Break-Even Units and Sales Revenue: Margin of Safety

Dupli-Pro Copy Shop provides photocopying service. Next year, Dupli-Pro estimates it will copy 2,990,000 pages at a price of $0.06 each in the coming year. Product costs include:

There is no variable selling expense; fixed selling and administrative expenses total $42,000.

Required:

In your computations that involve the contribution margin ratio, do not round the ratio.

1. Calculate the break-even point in units.
fill in the blank 1 units

2. Calculate the break-even point in sales revenue.
$fill in the blank 2

3. Calculate the margin of safety in units for the coming year.
fill in the blank 3 units

4. Calculate the margin of safety in sales revenue for the coming year.
$fill in the blank 4

5. What if the total selling and administrative expenses are reduced to $26,020? Recalculate the following:

QUESTION 2

Liyala Sdn Bhd is a successful family-run business. The board of directors is led by the founder of the company, Liyala who is both chairman and CEO. The other board members, a finance director and two non-executive directors, are also Liyala’s brother and daughter. The members of Liyala family own all the share capital of the company.The company does not have a company secretary, and its auditors are a local firm of accountants in the town where Liyala has its head office.

Liyala is proud of his entrepreneurial success. He has been prepared to take big risks with the company’s strategy in order to grow the business and, when necessary, he has been willing to cancel the annual dividend to shareholders to spend money on investment or to accept temporary decline in profits for the sake of longer-term success. He is aware that the company does not have a good reputation as an employer, but he believes that the company exists for the benefit of the Liyala family and employees should be grateful to have their jobs.

Liyala wants to retire in a few years’ time. He would like his daughter to take over the running of the company, but he would also like to take the company public. He is aware that the governance of the company have to undergo substantial change for this to happen, but he does not want to retire until all changes have been made and the company’s shares are being traded on Bursa Malaysia.

Required

a / Explain how the board’s attitude to its shareholders and other stakeholders will need to change if Liyala Sdn Bhd goes public ?

b / Giving your reasons, identify the main aspects of governance that the board of Liyala Sdn Bhd will have to consider before the companies goes public, and suggest changes that will have to be made?

Sales Data provides data on a sample of customers. An industry trade publication stated that the average profit per customer for this industry was at least $4,500. Using a test of hypothesis, do the data support this claim or not?

Problem Definition:

Problem: Given an array of integers print all pairs of integers a and b where a + b is equal to a given number.

For example, consider the following array and suppose we want to find all pairs of integers a and b where a + b = 16

A= [ 10, 4, 6, 15, 3, 5, 1, 13]

The following are pairs that sum to 16:

13, 3

6, 10

15, 1

Your program should print these pairs.

A poor Solutions:

There are several solutions to this problem. The most straightforward (but inefficient ) solution is to set up a nested loop structure that goes over the elements of the array one by one and for each element performs a sequential search on the entire array. The running time for this algorithm is quadratic due to the nested loop structure and the sequential search for each array element.

What you need to do for this assignment

When the size of the array is very large then the quadratic algorithm may be too slow to be useful. There are a number of strategies that can be employed to reduce the running time, and at this point we have covered enough topics to design a more efficient algorithm. Based on the material covered thus far in this course, design and implement a more efficient algorithm for this problem.

Hint, you might find it helpful to first sort the array. As for the searching aspect, there are two ways you can go about it that will be efficient and both solutions are valid. One involves utilizing the Binary Search while the other does not involve searching at all.

No additional libraries may be used. All code must be implemented by you or else you will receive a 0 for the assignment. This includes the Arrays class.

Your algorithm must at most have a running time of O(nlogn) where n is the number of elements in the array.

The framework for your algorithm should satisfy the following criteria:

1. The SumPairs class is given to you with a main method that will produce test code for you.
2. You just need to implement the printPairs method. This prints the pairs of numbers that sum to some given value.
3. You may implement any additional methods to help you solve the problem.
4. The efficiency of your algorithm must at most be O(n log n).

It is important that you adhere to the framework specification above to facilitate testing of your program.

What you need to turn in

1. Your SumPairs.java file with a proper implementation of printPairs and any other methods you implemented.
2. Include a document file with an explanation of your algorithm in your own words. You may use pseudocode to break down your algorithm. Include an explanation of your efficiency.
3. Include a document with test inputs you create. You can change the test input in main. Make sure to include the tests for when there are duplicate pairs, no pairs, and many pairs.

public class SumPairs {

   //-----Implement your algorithm here------
   public static void printPairs(int arr[], int sum) {
       return 0;
   }
  
   //-----End Student Implementation-----
  
   public static void main(String[] args) {
       int arr[] = {
           16, 53, 89, 28, 72, 51, 3, 26, 99,
           85, 57, 1, 92, 96, 2, 56, 11, 41,
           3, 80, 16, 41, 79, 85, 78, 53, 45,
           18, 91, 82, 39, 26, 23, 64, 32, 75,
           70, 11, 48, 45, 76, 53, 14, 67, 2,
           42, 92, 69, 24, 23, 78, 27, 100, 60,
16, 94, 65, 77, 45, 37, 98, 56, 6, 6,
3, 94, 64, 26, 50, 56, 74, 24, 37, 67,
74, 48, 35, 40, 42, 90, 15, 50, 16, 36,
42, 70, 4, 62, 39, 16, 53, 89, 89, 38, 3,
53, 35, 20, 17, 44
       };
      
       int sumToCheck = 58;
       printPairs(arr, sumToCheck);
   }

}

Consider the following situations and determine whether they exhibit simultaneous consumption, network effects, x-inefficiency or rent-seeking behavior. Assume the businesses referenced function as monopolies.

(a) A pharmaceutical company discovers a vaccine for the common cold. The company puts a significant effort into tests to get it FDA-approved and into hiring lawyers to obtain a patent.

(b) An Internet service provider adds thousands of new customers.

(c) The head of a family-owned, major hotel chain decides to hire his wild, socialite niece to work as an executive of the company after her reality TV career ends.

(d) An online profile company helps college and high school students from across the country to connect with each other.

The following trial balance relates to Rapcap plc at 31 December 2019:

The following notes are relevant:

1. At 1 January 2019, Rapcap plc had its land and buildings revalued to £400 million. This valuation includes a value for land of £80 million. The estimated remaining life of the building at that date was 40 years. Depreciation of buildings is charged on a straight-line basis and is allocated 70% to cost of sales, 20% to distribution costs and 10% to administrative expenses.

2. During the year, Rapcap plc manufactured an item of plant that it is using as part of its own operating capacity. The details of its cost, which is included in cost of sales in the trial balance, are:

The manufacture of the plant was completed on 30 September 2019 and the plant was brought into immediate use, but its cost has not yet been capitalised.

3. All plant is depreciated at 20% per annum (time apportioned where relevant) using the reducing balance method and charged to cost of sales.

4. On 1 January 2019, Rapcap plc acquired plant and machinery which had a cost of £30 million. The company traded in (part-exchanged) an old item of plant for a value of £10 million and paid cash of £20 million. The cash transaction has been accounted for in the trial balance above, but the trade-in has not yet been recorded. The plant traded in had been bought on 1 January 2017 at a cost of £12.5 million.

5. The investment property is let at commercial rates to tenants who are not connected to the company in any way. Rapcap plc adopts the fair value model in its accounting treatment of the asset. At 31 December 2019, the property had a value of £35 million.

6. The inventory at 31 December 2019 was valued at cost of £28.5 million. This includes £4.5 million of slow-moving goods. Rapcap plc is trying to sell these to another company, but has not been successful in obtaining a reasonable offer. The best price it has been offered is £2 million.

7. The Corporation tax account in the trial balance represents the under-provision of the previous year’s estimate. The estimated Corporation tax liability for the year ended 31 December 2019 is £9.2 million. At 31 December 2019 there were £42.5 million of taxable temporary differences. The Corporation tax rate is 20%.

Required:

1. Prepare for Rapcap plc, a Statement of Profit or Loss and Other Comprehensive Income for the year ended 31 December 2019 and
2. A Statement of Financial Position as at 31 December 2019

(Note: A Statement of Changes in Equity is NOT required)

3. A schedule of movements in property, plant and equipment for the year ended 31 December 2019
4. The following ratios have been extracted from industry averages:

Calculate the relevant ratios for Rapcap plc and comment on the liquidity position of the company and its management of working capital.

The following trial balance relates to Rapcap plc at 31 December 2019:

The following notes are relevant:

1. At 1 January 2019, Rapcap plc had its land and buildings revalued to £400 million. This valuation includes a value for land of £80 million. The estimated remaining life of the building at that date was 40 years. Depreciation of buildings is charged on a straight-line basis and is allocated 70% to cost of sales, 20% to distribution costs and 10% to administrative expenses.

2. During the year, Rapcap plc manufactured an item of plant that it is using as part of its own operating capacity. The details of its cost, which is included in cost of sales in the trial balance, are:

The manufacture of the plant was completed on 30 September 2019 and the plant was brought into immediate use, but its cost has not yet been capitalised.

3. All plant is depreciated at 20% per annum (time apportioned where relevant) using the reducing balance method and charged to cost of sales.

4. On 1 January 2019, Rapcap plc acquired plant and machinery which had a cost of £30 million. The company traded in (part-exchanged) an old item of plant for a value of £10 million and paid cash of £20 million. The cash transaction has been accounted for in the trial balance above, but the trade-in has not yet been recorded. The plant traded in had been bought on 1 January 2017 at a cost of £12.5 million.

5. The investment property is let at commercial rates to tenants who are not connected to the company in any way. Rapcap plc adopts the fair value model in its accounting treatment of the asset. At 31 December 2019, the property had a value of £35 million.

6. The inventory at 31 December 2019 was valued at cost of £28.5 million. This includes £4.5 million of slow-moving goods. Rapcap plc is trying to sell these to another company, but has not been successful in obtaining a reasonable offer. The best price it has been offered is £2 million.

7. The Corporation tax account in the trial balance represents the under-provision of the previous year’s estimate. The estimated Corporation tax liability for the year ended 31 December 2019 is £9.2 million. At 31 December 2019 there were £42.5 million of taxable temporary differences. The Corporation tax rate is 20%.

Required:

1. Prepare for Rapcap plc, a Statement of Profit or Loss and Other Comprehensive Income for the year ended 31 December 2019 and
2. A Statement of Financial Position as at 31 December 2019

(Note: A Statement of Changes in Equity is NOT required)

3. A schedule of movements in property, plant and equipment for the year ended 31 December 2019
4. The following ratios have been extracted from industry averages:

Calculate the relevant ratios for Rapcap plc and comment on the liquidity position of the company and its management of working capital.

ABC Company had the following transactions during 2019:

May 1: Received $6000 cash in advance for services to be provided over the coming 10 months.

August 5: Sold Merchandise for $7560 including 8% sales tax.

September 1: Borrowed $20000 from FNB bank by issuing 6 months, 6% interest bearing note.

October 10: Sold merchandise on account for $6000 plus 10% sales tax.

December 31: Prepare the adjusting entry to record the service revenue earned.

December 31: Prepare the adjusting entry to record the accrued interest to FNB bank.

December 31: Remitted the sales taxes to the government.

Answer the below questions related to the above transactions:

1) The entry of May 1 transaction should include a: *

a) Service Revenue $6,000

b) Accounts Receivable $6,000

c) Account Payable $6,000

d) Unearned Service Revenue $6,000

2) The Sales Revenue amount of the August 5 transaction is: *

a) $560

b) $604.8

c) $7,000

d) $7,560

3) The entry of August 5 transaction will include: *

a) Debit Cash $7,000

b) Debit Cash $7,560

c) Debit Accounts Receivable $7,000

d) Debit Accounts Receivable $7,560

4) The entry of September 1 transaction is: *

a) Debit Cash and Credit Notes Payable of $20,000

b) Debit Cash and Credit Notes Payable of $21,200

c) Debit Cash and Credit Notes Payable of $15,000

d) Debit Cash and Credit Accounts Payable of $15,000

5) The entry of October 10 will include a credit of: *

a) Sales Revenue $6,000

b) Sales Revenue $6,600

c) Sales Taxes Payable $6,000

d) Sales Taxes Expense $600

6) The entry of October 10 will include a debit of: *

a) Accounts Receivable $6,000

b) Cash $6,000

c) Accounts Receivable $6,600

d) Cash $6,600

7) The earned amount of the service revenue on December 31 is" *

a) $3,500

b) $4,800

c) $4,500

d) $5,000

8) The remaining balance of the Unearned Service Revenue after December 31 is: *

a) Zero

b) 1,200

c) $3,000

d) $4,000

9) The accrued interest amount on December 31 on the borrowed amount from FNB Bank is: *

a) $300

b) $400

c) $500

d) None of the above

10) The amount of Taxes Payable remitted to the government on December 31 is: *

a) $560

b) $1,160

c) $1,720

d) $1,820

Currently, Katie White (retail customers manager) and Jules De Martino (corporate customers manager) have their performance assessed based on how much profit/loss is made with their customers' loans and savings activities, but this has led to many disagreements. Based on figures from the previous year, the corporate customers' loans and savings activities have generated a profit of $124 million whereas the retail customers' loans and savings activities have generated a loss of $84 million. Jules is very happy with this outcome, but Katie argues Jules is lending money from her retail customers to his corporate customers.

Table 5 – RRB loans and savings activities

Values in million dollars Assets

Loans to customers Liabilities

Deposit from customers Interest income

Loans (8%) Interest expense

Deposits (6%)
Profit/Loss with customers

Retail Customers $75 $1,500 $6 $90

($84)

Corporate Customers $ 1,925 $500 $154 $30

$124

All Customers $2,000 $2,000 $ 160 $ 120

$40

RRB board is discussing implementing fund transfer pricing (FTP) for addressing Katie’s concern about her customers funding Jules’ activities. However, Jules argues implementing an arbitrary FTP rate will make the retail and customer managers performance evaluation too subjective. There has been some discussion in RRB board regarding implementing a Balanced Scorecard (BSC).

Required

1. a) Based on the figures from the previous year, what would be the adjusted profit/loss with retail customers and corporate customers if RRB set an FTP rate of 8% and which manager would benefit from this decision and why? (FTP2, 10 marks)