Mary's budget constraint is given by PxX+PyY=60, and Px=$5, Py=$2. Suppose Mary's utility function is given by the equation U = XY, where U is the level of utility measured in utility and X and Y refer to good X and good Y respectively. You are also told that the marginal utility of good X can be expressed as MUx = Y; and the marginal utility of good Y can be expressed as MUy = X. a. What are the X and Y in the market basket (X,Y) that maximize Mary's utility given her budget constraint? b. What is the marginal rate of substitution at the utility-maximizing market basket (X,Y). c. How does your answer to (a) change if the price of good X doubles? d. Can you identify a utility function for which the chosen bundle would not change when the price of good X doubled?
Answers
To maximize Mary's utility given her budget constraint, we first set up the Lagrange equation by combining the utility function U = XY with the budget constraint equation 5X + 2Y = 60.
a. To maximize Mary's utility given her budget constraint, we need to find the market basket (X, Y) that satisfies the budget constraint and maximizes the utility function U = XY.
We are given the budget constraint equation: PxX + PyY = 60, where Px = $5 and Py = $2. Substituting the values, we have:
5X + 2Y = 60.
To maximize utility, we can use the method of Lagrange multipliers. We set up the following equation:
L = XY + λ(5X + 2Y - 60),
where λ is the Lagrange multiplier.
Taking partial derivatives and setting them equal to zero, we have:
∂L/∂X = Y + 5λ = 0,
∂L/∂Y = X + 2λ = 0,
and the budget constraint equation: 5X + 2Y = 60.
Solving the system of equations, we find:
Y = -5λ,
X = -2λ.
Substituting these values into the budget constraint equation, we have:
5(-2λ) + 2(-5λ) = 60,
-10λ = 60,
λ = -6.
Substituting λ = -6 back into X and Y, we find:
X = -2(-6) = 12,
Y = -5(-6) = 30.
Therefore, the market basket (X, Y) that maximizes Mary's utility given her budget constraint is (12, 30).
b. The marginal rate of substitution (MRS) measures the rate at which Mary is willing to trade one good for another while maintaining the same level of utility. In this case, the MRS can be calculated as the ratio of the marginal utilities:
MRS = MUx / MUy = Y / X.
At the utility-maximizing market basket (X, Y) = (12, 30), the MRS is:
MRS = 30 / 12 = 2.5.
c. If the price of good X doubles, it means that Px = $10. In this case, the budget constraint equation becomes:
10X + 2Y = 60.
Using the same method as in part (a), we can solve for the new market basket (X, Y) that maximizes Mary's utility. However, the specific values of X and Y will change due to the new budget constraint equation.
d. To find a utility function for which the chosen bundle would not change when the price of good X doubles, we need to find a utility function that exhibits perfect complements between X and Y. One such utility function is the Leontief utility function:
U = min(aX, bY),
where a and b are positive constants.
With this utility function, the chosen bundle (X, Y) will not change when the price of good X doubles because the utility depends on the minimum of the quantities of X and Y. Thus, the consumer will continue to consume X and Y in fixed proportions regardless of the relative prices.
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Related Questions
returns to scale is a concept that operates part 2 a. only in the short run. b. only in the long run. c. in both the long run and the short run. d. in either the long run or the short run depending on the industry of the firm.
Answers
Returns to scale refer to the relationship between input and output in the production process. This concept does not operate only in the short run or only in the long run, but rather in both the short run and long run.
The scale of production, which refers to the level of output a firm is producing, is a key determinant of returns to scale. When a firm increases its scale of production, it may experience increasing returns to scale, constant returns to scale, or decreasing returns to scale, depending on the industry of the firm.
In industries where fixed costs are high, such as automobile manufacturing, a firm may experience increasing returns to scale when it expands its operations. In contrast, in industries where variable costs are high, such as farming, a firm may experience decreasing returns to scale when it increases its output. Constant returns to scale occur when a firm's output increases at the same rate as its inputs. In summary, returns to scale are a critical consideration for firms in both the short run and long run, and the industry in which a firm operates plays a significant role in determining the impact of changes in scale on returns to scale.
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Chloe, a textile designer, creates a flat fabric with a pattern that resembles the skin of a crocodile. Which design element is Chloe experimenting with?
A. undertone
B. shape
C. saturation
D. texture
Answers
Chloe, a textile designer, creates a flat fabric with a pattern that resembles the skin of a crocodile. Chloe is experimenting with texture.
Fabric is an umbrella term that includes numerous fiber-based materials, inclusive of fibers, yarns, filaments, threads, specific cloth types, and so forth. At first, the word "textiles" simplest cited woven fabric. However, weaving isn't always the only production method, many different methods were later developed to shape textile systems based on their meant use. Knitting and non-woven are different famous types of cloth manufacturing. Inside the cutting-edge world, textiles fulfill the fabric needs for flexible applications, from easy daily garb to bulletproof jackets, spacesuits, and medical doctor's gowns.
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Which of the following statements best characterizes the bottom line of security for e-commerce?
A) Good security is expensive but critical, and it is the responsibility of the customer to ensure that his or her private information is secure.
B) Good security is inexpensive but critical, and it is the responsibility of the customer to ensure that his or her private information is secure.
C) Good security is expensive but crítical, and it is the responsibility of the business to ensure that the customer's private information is secure.
D) Good security is inexpensive but critical, and it is the responsibility of the business to ensure that the customer's private information is secure.
Answers
Answer:
Good security is expensive but critical, and it is the responsibility of the business to ensure that the customer's private information is secure. C
Explanation:
What do you think Anielski means by the phrase
"a depletion of the social capital upon which an
economy depends"? Do you agree with him?
Answers
Answer: yes I agree the him
Explanation:
The Harris Company purchased equipment for $15,000 on December 1. It is estimated that annual depreciation on the computer will be $3,000. If financial statements are to be prepared on December 31, the company should make the following adjusting entry
Answers
The entry will include Depreciation Expenses for $1,750 and Accumulated Depreciation for $1,750
Here, we are to first calculate the Depreciation expenses while observing that the date runs for 1 month (From December 2 - December 31).
The depreciation expense will equals Annual depreciation of computer * 1/12
Depreciation expense = $3,000 * 1/12
Depreciation expense = $250
The adjusting entry will entails:
Date Account titles and explanation Debit Credit
31 Dec Depreciation expenses $250
Accumulated depreciation $250
(Entry to record depreciation expenses)
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what is the excecutive summary for candles?
Answers
Candles have become a popular choice for enhancing relaxation, creating mood lighting, and adding a touch of luxury to personal spaces.
The candle industry has witnessed steady growth in recent years, driven by factors such as increasing consumer demand for home fragrance products, rising popularity of aromatherapy, and a growing focus on creating a cozy and comforting ambiance.
1. Key Market Insights:
Market Size and Growth: The global candle market is estimated to reach $XX billion by 2027, reflecting a compound annual growth rate of X%. Market Segmentation: The candle market can be segmented based on types such as scented candles, pillar candles, votive candles, and decorative candles. Competitive Landscape: The candle industry is highly competitive, with both large multinational companies and smaller boutique brands vying for market share.2. Opportunities and Challenges:
Growing Demand for Natural and Eco-Friendly Candles: Consumers are increasingly seeking candles made from natural and sustainable materials, free from harmful chemicals. Expanding E-commerce Market: The rise of e-commerce has opened up new avenues for candle sales, allowing companies to reach a broader customer base globally. Rising Production Costs: Fluctuating prices of raw materials, such as wax, fragrance oils, and packaging materials, pose a challenge to candle manufacturers.For such more question on personal:
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Maintain a detailed working knowledge of all equipment deficiencies within the Work Center. The Work Center Supervisor will use the Current Ship's Maintenance Project (CSMP) as a daily working document for the scheduling of any maintenance actions not included on the PMS schedules. B. Use SKED's revision editor to ensure that all PMS changes have been properly annotated and applied to the schedule prior to the LCPO/LPO, Division Officer, and Department Head reviews and finalization. C. Schedule weekly Work Center maintenance and supervise its proper accomplishment. D. Ensure the status of Work Center planned maintenance is correctly reflected on the PMS schedules. E. Ensure the Division Officer and Division LCPO/LPO are advised of all 3-M System activity within the Work Center. F. Maintain an adequate supply of 3-M System materials within the Work Center. G. Ensure prompt reporting of all material deficiencies and completed maintenance actions as required. H. Ensure all equipment changes, adds and removals, regardless of whether the action is performed by command personnel or outside activities, is present or modified in the OMMS database and, if not present, is reported via 4790/CK to the Configuration Data Manager (CDM). A PMS FBR shall be submitted requesting a LOEP change for new adds and for equipment removals. This includes all alterations that result from maintenance actions which modify or change installed equipment as well as planned alterations, its called?
Answers
The correct answer is Maintain an adequate supply of 3-M System materials within the Work Center. The Maintenance Material Management (3-M) System is what this is known as.
The US Navy uses the system, a thorough maintenance management programme, to guarantee the material readiness of ships and submarines. In addition to maintaining accurate records of equipment deficiencies, maintenance actions, and material usage, the 3-M System contains methods for planning, scheduling, and tracking maintenance tasks.
The Current Ship's Maintenance Project (CSMP), Planned Maintenance System (PMS), SKED's revision editor, and the OMMS database are among the tools and papers used in this process. The system's goal is to guarantee that equipment is maintained in a way that is safe, dependable, and economical and that maintenance tasks are correctly planned, carried out, and recorded.
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Note that common skills are listed toward the top and less common skills are listed toward the bottom. According to O*NET, what are some common skills needed by Lawyers? Select four options.
installation
active listening
speaking
critical thinking
reading comprehension
equipment maintenance
Answers
The common skills needed by lawyers are active listening, speaking, critical thinking and reading comprehension.
The skills can be noted as -
Active Listening - To completely comprehend their viewpoints and obtain all pertinent facts, attorneys need to listen intently to their clients, witnesses, and other parties involved in a case.Speaking - Lawyers need to be able to communicate clearly both orally and in writing with their clients, juries, judges, and other lawyers.Critical Thinking - Lawyers must be able to evaluate intricate legal issues and create plans for resolving conflicts and attaining their clients' objectives.Reading comprehension - Complex legal papers, court rulings, and other important items must be read and understood by lawyers.Read more about lawyers on:
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How has Apple been able to sustain its competitive advantage in the smartphone industry?A. by reducing its network effects B. by targeting its new products and services toward laggards C. by driving the price for the end user to zero d. by regularly introducing incremental improvements in its products
Answers
The correct answer is D. By regularly introducing incremental improvements in its products.
Explanation:
Apple is a worldwide company that specializes in technology this includes smartphones, computers, smart watches, among others. Besides this, Apple is one of the most powerful and popular companies in this area and this reputation has been preserved for years. One of the factors that make Apple able to sustain its competitive industry is the fact this company is constantly improving its products and launching these to the products. Indeed, every year the company launches new improved versions of smartphones, computers, etc. which is essential because this keeps the interest in consumers.
josiah+owes+$3,500+on+his+credit+card+with+a+minimum+percentage+of+3%+or+a+minimum+payment+of+$100,+whichever+is+higher.+how+much+is+the+minimum+payment+due?
Answers
The minimum payment due for Josiah is $100. When an individual borrows money, they must repay it with interest.
Credit cards, as well as most types of loans, charge interest on the outstanding balance. In this case, Josiah owes $3,500 on his credit card. His minimum payment will be calculated by taking the maximum between $100 and 3% of his outstanding balance.
Minimum payment due = max (3% x $3,500, $100)
= max ($105, $100)
= $100
Therefore, Josiah must pay a minimum of $100 to avoid late fees and penalty interest charges on his credit card. If Josiah makes only the minimum payment, it will take him a long time to pay off his outstanding balance, and he will end up paying a lot of interest. This is because most of his minimum payment will go towards paying the interest charges and only a small portion towards reducing the outstanding balance.
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How does the R&D team support the product development process?
Answers
Research and development (R&D) includes the activities companies do to innovate and introduce new products and services. It is often the first step in the development process. The goal is usually to bring a new product or service to market and increase the company's revenue.
It support product development by -Sustainable innovation in products:
Small changes to products that make them cheaper or more powerful. These optimizations require some capital investment and can be difficult for competitors to replicate. It also provides a lead time of about a year for the competition to catch up.
Disruptive innovation:
A place where whole products can be replaced with new innovations. This is more often achieved when organizations split staff into smaller teams working on new projects. These new projects may complement or complement existing product lines. This largely depends on whether the organization is able to form such teams to work on new innovations and whether the organization has the means to foster new innovations as a separate department.
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if the government issues each firm a non-tradable permit to produce 700 tons of pollution per year, what will be the cost of pollution reduction?
Answers
if the government issues each firm a non-tradable permit to produce 700 tons of pollution per year, the cost of pollution reduction will be $700.
What is pollution permits?
Pollution permits involve giving firms a legal right to pollute a certain amount e.g. 100 units of Carbon Dioxide per year.If the firm produces less pollution it can sell its pollution permits to other firms.However, if it produces more pollution it has to buy permits from other firms or the government.This creates a market for pollution permits with the price set by demand and supply.The aim of pollution permits is to provide market incentives for firms to reduce pollution and reduce the external costs associated with it. For example, it is argued carbon dioxide emissions contribute towards global warming.Pollution permits can also be a way for the government to raise revenue, by selling firms these permits to allow pollution.To learn more about pollution permits
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Compare the product life cycle to the business cycle. Include at least one similarity and one difference.
Answers
Explanation:
A product life cycle refers to the life of a product in the market, and the processes that it goes through in relation to the business costs, as well as the sales measures. The business life cycle is the progression of a business in phases over time and is most commonly divided into five stages: launch, growth, shake-out, maturity, and decline. One major similarity between the product and project life cycles is that both are comprised of different and several phases or stages. These phases are very vital because they ensure that the requirements of the cycles are provided for and that both the goals and the objectives of the cycles are achieved. For instance, while some of the phases of the product cycle include the growth and maturation stages, those of the project life cycle include the birth and closure phases. The aim of integrating the phases in the life cycles is to ensure that there is proper coordination of the activities that take place in the cycles. The two cycles are closely related to each other. In some cases, a product may consist of more than one project, where the projects act as the subset of the product. This makes it necessary for the bigger product view to be put into consideration when it comes to project management. The product and project life cycles face various challenges which demand the adoption of strategies in the cycle phases, with the aim of ensuring that the cycles give the desired results.
Use an IF function in Cell G15 to calculate the Net Price. There is a discount of 2% applied to the Unit Price in E15 if 2 or more items are ordered and a discount of 5% applied if 10 or more are ordered. Refer to the appropriate discounts in cells E10, E11 and E12 for your IF function arguments. Use absolute and relative references when appropriate
Answers
By using this IF function with nested IF statements, you can calculate the appropriate net price based on the quantity ordered and apply the corresponding discount.
To calculate the Net Price using an IF function in cell G15, you can use the following formula:
=IF(D15>=10, E15*0.95, IF(D15>=2, E15*0.98, E15))
Here's a step-by-step explanation of how this formula works:
1. The first part of the formula, "D15>=10", checks if the value in cell D15 (representing the quantity ordered) is 10 or more.
2. If the quantity is 10 or more, the formula multiplies the unit price in cell E15 by 0.95 (representing a 5% discount) using the expression "E15*0.95".
3. If the quantity is less than 10, the formula moves to the next part of the IF function.
4. The second part of the formula, "D15>=2", checks if the quantity is 2 or more.
5. If the quantity is 2 or more, the formula multiplies the unit price in cell E15 by 0.98 (representing a 2% discount) using the expression "E15*0.98".
6. If the quantity is less than 2, the formula moves to the final part of the IF function.
7. The final part of the formula simply returns the unit price in cell E15 as the net price, without any discount.
By using this IF function with nested IF statements, you can calculate the appropriate net price based on the quantity ordered and apply the corresponding discount.
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10. According to the inventory life cycle,
after a retailer receives products, the next
step is
• A. to display products.
• B. that the retailer prices products.
• C. inventory is purchased.
• D. that the customer shops the store.
B
Answers
Answer:
B. that the retailer prices products.
Explanation:
In the inventory life cycle, after a retailer receives products, the usual next step is to display the products, arranging them properly for customer viewing and ensuring they have accurate price tags.
Explanation:According to the inventory life cycle in the retail business, after a retailer receives products, the next step is usually to display products (Option A). This is because once products are received, the goal is to prepare them for sale to customers as quickly as possible. Proper product display includes arranging goods attractively, often following visual merchandising principles, and making sure all items have accurate price tags so customers can make informed purchasing decisions. Following product display, customers can then shop the store (Option D).
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what time is it? pls tell meee
Answers
Answer:
it is 11.20 am in my phone
HOPE IT HELPS
Calculate tesla's current ratio (current assets / current liabilities) at the last two balance sheet dates. (round to two decimal places. )based on the current ratio, tesla was more liquid in 2020 than it was in 2019. Truefalse2 pointsquestion 9based on the debt to assets ratio (total liabilities / total assets), of tesla's assets were provided by debt in 2020 than in 2019. A. Moreb. Lessc. Same amountd. Cannot be determined2 pointsquestion 10according to the accrued liabilities note, tesla had $654 (in millions) in payroll and related costs that was unpaid at the most recent balance sheet date,a. Trueb. FALSE
Answers
Answer to Question 9:
Tesla had a higher debt to assets ratio in 2020 than in 2019. This indicates that a higher proportion of Tesla's assets were financed by debt in 2020 compared to 2019. Therefore, the correct answer is: A. More.
To calculate Tesla's debt to assets ratio, we need to divide its total liabilities by its total assets. Using the information from Tesla's annual reports for 2019 and 2020, we can find:
Debt to assets ratio for 2019 = Total liabilities / Total assets = 11,463 / 34,309 = 0.33
Debt to assets ratio for 2020 = Total liabilities / Total assets = 16,435 / 48,005 = 0.34
From the above calculation, we can see that Tesla had a higher debt to assets ratio in 2020 than in 2019. This indicates that a higher proportion of Tesla's assets were financed by debt in 2020 compared to 2019.
Therefore, the correct answer is: A. More.
Answer to Question 10:
According to the accrued liabilities note in Tesla's most recent balance sheet, Tesla had $654 million in payroll and related costs that were unpaid at the balance sheet date. Therefore, the correct answer is: A. True. This means that as of the balance sheet date, Tesla had $654 million in outstanding payroll and related expenses that it owed to its employees but had not yet paid. Accrued liabilities are a common type of short-term liability that arise when expenses are incurred but not yet paid. They are recorded on the balance sheet as a liability and reduce the company's equity.
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If the Table Analyzer finds unrelated data in a table, what does it suggest a user do?
O split the table into queries
O break the table into multiple tables
O move all the data to a new report
O move some data to a different database
Answers
Answer:
break the table into multiple tables
Explanation:
Answer:
B
Explanation:
QUESTION 4 Risk Management: The following phrase defines/explains Tier 1: • Tier 1 addresses the risk of an organization from the view of establishing and implementing a Governance structure that are inline with the strategic goals and objectives of organizations and the requirements defined by federal laws, directives, policies, regulations, standards, and missions/business functions. It also defines the following: o Structure • Establish the risk management strategy • Governance True O False
Answers
True By doing so, Tier 1 ensures that risk management is embedded in the organization's decision-making processes and aligns with its strategic direction.
The statement is true. Tier 1 in risk management refers to the level that focuses on establishing and implementing a governance structure aligned with the strategic goals and objectives of the organization. It involves ensuring compliance with federal laws, directives, policies, regulations, standards, and missions/business functions. Tier 1 is responsible for defining the risk management strategy and governance framework within the organization. This includes setting up the necessary structures and processes to effectively manage risks and ensure that risk management practices are integrated into the overall governance framework
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SRC Refrigeration Company manufactures and sells refrigerator display units for flowers. A salesperson for the company is calling on a large supermarket chain to try to interest them in SRC's new refrigeration unit. The salesperson has set as his sales call objective to replace all refrigeration units in the 235-store chain with SRC units. This sales call objective would be an example of a(n) ______________ call objective. Question 48 options: optimistic minimum primary crazy inspirational
Answers
Answer:
A. optimistic
Explanation:
A. optimistic
B. minimum
C. primary
D. secondary
E. basic
Minimum call objective can be regarded as basic business purpose which is a case that ones sales person needed to achieve so that the call can be successful. And the optimistic call objective can be regarded as optimistic outcome that sales person could think of in given sales.
Why would a person change their business status to a LLC?
A. To gain tax breaks
B. To limit their personal liability
C. To help obtain funding through the sale of stock
D. Because it is the easiest form for setting up your business
Answers
Answer:
A) to gain tax breaks
Explanation:
A common reason for changing a co. to an LLC is to avoid double taxation
Which of the following is an example of a long-term debt?
A. A student loan.
B. A debit card purchase.
C. A term life insurance policy.
D. A stock portfolio.
Answers
Which statement best defines tuition?
Tuition is federal money awarded to a student.
Tuition is aid given to a student by an institution.
Tuition is money borrowed to pay for an education.
Tuition is the price of attending classes at a school.
Answers
Answer:
D
Explanation:
Edge 2021
The statement that best describes tuition is the price of attending classes at a school.
What is tuition?Tuition is the payment made by a student for instruction or lessons received at a college or university. The tuition payed by a student depends on:
the complexity of the course: the more complex the course is, the higher tuition would be.the duration of the course: the longer the course is, the higher tuition would be.To learn more about tuition, please check: https://brainly.com/question/16882987
1. Choose a well-known company that you know of, and answer the following questions about it:
Answers
Answer:
what type of company
and which other questions
Four people are applying for a job. This chart shows the company’s favorite characteristic of each of these job applicants:
Answers
[Quality of Services Marketing]
1. Which of the following is an example of a B2B internet service? [Answer: Tech Support]
2. Many companies have sophisticated tracking software [Answer: Critical incident technique]
3. Which of the following is not a characteristic of a service? [Answer: Reliability]
4. What is the encounter between service-consumer that occurs during delivery of the service is known as? [Answer: Experince qualities]
5. Your local credit union offers a variety of services to its members [Answer: Fresh-baked cookies and gourmet cookies]
6. The measure of the difference between a customer's expectation [Answer: Gap analysis]
7. Shepherd University is launching new services to attract more students [Answer: Bachelor's degrees]
8. A large store that sells groceries also has a large pharmaceuticals section with a 24-hour pharmacy. [Answer: Offering free coffee tastings]
9. John always takes his car to the same place for an oil change. [Answer: Augmented]
10. Which of the following is not a service of quality attribute? [Answer: Response qualities]
- You can thank me by thanking my previous answers, would be very appreciated -
Answers
All of your answers are correct.
The questions given and their appropriate responses can be seen below:
1. Tech Support is an example of a B2B internet service.
2. Many companies have sophisticated tracking software - Critical incident technique.
3. Reliability is not a characteristic of a service.
4. Experience qualities is the encounter between service-consumer that occurs during delivery of the service
5. Your local credit union offers a variety of services to its members such as Fresh-baked cookies and gourmet cookies.
6. Gap analysis is the measure of the difference between a customer's expectation.
7. Shepherd University is launching new services such as Bachelor's degrees to attract more students.
8. Offering free coffee tastings is a large store that sells groceries also has a large pharmaceuticals section with a 24-hour pharmacy.
9. John always takes his car to the same place for an oil change - Augmented
10. Response qualities is not a service of quality attribute.
What is Service marketing?This is defined as the marketing that businesses that provide a service to their customers use to increase brand awareness and sales.
The answers to the questions given can be seen appropriately given above.
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prepare a double entry ledger entries January 3 took out of the cash till$50 and put into the business by cheque Jan 4 the proprietor put a further$5000 in to business by cheque .please I need it quick
Answers
Explanation:
In the first entry, $50 is taken out of the cash till and put into the business as drawings. The effect is a decrease in the cash balance and an increase in the drawings account.
In the second entry, the proprietor puts a further $5000 into the business by cheque. The effect is an increase in the capital account and an increase in the bank balance.
It's important to note that "Drawings" and "Capital" are the accounts used to record the personal transactions of the business owner in this case, it is assumed that the business is a proprietorship. Other forms of business may have different accounts to record the personal transactions of the owne
In a balanced balance sheet, if liabilities are $2,000 and owner’s equity is $3,300, what must assets be ____?
$5,300
$2,000
Not enough information to determine assets
$3,300
Answers
Answer:
5300
Explanation:
assets=equitys +liabilities
Dera diamonds inc. is a premium jeweler. its clientele includes movie stars, politicians, businessmen, and popular socialites. it has a team of jewelry experts that designs jewelry for each of its clients from scratch. everything is made to meet the specific requirements of the clients, and no two jewelry pieces produced by this company has ever been identical. this is an example of
Answers
Answer:
customization
Explanation:
From the question we are informed about Dera diamonds inc. which is a premium jeweler. its clientele includes movie stars, politicians, businessmen, and popular socialites. it has a team of jewelry experts that designs jewelry for each of its clients from scratch. everything is made to meet the specific requirements of the clients, and no two jewelry pieces produced by this company has ever been identical. The case above is an example of customization. Customization in business is also regarded as "built-to-order" it involves the modification of products/goods to suit the personal specification or preference of the clients/customer, it is a way to deliver the product of the customer according to the specified requirements. It a business strategy and when done very well, it makes the clients to always patronize again.
Tim Horton wants to raise funds to open a branch of their coffee shop in Trinidad. To raise the funds, Tim Horton would sell bonds 100 $1,000 par value with a coupon interest rate of 6%. The bonds would mature in 15 years and interest would be paid semi-annually. The required rate of return is expected to be 8%.
Requirement:
a) Calculate the value of one bond
b) What is the total amount Tim Horton would raise if all bonds were sold?
Answers
Answer:
a) The value of one bond is $837.08.
b) The total amount Tim Horton would raise if all bonds were sold is $83,708.
Explanation:
a) Calculate the value of one bond
This can be calculated as follows:
Annual coupon = Bond face value * Coupon interest rate = $1,000 * 6% = $60
Annual coupon discount factor = ((1 - (1 / (1 + r))^n) / r) .......... (1)
Where;
r = required semi-annual rate of return = required annual rate of return / number of semi-annual in a year = 8% / 2 = 0.08 / 2 = 0.04
n = number of semi-annuals = number of years * number of semi-annual in a year = 15 * 2 = 30
Substituting the values into equation (1), we have:
Semi-annual coupon discount factor = ((1-(1/(1 + 0.04))^30) / 0.04) = 17.2920333006645
Present value of coupon = ((Annual coupon / number of semi-annual in a year) * Semi-annual coupon discount factor) = (($60 / 2) * 17.2920333006645 = $528.76
Present value of the face value of the bond = Face value of the bond / (1 + r)^n = ($1,000 / (1 + 0.04)^30 = $308.32
Therefore, we have:
Bond value = Present value of coupon + Present value of the face value of the bond = $528.76 + $308.32 = $837.08
Therefore, the value of one bond is $837.08.
b) What is the total amount Tim Horton would raise if all bonds were sold?
Number of bonds expected to be sold = 100
Value of one bond = $837.08
Total amount that would be raised = Number of bonds expected to be sold * Value of one bond = 100 * $837.08 = $83,708
Therefore, the total amount Tim Horton would raise if all bonds were sold is $83,708.