Let (V, ||·||) be a normed space, and W a d^Norm_V,||·|| -closed vector subspace of V.

(a) Prove that a function |||·||| : V /W → R_≥0 can be consistently defined by ∀v ∈ V : |||v + W||| df= inf({||v + w|| : R_≥0 | w ∈ W}).

(b) Prove that |||·||| is a norm on V /W.

(c) Prove that if (V, ||·||) is a Banach space, then so is (V /W, |||·|||)

Let T be a connected graph and z ∈ℤ between the closed interval of 1 and the least degree of a vertex in T. Let a z - matching be a A ⊆ E s.t. there aren’t vertices with more than z edges in A. Let a z - cover be a X ⊆ E s.t. all vertices belong to at least z edges in X.

Let:

δ (T) = Max {|A| : A is a z - matching}

μ (T) = Min {|X| : X is a z - cover}

Show that δ (T) + μ (T) = zn

3. Suppose that a closed economy could be described by the following set of equations: Production Function: Y = 120K1/3 L2/3

̅̅ Factors of production: K=125; L=1000

̅̅ Government Behavior: G= 3000; T = 2500

Consumption Behavior: C = 400 + 0.8(Y –T)
Investment Behavior: I = 16500 – 1000r
a. Calculate the equilibrium level of output (Y)
b. Prove that the production function has the property of constant returns to scale.

c. Calculate the marginal product of labor (MPL)

d) Calculate the equilibrium levels of the following variables

(i) Consumption (C)

(ii) Private Savings

(iii) Public Savings

(iv) National Savings (S)

(v) real interest rate (r)

Exercise 18-14

Bramble Corporation purchased equipment very late in 2017. Based on generous capital cost allowance rates provided in the Income Tax Act, Bramble Corporation claimed CCA on its 2017 tax return but did not record any depreciation as the equipment had not yet been put into use. This temporary difference will reverse and cause taxable amounts of $25,800 in 2018, $36,400 in 2019, and $45,200 in 2020. Bramble’s accounting income for 2017 is $232,800 and $192,800 in each of 2018 and 2019, and the tax rate is 32%. There are no deferred tax accounts at the beginning of 2017. BrambleCorporation was informed on December 31, 2018 that the enacted rate for 2019 and subsequent years is 27%.

a. Calculate the deferred tax balances at December 31, 2018 and 2019.

b.Calculate taxable income and income tax payable for 2018 and 2019.

c.Prepare the journal entries to record income taxes for 2018 and 2019

d. Prepare the income tax expense section of the income statement for 2018, beginning with the line “Income before income tax.”

e. Prepare the income tax expense section of the income statement for 2019, beginning with the line “Income before income tax.”

Q8.

The post-closing trial balance of M/S. Shaheen Traders at 31 March 2020 is set out below

:

Shaheen Traders

Post Closing Trial Balance

As on 31^St March 2020

On the above date, Ajmal retired, and the following arrangements were agreed upon:

1. Goodwill of the firm is to be valued at OMR. 30,000.

2. The assets and liabilities are to be valued as under: Stock OMR19,000, Sundry Debtors        OMR15,500, Land and Building OMR35,600, Equipment OMR38,000 and Machinery OMR       12,000 and Sundry Creditors OMR21,000.

3. Azeem and Kamran were to introduce OMR23,000 and OMR8,000 respectively into the business and OMR18,200 was to be paid immediately and the balance transferred to his loan account.

4. To bring into books unrecorded investments OMR 5,000

5. Azeem and Kamran agreed not to retain goodwill in books.

6. Ajmal, Azeem and Kamran profit and loss sharing ratio are 4 : 2 : 1 respectively.

You are required to pass necessary Journal entries with proper narrations to record the above transactions. Prepare revaluation account, capital accounts, bank account and financial position of the new firm as at 1^st April 2020, after all above arrangement have been completed. Write down the impact of retirement with explanations cum values in the new balance sheet.  

Q8.

The post-closing trial balance of M/S. Shaheen Traders at 31 March 2020 is set out below

:

Shaheen Traders

Post Closing Trial Balance

As on 31^St March 2020

On the above date, Ajmal retired, and the following arrangements were agreed upon:

1. Goodwill of the firm is to be valued at OMR. 30,000.

2. The assets and liabilities are to be valued as under: Stock OMR19,000, Sundry Debtors        OMR15,500, Land and Building OMR35,600, Equipment OMR38,000 and Machinery OMR       12,000 and Sundry Creditors OMR21,000.

3. Azeem and Kamran were to introduce OMR23,000 and OMR8,000 respectively into the business and OMR18,200 was to be paid immediately and the balance transferred to his loan account.

4. To bring into books unrecorded investments OMR 5,000

5. Azeem and Kamran agreed not to retain goodwill in books.

6. Ajmal, Azeem and Kamran profit and loss sharing ratio are 4 : 2 : 1 respectively.

You are required to pass necessary Journal entries with proper narrations to record the above transactions. Prepare revaluation account, capital accounts, bank account and financial position of the new firm as at 1^st April 2020, after all above arrangement have been completed. Write down the impact of retirement with explanations cum values in the new balance sheet.  

Asia Pacific Ltd started operating on 1 July 2017 with 12 employees. Three years later all of those employees were still with the company. On 1 July 2019 the company hired 15 more people but by 30 June 2020 only 10 of those employed at the beginning of that year were still employed by Asia Pacific Ltd.

All employees are entitled to 13 weeks’ long-service leave after a conditional period of 10 years of employment with Asia Pacific Ltd.

At 30 June 2020 Asia Pacific Ltd estimates the following:

•  The aggregate annual salaries of all employees hired on 1 July 2017 is now $1,200,000.

•  The aggregate annual salaries of all current employees hired on 1 July 2019 is now $800,000.

•  The probability that employees hired on 1 July 2017 will continue to be employed for the duration

  of the conditional period is 40 per cent.

•  The probability that employees hired on 1 July 2019 will continue to be employed for the duration

  of the conditional period is 20 per cent.

•  Salaries are expected to increase indefinitely at 1 per cent per annum.

  The interest rates on high-quality corporate bonds are as follows:

  Corporate bonds maturing in seven years 6% Corporate bonds maturing in eight years 8% Corporate bonds maturing in nine years 8% Corporate bonds maturing in ten years 10%

  At 30 June 2019 the provision for long-service leave was $12,000.

  Required:

1. a) Calculate the total accumulated long-service leave benefit as at 30 June 2020.

Ravi and Kishor starts a business of Fruit and Vegetable processing and registered a company with the name Fruity Flavours Pvt Ltd having registered office in Kashipur in January 2020. Both the promoters contributed Rs 5.00 lakh each in the equity capital (divided in one lakh shares the face value of Rs 10 each). They also arranged a loan of Rs 10 lakhs from a bank under Stand-Up India Scheme. Kishor provided a building owned by him for processing facility for which the company agreed to pay him a rent of Rs 20,000 per month. Kishor will look after the production and operations; while Ravi is responsible for marketing. They will be entitled for a monthly salary of Rs 15,000 each. They also hired five employees. During first nine months the following transactions took place:

1. Legal and other expenses for incorporation of the company Rs 80,000.

2. Equipment purchased in January, 2020 for Rs 15 lakhs. Rs 10 lakh have been paid while Rs 5 lakhs still to be paid.

3. Raw material purchased Rs 25 lakhs directly from farmers. Rs 2 lakhs still to be paid to farmers. There was no raw material inventory on 30th September.

4. Chemicals and stores purchased Rs 2.50 lakhs, Chemicals and stores costing Rs 2.15 lakhs were consumed till 30th September.

5. Salary and wages paid (including salary to Ravi and Kishor) Rs 5,20,000. Salary to be paid for the month of September Rs 72,000 (this will be paid in the first week of October).

6. Power fuel and other expenses Rs 15 lakh.

7. Rent paid to Kishor Rs 1,80,000.

8. Sales revenue till 30th September was Rs 58.30 Lakh; of which Rs 15.00 lakhs still to be received.

9. Interest on loan Rs 50,000 charged by the bank. Instalment (including interest) paid to bank 2.50 lakhs.

The Company decides to change depreciation on equipment @ 20% per annum and write-off all the legal expenses.

Prepare the Income Statement for nine months and the Balance Sheet of Fruity Flavours Pvt Ltd as on 30th September, 2020, and answer the following questions:

(Question 1 carries 3 marks; remaining questions carry 2 marks each)

1. What is the Cash and Bank Balance as on 30th September, 2020?

2. What is the Cost of Raw Material and Stores consumed?

3. What is EBITDA for the nine months? [treat write-off also as depreciation].

4. What is the Net Profit for the period?

5. What is EPS for the period?

6. What is the value of Total Assets as on 30th September, 2020?

7. What is Total Equity as on 30th September, 2020?

An Anesthesiologist claims that a certain medication decreases the pain level of post-operative patients within 20 minutes. Fourteen Patients are randomly chosen and asked to give a number from 1-10 that represents his/her pain level as soon as waking up from surgery and then again in 20 minutes after taking the medication. The pain level for patients before and after the medication is recorded below.  Assume the pain levels are normally distributed. Use 0.05 as the level of significance, as well as d indicates the mean difference: patient pain level before medication -  patient pain level after medication.

Chose the appropriate hypotheses set up for this situation.

Based on your choice in part 1 , determine the direction of your hypothesis test.

Right skewed test.

Right-tailed test.

Left-tailed test.

Two-tailed test.

Calculate the test statistics.

Calculate the P-Value for this test statistic.

(Round your answer to 4 decimal places)

Based on your finding in part 4, what would be the appropriate decision?

Based on your finding from part 5,

a.) What type of error could have occurred potentially?

b.) Explain the reasoning of the type of error of your choice.

Based on your findings from previous parts (1-5), which one of the statements below would be true?

Shelly's Boutiques and Crafts had revenue of $5,700,000 this year on sales of 575,000 units. Variable costs were 35% and fixed costs totaled $3,150,000. Although the first five years were relatively profitable, increases in competition have led to a negative trend in profitability that has led them to the point where they have to make some changes to stay afloat. The company is evaluating two options to stay afloat.

Option 1: Purchase machinery to automate their operations. this machinery cost $625,000 but will decrease variable costs by 9%

Option 2: Outsource the production of one of their main components that requires a substantial amount of machinery and skilled labor. This will reduce fixed costs by $425,000, but increases variable costs from their current 35% of sales to 40% of sales.

a. determine break even points in units before changes. what is fixed cost total? what is the contribution margin per unit? what is the break even point in units?

b.) Assuming an income tax rate of 35%, what dollar value of sales is required to earn an after tax profit of $800,000 What before tax profit would be needed to earn an after tax profit of $800,000? what is the contribution margin raton? What dollar amount of sales would be required to earn the after tax profit described above?

c.) Calculate the operating leverage before applying any of the options: What is the contribution margin in Total? What is the operating income in total? what is the operating leverage factor?

d.) Calculate the break even point in units after applying Option 1: What is the new fixed cost in total? What is the new contribution margin per unit? What is the new break even point in units?

e.) Calculate the operating leverage after applying Option 1: What is the new contribution margin in Total? What is the new operating income in total? what is the new operating leverage factor?

f.) Calculate the break even point in units after applying Option 2: What is the new fixed cost in total? What is the new contribution margin per unit? What is the new break even point in units?

g.) Calculate the operating leverage after applying Option 2: What is the new contribution margin in Total? What is the new operating income in total? what is the new operating leverage factor?