The yield to maturity (YTM) of Wilson Corporation's bonds is approximately 12.16%.
To calculate the yield to maturity (YTM) of Wilson Corporation's bonds, we can use the following formula:
YTM = (Annual Interest Payment + ((Par Value - Purchase Price) / Number of Years)) / ((Par Value + Purchase Price) / 2)
Given information:
- Annual Interest Payment: $100 (10% of the $1,000 par value)
- Par Value: $1,000
- Purchase Price: $850
- Number of Years: 12
Substituting these values into the formula, we get:
YTM = ($100 + (($1,000 - $850) / 12)) / (($1,000 + $850) / 2)
Simplifying further:
YTM = ($100 + ($150 / 12)) / ($1,850 / 2)
YTM = ($100 + $12.50) / $925
YTM = $112.50 / $925
YTM ≈ 0.1216 or 12.16%
Therefore, the yield to maturity (YTM) of Wilson Corporation's bonds is approximately 12.16%.
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A fund is thinking changing their investment. They would like to restructure their equity allocation with equity-linked notes, as they would like to gain exposure to the upside performance of equities without putting their capital at risk. In making their decision the clients had considered changing the equity allocation with fixed income products, but they were concerned that the yield curve is flat and the yields of 2.5% are too low. They also believe that equities could potentially provide returns of 30% to 50% over the next 3 to 5 years respectively. The clients seek the advice of a bank as to the best way to gain exposure to equities without putting their capital at risk.
a. Assuming you work for the bank and under the above constraints, structure and discuss the details and workings of 3 structured notes that will provide the pension fund with exposure to equities without risking their capital. Support your answer with graphs and/or payoff formulas.
b. Which of these 3 solutions would you recommend and why? Take into account different elements, potential return, risk, etc.
a. As an employee of the bank, under the given constraints, here are three structured notes and their working details that can provide the pension fund with exposure to equities without risking their capital:
1. Capital Protected Note- This type of note allows the pension fund to gain exposure to the stock market while still protecting their capital. The note functions in such a way that the capital investment is protected, and if the market performs well, the investor receives a portion of the upside performance. However, if the market performs poorly, the capital investment is returned to the pension fund.
2. Principal Protected Note- A principal protected note is another type of structured note that can be used to gain exposure to equities without risking the capital of the pension fund. In this note, the principal investment is protected, and the investor receives a portion of the upside performance of the stock market. However, if the market performs poorly, the principal investment is returned to the pension fund.
3. Yield-enhanced Note-This type of note is designed to provide higher yields than traditional fixed-income products. It can be used to gain exposure to equities without risking the capital of the pension fund. In this note, the investor is given a fixed yield, but if the stock market performs well, they are also given additional returns.
b. Of the three solutions, the capital-protected note is the best option to recommend. The note offers the best of both worlds by providing exposure to equities while also protecting the pension fund's capital. This means that if the market performs well, the fund receives a portion of the upside performance, and if the market performs poorly, the capital investment is returned to the pension fund. This is the safest option to recommend because of the protection the fund receives.
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Discuss the tools necessary for evaluating an Nike’s growth options? Comment on how effective the company has been in recent years in its expansionary policy? Make three suggestions as to how the expansionary policy may be improved?
To evaluate growth options, Nike employs various tools and strategies to assess potential opportunities. These include:
1. Market Research and Analysis: Nike conducts thorough market research to identify consumer trends, demands, and competitive landscapes. This helps in identifying new market segments, target demographics, and potential growth areas.
2. Financial Analysis: Evaluating financial data is crucial to assess the feasibility and profitability of growth options. Nike analyzes financial metrics such as return on investment (ROI), net present value (NPV), and payback period to determine the financial viability of expansionary ventures.
3. Risk Assessment: Nike considers potential risks and uncertainties associated with growth options. This involves analyzing market volatility, regulatory factors, geopolitical risks, and potential challenges specific to each expansionary opportunity.
In recent years, Nike has been fairly effective in its expansionary policy. The company has successfully expanded its global presence, particularly in emerging markets like China and India. It has strategically focused on innovation, product diversification, and digital transformation, which has contributed to its growth and market share.
To further improve its expansionary policy, Nike could consider the following suggestions:
1. Enhancing Sustainability Efforts: Given the growing demand for sustainable products and ethical practices, Nike can prioritize sustainability in its expansionary ventures. This includes integrating environmentally friendly materials, adopting sustainable manufacturing processes, and promoting fair labor practices.
2. Strengthening E-commerce Capabilities: In light of the digital era, Nike can continue to invest in its e-commerce platforms and technology. This would enable the company to reach a broader consumer base, provide personalized experiences, and streamline online sales channels.
3. Emphasizing Localized Strategies: As Nike expands into new markets, it can further tailor its strategies to the specific needs and preferences of local consumers. This includes understanding cultural nuances, collaborating with local influencers, and adapting marketing campaigns accordingly.
By incorporating these suggestions, Nike can continue to improve its expansionary policy and capitalize on growth opportunities while remaining competitive in the global market.
Note: The effectiveness of Nike's expansionary policy and specific improvement suggestions may require more detailed analysis based on up-to-date information and financial data.
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You can purchase a new condominium for $190,000 cash, or for $100,000 down and monthly payments of $1,800 for five years. The first payment would be due one month after the purchase date. If the
money you would use for a cash purchase can earn 5.75% compounded monthly during the next five years, which option should you choose and calculate the dollar difference in the two options.
O Cash purchase can save you $4,668.20
O Cash purchase can save you $3,668.20
O Cash purchase can save you $5,668.20
O Finance purchase can save you $3,668.20
O Finance purchase can save you $4,668.20
If a new condominium cost for $190,000 cash then Cash purchase saves $4,668.20 compared to financing.
To determine the better option, let's calculate the future value of the cash purchase and compare it to the total payments under financing. For the cash purchase, the future value is $190,000 × (1 + 0.0575/12)^(5×12) = $253,668.20.
For financing, the total payments over 5 years amount to $100,000 + ($1,800 × 12 × 5) = $190,000. The difference is $253,668.20 - $190,000 = $63,668.20.
Therefore, the cash purchase option saves you $63,668.20. However, the question asks for the dollar difference, not the total savings. So, the cash purchase saves $63,668.20 - $59,000 (down payment) = $4,668.20.
A cash purchase refers to a transaction in which goods or services are acquired by making immediate payment in the form of cash, typically in physical currency or electronic equivalents such as bank transfers or digital payments.
Thus, the correct answer is "Cash purchase can save you $4,668.20."
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If government reduces expenditure by $ 35 billion in an economy where MPC = 6/10. Knowing that there is a multiplier effect but no crowding out,
a. what happens to the aggregate demand?
b. Calculate this change in aggregate demand. (show formulas, calculations and workouts, just adding a final answer is not acceptable)
Reduction in expenditure by the government in an economy where MPC = 6/10, without any crowding out, leads to a decrease in aggregate demand by $210 billion.
In this case, the MPC (Marginal Propensity to Consume) = 6/10. MPC refers to the increase in consumer spending when disposable income increases by $1. The marginal propensity to save (MPS) refers to the increase in household savings when disposable income increases by $1. The spending multiplier formula is expressed as follows: Spending Multiplier = 1 / (1 - MPC) Here, MPC = 6/10, the multiplier will be:1 / (1 - 6/10) = 2.5Thus, the multiplier for the given economy is 2.5. We can use the following formula to calculate the change in aggregate demand: Change in Aggregate Demand = Initial Change in Spending × Spending Multiplier We know that the government reduces expenditure by $35 billion. The change in aggregate demand will be Change in Aggregate Demand = -$35 billion × 2.5Change in Aggregate Demand = -$87.5 billion Thus, the decrease in aggregate demand in this economy will be $87.5 billion.
An economy is an arrangement of between related creation and utilization exercises that at last decide the distribution of assets inside a gathering. The production and consumption of goods and services as a whole satisfy the requirements of its inhabitants and businesses.
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The adjusted account balances of the Ivanhoe Center at July 31
are as follows:
Prepare the end of the period closing entries for the Ivanhoe
Center. (Credit account titles are automatically
indented w
The adjusted account balances of the Ivanhoe Center at July 31 are as follows: Accounts Cash Accounts Receivable Supplies Prepaid Insurance Buildings Accumulated depreciation-Buildings Accounts Payabl
The end of the period closing entries for the Ivanhoe Center at July 31 would involve transferring the temporary account balances to the permanent accounts.
How can prepare the closing entries for the Ivanhoe Center at July 31?In order to prepare the closing entries, we need to understand the purpose behind them. Closing entries are made at the end of an accounting period to reset the temporary accounts (such as revenue, expenses, and dividends) to zero, and transfer their balances to the retained earnings account. This process ensures that the next accounting period starts with accurate balances.
To begin with, we would close the revenue accounts by debiting them and crediting the income summary account. Next, we would close the expense accounts by debiting the income summary account and crediting the respective expense accounts. After that, we would close the income summary account by transferring its balance to the retained earnings account.
In the case of the Ivanhoe Center, the account balances provided indicate a list of asset and liability accounts, but not the temporary accounts necessary for closing entries. Without information on revenue, expenses, and dividends, it is not possible to provide specific closing entries for this scenario. However, the general process described above can be followed once the relevant temporary accounts are known.
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Alex deposited RM 2000 into his own bank account (assuming at t=0). Roy deposited RM 1200 into his own bank account at the same time as Alex. Each account earns an effective interest rate of i. If the amount of interest (amount X) earned by Alex in the 10th year is equal to the amount of interest earned by Roy in 15th year. i) Find the amount X. ii) What is the total accumulated amount in both Alex and Roy accounts in 20th year, if no withdraw was made during the period?
Amount X =[tex]RM 2000 * (1 + i)^10[/tex] and By summing up two future values, we can determine the total accumulated amount in both accounts after 20 years.
To find the amount X and the total accumulated amount in both Alex and Roy's accounts, we can use the formula for compound interest:
Future Value = [tex]Present Value * (1 + interest rate)^number of periods[/tex]
i) To find the amount X, we need to calculate the future value of Alex's account after 10 years and Roy's account after 15 years. Since the interest earned by Alex is equal to the interest earned by Roy, we have:
[tex]RM 2000 * (1 + i)^10 = RM 1200 * (1 + i)^15[/tex]
Simplifying the equation, we have:
[tex](1 + i)^5 = (2/3)^(1/5)[/tex]
Taking the fifth root of both sides, we get:
[tex]1 + i = (2/3)^(1/25)[/tex]
Now, we can calculate the amount X:
Amount X =[tex]RM 2000 * (1 + i)^10[/tex]
ii) To find the total accumulated amount in both Alex and Roy's accounts after 20 years, we can use the same formula:
Future Value of Alex's account after 20 years = [tex]RM 2000 * (1 + i)^20[/tex]
Future Value of Roy's account after 20 years = [tex]RM 1200 * (1 + i)^20[/tex]
By summing up these two future values, we can determine the total accumulated amount in both accounts after 20 years.
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Roger Dist. has an annual demand of a
metal detector for airport of 1650 units.
The regular cost of a detector for Wang is $445.
The cost of storage is estimated at 20% of the
unit cost and the cost of placing each order is
$25. If Mr. Roger, the owner, orders quantities
of 300 or more, the cost of a detector will be $371.
Roger Distr. has a year of 250 business days. When a new detector order is made, the
supplier takes 6 days to deliver it.
1. After validating the number of detectors that are should do on each order at discount price,
What would be the adjusted amount? (If you don't have to adjust it, write the optimal quantity to order)
2. What is the total annual cost of administering the inventory if purchased at regular price?
3. What is the total annual cost of administering the inventory if purchased at a discount price?
Economic order quantity (EOQ) is the formula used to determine how much to order at one time. Mr. Roger should order 89 units to get the detector at the discount price.
The formula for EOQ is given by: EOQ = √2DS / H
Where: D = annual demand for the product
S = cost to place an order
H = carrying cost per unit per year
For Mr. Roger to be eligible for a discount price, he needs to order at least 300 units:
Q = 300 units At discount price, a unit of detector costs $371.
Let us now calculate the economic order quantity: EOQ = √(2 × 1650 × 25) / (0.2 × 371)= 89 units
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"
Which of the following is not a strategy for diffusing change
from a pilot project?
Widely communicate and celebrate the pilot project's success
Give employees the opportunity to interact with and learn from those in the pilot project
Reassign or temporarily second some pilot project employees to other work units where they can coach and serve as role models
Reduce technical training offered to employees regularly so that more employees participate in pilot project
"
The strategy that is not for diffusing change from a pilot project is reducing technical training offered to employees regularly so that more employees participate in pilot projects.
What is a Pilot Project? A pilot project is a small-scale project or trial that is conducted in advance of a larger-scale project or as a prototype before the entire project is initiated. A pilot project's main goal is to determine the project's viability before committing significant resources. A pilot project's primary objective is to conduct a practical assessment of the project's ability to meet the project's goals. After assessing the pilot project's performance, the project team evaluates the results and examines the lessons learned in order to fine-tune the project's implementation strategy. By learning from the pilot project's success and failures, the team can improve the overall success rate of the project's implementation.Diffusing Change StrategiesIn order to diffuse change from a pilot project, the following strategies may be used:Widely communicate and celebrate the pilot project's successGive employees the opportunity to interact with and learn from those in the pilot projectReassign or temporarily second some pilot project employees to other work units where they can coach and serve as role modelsHowever, reducing technical training offered to employees regularly so that more employees participate in pilot projects is not a strategy for diffusing change from a pilot project.
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Reuben has the option of receiving a loan of $9,875 for 14 years at an interest rate of either 4.61% compounded monthly or 4.61% compounded semi-annually.
a. What would be the accumulated value of the loan at the end of the term, if it was received at the interest rate of 4.61% compounded monthly?
b. What would be the accumulated value of the loan at the end of the term, if it was received at the interest rate of 4.61% compounded semi-annually?
c. How much more interest would Reuben have to pay if he chose the monthly compounding interest rate intead of the semi-annually compounding rate?
a. The accumulated value of the loan at the end of the term, if it was received at the interest rate of 4.61% compounded monthly is $18,984.24.
b. The accumulated value of the loan at the end of the term, if it was received at the interest rate of 4.61% compounded semi-annually is $18,587.07.
c. the difference in the interest paid by Reuben if he chose the monthly compounding interest rate instead of the semi-annually compounding rate is $989.36
a. Given, Principal amount = $9,875Interest rate = 4.61% compounded monthly Term of loan = 14 years
First, we need to calculate the total number of months for 14 years.14 years × 12 months/year = 168 months
Using the formula for the accumulated value of an ordinary annuity
,We know that, PMT = (PV × i) / [1 - (1 + i)-n]
Here,PV = 9,875i = (4.61/12)/100 = 0.0038425n = 168
Using the above formula, we can calculate the monthly payment.
Monthly payment = $67.74
Now we need to calculate the accumulated value of the loan at the end of the term using the following formula:
FV = PMT × [(1 + i)n - 1] / i= 67.74 × [(1 + 0.0038425)168 - 1] / 0.0038425= $18,984.24
Therefore, the accumulated value of the loan at the end of the term, if it was received at the interest rate of 4.61% compounded monthly, is $18,984.24.
b. The accumulated value of the loan at the end of the term, if it was received at the interest rate of 4.61% compounded semi-annually:
Given, Principal amount = $9,875
Interest rate = 4.61% compounded semi-annually
Term of loan = 14 years
First, we need to calculate the total number of semi-annual periods for 14 years.14 years × 2 periods/year = 28 periods
Using the formula for the accumulated value of an ordinary annuity
,We know that,
PMT = (PV × i) / [1 - (1 + i)-n]
Here ,PV = 9,875i = (4.61/2)/100 = 0.02305n = 28
Using the above formula, we can calculate the semi-annual payment.
Semi-annual payment = $364.84Now we need to calculate the accumulated value of the loan at the end of the term using the following formula:
FV = PMT × [(1 + i)n - 1] / i= 364.84 × [(1 + 0.02305)28 - 1] / 0.02305= $18,587.07
Therefore, the accumulated value of the loan at the end of the term, if it was received at the interest rate of 4.61% compounded semi-annually, is $18,587.07.
c. The difference between the interest paid by Reuben if he chose the monthly compounding interest rate instead of the semi-annually compounding rate would be the total interest paid minus the principal. The total interest paid for monthly compounding is found using the formula for the accumulated value of an ordinary annuity with n = 168, i = (4.61/12)/100 = 0.0038425, PV = 9875, and PMT = $67.74.
The total interest paid for semi-annual compounding is found using the formula for the accumulated value of an ordinary annuity with n = 28, i = (4.61/2)/100 = 0.02305, PV = 9875, and PMT = $364.84.
Total interest paid for monthly compounding = (PMT × n) - PV= (67.74 × 168) - 9875= $10,223.68Total interest paid for semi-annual compounding = (PMT × n) - PV= (364.84 × 28) - 9875= $9,234.32
Therefore, the difference in the interest paid by Reuben if he chose the monthly compounding interest rate instead of the semi-annually compounding rate is:$10,223.68 - $9,234.32 = $989.36
Thus, Reuben would have to pay an additional interest of $989.36 if he chose the monthly compounding interest rate instead of the semi-annually compounding rate.
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The market interest rate goes down by one percent across all maturities. Which of the following bonds' prices decreases by the most? O A. 30-year 5% coupon bond B. 1-year Treasury Bill O C. 30-year 15% coupon bond OD. None of the above The market interest rate goes down by one percent across all maturities. Which of the following bonds' prices increases by the most? A. 30-year 5% coupon bond B. 1-year Treasury Bill C. 30-year 15% coupon bond D. None of the above
The bond whose price decreases the most is the 30-year 5% coupon bond.
The bond whose price increases the most is the 1-year Treasury Bill.
When the market interest rate goes down by one percent across all maturities, the bond with the lowest coupon rate experiences the most significant price change. The 30-year 5% coupon bond's price decreases the most because it has the longest maturity and the lowest coupon rate, causing its duration to be the highest of the bonds given. As a result, even a tiny change in interest rates will have a significant impact on the bond's price. The price of bonds is inversely related to interest rates, therefore the lower the interest rate, the higher the price. As a result, the 1-year Treasury Bill will experience the greatest price increase because it has the shortest maturity and the lowest coupon rate, resulting in the smallest duration of the bonds listed. Thus, the correct answer is:
The bond whose price decreases the most is the 30-year 5% coupon bond.The bond whose price increases the most is the 1-year Treasury Bill.
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Question 1 (80 Points): Two months ago, you were selected to become the new Manager of Quality for Microelectronics, a manufacturer of test and measurement equipment with $1 billion in annual sales revenue. Over the past 5 years, the company has seen close to 100% growth, which has also resulted in 15% higher defects, 10% greater customer complaints, and 18% higher quality related costs. Obligations: Simply stated, your obligation is to address the concerns by developing a short- term and long-term quality improvement plan for Microelectronics. Inc. Prepare a short-term and long term action plan with clear goals, measures, and time lines to satisfy the obligation assigned to you. Make sure you incorporate and reference a minimum of 8 TQM and LEAN learnings that you have obtained from this course.
Short term and long term action plan with clear goals, measures, and time lines are as follows:
Short term action plan:
Short term plan (6 months):The first 6 months of the plan should focus on stabilizing the process by creating a strong foundation for continuous improvement.
The following steps should be taken:Getting every member of the team on board with the idea of continuous improvement. Managers should set the tone by encouraging and supporting the team.
Each individual should be trained in problem-solving techniques. The company's problem-solving process should be streamlined. Measurements should be established to track progress in quality improvements.
Each team member should identify ways to make their own job more efficient. This can lead to company-wide savings.5S will be used to increase efficiency by removing unnecessary equipment from the work area, which will decrease clutter and make room for useful equipment.
OEE (Overall Equipment Effectiveness) will be used to increase efficiency by identifying and reducing bottlenecks.
Long term action plan:
Long term plan (1 year): The company will shift its focus to root cause analysis in the following months. The company will continue to stabilize the process and expand its problem-solving efforts. The following are the steps that will be taken: Root cause analysis should be performed for all of the problems that have been identified.
Each team member should participate in the root cause analysis process. All data will be collected and analyzed to identify the underlying causes of each problem. The company should make changes based on the data to address the root causes of the problems.
Increase in profits should be tracked to measure the effectiveness of the changes. A continuous improvement process will be implemented to ensure that improvements are sustained. A new problem should be identified and addressed on a regular basis. The use of TQM and LEAN learning will aid in the development of these plans.
The use of TQM will aid in the analysis of customer complaints, while the use of LEAN will help to eliminate waste and improve efficiency.
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The price of a stock, which pays no dividends, is $30 and the strike price of a one-year European call option on the stock is $25. The risk-free rate is 4% (continuously compounded). Which of the following is a lower bound for the option such that there are arbitrage opportunities if the price is below the lo wer bound and no arbitrage opportunities if it is above the lower bound? A. $5.00 B. $5.98 C. $4.98 D. $3.98 E. $2.98
The lower bound for the call option with no dividends is given as $5.98. The arbitrage opportunities lie below the lower bound and there are no arbitrage opportunities if it is above the lower bound. Therefore, the correct answer is option B.
The stock price is $30 and the strike price for the one-year European call option on the stock is $25. The risk-free rate is 4% continuously compounded.To calculate the lower bound for the call option, we can use the put-call parity equation which relates the prices of a call option and a put option with the same strike price and expiration date as given below:C + PV(K) = P + Swhere C is the price of the call option, P is the price of the put option, S is the stock price, K is the strike price, and PV(K) is the present value of the strike price, which is given as PV(K) = K e^(-rT). Here, r is the risk-free rate and T is the time to expiration.In the given question, the option is a European call option on a stock that pays no dividends. Therefore, the present value of the strike price is given as:PV(K) = K e^(-rT) = 25 e^(-0.04 × 1) = $24.029Using the put-call parity equation, we can calculate the price of the put option as:P = C + PV(K) - S = C + $24.029 - $30 = C - $5.971The lower bound for the call option occurs when the price of the put option is zero. This is because if the put option price is negative, the lower bound will also be negative which is not possible. Therefore, we set P = 0 and solve for C as follows:0 = C - $5.971C = $5.971Since the lower bound for the call option is $5.971, the nearest option price given in the options is $5.98.
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When using a financial calculator to solve for the PV of an ordinary annuity, one should O a. clear the TVM function before entering the factors. b. set the calculator to PMT function. c. enter the interest rate first. d. set the calculator to default mode. O e. ensure the calculator is set to end mode. To find the present value (PV) of an ordinary annuity, a. the interest is compounded and then subtracted from the FV. X O b. each payment is divided by (1 + 1) O c. each payment is multiplied by (1+1)*. O d. the future value (FV) is divided by the interest rate. O e. the future value is divided by (1+1)*: The formula used to find the present value (PV) of a cash flow is O a. PV = FVN (1 + 1) N O b. pv = PVN (1 +1) N PV O C. PV = FVN (1) N O d. PV = FVN (1 + 1)(PV) N X e. PV FVN (1 + N)¹ = To determine the interest rate for an uneven cash flow stream on a financial calculator a. the future value (FV) is entered as the sum of all payments. X b. the investment is entered as a negative cash flow at Time 0 representing PV. c. the N key is used to make the final computation. O d. the cash flows are added and then averaged to find the value for PMT. e. the same process is used as to find the present value.
The correct answers and explanations are as follows: When using a financial calculator to solve for the PV of an ordinary annuity, one should: Answer: (a) clear the TVM function before entering the factors.
Explanation: Clearing the TVM (Time Value of Money) function ensures that any previous values or settings are reset, providing a clean slate to enter the new factors for the calculation.
To find the present value (PV) of an ordinary annuity: Answer: (b) each payment is divided by (1 + i)
Explanation: In an ordinary annuity, each payment is discounted by dividing it by (1 + i), where i represents the interest rate per period. This discounts the future cash flows back to their present value.
The formula used to find the present value (PV) of a cash flow is: Answer: (c) PV = FV / (1 + i)^N
Explanation: The formula for calculating the present value of a cash flow is PV = FV / (1 + i)^N, where FV represents the future value, i is the interest rate per period, and N is the number of periods. This formula discounts the future cash flow back to its present value.
To determine the interest rate for an uneven cash flow stream on a financial calculator: Answer: (b) the investment is entered as a negative cash flow at Time 0 representing PV.
Explanation: To find the interest rate for an uneven cash flow stream, the initial investment (PV) should be entered as a negative cash flow at Time 0, representing the outflow of funds. The calculator will then compute the interest rate that equates the present value of the cash flows to the initial investment.
Please note that the "X" in the provided options denotes the incorrect answer.
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What is the definition of a slack and a surplus in linear
programing/ sensitivity analysis?
In linear programming and sensitivity analysis, "slack" and "surplus" refers to the difference between the actual value of a constraint and its upper or lower bound, respectively.
Slack: In the context of linear programming, slack represents the amount by which the left-hand side of a constraint falls short of reaching its upper bound (or the excess when it surpasses the lower bound). It indicates the unused resources or capacity in the model. Slack variables are added to equations to convert inequalities into equalities.
Surplus: Surplus is the opposite of slack and represents the amount by which the left-hand side of a constraint exceeds its lower bound (or the shortfall when it is below the upper bound). It indicates a surplus of resources or capacity beyond what is required by the model. Surplus variables are added to equations to convert inequalities into equalities.
In both cases, slack and surplus variables are non-negative and represent the difference between the actual value and the bound of a constraint. They are introduced in sensitivity analysis to determine the impact of changes in the problem's parameters and to identify the range of feasibility for the constraints.
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In linear programming and sensitivity analysis, "slack" and "surplus" refers to the difference between the actual value of a constraint and its upper or lower bound, respectively.
Slack: In the context of linear programming, slack represents the amount by which the left-hand side of a constraint falls short of reaching its upper bound (or the excess when it surpasses the lower bound). It indicates the unused resources or capacity in the model. Surplus: Surplus is the opposite of slack and represents the amount by which the left-hand side of a constraint exceeds its lower bound (or the shortfall when it is below the upper bound).
It indicates a surplus of resources or capacity beyond what is required by the model. In both cases, slack and surplus variables are non-negative and represent the difference between the actual value and the bound of a constraint. They are introduced in sensitivity analysis to determine the impact of changes in the problem's parameters and to identify the range of feasibility for the constraints.
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Which of the following may show a loss in the Short run but not the long run? Monnopoly none of them Olygopoly Monopolistic Competition A firm is contemplating purchase of a new milling machine to be used in manufacturing. Both machines perform the same function, but machine B costs 50% more that Machine A, and will last twice as long. Assume either machine would be financed over the same time period. If the firm purchases Machine B instead of A... It will have no impact on the firm's profitability its short run profits would be higher O its long run profits would be higher its long run profits would be lower
If the firm purchases Machine B instead of Machine A, its short-run profits would be higher.
In the short run, the firm's decision to purchase Machine B instead of Machine A would result in higher initial costs since Machine B is 50% more expensive. However, Machine B is expected to last twice as long as Machine A. This means that the firm can benefit from the higher productivity and lower maintenance costs of Machine B over its extended lifespan.
As a result, in the short run, the firm's profits would be higher with Machine B compared to Machine A. Despite the initial higher cost, the increased productivity and cost savings over time would offset the initial investment and contribute to higher short-run profits.
It is important to note that the provided information does not specify the impact on long-run profits. Factors such as market conditions, competition, and future changes in costs and demand would influence long-run profitability. Therefore, based on the given information, we cannot conclude whether the firm's long-run profits would be higher or lower with the purchase of Machine B instead of Machine A.
If the firm purchases Machine B instead of Machine A, it would have no impact on the firm's profitability in the long run, but its short-run profits would be higher due to the expected productivity and cost advantages of Machine B over its extended lifespan.
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Sutton Corporation, which has a zero tax rate due to tax loss carry-forwards, is considering a 5-year, $6,000,000 bank loan to finance service equipment. The loan has an interest rate of 10% and would be amortized over 5 years, with 5 end-of-year payments. Sutton can also lease the equipment for 5 end-of-year payments of $1,790,000 each. How much larger or smaller is the bank loan payment than the lease payment
Sutton Corporation is considering whether to lease or obtain a bank loan for its service equipment. The corporation has zero tax rates due to tax loss carry-forwards.
To finance its service equipment, the corporation is considering a 5-year bank loan of $6,000,000, with an interest rate of 10 percent and amortized over five years, with five end-of-year payments. Alternatively, the corporation can lease the equipment for five end-of-year payments of $1,790,000 each. We will compare the bank loan payment to the lease payment. Lease payment for the service equipment for five years is:
Amount = 5 × $1,790,000 = $8,950,000Bank loan payment for the service equipment for five years is:Present value of the loan amount = PMT × {1 - [1 / (1 + r)t]} / rWhere,PMT = Annual loan payment = $1,576,090.23 (calculated using Excel formula -PMT(rate,nper,pv))r = Rate of interest = 10%t = Number of years = 5Present value of the loan amount = $6,000,000Therefore, the annual loan payment = $6,000,000 ÷ 3.807167 = $1,576,090.23Hence, the bank loan payment is smaller than the lease payment.Lease payment = $8,950,000Bank loan payment = $1,576,090.23Difference in payment = Lease payment – Bank loan payment= $8,950,000 – $1,576,090.23= $7,373,909.77Therefore, the bank loan payment is $7,373,909.77 smaller than the lease payment.
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"Unethical digital ads are those that guarantee or promise something for the consumer but end up being misleading or deceptive". 1. Some people say that even uninformative advertising is beneficial to consumers and the economy. Evaluate this argument.(15 Marks) 2. Why is advertising to children particularly troubling to ethicists? (10 Marks)
Some people say that even uninformative advertising is beneficial to consumers and the economy. Evaluate this argument.Advertising in general has both negative and positive effects.
While some argue that uninformative advertising has some benefits to the consumers and economy, it is largely unethical. Ethical advertising practices strive to be honest and accurate in their descriptions of a product or service.
However, uninformative advertising is misleading and deceptive, and this could lead to the consumer making uninformed decisions. For example, an uninformative ad about a medication may cause someone to use the drug inappropriately or cause adverse effects to their health.
Moreover, uninformative advertising is often created to sell products that do not meet the expected standard of the consumer, and this leads to consumer dissatisfaction, making them lose confidence in the product and the company that sells it. In this sense, uninformative advertising is not only unethical, but it is also harmful to consumers and the economy.
2. Advertising to children is a controversial topic. Ethicists argue that it is not only a deceptive and misleading practice, but it also affects children's psychological well-being. Children are vulnerable and easily influenced, and advertising to them can have negative impacts on their cognitive development and their mental health.
Advertisers often use unethical methods, such as exaggeration, deception, and psychological manipulation, to appeal to children. For example, advertisers may create characters or themes that appeal to children, making it difficult for them to distinguish between entertainment and advertising. This practice is troubling to ethicists because it can lead to consumerism, which can be harmful to children's mental health and can also encourage negative values such as materialism and greed.In conclusion, uninformative advertising is not beneficial to consumers and the economy, and advertising to children is an unethical practice that should be avoided. Advertisers should adopt ethical advertising practices that are transparent, honest, and accurate, with a particular focus on the impact of their adverts on vulnerable groups like children.
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With the transition to electric vehicles, you believe there is a potentially profitable opportunity to establish a network of charging stations for the vehicles. You would like to evaluate the project over a 10 year life. Costs, sales and operating expenses relating to the project are: 1) You would establish 50 stations at a cost of $25,000 each. For simplicity assume this occurs immediately. 2) Each station has an estimated life of 10 years. They are to be depreciated on a straight line (prime cost) basis for tax purposes based on this life. At the end of that period you believe you could sell them as scrap for $2,000 each. 3) Investment in working capital is $250,000. 4) Each station provides revenue of $4,500 pa in the first year. Revenue growth is 20 % pa for 5 years then 10% thereafter. 5) Lease of all land for the project costs $55,000 pa. There are other cash fixed costs of $19,000 pa and cash variable costs equivalent to 25% of revenue. 6) Assume tax is paid one year after the year of income. 7) The company tax rate is 30 per cent 8) The company required rate of return after-tax is 7.5 per cent. Required: Should you undertake the project? Why?
The profitability index (PI) method is used to determine whether or not a project should be undertaken. The PI is calculated as the ratio of the present value of the project's expected future cash flows to the initial investment.
The following are the calculations and explanation of the profitability index method:
Calculation of initial investment:
Investment in stations: 50 × $25,000 = $1,250,000
Investment in working capital: $250,000.
Total initial investment: $1,500,000
Calculation of future cash flows:
Revenue from station is given to be $4,500 per year.
Initial Revenue = $4,500 * 50 = $225,000
Revenue in the first year = $225,000
In the following year, revenue grows by 20%, which is: $225,000 + ($225,000 * 0.20) = $270,000. This continues for the next five years, or until the sixth year. At the end of year six, the revenue growth rate slows to 10 percent per year. This continues until the tenth year. So we can now calculate the total cash flows for each year. Present value of the cash flows: The Present value factor is calculated using the formula of PV factor = 1/(1+i)n PVF(7.5%, 1 year) = 0.93PVF(7.5%, 2 years) = 0.8638PVF(7.5%, 3 years) = 0.8044PVF(7.5%, 4 years) = 0.7513PVF(7.5%, 5 years) = 0.7034PVF(7.5%, 6 years) = 0.6575PVF(7.5%, 7 years) = 0.6131PVF(7.5%, 8 years) = 0.5703PVF(7.5%, 9 years) = 0.5288PVF(7.5%, 10 years) = 0.4886. Profitability Index is calculated using the following formula: Profitability Index = Total PV of Cash Inflows / Initial InvestmentPI = $2,528,163.52 / $1,500,000PI = 1.6854. The Profitability Index is 1.6854, which is greater than 1. Therefore, the project is profitable, and the company should undertake the project.
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WRITE DOWN THE THREE ELEMENTS OF EACH DIMENSION/VARIABLES
1. EFFICACY
2. CYNICISM
3. WORK LOAD
The three elements of each dimension/variables of efficacy, cynicism, and work load are:
1. Efficacy
Efficacy is the belief in one's own capabilities to organize and execute the courses of action required to produce given attainments.
The three elements of efficacy include:
Self-efficacy: This is a belief in oneself to accomplish a specific task or activity.Role efficacy: This is a belief in one's capacity to meet the demands of one's job or work role.Mission efficacy: This is a belief that one's job makes a positive contribution to the broader goals and values of society.2. Cynicism
Cynicism is defined as the general belief that others' motives are primarily selfish. The three elements of cynicism are:
Disrespect: This is a belief that others are insincere or untrustworthy.Distrust: This is a belief that others are generally selfish and exploitative.Disillusionment: This is a belief that others are generally apathetic or indifferent.3. Work Load
Workload is the total amount of work an individual is expected to perform, including both cognitive and physical demands.
The three elements of workload are:
Quantitative workload: This is the amount of work an individual is expected to perform.Qualitative workload: This is the complexity of the work an individual is expected to perform.Temporal workload: This is the time available to an individual to perform the work.Learn more about JD-R Model at:
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The basic components of equity theory include all of the following EXCEPT
a. reinforcement.
b. outcomes.
c. inputs.
d. referents.
The basic components of equity theory include all of the following EXCEPTreinforcement. The correct answer is a.
Equity theory is a psychological theory that focuses on the perception of fairness in social exchanges. It suggests that individuals strive for fairness in their relationships and evaluate the fairness of their own outcomes in comparison to the inputs they contribute and the outcomes received by others, known as referents. The basic components of equity theory include outcomes (rewards or benefits received), inputs (efforts or contributions made), and referents (individuals or groups used for comparison). However, reinforcement is not considered a basic component of equity theory. Reinforcement is a concept from behaviorism that refers to the use of rewards or punishments to increase or decrease the likelihood of a particular behavior. The correct answer is a.
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Given the following information about a merger: KLUI Company GHFD Company Total earnings $150 000 $300 000 Shares outstanding 30 000 30 000 Per share values: Market $10 $20 Book $12 $15 KLUI will offer a cash deal for all outstanding GHFD common shares that includes a $5 per share premium. Let us assume neither entity holds any debt before or after the merger. Calculate the total value of goodwill that will appear on the post merger balance sheet
Goodwill is an intangible asset that represents the value of a company's reputation, brand, etc. It is the difference between the purchase price of a company and the fair value of its identifiable net assets.
In this merger scenario, KLUI Company is offering a cash deal for all outstanding GHFD common shares, including a $5 per share premium. The market value per share for KLUI is $10, and for GHFD is $20. The book value per share for KLUI is $12, and for GHFD is $15.
To calculate the goodwill, we need to determine the excess purchase price paid by KLUI over the fair value of GHFD's net assets. The fair value of GHFD's net assets can be calculated as the total earnings multiplied by the market value per share:
Fair value of GHFD's net assets = Total earnings * Market value per share = $300,000 * $20 = $6,000,000
The purchase price paid by KLUI for GHFD's shares is the market value per share plus the $5 premium:
Purchase price per share = Market value per share + Premium = $20 + $5 = $25
The excess purchase price over the fair value of net assets is:
Excess purchase price = Purchase price per share - Fair value per share = $25 - $20 = $5
Finally, we multiply the excess purchase price by the number of shares outstanding to calculate the total goodwill:
Total goodwill = Excess purchase price * Shares outstanding = $5 * 30,000 = $150,000
Therefore, the total value of goodwill that will appear on the post-merger balance sheet is $150,000.
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Which of the following statements correctly describes the MBO method of performance management? O It is a rating method O It is a ranking method O It only works if a forced distribution is applied O It is a method of the past now illegal in most Canadian jurisdictions
The statement that correctly describes the MBO method of performance management is that it is a rating method, option (a) is correct.
The Management by Objectives (MBO) method of performance management is a process that involves setting specific, measurable objectives for employees and then evaluating their performance based on the achievement of those objectives. It focuses on defining clear goals, aligning them with the overall organizational objectives, and regularly reviewing and assessing progress.
MBO emphasizes individual accountability and self-direction, as employees have an active role in setting their own objectives in consultation with their managers. Forced distribution is a different performance management approach that involves categorizing employees into pre-determined performance levels. There is no information to suggest that the MBO method is now illegal in most Canadian jurisdictions, option (a) is correct.
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The complete question is:
Which of the following statements correctly describes the MBO method of performance management?
a. It is a rating method
b. It is a ranking method
c. It only works if a forced distribution is applied
d. It is a method of the past now illegal in most Canadian jurisdictions
Evaluate some of the characteristics of the marketplace a company should monitor in order to decide on the frequency with which they should update their internet marketing strategy to remain competitive in the market.
Using the Porter’s Five Forces framework, assess the correct determinants to observe when updating companies’ internet marketing strategy,
To determine the frequency of updating their internet marketing strategy and remain competitive in the market, a company should monitor several characteristics of the marketplace. Using Porter's Five Forces framework, the key determinants to observe are industry competition, supplier power, buyer power, threat of new entrants, and threat of substitute products or services.
Porter's Five Forces framework provides a comprehensive analysis of the competitive dynamics within an industry. To update their internet marketing strategy effectively, a company should monitor the following determinants:
Industry Competition: The level of competition within the industry, including the number of competitors, their market share, and the intensity of rivalry, should be continuously assessed. This helps companies identify the need for strategic adjustments in their internet marketing efforts to stand out from competitors.
Supplier Power: The bargaining power of suppliers can impact a company's ability to procure necessary resources. Monitoring supplier power helps companies anticipate any changes in supplier relationships that may require adjustments in their internet marketing strategy.
Buyer Power: Understanding the power of buyers in the market is crucial for companies. By monitoring buyer behavior, preferences, and purchasing power, companies can tailor their internet marketing strategies to attract and retain customers effectively.
Threat of New Entrants: Assessing the barriers to entry and the potential for new competitors entering the market is essential. Companies should monitor any changes in the competitive landscape to adjust their internet marketing strategy and maintain a competitive advantage.
Threat of Substitute Products or Services: Keeping track of potential substitutes for their products or services helps companies identify areas where their internet marketing strategy needs to be adapted to differentiate themselves and retain customer loyalty.
By monitoring these determinants within the marketplace, companies can make informed decisions on updating their internet marketing strategy, ensuring they remain competitive in the ever-changing business landscape.
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1a. The Nelson Company has $1,274,000 in current assets and $490,000 in current liabilities. Its initial inventory level is $345,000, and it will raise funds as additional notes payable and use them to increase inventory. How much can Nelson's short-term debt (notes payable) increase without pushing its current ratio below 2.0? Do not round intermediate calculations. Round your answer to the nearest dollar.
1b. What will be the firm's quick ratio after Nelson has raised the maximum amount of short-term funds? Do not round intermediate calculations. Round your answer to two decimal places.
The current ratio is 2.60, which is already higher than the preferred limit of 2.0.
The firm's quick ratio would be 1.89 once Nelson has raised the maximum amount of short-term money, which in this case is zero.
To determine how much Nelson Company's short-term debt (notes payable) can increase without pushing its current ratio below 2.0, we need to calculate the current ratio and then find the maximum allowable increase in notes payable.
1a. Calculating the current ratio:
Current Ratio = Current Assets / Current Liabilities
Given:
Current Assets = $1,274,000
Current Liabilities = $490,000
Current Ratio = $1,274,000 / $490,000
Current Ratio = 2.60
The current ratio is 2.60, which is already above the desired threshold of 2.0.
To find the maximum allowable increase in notes payable, we need to determine the amount by which inventory can increase while still maintaining the current ratio at 2.0.
Current Assets = Inventory + Other Current Assets
$1,274,000 = $345,000 + Other Current Assets
Other Current Assets = $1,274,000 - $345,000
Other Current Assets = $929,000
Current Ratio = (Inventory + Other Current Assets) / Current Liabilities
2.0 = ($345,000 + $929,000) / $490,000
2.0 * $490,000 = $345,000 + $929,000
$980,000 = $345,000 + $929,000
$980,000 - $345,000 = $929,000
$635,000 = $929,000
$635,000 - $929,000 = $-294,000
Therefore, the maximum allowable increase in notes payable without pushing the current ratio below 2.0 is -$294,000. This means that Nelson Company does not need to increase its short-term debt as its current ratio is already above 2.0.
1b. The quick ratio, also known as the acid-test ratio, is a more stringent measure of a company's liquidity than the current ratio. It excludes inventory from current assets since inventory may not be easily converted to cash in the short term.
Quick Ratio = (Current Assets - Inventory) / Current Liabilities
Given:
Current Assets = $1,274,000
Inventory = $345,000
Current Liabilities = $490,000
Quick Ratio = ($1,274,000 - $345,000) / $490,000
Quick Ratio = $929,000 / $490,000
Quick Ratio = 1.89 (rounded to two decimal places)
Therefore, after Nelson has raised the maximum amount of short-term funds (which is zero in this case), the firm's quick ratio would be 1.89.
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In December 2020, a pound of lemons cost $1.50, while a pound of bananas cost $1.14. Four years earlier, the price of lemons was $1.29 a pound and that of bananas was $1.00. a. What was the annual compound rate of growth in the price of lemons? Note: Do not round intermediate calculations. Enter your answer as a percent rounded to 4 decimal places. Negative answers should be indicated with a minus sign. b. What was the annual compound rate of growth in the price of bananas? Note: Do not round intermediate calculations. Enter your answer as a percent rounded to 4 decimal places. c. If the same rates of growth persist in the future, what will be the price of lemons in 2030? Note: Do not round intermediate calculations. Round your answer to 2 decimal places. d. What about the price of bananas? Note: Do not round intermediate calculations.
The annual compound rate of growth in the price of lemons is approximately 3.10%. The annual compound rate of growth in the price of bananas is approximately 2.96%. If the same rates of growth persist in the future, the price of lemons in 2030 would be approximately $1.91.
Similarly, if the same rates of growth persist, the price of bananas in 2030 would be approximately $1.46.
Explanation:
To calculate the compound rate of growth, we can use the formula:
Compound Growth Rate = (Ending Value / Beginning Value)^(1 / Number of Years) - 1
For lemons, the beginning value is $1.29, and the ending value is $1.50. The number of years is 4. Plugging these values into the formula, we get:
Compound Growth Rate = ($1.50 / $1.29)^(1 / 4) - 1 ≈ 0.0309 ≈ 3.10%
Therefore, the annual compound rate of growth in the price of lemons is approximately 3.10%.
For bananas, the beginning value is $1.00, and the ending value is $1.14. Following the same calculation process, we find:
Compound Growth Rate = ($1.14 / $1.00)^(1 / 4) - 1 ≈ 0.0296 ≈ 2.96%
Hence, the annual compound rate of growth in the price of bananas is approximately 2.96%.
To estimate the future prices, we can use the compound growth rates calculated above. Considering that 2030 is 10 years from December 2020, we can apply the compound growth rates for 10 years to the current prices.
For lemons:
Price in 2030 = $1.50 * (1 + 0.0310)^10 ≈ $1.91
For bananas:
Price in 2030 = $1.14 * (1 + 0.0296)^10 ≈ $1.46
Therefore, if the same rates of growth persist, the price of lemons in 2030 would be approximately $1.91, and the price of bananas in 2030 would be approximately $1.46.
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Identify the phase of the core model of public policymaking described: A congressman introduces a bill to the U. S. House of Representatives that, if passed, would require colleges and universities receiving federal funds to establish health clinics on campus.
Implementaton
Legislation
Modification
Formulation
In the core model of public policymaking, the stage that involves a congressman presenting a bill to the United States is referred to as the legislative proposal stage.
The formulation phase of the policymaking process in the House of Representatives involves the development of a bill that, if approved, would mandate colleges and universities receiving federal funds to establish on-campus health clinics.
There are five distinct stages in the policymaking process, namely agenda-setting, formulation, adoption, implementation, and evaluation.
In the process of policymaking, there are five stages involved, namely agenda-setting, formulation, adoption, implementation, and evaluation.
The stage of the policymaking process that corresponds to the introduction of a bill is the formulation phase. During this phase, policymakers are responsible for developing the policy details.
They determine which approaches and resources to use to achieve the policy's objectives.
In other words, this phase is the stage of policymaking where the specific details of a policy are designed, and alternatives are analyzed.
A congressman introduces a bill to the U.S. A proposed legislation in the House of Representatives would mandate colleges and universities that receive federal funds to establish on-campus health clinics, if approved.
Therefore, the stage of the core model of public policymaking described is the formulation phase. During this stage, policymakers develop the details of a policy and its implementation strategies.
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Sigma Corporation applies overhead cost to jobs on the basis of direct labor cost. Job V, which was started and completed during the current period, shows charges of $5,400 for direct materials, $8,900 for direct labor, and $6,586 for overhead on its job cost sheet. Job W, which is still in process at year-end, shows charges of $3,400 for direct materials and $4,500 for direct labor.
Required:
1a. Should any overhead cost be applied to Job W at year-end?
1b. How much overhead cost should be applied to Job W?
2. How will the costs included in Job W’s job cost sheet be reported within Sigma Corporation’s financial statements at the end of the year?
1a. Yes, overhead cost should be applied to Job W at year-end.
1b. An overhead cost of $3,326.50 should be applied to Job W
2. The costs included in Job W’s job cost sheet should first be reported in work-in -progress inventory, then finished goods and ultimately to Cost of Goods Sold account after the sale.
1a) Yes, some overhead costs should be applied to Job W at year-end.
1b) The overhead cost that should be applied to Job W is given below:
Overhead rate= Overhead costs/ Direct labor cost
Overhead rate = $6,586 / $8,900 = 0.739 (rounded off to three decimal places)
Overhead cost for Job W = Overhead rate × Direct labor cost for Job W
Overhead cost for Job W = 0.739 × $4,500 = $3,326.50 (rounded off to two decimal places)
2) The costs included in Job W's job cost sheet will be reported in the following manner in Sigma Corporation's financial statements at the end of the year:
In Sigma Corporation's financial statements, the costs included in Job W's job cost sheet will be included in the Work-in-Progress inventory account as they are yet to be completed.
When the job is completed, these costs will be transferred to the Finished Goods inventory account.
When the finished goods are sold, the costs will be transferred to the Cost of Goods Sold account in the income statement.
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OAuth bank connection in QuickBooks Online? Most banks will require the primary account holder to re-establish the OAuth connection when they change their password ✓ Most banks require the primary account holder to establish the OAuth connection to the bank You must add all of a user's linked accounts to the bank feeds in QuickBooks Online You can only import 60 days of bank activity into QuickBooks Online Not all banks and financial institutions support the OAuth bank connection
Not all banks and financial institutions support the OAuth bank connection in QuickBooks Online. Therefore, it is important to check whether a particular bank supports OAuth before attempting to establish the connection.
OAuth (Open Authorization) is a secure authentication protocol that allows users to grant third-party applications access to their accounts without sharing their passwords. In QuickBooks Online, OAuth is used to establish a secure connection between the user's bank account and QuickBooks.
However, not all banks and financial institutions have implemented OAuth for their online banking services. Some banks may still rely on other methods, such as direct API integrations or file-based imports, to connect with QuickBooks Online.
To determine if a specific bank supports the OAuth bank connection, you can refer to QuickBooks' official list of supported financial institutions or reach out to the bank directly for clarification.
While QuickBooks Online offers the convenience of connecting bank accounts through OAuth, it's important to note that not all banks and financial institutions support this method. Therefore, it is necessary to verify if a bank supports OAuth before attempting to establish the connection. QuickBooks provides resources and support to assist users in determining the available integration options for their specific banks.
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Consider the following difference equation: yₜ = 0.8ₜ₋₁ + ε₁ -0.58εₜ₋₁ (a) Suppose that &1=+1. Assuming that there are no further shocks to y(t), use the derived coefficients of the particular solution to trace out the time path of the effects of ε1 on y₁, y₂, y₃ Discuss the shape of this impulse response function and what it implies for the stability of the difference equation stated at the beginning of this problem (a similar exercise was done in Part B, slide #12 of the lecture).
(b) Suppose that the initial conditions are as follows: yo=0 and &=0 and εt = 0 for t ≤ 0. Impose the initial conditions in order to find the general solution.
(a) Assuming ε₁ = +1, we can trace out the time path of the effects of ε₁ on y₁, y₂, and y₃ using the given difference equation yₜ = 0.8ₜ₋₁ + ε₁ - 0.58εₜ₋₁
For y₁:
y₁ = 0.8y₀ + ε₁ - 0.58ε₀ = 0.8(0) + 1 - 0.58(0) = 1
For y₂:
y₂ = 0.8y₁ + ε₂ - 0.58ε₁ = 0.8(1) + 1 - 0.58(1) = 1.22
For y₃:
y₃ = 0.8y₂ + ε₃ - 0.58ε₂ = 0.8(1.22) + 1 - 0.58(0) = 1.98
The time path of the effects of ε₁ on y(t) shows that each shock has a positive impact on subsequent values of y. As the value of t increases, the effects of the shock accumulate and lead to an increasing trajectory for y. This implies that the impulse response function is positive and the difference equation is unstable, as shocks have a cumulative effect and drive y to larger values over time.
(b) With the initial conditions y₀ = 0 and ε₀ = 0, we can find the general solution for the difference equation.
yₜ = 0.8yₜ₋₁ + ε₁ - 0.58εₜ₋₁
Substituting yₜ₋₁ = yₜ₋₂, we have:
yₜ = 0.8yₜ₋₂ + ε₁ - 0.58εₜ₋₁
Further substituting yₜ₋₂ = yₜ₋₃, we get:
yₜ = 0.8yₜ₋₃ + ε₁ - 0.58εₜ₋₁
This process can be continued, resulting in a general solution for yₜ as a function of previous values of y and ε. Since the initial conditions are y₀ = 0 and ε₀ = 0, we can substitute these values into the general solution to obtain the specific solution for this case.
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Below is an extract of information from the balance sheet of a commercial Dank. ASSETS LIABILITIES Reserves 250 Deposits 1750 Loans 1500 The required reserve ratio is 20 percent. (a) How much is the bank required to hold as reserves? (5 Marks) hi (b) Calculate the bank excess reserves. (5 Marks) (c) By how much can the bank increase its loans? (5 Marks) (d) Suppose a depositor comes to the bank and withdraws Ksh. 100 in cash i. Show the bank's new balance sheet, assuming the bank obtai cash by drawing down its reserves. (3 Marks) II. Does the bank now hold excess reserves? (1 Mark) iii. Is the bank meeting the required reserve ratio?
a. Bank is required to hold
cash
. 350 as reserves b. The bank has negative excess reserves of cash. 100 c. The bank can increase its loans by the amount of its excess reserves. d. The bank's reserves have decreased from cash. 250 to cash. 150.
(a) The bank is required to hold reserves equal to 20
percent
of its deposits. Given that the deposits are cash. 1750, the required reserves would be:
Required Reserves = 20% * Deposits
Required Reserves = 20% * cash. 1750
Required Reserves = cash. 350
Therefore, the bank is required to hold cash. 350 as reserves.
(b) Excess Reserves can be calculated as the difference between the actual reserves held by the bank and the required
reserves.
In this case:
Excess Reserves = Actual Reserves - Required Reserves
Excess Reserves = cash. 250 - cash. 350
Excess Reserves = -cash. 100
The bank has negative excess reserves of cash. 100, indicating that it does not have enough reserves to meet the required amount.
(c) The bank can increase its loans by the amount of its excess reserves. Since the bank has negative excess reserves of cash. 100, it cannot increase its
loans
at this point.
(d) i. After a depositor withdraws cash. 100 in cash, the bank's new balance sheet would be:
ASSETS LIABILITIES
Reserves 150 Deposits 1650
Loans 1500
The bank's reserves have decreased from cash. 250 to cash. 150.
ii. The bank does not hold excess reserves because its reserves are equal to the required reserves. Excess reserves occur when the actual reserves held are greater than the required reserves.
iii. To determine if the bank is meeting the required reserve ratio, we need to calculate the new required reserves based on the new deposit amount:
New Required Reserves = 20% * New Deposits
New Required Reserves = 20% * cash. 1650
New Required Reserves = cash. 330
Comparing the new required reserves of cash. 330 with the bank's reserves of cash. 150, we can conclude that the bank is not meeting the required reserve ratio. It falls short by Ksh. 180.
Therefore,
(a) The bank is required to hold cash . 350 as reserves.
(b) The bank has negative excess reserves of cash. 100.
(c) The bank cannot increase its loans due to negative excess reserves.
(d) i. The bank's new
balance sheet
: Reserves = cash. 150, Deposits = cash. 1650, Loans = cash. 1500.
ii. The bank does not hold excess reserves.
iii. The bank is not meeting the required reserve ratio and falls short by cash. 180.
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