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In Lesson Eight you've learned how to construct confidence intervals for population parameters and proportions, based on data from samples.
In: Statistics and Probability
In this simple insurance model, a company has a
monopoly over a small market. There are 100K potential customers
with a low risk profile, 60K potential customers with a medium risk
profile, and 10K potential customers with a high risk
profile. A person’s risk profile is important as it
determines how much insurance is worth to the customer and how much
money the customer will cost on average to the insurance company.
The following table summarizes the estimates put together by the
company:
Low risk profile
Medium risk profile
High risk profile
Number of potential customers
100,000
60,000
10,000
Expected expense per customer
$2K
$6K
$14K
Maximal price the customer is
ready to pay for insurance
$3K
$7K
$15K
Remark: Explaining where these numbers come from would
require a subtler model that describes the risk covered by the
insurance policy. While there is no need to do this for the purpose
of this exercise, notice though how the maximal price a customer is
ready to pay is always larger than the expected expense the
insurance company would incur for that customer. This is the case,
for instance, if potential customers are risk averse while the
insurance company is risk neutral.
QUESTIONS:
(a) What is the average cost per customer
if the insurance company insures all 170K potential
customers?
(b) The number computed in (a) is thus the
minimal price the company would need to charge to make it
profitable to serve everyone. Assume here that customers know their
risk profile. Would all potential customers want to buy insurance
at that price?
(c) Suppose the insurance company chooses the price at
which it sells its policy. Consider a classic case of asymmetric
information: customers know their risk profile, but the insurance
company cannot identify the risk profile of its potential
customers. By deciding to sell at a price $p, all customers with a
maximal price larger or equal to $p will buy the policy (and the
firm must incur the expected expense associated to its customers,
that is, it cannot renege on the terms of its policy). At which
price will the insurance company sell its policies (assuming it
aims to maximize profit)? What is the profit it realizes?
Hint: The company will always charge the maximal price
customers of some risk profile are ready to pay. So it will charge
either $3K (in which case customers of all risk profiles will buy
the policy), or $7K (in which case only customers with medium to
high risk will buy the policy), or $15K (in which case only high
risk customers will buy the policy). What scenario gives the best
profit?
Remark: This question illustrates well the concept of
adverse selection. Notice how customers who are ready to pay more
for the policy are also more costly to the insurance
company.
(d) Suppose now the company can identify
each potential customer’s risk profile (e.g. by doing a thorough
physical exam in case of some medical insurance). To maximize
profit, at what price will it sell its policy to low risk
customers, at what price will it sell its policy to medium risk
customers, and at what price will it sell its policy to high risk
customers? What is the total profit in this case, and how does it
compare to profit in (c)? This should illustrate the substantial
loss in profit that asymmetric information can generate.
In: Economics
Edward Sayers has collected information showing that the average Amazon Prime customer spent $2,486 over the last twelve months compared to $544 for non-Prime Amazon customers. It is known that the amount spent by Amazon Prime customers is normally distributed, with a standard deviation of $125.
What is the probability that an Amazon Prime customer spent more than $2,771 over the last twelve months? Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer to 4 decimal places, using conventional rounding rules.
ANSWER:
What is the probability that an Amazon Prime customer spent less than $2,301 over the last twelve months? Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer to 4 decimal places, using conventional rounding rules.
ANSWER:
What is the probability that an Amazon Prime customer spent more than $2,206 over the last twelve months? Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer to 4 decimal places, using conventional rounding rules.
ANSWER:
What percent of the Amazon Prime customers spent between $2,366 and $2,846 over the last twelve months? Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer to 2 decimal places, using conventional rounding rules.
ANSWER: %
What percent of the Amazon Prime customers spent less than $2,806 over the last twelve months? Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer to 2 decimal places, using conventional rounding rules.
ANSWER: %
Four percent of the Amazon Prime customers spent less than what amount over the last twelve months? Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer to 2 decimal places, using conventional rounding rules.
ANSWER: $
In: Statistics and Probability
Wally’s Widget Company (WWC) incorporated near the end of 2011. Operations began in January of 2012. WWC prepares adjusting entries and financial statements at the end of each month. Balances in the accounts at the end of January are as follows: Cash $ 21,470 Unearned Revenue (25 units) $ 5,300 Accounts Receivable $ 12,500 Accounts Payable (Jan Rent) $ 3,200 Allowance for Doubtful Accounts $ (1,850) Notes Payable $ 15,500 Inventory (30 units) $ 2,400 Contributed Capital $ 6,900 Retained Earnings – Feb 1, 2012 $ 3,620 • WWC establishes a policy that it will sell inventory at $165 per unit. • In January, WWC received a $5,300 advance for 25 units, as reflected in Unearned Revenue. • WWC’s February 1 inventory balance consisted of 30 units at a total cost of $2,400. • WWC’s note payable accrues interest at a 12% annual rate. • WWC will use the FIFO inventory method and record COGS on a perpetual basis. February Transactions 02/01 Included in WWC’s February 1 Accounts Receivable balance is a $1,700 account due from Kit Kat, a WWC customer. Kit Kat is having cash flow problems and cannot pay its balance at this time. WWC arranges with Kit Kat to convert the $1,700 balance to a note, and Kit Kat signs a 6-month note, at 9% annual interest. The principal and all interest will be due and payable to WWC on August 1, 2012. 02/02 WWC paid a $600 insurance premium covering the month of February. The amount paid is recorded directly as an expense. 02/05 An additional 170 units of inventory are purchased on account by WWC for $12,750 – terms 2/15, n30. 02/05 WWC paid Federal Express $510 to have the 170 units of inventory delivered overnight. Delivery occurred on 02/06. 02/10 Sales of 140 units of inventory occurred during the period of 02/07 – 02/10. The sales terms are 2/10, net 30. 02/15 The 25 units that were paid for in advance and recorded in January are delivered to the customer. 02/15 20 units of the inventory that had been sold on 2/10 are returned to WWC. The units are not damaged and can be resold. Therefore, they are returned to inventory. Assume the units returned are from the 2/05 purchase. 02/16 WWC pays the first 2 weeks wages to the employees. The total paid is $2,700. 02/17 Paid in full the amount owed for the 2/05 purchase of inventory. WWC records purchase discounts in the current period rather than as a reduction of inventory costs. 02/18 Wrote off a customer’s account in the amount of $1,950. 02/19 $6,400 of rent for January and February was paid. Because all of the rent will soon expire, the February portion of the payment is charged directly to expense. 02/19 Collected $9,900 of customers’ Accounts Receivable. Of the $9,900, the discount was taken by customers on $7,500 of account balances; therefore WWC received less than $9,900. 02/26 WWC recovered $590 cash from the customer whose account had previously been written off (see 02/18). 02/27 A $900 utility bill for February arrived. It is due on March 15 and will be paid then. 02/28 WWC declared and paid a $850 cash dividend. Adjusting Entries: 02/29 Record the $2,700 employee salary that is owed but will be paid March 1. 02/29 WWC decides to use the aging method to estimate uncollectible accounts. WWC determines 8% of the ending balance is the appropriate end of February estimate of uncollectible accounts. 02/29 Record February interest expense accrued on the note payable. 02/29 Record one month’s interest earned Kit Kat’s note (see 02/01).
In: Accounting
Gallatin Carpet Cleaning is a small, family-owned business operating out of Bozeman, Montana. For its services, the company has always charged a flat fee per hundred square feet of carpet cleaned. The current fee is $23.95 per hundred square feet. However, there is some question about whether the company is actually making any money on jobs for some customers—particularly those located on remote ranches that require considerable travel time. The owner’s daughter, home for the summer from college, has suggested investigating this question using activity-based costing. After some discussion, she designed a simple system consisting of four activity cost pools. The activity cost pools and their activity measures appear below:
| Activity Cost Pool | Activity Measure | Activity for the Year | |
| Cleaning carpets | Square feet cleaned (00s) | 11,000 | hundred square feet |
| Travel to jobs | Miles driven | 230,000 | miles |
| Job support | Number of jobs | 2,100 | jobs |
| Other (organization-sustaining costs and idle capacity costs) | None | Not applicable | |
The total cost of operating the company for the year is $358,000 which includes the following costs:
| Wages | $ | 143,000 |
| Cleaning supplies | 21,000 | |
| Cleaning equipment depreciation | 17,000 | |
| Vehicle expenses | 30,000 | |
| Office expenses | 68,000 | |
| President’s compensation | 79,000 | |
| Total cost | $ | 358,000 |
Resource consumption is distributed across the activities as follows:
| Distribution of Resource Consumption Across Activities | ||||||||||
| Cleaning Carpets | Travel to Jobs | Job Support | Other | Total | ||||||
| Wages | 75 | % | 14 | % | 0 | % | 11 | % | 100 | % |
| Cleaning supplies | 100 | % | 0 | % | 0 | % | 0 | % | 100 | % |
| Cleaning equipment depreciation | 69 | % | 0 | % | 0 | % | 31 | % | 100 | % |
| Vehicle expenses | 0 | % | 75 | % | 0 | % | 25 | % | 100 | % |
| Office expenses | 0 | % | 0 | % | 65 | % | 35 | % | 100 | % |
| President’s compensation | 0 | % | 0 | % | 27 | % | 73 | % | 100 | % |
Job support consists of receiving calls from potential customers at the home office, scheduling jobs, billing, resolving issues, and so on.
Required:
1. Prepare the first-stage allocation of costs to the activity cost pools.
2. Compute the activity rates for the activity cost pools.
3. The company recently completed a 600 square foot carpet-cleaning job at the Flying N Ranch—a 54-mile round-trip journey from the company’s offices in Bozeman. Compute the cost of this job using the activity-based costing system.
4. The revenue from the Flying N Ranch was $143.70 (600 square feet @ $23.95 per hundred square feet). Calculate the customer margin earned on this job.
Prepare the first-stage allocation of costs to the activity cost pools.
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Compute the activity rates for the activity cost pools. (Round your answers to 2 decimal places.)
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The company recently completed a 600 square foot carpet-cleaning job at the Flying N Ranch—a 54-mile round-trip journey from the company’s offices in Bozeman. Compute the cost of this job using the activity-based costing system. (Round your intermediate calculations and final answer to 2 decimal places.)
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The revenue from the Flying N Ranch was $143.70 (6 hundred square feet @ $23.95 per hundred square feet). Calculate the customer margin earned on this job. (Negative customer margins should be indicated with a minus sign. Round your intermediate calculations and final answers to 2 decimal places.)
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In: Accounting
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Wally’s Widget Company (WWC) incorporated near the end of 2011. Operations began in January of 2012. WWC prepares adjusting entries and financial statements at the end of each month. Balances in the accounts at the end of January are as follows: |
| Cash | $ | 20,570 | Unearned Revenue (40 units) | $ | 5,000 | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| Accounts Receivable | $ | 11,600 | Accounts Payable (Jan Rent) | $ | 2,600 | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| Allowance for Doubtful Accounts | $ | (1,550) | Notes Payable | $ | 16,500 | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| Inventory (45 units) | $ | 4,050 | Contributed Capital | $ | 6,300 | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| Retained Earnings – Feb 1, 2012 | $ | 4,270 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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In: Accounting
Chinsali Division, a subsidiary of Mungwi Group Plc has the following budgeted results: K’000 Capital Employed 6,400 Operating Profit 1,600 Mungwi Group uses the Return on (ROI) and the Residual Income (RI) to evaluate the performance of division managers. The non-current assets are valued at net book value at year end while net current assets are valued at the average for the year. Depreciation is calculated on straight line basis. Mungwi Group expects all new projects to earn a minimum 18% discounted cashflow return over four years. In addition to the budgeted results, Chinsali division is considering investment in the following three new independent projects: Project 1 Investment outlay of K1,200,000 in a processing plant Benefit - the plant will reduce annual revenue costs by K400,000’ The plant would be purchased at the beginning of next year, with a useful life of four years and no scrap value. Project 2 Investment outlay of K32,000 in computerized inventory control system at start of next year. Plus an additional member of staff to be employed specifically to manage the system at an annual salary of K36,000. Benefit of new system – reduction in inventory levels by an average of K180,000 over the year. This project investment to be regarded as a revenue expense lasting only one year. The extra cash to be remitted to Mungwi group head office. Project 3 Head office be allowed to assist chinsali handle its accounts receivable by injecting some extra cash. This assistance will enable chinsali increase accounts receivable by an average of K140,000 over a year. This will result in increased sales generating an additional annual contribution of a K100,000. Ignore inflation and taxation
Required: (1) Calculate the existing return on investment (ROI) and residual income (RI) for Chinsali Division without the proposed new investment projects’ (2)
Calculate Chinsali division’s return on investment and residual income for the next year for each of the three new independent projects. (3)
Recommend the new project(s) that are likely to encourage goal congruence between Mungwi group plc and chinsali division. Comment on the residual income decision rules. Discount factors (18%) Year 0 Year 1 Year 2 Year 3 Year4 Year5 1 0.847 1.566 2.174 2.690 3.127
In: Accounting
We can make good decisions with good information and we can make bad decisions with good information. How would you apply the advice given in Job 28: 27-28 NIV to the information generated in accounting, 27 "then he looked at wisdom and appraised it; he confirmed it and tested it. 28 And he said to man, 'The fear of the Lord - that is wisdom, and to shun evil is understanding.'"
In: Accounting
An instructor wishes to see if the way people obtain information is independent of their educational background. A survey of 400 high school and college graduates yielded this information. At a=5%, test the claim that the way people obtain information is independent of their educational background.
Table:
| Television | newspaper | other sources | |
| high school | 159 | 90 | 51 |
| college | 27 | 42 | 31 |
College 27 42 31
In: Statistics and Probability
In: Economics