work in process inventory, we can use the FIFO method. Since the cost of the oldest work in process inventory is used first, we can assume that the $22,000 beginning work in process inventory was completed first and that the ending work in process inventory was started and completed during the month. Therefore, the cost of ending work in process inventory can be calculated as follows:Cost of units completed during the month= $135,000Costs added during the month= $156,000Total cost of units started during the month= $291,000Cost of beginning work in process inventory= $22,000Total cost to be accounted for= $313,000Total cost to be accounted for= Cost of units completed during the month+ Cost of ending work in process inventoryCost of ending work in process inventory= Total cost to be accounted for - Cost of units completed during the month= $313,000 - $135,000= $178,000Therefore, the total cost to be accounted for would be $313,000.
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A vending machine dispenses hot chocolate or coffee. Service time is 15 seconds per cup and is constant. Customers arrive at a mean rate of 62 per hour, and this rate is Poisson-distributed. a. Determine the average number of customers waiting in line. (Round your answer to 2 decimal places.) Average number of customer ________
b. Determine the average time customers spend in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average time ______ minutes c. Determine the average number of customers in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average number ________ customers
a. The average number of customers waiting in line is approximately 9.43.
b. The average time customers spend in the system is approximately 9.39 minutes.
c. The average number of customers in the system is approximately 9.69 customers.
a. To determine the average number of customers waiting in line, we can use the queuing theory formula for the M/M/1 queue (a single-server queue with Poisson arrivals and exponential service times). The average number of customers waiting in line can be calculated using the following formula:
Lq = λ^2 / (μ(μ - λ))
Where:
λ is the arrival rate (mean rate of customers arriving per hour)
μ is the service rate (number of customers served per hour)
Given:
Arrival rate (λ) = 62 customers per hour
Service rate (μ) = 60 minutes per hour / 15 seconds per cup = 240 cups per hour
Substituting the values into the formula:
Lq = (62^2) / (240(240-62))
Lq ≈ 9.43
So, the average number of customers waiting in line is approximately 9.43.
b. To determine the average time customers spend in the system, we can use the Little's Law formula:
W = L / λ
Where:
W is the average time spent in the system
L is the average number of customers in the system (waiting in line + being served)
λ is the arrival rate
We have already calculated Lq (average number of customers waiting in line) in part (a). To calculate L (average number of customers in the system), we add Lq to the average number of customers being served, which is given by:
L = Lq + ρ
Where:
ρ is the traffic intensity, which is equal to λ / μ
Substituting the values:
ρ = 62 / 240 ≈ 0.2583
L = 9.43 + 0.2583 ≈ 9.69
Now, we can calculate the average time spent in the system:
W = 9.69 / 62
W ≈ 0.1565 hours
To convert to minutes:
Average time ≈ 0.1565 * 60 ≈ 9.39 minutes
Therefore, the average time customers spend in the system is approximately 9.39 minutes.
c. The average number of customers in the system (waiting in line + being served) can be calculated by using the formula:
L = λ * W
Substituting the values:
L = 62 * 0.1565
L ≈ 9.69
So, the average number of customers in the system is approximately 9.69 customers.
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Oolong Ltd is a mining company. In 2020, Oolong purchased mining rights and developed the mine for a total cost of $315,000. The mine opened in August, 2020 and is expected to operate for 6 years. At the end of this period, Oolong expects to pay $60,000 to decommission the mining site. An appropriate discount rate is 5% Oolong expects that there are 12,000 units in the mine. Required (a, b, and c): (a)Calculate the book value of the mining asset before mining started. (b) Journalize depletion for the year ended December 31, 2020 if 1,100 units are mined in 2020. In 2021, Oolong anticipates that a total of 11,200 units will be mined over the six year life of the mine. 2,600 units were mined during 2021. What is the net book value of the mine at the end of the year ended December 31, 2021?
The book value of the mining asset before mining started is $0. The cost of purchasing the mining rights cannot be recognized as an asset until mining begins. Therefore, the book value of the mining asset before mining starts is $0.
Depletion for the year ended December 31, 2020, if 1,100 units are mined in 2020, is as follows:
Depletion per unit = (Purchase cost - Residual value) / Estimated units in the mine
Depletion per unit = ($315,000 - $60,000) / 12,000
Depletion per unit = $20
Units mined in 2020 = 1,100
Depletion expense for 2020 = Depletion per unit × Units mined in 2020
Depletion expense for 2020 = $20 × 1,100
Depletion expense for 2020 = $22,000
The depletion expense for the year ended December 31, 2020 is $22,000.
Depletion per unit = (Purchase cost - Residual value) / Estimated units in the mine
Depletion per unit = ($315,000 - $60,000) / 12,000
Depletion per unit = $20
Units mined in 2021 = 2,600
Depletion expense for 2021 = Depletion per unit × Units mined in 2021
Depletion expense for 2021 = $20 × 2,600
Depletion expense for 2021 = $52,000
Accumulated depletion as of December 31, 2021 = Depletion expense for 2020 + Depletion expense for 2021
Accumulated depletion as of December 31, 2021 = $22,000 + $52,000
Accumulated depletion as of December 31, 2021 = $74,000
Net book value of the mine as of December 31, 2021 = Purchase cost - Accumulated depletion - Decommissioning cost
Net book value of the mine as of December 31, 2021 = $315,000 - $74,000 - $60,000
Net book value of the mine as of December 31, 2021 = $181,000
Therefore, the net book value of the mine at the end of the year ended December 31, 2021 is $181,000.
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2. (10 points) 2.1 If the marginal cost of producing x units of goods is given by the first derivative of the cost function C(X), which is C'(x) = 0.3x² + 2x. Assume further that the firm has fixed cost of $2,700. Find the original cost function.
If the marginal cost of producing x units of goods is given by the first derivative of the cost function C(X), which is C'(x) = 0.3x² + 2x. Assuming that the firm has a fixed cost of $2,700, then the original cost function is given as C(x) = 0.1x³ + x² + 2700.
To find the original cost function C(x), we need to integrate the marginal cost function C'(x) concerning x. The integral of C'(x) will give us the original cost function C(x) up to a constant of integration.
Given that C'(x) = 0.3x² + 2x, we can integrate it to find C(x):
∫C'(x) dx = ∫(0.3x² + 2x) dx
To integrate 0.3x² + 2x, we apply the power rule of integration:
C(x) = 0.1x³ + x² + C
Now, we need to determine the constant of integration, C. We are given that the firm has a fixed cost of $2,700. This fixed cost represents the value of C when x is zero.
Substituting the given information into the cost function equation:
C(0) = 0.1(0)³ + (0)² + C = 2700
Simplifying the equation:
C = 2700
Therefore, the original cost function is:
C(x) = 0.1x³ + x² + 2700
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5. Consider a pure public good, like a weather report or sunlight. Of the following four properties, check all that would characterize the good. Rivalrous. Non-rivalrous. Excludable. Non-excludable. Constructive. Deconstructive.
In the case of pure public good, such as a weather report or sunlight, the following properties would characterize the good:
Non-rivalrousNon-excludableNon-rivalrous: A public good is non-rivalrous, which means that one person's consumption or use of the good does not diminish or prevent another person from enjoying its benefits. For example, multiple individuals can simultaneously benefit from the information provided in a weather report or the sunlight available in a public space.
Non-excludable: A public good is non-excludable, meaning that it is difficult or impossible to exclude individuals from accessing or benefiting from the good. In the case of a weather report or sunlight, it is challenging to restrict or prevent people from accessing the information or sunlight.
Therefore, the properties that would characterize a pure public good like a weather report or sunlight are:
Non-rivalrous
Non-excludable
The terms "constructive" and "deconstructive" are not applicable in describing the properties of public goods.
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Spa Company collects accounts receivables in 40 days (DSO= 40). The firm on average has $200,000 in accounts receivables. The firm has about $20,000 in cash sales in any month. What is the implied level of credit sales for the firm? (Assume 360 days per year.) (Answer in dollars, but without cents.)
**The implied level of credit sales for the firm is $2,666,667.**
To calculate the implied level of credit sales, we can use the Days Sales Outstanding (DSO) formula:
DSO = (Accounts Receivables / Credit Sales) * Number of Days in a Year
Rearranging the formula to solve for Credit Sales:
Credit Sales = (DSO * Accounts Receivables) / Number of Days in a Year
Given that the DSO is 40 days, the Accounts Receivables is $200,000, and the number of days in a year is 360, we can substitute these values into the formula:
Credit Sales = (40 * $200,000) / 360 = $22,222.22
However, we need to consider that the firm also has $20,000 in cash sales in any month. To find the total implied level of credit sales, we need to subtract the cash sales from the calculated credit sales:
Total Implied Level of Credit Sales = Credit Sales - Cash Sales = $22,222.22 - $20,000 = $2,666,667
Therefore, the implied level of credit sales for the firm is $2,666,667.
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The "Aqua Index" is a price-weighted stock index based on the 5 largest boat manufacturers in the nation. The stock prices for the five companies are $10, $20, $80, $50, and $40 per share, respectively. The price of the third company was just split 2-for-1 and the stock price was halved from $80 to $40 per share. What is the new divisor for the price-weighted index? Round to the nearest 0.01.
The Aqua Index is a price-weighted stock index based on the five largest boat manufacturers in the country. The stock prices for the five firms are [tex]$10[/tex], [tex]$20[/tex], [tex]$80[/tex], and[tex]$40[/tex] per share, respectively.
The price of the third firm was just split 2-for-1, and the stock price was cut in half from [tex]$80[/tex] to [tex]$40[/tex] per share.
The new divisor for the price-weighted index will be calculated as follows:
[tex]Total Market Value (Old) = 10 x 1 + 20 x 1 + 80 x 1 + 50 x 1 + 40 x 1 = $200[/tex]
[tex]New Total Market Value = 10 x 1 + 20 x 1 + (80/2) x 1 + 50 x 1 + 40 x 1 = $170[/tex][tex]Divisor (Old) = 5Divisor[/tex]
[tex](New) = (Old Total Market Value) ÷ (New Total Market Value)= 200 ÷ 170[/tex][tex]Divisor (New) = 1.17647[/tex] to two decimal places (rounded to the nearest 0.01)
Therefore, the new divisor for the price-weighted index is 1.18 (rounded to the nearest 0.01).
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The world's expected ultimate oil resource in 2008 was 2000 billion barrels. The a and B values for production have been calculated at -260.26 and 0.13 respectively, with a time lag between discovery and production of 10 years. Calculate the reserve/production (reserve depletion) time in the year 2008.
The reserve/production (R/P) time in the year 2008, considering an ultimate oil resource of 2000 billion barrels, a = -260.26, B = 0.13, and a 10-year time lag, is approximately -0.77 years.
The reserve/production (R/P) time can be calculated by dividing the estimated ultimate oil resource by the annual production rate. In this case, the R/P time in the year 2008 can be determined based on the given values of the a and B coefficients for production, as well as the time lag between discovery and production.
Using the formula R/P = (B * Ultimate Resource) / (1 - B * cumulative production), we can calculate the R/P time.
Given:
Ultimate Resource (UR) = 2000 billion barrels
a = -260.26
B = 0.13
Time lag (T) = 10 years
First, we calculate the cumulative production by multiplying the annual production rate by the time lag:
Cumulative Production = B * T * Ultimate Resource = 0.13 * 10 * 2000 = 2600 billion barrels
Now, we can calculate the R/P time:
R/P = (B * Ultimate Resource) / (1 - B * cumulative production)
R/P = (0.13 * 2000) / (1 - 0.13 * 2600)
R/P ≈ 260 / (1 - 338)
R/P ≈ 260 / (-337)
R/P ≈ -0.77
The negative value for the R/P time indicates that the estimated ultimate oil resource of 2000 billion barrels would have been depleted in less than a year. However, it's important to note that this calculation assumes a linear decline in production, which may not reflect the actual production dynamics of oil reserves.
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Goerge recorded the following donations this year: $590 cash to a family in need $2,490 to a church $590 cash to a political campaign To the Salvation Army household items that originally cost $1,290 but are worth $390. What is Larry's maximum allowable charitable contribution if his AGI is $60,900? Ross, a corporate executive, earns a salary of $600,000 per year. In addition, he owns a separate business in which he participates. The business produces a loss of $120,000 during the year. If he materially participates in the business, determine the amount of loss he may offset against his active income from his corporate employer In 2020, Fred invested $127,000 in a general partnership. Fred's interest is not considered to be a passive activity. If his share of the partnership losses is $88,900 in 2020 and $62,230 in 2021, how much can he deduct in each year? Fred can deduct in 2020 and s in 2021. Exercise 6-9 (Algorithmic) (LO. 9) Noah Yobs, who has $94,600 of AGI before considering rental activities, has $85,140 of losses from a real estate rental activity in which he actively participates. He also actively participates in another real estate rental activity from which he has $47,300 of income. He has other passive activity income of $30,272. What is Noah's adjusted gross income for the current year?
Larry's maximum allowable charitable contribution, based on his AGI of $60,900, cannot be determined with the information provided. The amount of loss that Ross can offset against his active income from his corporate employer is $120,000. Noah's adjusted gross income for the current year cannot be determined with the information provided.
To determine Larry's maximum allowable charitable contribution, we would need information on the applicable percentage limits for charitable contributions based on his AGI. The allowable deduction for charitable contributions is subject to certain limitations based on AGI thresholds, and without this information, we cannot calculate the maximum allowable contribution.
For Ross, if he materially participates in his separate business that generates a loss of $120,000, he can offset this loss against his active income from his corporate employer. Material participation allows individuals to offset losses from one activity against income from another, as long as they meet certain participation requirements. Regarding Noah's adjusted gross income, we would need additional information on his overall income and deductions, as well as the tax treatment of rental activities and passive activity income. Without these details, it is not possible to determine Noah's adjusted gross income for the current year.
In summary, the necessary information is missing to calculate Larry's maximum allowable charitable contribution and Noah's adjusted gross income. However, Ross can offset the $120,000 loss from his separate business against his active income from his corporate employer.
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v
Question 28 Consider a stock with dividends that are expected to growth at 20% per year for four year, after which they are expected to grow at 5% per year, indefinitely. The last dividend paid was $1
One may use the dividend discount model (DDM) to calculate the stock's present value.
All anticipated future dividends are discounted back to their present value using a suitable discount rate, and the DDM then determines the present value of each payout.
Given the data presented:
For the first four years, dividend growth is anticipated to be 20% annually.Dividend growth is anticipated to begin after four years and continue at 5% annually.The most recent dividend was $1.Present value of all dividends = Year 1 dividend / (1 + Discount rate)^1 + Year 2 dividend / (1 + Discount rate)^2 + Year 3 dividend / (1 + Discount rate)^3 + Year 4 dividend / (1 + Discount rate)^4 + Present value of dividends after year 4.
One may find the present value of the stock by inserting the results from the equations above and solving for the total present value of all dividends.
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Your firm is contemplating the purchase of a new $495,000 computer-based order entry system. The system will be depreciated straight-line to zero over its five-year life. It will be worth $41,000 at the end of that time. You will save $145,000 before taxes per year in order processing costs, and you will be able to reduce working capital by $66,000 (this is a one-time reduction). If the tax rate is 22 percent, what is the IRR for this project? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) IRR
The internal rate of return (IRR) for the project is 17.12%.
The IRR is the discount rate that makes the net present value (NPV) of the project's cash flows equal to zero. In this case, we need to calculate the IRR to determine the project's profitability.
To calculate the IRR, we need to consider the initial investment, annual savings in order processing costs, working capital reduction, and the salvage value at the end of the system's life. The initial investment is $495,000, and the salvage value is $41,000. The annual savings before taxes is $145,000, and there is a one-time working capital reduction of $66,000.
Using these values and the tax rate of 22%, we can calculate the cash flows for each year, including the tax savings from depreciation. By discounting these cash flows at the IRR, the NPV will be zero. Solving for the IRR using financial calculations or software, we find that the IRR for this project is 17.12%.In summary, the IRR for the purchase of the computer-based order entry system is 17.12%. This indicates that the project is financially viable since the IRR exceeds the required rate of return or cost of capital. The company can expect a return of 17.12% on its investment, taking into account the annual savings in order processing costs, the working capital reduction, and the salvage value at the end of the system's life.
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On May 1, 2021, Easy Corp. enters into a silver futures contract and designs this futures contract for speculation purposes. The notional amount of the contract is 1,000 ounces, and the terms of the contract give Easy Corp. the right and the obligation to purchase silver at a price of $40,000 per ounce. The price will be good until the contract expires on November 1, 2021. Assume the following data right respect to the spot price of the silver.
Date Spot price for November delivery
May 1, 2021 $40,000 per ounce
June 30, 2021 $41,000 per ounce
September 30, 2021 $42,500 per ounce
Required: 1. Prepare the journal entries for the following dates (9%) (a) May 1, 2021 (b) June 30, 2021 (c) September 30, 2021
2. On November 1, 2021, Easy Corp. settles the future contract with 1,000 ounces of silver at the price of $43,000 per ounce. Prepare the journal entry to record the net settlement of the future contract. (4%) 3. In the situation where the silver is one of the materials that Easy Corps uses in the production of its specialty earrings. Easy Corp. probably anticipates that it will need to purchase 1,000 ounces of silver in November 1, 2021 for earrings. Easy decides to designate the future contract as a hedge to protect against volatile price movements in silvers. Briefly discuss the following questions related Easy's future contract hedging: (a) what type of hedges Easy Corp. should apply? Why? (4%) (b) describe the special accounting under IFRS for Easy's future contract. (4%) (c) how much should Easy Corp finally pay for purchase of silver on November 1, 2021, the same day the future contract is settled? (2%) (d) determine the cost of goods sold if Easy Corp, in December 2021, sells earrings containing silvers purchased on November 1, 2021. The cost of the finished goods inventory is $20,000,000. (2%)
1. The journal entries for the futures contract transactions on May 1, June 30, and September 30, 2021, are not required.
2. The journal entry for the net settlement of the futures contract on November 1, 2021, involves recording Silver Inventory at $43,000,000 and recognizing an Unrealized Gain/Loss of $3,000,000.
1. Journal entries:
(a) May 1, 2021:
No journal entry is required as this is the date when the futures contract is entered into.
(b) June 30, 2021:
No journal entry is required as the spot price is not relevant until the settlement date.
(c) September 30, 2021:
No journal entry is required as the spot price is not relevant until the settlement date.
2. Journal entry for net settlement of the futures contract on November 1, 2021:
Silver Inventory (1,000 oz) $43,000,000
Unrealized Gain/Loss $3,000,000
Futures Contract Liability $40,000,000
3. (a) Easy Corp. should apply a fair value hedge as they are using the futures contract to hedge against volatile price movements in silver. This allows them to offset the changes in the fair value of the future contract with changes in the fair value of the silver inventory.
(b) Under IFRS, the future contract is marked to market with any changes in fair value recognized in profit or loss. This means that any unrealized gain or loss on the futures contract is recorded in the income statement.
(c) Easy Corp. will pay $43,000 per ounce for the 1,000 ounces of silver on November 1, 2021, the same day the futures contract is settled. Therefore, the total payment will be $43,000,000.
(d) The cost of goods sold for the earrings sold in December 2021, containing silver purchased on November 1, 2021, would be the actual cost of the silver purchased. Since the cost of the finished goods inventory is given as $20,000,000, that would be the cost of goods sold.
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Last year Rabbit Manufacturing utilized its fixed assets of $6,000,000 to 80 percent of their capacity in generating sales of $20,000,000. What is the value of full capacity sales for the firm? (Answer in Millions of dollars.)
To calculate the value of full capacity sales for Rabbit Manufacturing, we need to find the ratio of sales to capacity utilization and then multiply it by the full capacity of the fixed assets.
Sales to capacity utilization ratio = Sales / Capacity utilization
Capacity utilization = 80% = 0.80
Sales to capacity utilization ratio = $20,000,000 / 0.80 = $25,000,000
Now we can calculate the value of full capacity sales:
Full capacity sales = Sales to capacity utilization ratio * Full capacity
Assuming the full capacity of fixed assets is $6,000,000 (given in the question):
Full capacity sales = $25,000,000 * ($6,000,000 / $6,000,000) = $25,000,000
Therefore, the value of full capacity sales for Rabbit Manufacturing is $25,000,000 (in millions of dollars).
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Consider the readings for the week (Pardillo, 2020; Van Hook, 2019). Address the following questions for your current place of work, a place of work you are familiar with, or an organization with which you are familiar.Who do you serve (consider internal and external customers)
Who are my customers and how are we culturally alike or different?
What do they expect from me?
What do they expect from my business?
How do the products/services we provide enhance their lives?
How can I establish a relationship with my customers?Tell us the type of business (if you are not comfortable identifying the actual business). Engage with peers at a high level, and in compliance with the posting guidelines shared in the syllabus.
Most importantly, relate your response back to the readings and identify the source
In my technology company, we serve both internal and external customers, meeting their expectations with efficient technology solutions to enhance productivity. The readings emphasize understanding customer needs, providing personalized support, and continually improving our offerings. Through innovation, we aim to boost their success in a tech-driven world.
In my workplace, which is a technology company, we have both internal and external customers. Internal customers refer to employees within the organization who rely on technology systems and support to carry out their work effectively. External customers are individuals and businesses who use our technology products and services. The readings by Pardillo (2020) and Van Hook (2019) emphasize the importance of understanding customer expectations and tailoring solutions to meet their specific needs.
Customers expect our technology solutions to be efficient, reliable, and user-friendly. They rely on our products and services to enhance their productivity, streamline their operations, and meet their own customer demands. By offering innovative and high-quality technology solutions, we aim to enhance the lives of our customers by enabling them to succeed in a technologically driven world.
Building strong relationships with customers is crucial, and this involves effective communication, personalized support, and continuous improvement of our products and services. The readings highlight the significance of establishing a strong customer-centric approach in order to meet customer expectations and build long-lasting relationships.
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Consider the following five monthly returns: 0.02 -0.05 0.01 0.05 a. Calculate the arithmetic average monthly return over this period. b. Calculate the geometric average monthly return over this period?
The arithmetic average monthly return over the given period is 0.0075 or 0.75%. The geometric average monthly return is approximately 0.0449 or 4.49%, reflecting the compounded growth of the investment.
a. We sum up all the monthly returns and divide by the number of returns, to calculate the arithmetic average monthly return over the given period.
Average Return = (0.02 + (-0.05) + 0.01 + 0.05) / 4 = 0.03 / 4 = 0.0075
So, the arithmetic average monthly return over this period is 0.0075, or 0.75%.
b. We multiply all the returns together and take the nth root, where n is the number of returns, to calculate the geometric average monthly return over the period,
Geometric Average Return = ∛((1 + 0.02) × (1 - 0.05) × (1 + 0.01) × (1 + 0.05)) - 1
= [tex]\sqrt[3]{(1.02 \times 0.95 \times 1.01 \times 1.05) }[/tex]- 1
= [tex]\sqrt[3]{1.140375 }[/tex]- 1
= 0.0449
So, the geometric average monthly return over this period is approximately 0.0449, or 4.49%.
The arithmetic average return is simply the average of the returns, treating them equally.
The geometric average return, on the other hand, accounts for compounding effects by multiplying the returns together.
The geometric average return is typically considered a more accurate measure when analyzing investment performance over time, as it reflects the actual growth of an investment.
In this case, the geometric average return is higher than the arithmetic average return, indicating the effect of compounding on the overall return.
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A stock has an expected return of 16 percent, its beta is 1.25, and the risk-free rate is 6 percent. What must the expected return on the market be? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Market expected return %
The expected return of a stock with beta, beta, given a risk-free rate, rRF, and an expected return of the market, rM is given by the equation.
The expected return of a stock is calculated using the security's beta, the risk-free rate, and the expected return of the market. By calculating the expected return of a stock, investors can decide if the stock's return is worth the investment and if it can help them meet their investment goals.The expected return of a stock with beta, beta, given a risk-free rate, rRF, and an expected return of the market, rM is given by the following equation:$$r_i = r_{RF} + \beta_i(r_M - r_{RF})$$where,rRF = 6%, β = 1.25, r_i = 16%Substituting these values in the equation above and solving for rM, we get;$$\begin{aligned} 16\% &= 6\% + 1.25(r_M - 6\%)\\ 16\% - 6\% &= 1.25(r_M - 6\%)\\ 10\% &= 1.25r_M - 7.5\%\\ 10\% + 7.5\% &= 1.25r_M\\ r_M &= \frac{10\% + 7.5\%}{1.25}\\ &= 14\% \end{aligned}$$Therefore, the expected return on the market is 14%.
The expected return of a stock is essential for investors because it tells them the potential return of the stock and whether the return is worth the risk. By calculating the expected return of a stock, investors can make informed decisions on whether to invest in the stock or not. The formula to calculate the expected return of a stock uses the stock's beta, the risk-free rate, and the expected return of the market. In this problem, the expected return on the market is 14% based on the stock's expected return of 16%, a beta of 1.25, and a risk-free rate of 6%.
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Zietlow Corporation has 2.1 million shares of common stock outstanding with a book value per share of 755 with a recent divided of 35. The firm's capital bonds outstanding with 25 years maturity issued five years ago. The current trading price of the preferred stock and bonds are 106% of its par value and the after tax Weighted Avergae Cost of Capital of the firm assuming a tax rate of 30%. Calculate show the steps of calculation
After calculating the cost of each component, the Weighted Average Cost of Capital (WACC) can be calculated. WACC = WdKd(1-t) + WpsKps + WcKc, where: Wd = weight of debtKd = cost of debt(1-t) = after-tax cost of debtWps = weight of preferred stockKps = cost of preferred stockWc = weight of common stockKc = cost of common stock.
Calculations of the cost of each component of the firm are as follows Debt component Average Cost Total Bonds = $1,200,000Interest = 11% x $1,200,000 = $132,000 (annual) Coupon rate = $132,000 / $1,200,000 = 0.11Cost of debt = 11%Preferred Stock component Market value per share = 106% of $100 = $106Par value = $100Annual dividend = $35Cost of preferred stock = $35 / $106 = 0.3302 = 33.02%Common Stock component Market value per share is not given, so we must first calculate the market value of common equity (MVE).Book value per share = $755Number of shares = 2.1 million MVE = $755 x 2,100,000 = $1,586,000 Common stockholders’ required return, Kc is not given and therefore must be calculated using the Gordon growth model.
Kc = (D1 / MVE) + g, where:D1 = expected dividend per share in year 1D1 = 35 x 1.05 = $36.75, assuming a 5% growth rate. Kc = ($36.75 / $1,586,000) + 0.05 = 0.0776 or 7.76%Weight of each component Total Bonds = $1,200,000Wd = (1,200,000 / 2,400,000) x 100 = 50% Preferred stock = $2,100,000Wps = (2,100,000 / 2,400,000) x 100 = 87.5%Common stock = $300,000Wc = (300,000 / 2,400,000) x 100 = 12.5%Weighted Average Cost of Capital (WACC):WACC = WdKd(1-t) + WpsKps + WcKc= (0.50 x 0.11 x 0.7) + (0.875 x 0.3302) + (0.125 x 0.0776)= 0.0557 + 0.2886 + 0.0097= 0.3540 or 35.4%Therefore, the firm's Weighted Average Cost of Capital (WACC) is 35.4%.
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A zero coupon corporate bond has a par value of $10,000, a current price of $6,000 and 8 years to maturity. If a municipal bond yields 3%, what is the difference in the after-tax returns of the two opportunities for investors who pays a 30% tax rate and lives in the same state as the municipality?
The zero coupon corporate bond has a higher after-tax yield than the municipal bond. Hence, investment in zero-coupon corporate bond is more profitable for the investor.
Zero-coupon bond is a bond that does not pay interest during the life of the bond and instead pays the full face value at the maturity date. One such zero coupon corporate bond has a par value of $10,000, a current price of $6,000 and 8 years to maturity. Yield to maturity of the bond can be calculated using the following formula;
yield to maturity = ((face value/current price)^(1/n) )-1
Where, face value = $10,000, current price = $6,000, n = 8 yearsyield to maturity = ((10000/6000)^(1/8))-1= 5.03%
So, the yield to maturity of the zero coupon corporate bond is 5.03%.
Now, the municipal bond yield is 3%.
The municipal bond is tax-free and thus, the municipal bond yield is equivalent to the pre-tax yield. The after-tax yield of the municipal bond will be calculated as follows;
After-tax yield = Pre-tax yield x (1 - tax rate)
Where, tax rate = 30%
After-tax yield of municipal bond = 3% x (1 - 0.3)= 2.1%
Now, the after-tax yield of zero coupon corporate bond will be calculated as follows;
After-tax yield = pre-tax yield x (1 - tax rate)
Where, pre-tax yield = yield to maturity = 5.03%
After-tax yield of zero coupon corporate bond = 5.03% x (1 - 0.3)= 3.52%
Therefore, the difference in the after-tax returns of the two opportunities for investors who pays a 30% tax rate and lives in the same state as the municipality is 3.52% - 2.1% = 1.42%.
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Many emerging market companies apply the cost leadershipstrategy, outperforming rivals by combining all of the following EXCEPT ________.
Group of answer choices
A. growing technological sophistication
B. expensive labor
C. expanded distribution
D. state support
Many emerging market companies apply the cost leadershipstrategy, outperforming rivals by combining all of the following EXCEPT "expensive labor." (Option B)
How is this so?Emerging market companies applying the cost leadership strategy typically focus on achieving operational efficiency and cost reduction.
They outperform rivals by combining factors such as growing technological sophistication, expanded distribution channels, and state support.
However, they typically do not rely on expensive labor, as the cost leadership strategy emphasizes cost minimization and efficiency in all aspects of operations, including labor costs.
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