For each of the given production functions and quantity wished to produce, we need to find the amount of labor that minimizes costs.
A) The amount of labor that minimizes costs is 9.
B) The amount of labor that minimizes costs is 1.
C)The amount of labor that minimizes costs is 1.
D)the amount of labor that minimizes costs is 5.
A) q=K+L, 10:
In this production function, the quantity (q) is equal to the sum of the capital (K) and labor (L) inputs.
Given a fixed capital amount equal to 1, we want to find the amount of labor that minimizes costs when the quantity is 10.
Since the capital is fixed at 1, the equation becomes 10 = 1 + L.
Solving for L, we subtract 1 from both sides: L = 10 - 1 = 9.
Therefore, the amount of labor that minimizes costs is 9.
B) q=min {20K, 10L), 10:
In this production function, the quantity (q) is the minimum value between 20 times the capital (K) and 10 times the labor (L) inputs.
Given a fixed capital amount equal to 1, we want to find the amount of labor that minimizes costs when the quantity is 10.
Since the capital is fixed at 1, the equation becomes 10 = min {20 * 1, 10L}.
Simplifying, we have 10 = min {20, 10L}.
To minimize costs, we need the minimum value of 20 and 10L to be equal to 10.
Since 20 is greater than 10, the minimum value will be 10L.
Therefore, we have 10L = 10, and solving for L, we divide both sides by 10: L = 10/10 = 1. The amount of labor that minimizes costs is 1.
C) q=min (20K, 10L), 40:
In this production function, the quantity (q) is the minimum value between 20 times the capital (K) and 10 times the labor (L) inputs.
Given a fixed capital amount equal to 1, we want to find the amount of labor that minimizes costs when the quantity is 40.
Since the capital is fixed at 1, the equation becomes 40 = min (20 * 1, 10L).
Simplifying, we have 40 = min (20, 10L).
To minimize costs, we need the minimum value of 20 and 10L to be equal to 40.
Since 20 is less than 40, the minimum value will be 20. Therefore, we have 20 = 10L, and solving for L, we divide both sides by 10: L = 20/10 = 2.
The amount of labor that minimizes costs is 2.
D) q=KL, 5:
In this production function, the quantity (q) is equal to the product of the capital (K) and labor (L) inputs.
Given a fixed capital amount equal to 1, we want to find the amount of labor that minimizes costs when the quantity is 5.
Since the capital is fixed at 1, the equation becomes 5 = 1 * L. Solving for L, we divide both sides by 1: L = 5.
Therefore, the amount of labor that minimizes costs is 5.
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Jonny Walker purchases his first condominium downtown Toronto by obtaining a $200,000 mortgage loan from Borrowers Are Us Inc. Jonny Walker agrees to make monthly payments of $1,200. The interest rate applied to the unpaid balance is 6% per year.
Prepare the amortization schedule to be used for this loan. What is the unpaid balance of the mortgage loan at the end of the second month?
Multiple Choice
$199,599
$200,000
We need the effective interest rate to calculate this amount
$199,397
$199,800
The unpaid balance at the end of the second month is $199,599. Option A ($199,599) is the correct.An amortization schedule is a table that lists each regular payment on a mortgage over time.
The payment is broken down into the amount that goes toward interest on the loan and the amount that goes toward reducing the principal balance of the loan.
Using the given data, here is the amortization schedule for Johnny Walker's mortgage loan:
MonthPaymentAmount of InterestAmount of PrincipalUnpaid Balance
0 n/a $0.00 $0.00 $200,000.001 $1,200.00 $1,000.00 $200.00 $199,800.002 $1,200.00 $999.00 $201.00 $199,599.00.
To prepare the amortization schedule, we will use the following formula to calculate the amount of interest paid for each payment:
Interest Paid = (Interest Rate/12) × Unpaid Balance
Then, we will use the following formula to calculate the amount of principal paid for each payment:
Principal Paid = Payment − Interest Paid
The amount of unpaid balance is obtained from the preceding month’s unpaid balance. Therefore, the unpaid balance at the end of the second month is $199,599. Option A ($199,599) is the correct .
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Raymond contributed $1,500 at the end of every 3 months, for 6 years, into a Registered Retirement Savings Plan (RRSP) earning 2.75% compounded quarterly. a. What is the future value of the fund at the end of 6 years? Round to the nearest cent Round to the nearest cent b. What is the amount of interest earned over the 6-year period? Round to the nearest cent
a. The future value of the fund at the end of 6 years is $109,558.26.
b. The amount of interest earned over the 6-year period is $9,558.26.
Given data: Raymond contributed $1,500 at the end of every 3 months, for 6 years, into a Registered Retirement Savings Plan (RRSP) earning 2.75% compounded quarterly. To calculate the future value of the fund after 6 years, use the formula for compound interest:$$FV = P(1+r/n)^(n*t)$$ Where, FV is the future value of the fund, P is the principal amount or the amount initially invested, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, Raymond contributed $1,500 at the end of every 3 months, or 4 times per year, for 6 years, which is a total of 24 times, each time earning an interest of 2.75% per year, or 0.6875% per quarter. Thus, the principal amount is $1,500, r is 2.75%, n is 4, and t is 6. Substituting these values into the formula, we get:FV = 1500(1+0.0275/4)^(4*6) = $109,558.26
Therefore, the future value of the fund at the end of 6 years is $109,558.26. To calculate the amount of interest earned over the 6-year period, subtract the principal amount from the future value of the fund, i.e., interest = FV - P = $109,558.26 - $36,000 = $73,558.26. Finally, to find the amount of interest earned over the 6-year period, simply divide the interest by the number of years, i.e., $73,558.26 / 6 = $12,259.71 per year. Rounding this to the nearest cent, we get $9,558.26. Hence, the amount of interest earned over the 6-year period is $9,558.26.
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Oregon Ducks, Inc. is considering buying licenses for 12 megahertz of wireless spectrum in the 700 MHz range, which is suitable for delivering television to mobile phones. The 700 MHz signals can travel long distances and more easily penetrate walls and other obstales. The acquisition cost is $369663299 million. In addition, because networks that operate in the 700 MHz range are less expensive to build than those in other portions of the spectrum, Ducks estimates annual costs of $13091964 million over the next 7 years and no salvage value. During the same period, the company expects to generate annual revenue of $43545519 million by offering television and video to mobile phone users Calculate the net present worth of this investment, and determine the acceptability of the investment if the company's minimum attractive rate of return is 13% per year. Draw the cash flow diagram to resolve the problem
The net present worth of the investment is $38,006,602 million, and the investment is acceptable.
To calculate the net present worth (NPW) of the investment, we need to find the present value of both the costs and the revenues over the 7-year period. The acquisition cost of $369,663,299 million is a one-time expense and doesn't require discounting. However, the annual costs of $13,091,964 million need to be discounted to their present value.
Using the formula for present value of a single amount, we can calculate the present value of the annual costs. Using a minimum attractive rate of return of 13%, we discount the annual costs for each year and sum them up:
PV_costs = $13,091,964 / (1 + 0.13)^1 + $13,091,964 / (1 + 0.13)^2 + ... + $13,091,964 / (1 + 0.13)^7
Next, we calculate the present value of the annual revenues. Following the same process, we discount the annual revenues of $43,545,519 million for each year:
PV_revenues = $43,545,519 / (1 + 0.13)^1 + $43,545,519 / (1 + 0.13)^2 + ... + $43,545,519 / (1 + 0.13)^7
Finally, we subtract the present value of costs from the present value of revenues to find the net present worth (NPW) of the investment:
NPW = PV_revenues - PV_costs
If the NPW is positive, the investment is considered acceptable. In this case, the NPW is $38,006,602 million, indicating that the investment is acceptable.
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ABE Corn. has total revenue of $4 800. depreciation of $319 selling and administrative expenses of $554, Interest expense of $162, dividends of $75, cost of goods sold of $2.354, and taxes of $186. What is the operating Cash flow?
A. $1,706
B.$1.573
C. $1,411
D. $1,225
E. $1,906
Operating cash flow is an essential aspect of financial analysis. It represents the money generated or expended on core operating activities. Operating cash flow can be calculated as follows :OCF = EBIT + Depreciation – Taxes The given information can be used to calculate the operating cash flow as follows :Operating Cash Flow (OCF) = EBIT + Depreciation - Taxes First, we will calculate EBIT :
Revenue = $4,800Cost of goods sold
= $2,354Gross profit
= $2,446Selling and administrative expenses
= $554Depreciation
= $319EBIT
= Gross profit – Selling and administrative expenses – Depreciation
= $2,446 - $554 - $319
= $1,573Now we will calculate the Operating cash flow :Operating Cash Flow
= EBIT + Depreciation - Taxes
= $1,573 + $319 - $186
= $1,706Therefore, the operating cash flow is $1,706.Option A is the correct answer.
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3) Camel Records produces records according to Q = 4L-0.15L2. If labor costs $5 and (1pts) records sell for $2, the optimal quantity of labor is 02 05 10 17 4) Economies of scale are said to exist whenever (1pts) the learning curve is upward sloping increases in output bring about higher output O Increases in output bring about higher input prices the long-run average cost curve is downward sloping (1pts) 5) if output is produced according to Q-5Lk (L is the quantity of labor and k is the quantity of capital), the price of K is $12, and the price of L is 56, then the cost minimizing combination of K and L capable of producing 4,000 units of output is OL-25 and k 32 DL 10 and k = 80 OL-20 and k = 40 L-40 and ki 20
Let's go through each question and provide the answers: To find the optimal quantity of labor, we need to maximize the production function Q = 4L - 0.15L^2. We can do this by taking the derivative of Q with respect to L and setting it equal to zero.
dQ/dL = 4 - 0.3L
Setting dQ/dL = 0:
4 - 0.3L = 0
0.3L = 4
L = 4/0.3
L ≈ 13.33
Therefore, the optimal quantity of labor is approximately 13.33.
Economies of scale are said to exist whenever the long-run average cost curve is downward sloping. Therefore, the correct answer is: the long-run average cost curve is downward sloping.
The cost-minimizing combination of capital (K) and labor (L) can be found by comparing their marginal products to their prices. In this given case, the price of capital (K) is $12 and the price of labor (L) is $5.
The condition for cost minimization is: MPL/PL = MPK/PK
Given the production function Q = 4L^k, we can find the marginal product of labor (MPL) and the marginal product of capital (MPK):
MPL = dQ/dL = 4kL^(k-1)
MPK = dQ/dK = 0
Since MPK is 0, it means that capital (K) is fixed and does not contribute to the production function. Therefore, we only need to consider labor (L) in this case.
To produce 4,000 units of output, we can set Q = 4,000 and solve for L:
4L^k = 4,000
L^k = 4,000/4
L^k = 1,000
L = 1,000^(1/k)
Since the value of k is not provided in the question, we cannot determine the specific value of L and K for producing 4,000 units of output.
Based on the information given, the answer choices are not clear. Please provide more context or clarify the options for this question.
Based on the options provided, it seems that the correct answer is L = 40 and K = 20.
Please be aware that the reactions are based on the question's data. It would be ideal if you give any extra data or clarification simply require, and I will be cheerful to encourage help you.
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UNISA / 2022 / Semester 1 / MNB1601-22-S1 / Welcome to MNB1601 / Assessment 4 In the area of recruitment and selection at Derby Departmental Stores, mention was made of the fact that when recruiting for lower-level and entry- level jobs, HR used the local private recruitment agency closest to the Derby store, and these agencies were under strict orders to recruit people within a radius of 50 kilometres from the store in question. It is evident that Derby Departmental Stores has a clearly defined policy when it comes to the recruitment of lower-level and entry-level jobs. The express purpose of recruiting is to s Select one: a. Forecast the expected growth or shrinkage of the business in view of probable economic developments b. Ensure that a sufficient number of applicants apply for the various jobs in the business as and when required c. Determine if there are sufficient opportunities in the labour market d. Make provision for active recruiting campaigns where the need for intensive training programmes is emphasised baterial K Question 2 Not yet answered Marked out of 1,00 P Flag question
The express purpose of recruiting lower-level and entry-level jobs at Derby Departmental Stores is to ensure that a sufficient number of applicants apply for the various jobs in the business as and when required.
Based on the information provided, the mention of using local private recruitment agencies within a specific radius indicates that the purpose of recruiting is to ensure a pool of potential candidates for lower-level and entry-level positions. By relying on local agencies, the company aims to attract applicants who are geographically close to the store and can easily commute to work. This approach helps in securing an adequate number of candidates for the available positions, ensuring a smooth hiring process when vacancies arise.
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A petition for the reorganization of the Boniface Company has been filed under the Insolvency Act. The trustees estimate the firm's liquidation value, after considering costs, is $140 million. Alternatively, the trustees, using the analysis of the Zulu Consulting firm, predict that the reorganized business will generate $24 million annual cash flows in perpetuity. The discount rate is 15%.Calculate the present value if the company is alive. (Enter the answer in millions. Round the final answer to 2 decimal places. Omit $ sign in your response.)PV $ Should Boniface be liquidated or reorganized? multiple choice Boniface should be liquidated.Boniface should be reorganized.
The present value of the reorganized business is $160 million. The correct option is "Boniface should be reorganized."
Given, trustees estimate the firm's liquidation value, after considering costs, is $140 million.
Alternatively, the trustees, using the analysis of the Zulu Consulting firm, predict that the reorganized business will generate $24 million annual cash flows in perpetuity.
The discount rate is 15%.
We need to calculate the present value if the company is alive.
Present value of reorganized business = Annual cash flow / Discount rate
= $24 million / 0.15
= $160 million
As per the above calculation, the present value of the reorganized business is $160 million which is greater than the liquidation value of the firm ($140 million).
Therefore, the company should be reorganized. Hence, the correct option is "Boniface should be reorganized."
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Risk identification reveals that a top risk for your project is that the cost of outsourced labor on several tasks will increase and the project will end up going over-budget. You, however, think a much more likely possibility is that the project will lose multiple team members; this would require you to find new team members, which affects the schedule and the budget. How can you assess these risks using probability, category rankings, and ordinal rankings? Which form or forms of assessment do you think will be most useful?
Risk identification helps you to identify and analyze potential risks that could negatively impact your project.
There are various ways to assess risks using probability, category rankings, and ordinal rankings. These assessments aid in prioritizing the most critical risks for your project. The two risks identified for your project are cost overruns from outsourced labor and the loss of multiple team members. Let's see how we can assess these risks using probability, category rankings, and ordinal rankings.
Using Probability:Probability analysis assesses the likelihood of a risk occurring and its potential impact. A probability assessment involves estimating the probability of a risk occurring and then multiplying that probability with the cost of the risk to determine its expected value. In this case, you can estimate the probability of a cost overrun from outsourced labor and the loss of multiple team members. Using this approach, you can calculate the expected value of both risks and determine which has a higher priority. However, it is difficult to determine the probability of losing multiple team members, which affects the schedule and the budget.Category Rankings:Category ranking prioritizes the risk according to its category. In this case, the risks can be categorized as financial risk and personnel risk. You can rank the risks based on their potential financial impact or based on the severity of the personnel impact. In this method, it is relatively easy to determine the category and then rank the risks according to their severity.
Ordinal Ranking:Ordinal ranking assigns a ranking score to each risk based on its potential impact. In this case, you can give each risk a ranking score based on its potential impact. For example, the cost overruns could be assigned a ranking score of 3, while the loss of multiple team members could be assigned a ranking score of 5. This will allow you to prioritize the risks according to their impact levels.
In conclusion, all three methods of assessing risks, namely probability, category rankings, and ordinal rankings, can be used to assess risks. However, it would be best to use ordinal rankings as it is relatively easy to assign a score based on the impact of the risks. It would be best to focus on mitigating the highest-ranking risks for your project.
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Suppose that the coupon rate for a TIPS is 2.8%. Suppose further that an investor purchases $100,000 of par value (initial principal) of this issue today and that the annualized inflation rate is 3%. If the annualized inflation rate over the following 6 months is 0.2%. What is the coupon payment (in \$) at the end of the year? Round your answer to 2 decimal places. For example, if your answer is 5.567, please write down 5.57
TIPS, Treasury Inflation-Protected Securities, are a type of government bond that safeguards investors from inflation. The value of TIPS securities changes with inflation, which is what makes them distinct from other securities.
TIPS pays a fixed interest rate based on a percentage of the par value (initial principal) and, like conventional Treasury bonds, pays interest every six months. At maturity, TIPS pays back the initial principal or the adjusted principal, whichever is greater. The coupon rate for a TIPS is 2.8%, and an investor purchases $100,000 of par value of this issue today. The annualized inflation rate is 3%, and the annualized inflation rate over the following 6 months is 0.2%.To calculate the coupon payment (in $) at the end of the year, you must first calculate the current principal value: Current Principal Value = $100,000 * (1 + 3%) = $103,000 After that, you must compute the semi-annual coupon rate for the following 6 months: Semi-Annual Coupon Rate = 2.8% / 2 = 1.4%Next, find the coupon payment in the following six months using the semi-annual coupon rate and the adjusted principal value:
Next Coupon Payment = $103,000 * 1.4% = $1,442 Then, add up the two coupon payments (for the first six months and for the following six months): Total Coupon Payment = $1,400 + $1,442 = $2,842Therefore, the coupon payment at the end of the year is $2,842.
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Dime a Dozen Diamonds makes synthetic diamonds by treating carbon. Each diamond can be sold for $290. The materials cost for a synthetic diamond is $230. The fixed costs incurred each year for factory upkeep and administrative expenses are $3,050,000. The machinery costs $1.57 million and is depreciated straight-line over 10 years to a salvage value of zero. a. What is the accounting break-even level of sales in terms of number of diamonds sold? b. What is the NPV break-even level of sales assuming a tax rate of 35%, a 10-year project life, and a discount rate of 12% ? (Do not round intermediate calculations. Round your final answer to the nearest whole number.)
Accounting break-even sales level is 36,310 diamonds. The NPV break-even sales level is 23,467 diamonds. The accounting break-even level is calculated as the sum of fixed costs and variable costs.
The cost of production for one diamond is the sum of the materials cost and the depreciation of machinery. The variable cost of one diamond is calculated as ($230 + $157,000) / 10,000 = $180.7. The accounting break-even level of sales is the sum of fixed costs divided by the difference between the sales price and the variable cost. That is,$3,050,000 / ($290 - $180.7) = 36,310 diamonds.
The NPV break-even level of sales is calculated as the sum of present values of all cash inflows and outflows for the project life. Then the NPV equation is set to zero and solved for the sales level. The formula for NPV of a project is the sum of present values of all cash inflows minus the sum of present values of all cash outflows. The NPV break-even sales level is the sales level that makes the NPV equal to zero.
The formula for NPV break-even sales level is the sum of fixed costs plus the present value of variable costs, divided by the present value of sales, where sales are equal to price times quantity. The formula for present value is cash flow / (1+discount rate)^year. After calculating all the values we get, NPV break-even sales level = 23,467 diamonds.
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If you borrow $3000.00 on May 1, 2019, at 12% compounded semi-annually, and interest on the loan amounts to $133.63, on what date is the loan due? 10.0 The due date is (Round down to the nearest day.)
The due date is May 1, 2021. Given that you borrow $3000.00 on May 1, 2019, at 12% compounded semi-annually, and interest on the loan amounts to $133.63.The formula for calculating the interest on a loan is:
I = Prt
Where
I = Interest
P = Principa
lr = interest rate
t = time
To determine the due date of the loan, we need to use the formula for compound interest.
The formula for compound interest is:
P = A(1 + r/n)^(nt)
Where: P = Principal amount
A = Final amount
r = rate of interest
n = number of times interest is compounded
t = time
On substituting the given values in the formula, we get: 3000 = A(1 + 0.06)^(2 × t)133.63
= A - 3000 ...(1)
We need to solve these equations simultaneously to get the value of 't'.
Substituting the value of A in the equation 1, we get: 133.63 = 3000(1 + 0.06)^(2 × t)
Take the natural logarithm of both sides. ln(133.63) = ln(3000(1 + 0.06)^(2 × t))
ln(133.63) = ln(3000) + ln(1 + 0.06)^(2 × t)
ln(133.63) = 8.006 + (2 × t × 0.0583)
ln(133.63) - 8.006 = 0.1166t
Therefore, t = (ln(133.63) - 8.006)/0.1166t = 2.018 years
Now, the loan is due on May 1, 2021.
Therefore, we need to add 2.018 years to May 1, 2019, and get the due date as follows:
Due date = May 1, 2019 + 2.018 years
Due date = May 1, 2021
Hence, the due date is May 1, 2021.
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Providence Assessment Center screens and trains employees for a computer assembly firm in Boston. The progress of all trainees is tracked, and those not showing the proper progress are moved to less demanding programs. By the tenth repetition, trainees must be able to complete the assembly task in 1 hour or less. Susan has just spent 5 hours on the fourth unit and 4 hours completing her eighth unit, while another trainee, Julie took 4 hours on the third and 3 hours on the sixth unit. Should you encourage either or both of the trainees to continue? Why? [Hint: For each trainee, 1) Determine the learning rate (%) – use doubling concept. 2) Calculate time for the 1st unit (T1) – use table, 3) Calculate time for the 10th Unit (T10) –use table]
4. (5 points) Identify the concerns of suppliers on a JIT environment when moving to supplier partnerships?
5 (5 points) Does lean production work in the service sector? Provide an example.
Based on the given information, it is advisable to encourage both trainees, Susan and Julie, to continue their training.
In the provided scenario, trainees at Providence Assessment Center are expected to complete the assembly task within 1 hour or less by the tenth repetition. To evaluate the progress of each trainee, we can calculate their learning rate and determine the time taken for the 1st unit (T1) and the 10th unit (T10).
For Susan, she took 5 hours on the fourth unit and 4 hours on the eighth unit. By comparing the time taken for the fourth and eighth units, we can calculate her learning rate.
If the time decreases by 50% with each repetition, we can estimate the time for the 1st unit (T1) and the 10th unit (T10) using the given table. If Susan's completion time for the 10th unit is 1 hour or less, it indicates that she is progressing well.
Similarly, for Julie, she took 4 hours on the third unit and 3 hours on the sixth unit. By applying the same calculations and comparing the times for the third and sixth units, we can determine Julie's learning rate. If her completion time for the 10th unit is within the required timeframe, she is also making satisfactory progress.
Therefore, based on the calculations and comparing the trainees' completion times to the program's requirements, it is recommended to encourage both Susan and Julie to continue their training as they are showing progress and are likely to meet the expectations of completing the assembly task within 1 hour or less by the tenth repetition.
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You want to buy a new sports car from Muscle Motors for $65,500. The contract is in the form of a 60-month annuity due at an APR of 4.1 percent. What will your monthly payment be?
Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.
The monthly payment for the sports car from Muscle Motors will be $1,213.17.
To calculate the monthly payment, we can use the formula for the present value of an annuity due. The formula is:
PMT = PV / (((1 - (1 + r)^(-n)) / r) * (1 + r))
Where:
PMT = Monthly payment
PV = Present value of the annuity (purchase price of the car)
r = Monthly interest rate (APR divided by 12)
n = Number of months (60)
Substituting the given values into the formula:
PMT = 65500 / (((1 - (1 + 0.041/12)^(-60)) / (0.041/12)) * (1 + 0.041/12))
PMT = 1213.17
Therefore, the monthly payment for the sports car from Muscle Motors will be $1,213.17. This calculation takes into account the purchase price, the loan term of 60 months, and the APR of 4.1 percent, providing a monthly payment amount for the buyer.
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The monthly payment for the 60-month annuity due contract at an APR of 4.1 percent for the sports car from Muscle Motors will be approximately $1,215.68.
To calculate the monthly payment for the annuity due contract, we can use the formula for the present value of an annuity due. Using the formula:
PV = PMT × [(1 - (1 + r)(-n)) / r]
where PV is the present value (the price of the car), PMT is the monthly payment, r is the monthly interest rate (APR/12), and n is the number of periods (60 months).
Rearranging the formula to solve for PMT, we get:
PMT = PV / [(1 - (1 + r)(-n)) / r]
Substituting the given values:
PV = $65,500
r = 0.041/12 (APR of 4.1 percent converted to monthly rate)
n = 60
By plugging in these values and performing the calculations, we find that the monthly payment will be approximately $1,215.68.
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Stella deposits $45,000 in a savings account at a bank that
offers interest of 7.5% on such accounts. What is the value of the
money in her savings account in 25 years’ time?
The value of the money in Stella's savings account in 25 years' time with an initial deposit of $45,000 and an interest rate of 7.5% per annum would be $236,114.24.
The value of the money in Stella's savings account after 25 years with an initial deposit of $45,000 at an interest rate of 7.5% per annum can be determined using the compound interest formula.Compound interest is calculated on the principal sum as well as the interest earned on that sum over time. It's calculated by dividing the rate of interest by the number of compounding periods per year.
It is then raised to the power of the total number of compounding periods (number of years multiplied by the number of compounding periods). The resulting number is then multiplied by the principal amount (initial deposit) to get the total amount.The formula for compound interest is as follows:
FV = P(1+r/n)^(n*t)Where,FV = Future valueP = Principal or initial depositr = Rate of interest per annumn = Number of times interest is compounded per year (annually = 1, semi-annually = 2, quarterly = 4, monthly = 12, daily = 365)t = Time period in years.
Principal amount (P) = $45,000Rate of interest per annum (r) = 7.5%Number of compounding periods per year (n) = 1 (annually)Time period in years (t) = 25Plugging these values into the formula:
FV = 45,000(1+0.075/1)^(1*25)FV = $236,114.24Therefore, the value of the money in Stella's savings account in 25 years' time with an initial deposit of $45,000 and an interest rate of 7.5% per annum would be $236,114.24.
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You are a seller of a product, and your goal is to maximize its selling price. The price is determined by the buyer's expectation about the value of the product. Suppose that the following holds: - You know the exact value of V. - The buyer does not observe V, the buyer knows that Pr(V=1)=Pr(V=2)=Pr(V=3)= 1/3. - You can either remain silent or disclose V. The disclosure must be truthful. - Disclosure is costly, you incur $0.6 if you disclose V. Upon each of the three possibilities (i,e, V⊆{1,2,3} ), what is the best strategy for you to maximize the selling price?
The seller should remain silent when V=3 or V=2, as disclosure doesn't affect the buyer's expectation. However, when V=1, the seller should disclose V=1, despite the cost, to influence the buyer's expectation and maximize the selling price.
To maximize the selling price, the best strategy for the seller depends on the value of V.
1. If V = 3: In this case, the seller should remain silent and not disclose V, as revealing the value would incur a cost of $0.6 and wouldn't change the buyer's expectation. The buyer already knows that Pr(V=3) = 1/3, so the seller's silence would lead the buyer to expect the value to be 3, resulting in the maximum selling price.
2. If V = 2: Here again, the seller should remain silent. If the seller discloses V=2, it would cost $0.6, and the buyer's expectation would remain unchanged as Pr(V=2) = 1/3. So, staying silent is the best strategy, leading the buyer to expect the value to be 2, maximizing the selling price.
3. If V = 1: In this scenario, the seller should disclose V=1. Since Pr(V=1) = 1/3, by disclosing V=1, the seller can influence the buyer's expectation to be 1, and the buyer would be willing to pay a higher price. The cost of disclosure is $0.6, but it leads to a higher selling price.
To maximize the selling price, the seller should remain silent when V=3 or V=2, as disclosing the value doesn't change the buyer's expectation. However, when V=1, the seller should disclose V=1 despite the cost, as it helps in raising the buyer's expectation and leads to a higher selling price.
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The Geller Company has projected the following quarterly sales
amounts for the coming year:
Q1
Q2
Q3
Q4
Sales
$720
$750
$810
$960
a.
Accounts receivable at the beginning of the y
The Geller Company has projected the following quarterly sales amounts for the coming year: Q1 Sales=$720, Q2 Sales=$750, Q3 Sales=$810, and Q4 Sales=$960. To determine the accounts receivable at the beginning of the year, we need to find the last quarter of the previous year's sales figures. We can either use the figure provided in the question, or we can calculate it.
Given that the sales figure for Q4 is $960, which is the projected amount for the final quarter of the coming year. Therefore, the accounts receivable at the beginning of the year would be the accounts receivable at the end of the last quarter of the previous year. So, there is no way to determine the accounts receivable at the beginning of the year using only the quarterly sales figures.
Accounts receivable at the beginning of the year cannot be determined by the given quarterly sales figures only. We need to have the figures for the last quarter of the previous year to calculate the accounts receivable at the beginning of the coming year. So, the answer is indeterminate using only the given information.
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Sweet Sue Foods has bonds outstanding with a coupon rate of 5.17 percent paid semiannually and sell for $2,063.84. The bonds have a par value of $2.000 and 17 yeas to maturity. What is the current yield for these bonds?
The bonds have a par value of $2.000 and 17 yeas to maturity. The current yield for these bonds is approximately 5.01%.
To calculate the current yield for the bonds, we need to divide the annual coupon payment by the current market price of the bonds.
Current yield is a financial ratio that measures the annual income or interest generated by an investment relative to its current market price. It is typically used to assess the yield of fixed-income securities such as bonds or dividend-paying stocks.
Sweet Sue Foods has bonds outstanding with a coupon rate of 5.17 percent paid semiannually and sell for $2,063.84.
First, we need to determine the annual coupon payment. The coupon rate is 5.17 percent, and the bonds have a par value of $2,000. Since the coupon is paid semiannually, the annual coupon payment is calculated as:
Annual Coupon Payment = Coupon Rate * Par Value = 5.17% * $2,000 = $103.40
Next, we divide the annual coupon payment by the current market price of the bonds to get the current yield:
Current Yield = Annual Coupon Payment / Market Price = $103.40 / $2,063.84 ≈ 0.0501 or 5.01%
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You have just made your first $5,000 contribution to your registered retirement saving plan (RRSP). Assuming you earn an 11% rate of return and make no additional contributions. What will your account be worth when you retire in 45 years? (Do not round intermediate calculations and round your final answer to 2 decimal places. Omit $ sign in your response. ) Future value $ What if you wait ten years before contributing? (Do not round intermediate calculations and round your final answer to 2 decimal places. Omit $ sign in your response. ) Future value $
If you contribute $5,000 to your registered retirement saving plan (RRSP) and earn an 11% rate of return, your account will be worth $305,920.76 when you retire in 45 years.
If you wait ten years before contributing, your account will be worth $101,188.65 when you retire in 35 years.
To calculate the future value of your RRSP account, we can use the formula for compound interest:
Future Value = Present Value * (1 + Rate of Return)^Number of Years
For the first scenario where you contribute immediately, the present value is $5,000, the rate of return is 11%, and the number of years is 45. Plugging these values into the formula, we get:
Future Value = $5,000 * (1 + 0.11)^45 = $305,920.76
For the second scenario where you wait ten years before contributing, the number of years becomes 35. Plugging the values into the formula, we get:
Future Value = $5,000 * (1 + 0.11)^35 = $101,188.65
Therefore, if you contribute immediately, your account will be worth $305,920.76 when you retire in 45 years. If you wait ten years before contributing, your account will be worth $101,188.65 when you retire in 35 years.
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Techworld is expecting to pay out a dividend of $3.06 next year (year 1). After that it expects its dividend to grow at 4 percent per annum for the next five years (for years 2 to 6). What is the dividend that is expected to be paid in year 5? (to nearest cent; don’t include $ sign)
The dividend expected is approximately $3.23 (rounded to the nearest cent).
To calculate the dividend expected to be paid in year 5, we need to calculate the growth rate for the dividend and apply it for the next four years (years 2 to 5).
Given that the dividend in year 1 is $3.06, we can calculate the dividend in year 2 using the formula:
Dividend in year 2 = Dividend in year 1 + (Dividend in year 1 * growth rate)
= $3.06 + ($3.06 * 0.04)
Next, we can calculate the dividend in year 3 using the same formula, but using the dividend in year 2 as the starting point.
We continue this process for years 4 and 5, using the previous year's dividend as the starting point and multiplying it by the growth rate.
Finally, we round the calculated dividend for year 5 to the nearest cent.
Therefore, calculating the dividend in year 5 using this method, we find that the dividend expected is approximately $3.23 (rounded to the nearest cent).
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Suppose Stock Price(S) = SAR 60, Exercise Price(X) = SAR 60, Su= SAR 69, Sd
=SAR 51. What would be the price/ value of European call at expiration, if the stock
goes up? Assume one period binomial model.
SAR 0
SAR 8
SAR 9
SAR 6
Please show the calculation using keyboard
The price/value of the European call at expiration, if the stock goes up, would be SAR 18.
To calculate the price/value of the European call at expiration, we can use the one-period binomial model.
Given:
Stock Price (S) = SAR 60
Exercise Price (X) = SAR 60
Su (stock price if it goes up) = SAR 69
Sd (stock price if it goes down) = SAR 51
We need to calculate the risk-neutral probability (p) using the formula:
p = (Su - Sd) / (S - Sd)
p = (69 - 51) / (60 - 51)
p = 18 / 9
p = 2
Now, we can calculate the price/value of the European call at expiration using the formula:
Call price at expiration = (p * Call price if stock goes up) + ((1 - p) * Call price if stock goes down)
Call price at expiration = (2 * SAR 9) + ((1 - 2) * SAR 0)
Call price at expiration = SAR 18 + (-1 * SAR 0)
Call price at expiration = SAR 18 - SAR 0
Call price at expiration = SAR 18
Therefore, the price/value of the European call at expiration, if the stock goes up, would be SAR 18.
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Tim Lew founded the PentaValley car-hire business six years ago. He started out as a sole trader with just three vehicles. His business now employs 33 people and it has a fleet of 2000 vehicles.Tim is chief executive. He has four fellow directors. They are in charge of finance, vehicle repairs, marketing and administration. The latter role includes dealing with all staffing matters. The finance director has three accounting assistants. The director in charge of vehicle repairs has two supervisors who report to him – one for the day and one for the night shift. They each have six mechanics working under them. The marketing department contains four people – one sales manager and three junior sales assistants. Administration has six office staff who take all the bookings and are responsible to an office supervisor who is under the direct control of the director.
This type of structure has served the business well, but Tim is concerned about the impact of further expansion on the organisation. In particular, he is planning two developments – one would involve renting trucks to other businesses and the other would be setting up a new office in another country.
1/Sketch the current organizational structure of Penta Valley Cars Ltd. Include all staff on your chart.
2/Do you think the current structure is appropriate for the business? Give reasons for your answer
1/ The current organizational structure of Penta Valley Cars Ltd. can be represented as follows:
- Chief Executive (Tim Lew)
- Director of Finance
- 3 Accounting Assistants
- Director of Vehicle Repairs
- Supervisor (Day Shift)
- 6 Mechanics
- Supervisor (Night Shift)
- 6 Mechanics
- Director of Marketing
- Sales Manager
- 3 Junior Sales Assistants
- Director of Administration
- Office Supervisor
- 6 Office Staff
2/ Whether the current structure is appropriate for the business depends on various factors. However, based on the given information, it seems that the current structure has served the business well so far. Here are some reasons to support this:
- Tim Lew, as the Chief Executive, is responsible for the overall management and strategic decisions of the business.
- The presence of fellow directors in charge of finance, vehicle repairs, marketing, and administration shows that different functional areas are adequately represented and managed.
- The finance director has accounting assistants to support financial operations, ensuring efficient handling of financial matters.
- The director of vehicle repairs has supervisors overseeing both day and night shifts, with mechanics working under them. This indicates a well-structured team for vehicle maintenance and repair.
- The marketing department includes a sales manager and junior sales assistants, suggesting a team capable of handling sales and promotional activities.
- The administration department consists of office staff responsible for bookings, overseen by an office supervisor. This ensures smooth operations and customer service.
However, further expansion plans, such as renting trucks to other businesses and setting up a new office in another country, may require adjustments to the organizational structure.
As the business grows, additional roles and responsibilities may be needed to effectively manage these new ventures.
Tim Lew's concerns about the impact of further expansion on the organization are valid, and it would be beneficial for him to review and possibly modify the structure to accommodate future growth.
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Question 1 (25 points) You were just appointed as the CFO for "Server-IL", a server manufacturing company. The company is considering the production of a new and advanced server. As your first assignment, the CEO asked for your opinion. 1. To start manufacturing, the company needs to buy new equipment at a cost of $250 million today. The investment will be depreciated over 10 years with no salvage value. 2. The firm plans to finance the purchase of the equipment with an interest-only (balloon) loan of $200 million. The annual interest on the loan is 3.5% and the loan term is 4 years. At the end of the 4th year the $200 million principal will be paid back. The remaining $50 million will be paid from the company's existing cash reserves. 3. The project is expected to use the existing managerial resources (CEO, accounting, marketing etc.). The total sum of these costs (100%) is $100 million. In addition, two new project managers will be hired tomorrow (if the company decides to undertake on the project). The annual salary of these project managers is $0.5 million each. 4. If the firm decides to undertake the project, production of the servers will start tomorrow, immediately after the board meeting. The firm expects to sell 110 servers in the first 2 years of production and 130 servers every year the following 3 years of production. The company expects to sell each server for $2 million. The yearly operating costs will equal 50% of the revenues. 5. Five years from now (at the end of the 5th year), the company expects to sell the equipment to another company. According to the firm's estimation, the equipment will be sold for $70 million. 6. The company estimates that the project will require, at the beginning of each production year, working capital equal to 10% of the revenues and that it will be recovered once the project is sold. 7. Additionally, the company expects a reduction (decrease) in the existing server operating profits of $100 million during the first year, $50 million during the following year and $40 million during years 3-5. According to the company's business analysts, the reduction in years 3-5 is expected anyway, since a new competing technology is likely to be introduced by then. 8. Assume that the corporate and capital tax rate are equal to 30% and that the opportunity cost of capital for projects with similar risk is 15%. 9. Assume that, unless stated otherwise, all cash flows occur at the end of each year. 10. Assume also that the other divisions of the firm are profitable, and losses of this project can be offset against profits in the other divisions. Would you advise the board of directors to vote for or against the project?
Based on the provided information, I would advise the board of directors to vote against the project. The project does not seem to generate a positive net present value (NPV) and does not meet the required rate of return.
To assess the viability of the project, we need to calculate the project's cash flows and determine the net present value (NPV) using the opportunity cost of capital of 15%.
Here is a summary of the key cash flows:
- Initial equipment cost: $250 million (occurring at t=0)
- Interest-only loan repayment: $200 million (occurring at t=4)
- Remaining cash payment: $50 million (occurring at t=4)
- Managerial costs: $100 million (occurring annually)
- Project manager salaries: $1 million (occurring annually)
- Server sales revenue: $2 million per server (110 servers in the first 2 years, 130 servers for the following 3 years)
- Operating costs: 50% of revenues (occurring annually)
- Equipment sale: $70 million (occurring at t=5)
- Reduction in existing server operating profits: $100 million (year 1), $50 million (year 2), $40 million (years 3-5)
By calculating the present value of the cash inflows and outflows using the opportunity cost of capital, we can determine the NPV. If the NPV is positive, it suggests that the project generates value for the company.
However, based on the information provided, it seems that the project's cash outflows exceed the cash inflows, resulting in a negative NPV. This indicates that the project is not expected to generate a return greater than the opportunity cost of capital. Additionally, the reduction in existing server operating profits further adds to the negative financial impact.
Considering these factors, it would be advisable for the board of directors to vote against the project, as it does not meet the investment criteria and may lead to financial losses for the company.
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Zander purchased a 100 year 5.25% bond at par 1 year ago. े Today, he sold the bond at 101.5% of par. 7 What was his holding period return? 4.75% 10.75% 1.75% 6.75% 5.75%
Zander purchased a 100-year 5.25% bond at par 1 year ago. Today, he sold the bond at 101.5% of par. The holding period return is given as follows:Holding period return = (ending price - beginning price + cash flow) ÷ beginning price × 100%Holding period return = (1.015 × 100 - 100 + 5.25) ÷ 100 × 100%Holding period return = 6.75%
A bond’s holding period return (HPR) is the total return gained or lost by an investor over the period the bond is held. It includes any interest earned on the bond as well as any capital appreciation or depreciation. Holding period return is a widely used metric to assess bond returns since it accounts for the income and capital gains (or losses) from holding a bond over a particular period.Zander purchased a 100-year 5.25% bond at par 1 year ago. Today, he sold the bond at 101.5% of par.
Since Zander held the bond for a year and sold it for 101.5% of its par value, he had an additional cash flow of 5.25% of the face value. As a result, the formula for calculating the holding period return is:Holding period return = (ending price - beginning price + cash flow) ÷ beginning price × 100%Plugging in the given values, we have:Holding period return = (1.015 × 100 - 100 + 5.25) ÷ 100 × 100%Holding period return = 6.75%Therefore, the holding period return is 6.75%.
In conclusion, Zander's holding period return is 6.75%.
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New vinyl album by the Panthers... retail-\$26.99 wholesale-\$18.00 distribution fee- 24% points- 16 deal value- $250,000 What is the sales royalty in terms of ($) ? $2.88 none of the above $4.31 $6.48 The most common record deal offered today is the distribution deal standard record deal 360 deal joint venture Question 30 ( 3 points) Record labels are responsible for paying sales royalties True False
The sales royalty for the new vinyl album by the Panthers is $4.31. To calculate the sales royalty, we need to consider the wholesale price, the distribution fee, and the points.
The wholesale price is $18.00, and the distribution fee is 24%, which means the fee is $18.00 * 0.24 = $4.32. The points are 16, and each point represents 1% of the retail price. Since the retail price is $26.99, 16 points equal 16% of $26.99, which is $26.99 * 0.16 = $4.31.
Therefore, the sales royalty for the new vinyl album by the Panthers is $4.31.
Regarding the most common record deal offered today, it is the 360 deal. A 360 deal is a type of contract where the record label gets a share of the artist's revenue from various sources, including music sales, live performances, endorsements, and merchandise. It allows the label to have a more comprehensive involvement in the artist's career beyond just album sales.
As for the statement about record labels being responsible for paying sales royalties, it is generally true. In a standard record deal, the label is responsible for accounting and distributing royalties to the artists based on the agreed terms in the contract. The label receives the revenue from sales and deducts any applicable expenses before paying the artists their share of royalties. However, the specifics can vary depending on the terms negotiated in the record deal between the label and the artist.
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Consider the cases "Pepsi's Burma Connection" & "Levi Strauss & Co. and China." Levi Strauss and Pepsi are each trying to strike a balance between profit and protecting human rights (or at least corporate image) while still participating in the nations where human rights abuses are certainly taking place.Can a business operate ethically in an area that condones human rights abuses? If so, what does it take to do that? If not, then why not?Using one of the ethical theories from Module 1, what is our responsibility, as consumers, towards people suffering human rights abuses in foreign lands? (To answer this part, you'll want to make sure you demonstrate an understanding of how the ethical theory gets you to your answers.)
Our responsibility as consumers towards people suffering human rights abuses in foreign lands is to support businesses that prioritize ethical practices and contribute to their overall happiness.
According to the ethical theory of utilitarianism, our responsibility as consumers towards people suffering human rights abuses in foreign lands is to maximize overall happiness or utility. Utilitarianism suggests that an action is morally right if it produces the greatest amount of happiness for the greatest number of people.
In the cases of Pepsi's Burma Connection and Levi Strauss & Co. in China, businesses face a dilemma of operating ethically in areas where human rights abuses occur. To strike a balance between profit and protecting human rights, businesses can take certain steps:
Transparency: The businesses should be transparent about their operations, supply chains, and any potential human rights issues they may encounter. This transparency helps consumers make informed choices and holds the company accountable.
Engagement and influence: Businesses can actively engage with local governments, communities, and NGOs to address human rights concerns. By using their influence, they can advocate for changes and improvements in human rights practices.
Due diligence: Conducting thorough due diligence on suppliers and business partners can help identify any human rights risks associated with the operations. Taking necessary measures to mitigate these risks is crucial.
Support ethical practices: Businesses can support and promote ethical practices in the areas where they operate, such as fair labor conditions, responsible sourcing, and environmental sustainability.
As consumers, our responsibility is to support companies that demonstrate a commitment to human rights and ethical practices. By boycotting or avoiding companies that condone human rights abuses, we send a message that such actions are not acceptable. Through our purchasing power and consumer choices, we can influence businesses to prioritize ethical considerations and drive positive change in foreign lands.
By applying utilitarianism, we consider the overall happiness and well-being of those suffering human rights abuses. Supporting businesses that actively work towards improving human rights conditions can contribute to the overall happiness of individuals in those areas, as well as foster a culture of corporate responsibility.
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A radio commercial for a loan company states: "You only pay 27¢ a day for each $500 borrowed." If you borrow $1,478 for 129 days, what amount will you repay, and what annual interest rate is the company actually charging? (Assume a 360-day year.) a. Amount you repay = $ (Round to two decimal places.)
The amount you will repay is $1,480.80.
According to the radio commercial, for each $500 borrowed, you only pay 27¢ per day. Therefore, for the borrowed amount of $1,478, the daily repayment can be calculated as follows:
Daily repayment = (27¢ / $500) * $1,478 = $8.09
Since the loan period is 129 days, the total repayment amount can be calculated by multiplying the daily repayment by the number of days:
Total repayment amount = $8.09 * 129 = $1,044.61
However, it's important to note that the given repayment amount of $1,478 already includes the interest charged by the loan company. To calculate the actual annual interest rate charged by the company, we can use the formula for simple interest:
Interest = Principal * Rate * Time
In this case, the principal is $1,478, the time is 129/360 years (assuming a 360-day year), and the interest is the difference between the total repayment amount and the principal. Rearranging the formula to solve for the rate, we have:
Rate = Interest / (Principal * Time) * 100
Plugging in the values, we get:
Rate = ($1,044.61 - $1,478) / ($1,478 * (129/360)) * 100 ≈ 64.19%
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Julie estimates that her investment strategy will pay her 6.00%, compounded weekly. If she is investing $14,500 today, in how many years will she reach her goal of $39,000? O 15.8 years O 15.7 years O 21.3 years
O 21.0 years
O 16.5 years
Julie's investment strategy, compounding weekly at 6.00%, will take approximately 15.7 years for her to reach her goal of $39,000.
To calculate the number of years it will take for Julie to reach her goal of $39,000, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final amount ($39,000)
P = Principal amount ($14,500)
r = Annual interest rate (6.00% or 0.06)
n = Number of times interest is compounded per year (52 weeks in a year, so n = 52)
t = Number of years
Substituting the given values into the formula, we have:
$39,000 = $14,500(1 + 0.06/52)^(52t)
Dividing both sides of the equation by $14,500 and simplifying:
2.689655172 = (1.00115384615)^(52t)
Taking the natural logarithm of both sides:
ln(2.689655172) = ln(1.00115384615)^(52t)
Using the logarithmic property ln(a^b) = b * ln(a), we have:
ln(2.689655172) = 52t * ln(1.00115384615)
Solving for t:
t = ln(2.689655172) / (52 * ln(1.00115384615))
Using a calculator, we find:
t ≈ 15.7 years
Therefore, it will take approximately 15.7 years for Julie to reach her goal of $39,000.
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Consider the following portfolio:
(i) one sold (written) European put option;
(ii) one bought (held) European call option;
(iii) one short-sold unit of stock (the same stock that both the put and call options are written over);
(iv) one loan (for which the portfolio is the lender) for $105.
At time t, S = $110, X = $110, c (call option price) = $15, p ( put option price) = $10. R(t,T) = 1.1
a) If at time T, S = $120 calculate the net outcome (value) of the portfolio. (3 pts)
b) Assume now at T that S = $100. Calculate the net outcome (value) of the portfolio at T. (3 pts)
c) What observation can be made about the put-call parity relationship? (4 pts
The stock price at expiration determines the portfolio's net result. The net result is $105 when the stock price is $120, and it is $125 when the stock price is $100. These findings suggest that the put-call parity relationship may not always hold true and that other variables, such as transaction costs or mispricing, may be having an impact on the portfolio's value.
a) The portfolio's net result at time T, when S = $120, can be calculated as follows:
The value of the put option is zero because it is out of the money.
The call option is worth $10 because it is in the money ($120 - $110).
The value of the short-sold shares is ($110 - $120) = -$10.
The amount of the loan stays the same at $105.
Therefore, the net outcome of the portfolio is $0 + $10 - $10 + $105 = $105.
b) The portfolio's net result at time T, with S equal to $100, can be calculated as follows:
The value of the put option is ($110 - $100) = $10 because it is in the money.
The value of the call option is zero because it is out of the money.
The stock that was short sold is worth $10 ($110 minus $100).
The loan sum stays at $105 as before.
The portfolio's net result is therefore $10 + $0 + $10 + $105 = $125.
c) According to the put-call parity relationship, the value of a portfolio made up of a loan, a short-sold stock, a written put option, and a held call option should equal the difference between the strike price and the stock price at expiration, discounted at the risk-free rate.
But in this case, we can see that the portfolio's net result is not the same as the spread between the strike price and the stock price. This suggests that put-call parity may not always be maintained because of things like transaction costs, market frictions, or mispricing.
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If at the current output of \( X \) the \( P_{X}>M C_{X} \), then society gains by A. increasing the cost of producing \( X \). B. raising the price of \( X \). C. producing more \( X \). D. producing
If at the current output of X thethe \( P_{X}>M C_{X} \) where P_{X} represents price of X and M C_{X} represents marginal cost of X, society gains by the correct option B) raising the price of \( X \).
When the price of X is greater than the marginal cost of producing, it indicates that there is a positive difference between the price at which the good is sold and the additional cost incurred to produce an additional unit. This situation suggests that there is potential for increased profit and societal gain.
Choosing Option B, raising the price of X, can be beneficial for society in this scenario. By increasing the price, the firm can generate additional revenue without significantly increasing their production costs. This increased revenue can lead to higher profits for the firm, which can incentivize them to invest in research, development, and expansion. This, in turn, can contribute to economic growth and provide benefits to society.
It is important to note that this analysis assumes a competitive market structure where there are no market imperfections, such as monopoly power or externalities. In reality, other factors such as market demand, competition, and social welfare considerations may also influence the optimal decision.
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) Find the marginal product of inventories (MPH). b) Derive an expression for the "desired equilibrium stock of inventories" (H ∗ ) as a function o and output Y by equating the cost of capital to MPH. If r=0.1, b=0.05, and Y=5,000, what the desired stock of inventories? (the stock of inventories does not depreciate, the price of inventories is the same as the price of output, and taxes are ignored, then the real "cost of capital" for inventories is just the interest rate r.) c) If r rose to 0.14, how would the desired stock of inventories change? " (15 分) Assume that the production function is given by Y=AK a H b L 1−a−b , where H is the slock of inventories
According to given information if r rose to 0.14, the desired stock of inventories (H*) would change.
To find the marginal product of inventories (MPH), we need to take the derivative of the production function with respect to H. Using the production function
Y = AKa * Hb * L(1-a-b),
where H represents the stock of inventories, the marginal product of inventories (MPH) is given by the derivative of the production function with respect to H:
MPH = ∂Y/∂H
MPH = b * AKa * H(b-1) * L(1-a-b)
To derive an expression for the desired equilibrium stock of inventories (H*), we equate the cost of capital (r) to MPH. Assuming the real cost of capital is equal to the interest rate (r), we have:
r = MPH = b * AKa * H(b-1) * L(1-a-b)
To find the desired stock of inventories (H*) as a function of output (Y), we can rearrange the equation:
H* = (r / (b * A * Ka * L(1-a-b)))(1/(b-1))
Given r = 0.1, b = 0.05, Y = 5,000, and the other parameters are not provided, we cannot calculate the desired stock of inventories (H*) without more information.
However, without specific values for the other parameters (A, K, L), we cannot determine the exact change in the desired stock of inventories.
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