Deck 4: Wholly Owned Subsidiaries: Reporting Subsequent Acquisitions

Question 1

Piri Ltd. acquired 100% of the commons shares of Golden Co. This business combination resulted in $100,000 of goodwill. Piri allocated the goodwill to three cash-generating units. At its year-end, Piri conducts a goodwill impairment test. Which of the following statements about the impairment test is true?

A)The impairment test is applied to Golden Co. as a whole.
B)The impairment test is applied to the business combination as a whole.
C)The impairment test is applied to each of the three cash-generating units to which goodwill has been allocated.
D)Piri is not required to conduct an impairment test unless its circumstances have changed materially from its previous year.

Answer 1

C

Question 2

Flatt Ltd. is a wholly-owned subsidiary of Franco Ltd. For consolidation purposes, how does the treatment of unrealized profits on upstream sales differ from the treatment of unrealized profits on downstream sales?

A)Unrealized profits must be eliminated on upstream sales, but not on downstream sales.
B)Unrealized profits must be eliminated on downstream sales, but not on upstream sales.
C)Unrealized profits must be eliminated for both upstream and downstream sales.
D)Unrealized profits are not eliminated on either upstream or downstream sales.

Answer 2

C

Question 3

A subsidiary sold goods to its parent company. At its year-end, the parent company still had some of the goods in inventory. Included in the value of these inventories is $15,000 of unrealized profits. What journal entry should be made to eliminate these unrealized profits?

A) $$\begin{array} { | l | c | } \hline \text { DR Sales } & 15,000 \\\hline \text { CR Inventory } & 15,000 \\\hline\end{array}$$
B) $$\begin{array} { | l | c | } \hline \text { DR Cost of sales } & 15,000 \\\hline \text { CR Inventory } & 15,000 \\\hline\end{array}$$
C) $$\begin{array} { | c | c | } \hline \text { DR Selling expenses } & 15,000 \\\hline \text { CR Inventory } & 15,000 \\\hline\end{array}$$
D) $$\begin{array} { | c | c | } \hline \text { DR Inventory } & 15,000 \\\hline \text { CR Sales } & 15,000 \\\hline\end{array}$$

Answer 3

B

Question 4

Coral Ltd. owns 100% of Ambrose Ltd. Coral uses the cost method to record this subsidiary. Coral received $150,000 in dividends from Ambrose. What journal entry should Coral make on its consolidation worksheet with respect to the dividends?

A) $$\begin{array} { | c | c | } \hline \text { DR Dividends declared (Ambrose) } & 150,000 \\\hline \text { CR Dividend income (Coral) } & 150,000 \\\hline\end{array}$$
B) $$\begin{array} { | c | c | } \hline \text { DR Dividends declared (Ambrose) } & 150,000 \\\hline \text { CR Investment in Ambrose (Coral) } & 150,000 \\\hline\end{array}$$
C) $$\begin{array} { | c | c | } \hline \text { DR Dividend income (Coral) } & 150,000 \\\hline \text { CR Dividends declared (Ambrose) } & 150,000 \\\hline\end{array}$$
D) $$\begin{array} { | c | c | } \hline \text { DR Investment in Ambrose (Coral) } & 150,000 \\\hline \text { CR Dividends declared (Ambrose) } & 150,000 \\\hline\end{array}$$

Question 5

Goodwill impairment testing can involve comparing the recoverable amount of a cash-generating unit to its ________.

A)carrying value, excluding goodwill
B)carrying value, including goodwill
C)carrying value of tangible assets and the fair value of its intangible assets
D)fair value of tangible assets and the carrying value of its intangible assets

Question 6

Waite Co. is a wholly-earned subsidiary of Star Ltd. During the year, Waite earned net income of $65,000. Star recorded this income on its books using the equity method. What elimination entry does Star have to make in the consolidation process with respect to this income?

A) $$\begin{array} { | c | c | } \hline \text { DR Equity earnings in Waite } & 65,000 \\\hline \text { CR Retained earnings } & 65,000 \\\hline\end{array}$$
B) $$\begin{array} { | c | c | } \hline \text { DR Equity earnings in Waite } & 65,000 \\\hline \text { CR Investment in Waite } & 65,000 \\\hline\end{array}$$
C) $$\begin{array} { | l | c | } \hline \text { DR Investment in Waite } & 65,000 \\\hline \text { CR Equity earnings in Waite } & 65,000 \\\hline\end{array}$$
D)No entry is required under the equity method.

Question 7

Thivan Ltd. is a wholly-owned subsidiary of Bateman Co. Thivan has declared dividends of $100,000.

- Under the equity method, what entry should Bateman record on its books?

A) $$\begin{array} { | c | c | } \hline \text { DR Investment in Thivan } & 100,000 \\\hline \text { CR Dividend income } & 100,000 \\\hline\end{array}$$
B) $$\begin{array} { | l | c | } \hline \text { DR Investment in Thivan } & 100,000 \\\hline \text { CR Equity in earnings of Thivan } & 100,000 \\\hline\end{array}$$
C) $$\begin{array} { | c | c | } \hline \text { DR Dividends receivable } & 100,000 \\\hline \text { CR Investment in Thivan } & 100,000 \\\hline\end{array}$$
D)No entry is required until the dividends are paid.

Question 8

Thivan Ltd. is a wholly-owned subsidiary of Bateman Co. Thivan has declared dividends of $100,000.

- Bateman uses the equity method to record this investment and has properly reflected Thivan's dividend declaration on its books. What journal entry should Bateman make when it receives the dividends?

A) $$\begin{array} { | l | c | } \hline \text { DR Cash } & 100,000 \\\hline \text { CR Investment in Thivan } & 100,000 \\\hline\end{array}$$
B) $$\begin{array} { |l | c | } \hline \text { DR Cash } & 100,000 \\\hline \text { CR Dividend revenue } & 100,000 \\\hline\end{array}$$
C) $$\begin{array} { | l | c | } \hline \text { DR Cash } & 100,000 \\\hline \text { CR Dividends receivable } & 100,000 \\\hline\end{array}$$
D)No entry is required as the journal entry for dividends declared was already received.

Question 9

Mitzi's Muffins Ltd. purchased a commercial baking system for $150,000 at the beginning of 20X1. The estimated economic life of the system is 10 years and Mitzi's uses straight-line amortization. At the beginning of 20X3, Delicious Bakeries Ltd. acquired Mitzi's in a business combination.

-At the time of the acquisition, Mitzi's baking system had a fair value of $140,000 and a remaining useful life of eight years. With respect to the baking system, how much amortization expense should Delicious Bakeries report on its consolidated financial statements at the end of 20X3?

A)$ 2,500
B)$14,000
C)$15,000
D)$17,500

Question 10

A parent company records an investment in its subsidiary using the equity method. Which of the following statements about consolidated net income is true?

A)Consolidated net income is higher than the net income under the equity method.
B)Consolidated net income is lower than the net income under the equity method.
C)Consolidated net income is higher than the net income under the equity method only if the subsidiary is profitable and has not paid any dividends.
D)Consolidated net income is the same as the net income under the equity method.

Question 11

DC Company purchased 100% of the outstanding common shares of FA Company on December 31, 20X3, for $170,000. At that date, FA had $100,000 of outstanding common shares and retained earnings of $30,000. It was agreed that the net assets were fairly valued except that the fair value of the capital assets exceeded their net book value by $20,000 and the carrying value of the inventory exceeded its fair value by $10,000. The capital assets had a remaining useful life of eight years as of the acquisition date and have no residual value. Inventory turns over four times a year.

- What adjustment should be made to the consolidated financial statements for the year ended December 31, 20X4, with respect to the $10,000 fair value adjustment to inventory?

A)An adjustment should be made through opening retained earnings.
B)An adjustment should be made to cost of sales.
C)No adjustment is required as an adjustment would have already been made to inventory at the time of sale.
D)No adjustment is required as an adjustment would have already been made to cost of sales at the time of sale.

Question 12

Amber Ltd. acquired Luna Ltd. in a business combination. One of the main reasons for the acquisition is that Amber wanted access to Luna's extensive customer list. The list is not recorded on Luna's books and has an estimated value of $100,000 and an estimated life of seven years. On Amber's consolidated statement of financial position, what value should be shown for Luna's customer list?

A)$0, since it was not recorded on Luna's books
B)$100,000 less any impairment losses
C)$100,000 less any accumulated amortization (calculated over five years)and any impairment losses
D)$100,000 less any accumulated amortization (calculated over seven years)and any impairment losses

Question 13

A company has a subsidiary that has an intangible capital asset. It has not been recorded on the subsidiary's books, but at the date of acquisition, the asset had a fair value of $200,000 and an indefinite economic life. How should the company show the asset on its consolidated statement of financial position?

A)$200,000 less any impairment losses
B)$200,000 less accumulated amortization (calculated over 10 years)and any impairment losses
C)$200,000 less accumulated amortization (calculated over 40 years)and any impairment losses
D)The company should not show the asset on the consolidated financial statement as the subsidiary does not do so.

Question 14

DC Company purchased 100% of the outstanding common shares of FA Company on December 31, 20X3, for $170,000. At that date, FA had $100,000 of outstanding common shares and retained earnings of $30,000. It was agreed that the net assets were fairly valued except that the fair value of the capital assets exceeded their net book value by $20,000 and the carrying value of the inventory exceeded its fair value by $10,000. The capital assets had a remaining useful life of eight years as of the acquisition date and have no residual value. Inventory turns over four times a year.

- What adjustment should be made to the consolidated financial statements for the year ended December 31, 20X6, for the fair value increment related to the capital assets?

A)The retained earnings at January 1, 20X6, will be increased by $20,000.
B)Amortization expense on the capital assets for 20X6 will be increased by $2,500.
C)Amortization expense on the capital assets for 20X6 will be increased by $7,500.
D)Retained earnings at the end of 20X6 will be increased by $12,500.

Question 15

Under the direct method, what values should be entered for the assets, liabilities, and shareholders' equity to start the consolidation process?

A)Carrying values for both the parent and the subsidiary companies
B)Carrying values for the parent company and fair values for the subsidiary company
C)Fair values for the parent company and carrying values for the subsidiary company
D)Fair values for both the parent and the subsidiary companies

Question 16

DC Company purchased 80% of the outstanding common shares of FA Company on December 31, 20X3, for $170,000. At that date, FA had $100,000 of outstanding common stock and retained earnings of $30,000. It was agreed that the net assets were fairly valued except that the fair value of the capital assets exceeded their net book value by $20,000 and the carrying value of the inventory exceeded its fair value by $10,000. The capital assets had a remaining useful life of eight years as of the acquisition date and have no salvage value. Inventory turns over four times a year. It is now 20X6 and DC has been very pleased with how profitable its investment in FA has been. On DC's consolidated financial statements at December 31, 20X6, what balance should be reported for goodwill assuming no impairment has occurred?

A)$0
B)$10,000
C)$52,500
D)$58,500

Question 17

Paranich Co. acquired Crowley Co. in a business combination at December 31, 20X4. Crowley has a capital asset that it has been amortizing at a rate of $10,000 per year. At the time of the acquisition, the asset had a book value of $70,000 and a fair value of $77,000. The asset has a remaining life of seven years. With respect to this asset, how much amortization expense should Paranich report on its December 31, 20X5, consolidated financial statements?

A)$ 1,000
B)$ 7,700
C)$10,000
D)$11,000

Question 18

Fair value increments on depreciable assets ________.

A)should be amortized in accordance with the subsidiary's depreciation policies
B)should be amortized in accordance with the parent company's depreciation policies
C)should always be recorded on the subsidiary's books
D)should be expensed immediately

Question 19

Mitzi's Muffins Ltd. purchased a commercial baking system for $150,000 at the beginning of 20X1. The estimated economic life of the system is 10 years and Mitzi's uses straight-line amortization. At the beginning of 20X3, Delicious Bakeries Ltd. acquired Mitzi's in a business combination.

-At the time of acquisition, Mitzi's baking system had a fair value of $140,000. At the end of 20X3, how much amortization expense should Mitzi report?

A)$0
B)$14,000
C)$15,000
D)$17,500

Question 20

Inventory was acquired as part of a business combination at the end of 20X1. The inventory was sold in 20X2. How should the fair value increment for the inventory at acquisition be treated for consolidation at the end of 20X2?

A)It should be added to inventory.
B)It should be added to sales.
C)It should be added to the cost of goods sold.
D)It should be added to retained earnings.

Question 21

On September 1, 20X5, CanAir Limited decided to buy 100% of the shares outstanding of SkyAir Inc. for $900,000. CanAir will pay for this acquisition by using cash of $500,000 and issuing share capital for the remaining amount. The balances showing on the statement of financial position for the two companies at August 31, 20X5, are as follows: After a review of the financial assets and liabilities, CanAir determines that some of the assets of SkyAir have fair values different from their carrying values. These items are listed below:
• Land has a fair value of $225,000.
• The building has a fair value of $1,090,000. The remaining useful life of the building is 20 years.
• Internet domain name has a fair value is $55,000. The domain name is estimated to have a useful life of five years.
• Customer lists have a fair value is $35,000. It is estimated that the customer lists will have a useful life of seven years.
During the 20X9 fiscal year, the following events occurred:
1. On March 1, 20X9, SkyAir sold land to CanAir for $390,000, which had a carrying value of $275,000. CanAir paid for this with $90,000 cash and a note payable for the difference. This note pays interest at 10%, which is paid monthly.
2. CanAir provided management expertise to SkyAir and charged management fees of $890,000.
3. CanAir sold supplies (included in CanAir sales)to SkyAir for $200,000. CanAir charged SkyAir an amount that was 25% above cost. SkyAir still has supplies on hand of $70,000.
4. In 20X8, SkyAir provided seat space on flights to Can Air for a value of $500,000. This amount was included in sales for SkyAir. Profit margin on these sales is 40%. At the end of August, 20X8, CanAir still had an amount of $200,000 in these prepaid seats that had not yet been used. (CanAir includes this in inventory.) Required:
Calculate the consolidated retained earnings as at August 31, 20X9.
Prepare the consolidated statement of financial position for the year ended August 31, 20X9.

Question 22

Which of the following statements about goodwill impairment testing under IFRS and ASPE is true?

A)Goodwill impairment testing is done at the lowest reporting level under both IFRS and ASPE.
B)Goodwill impairment testing is done at the smallest cash-generating unit level under both IFRS and ASPE.
C)Goodwill impairment testing is done at the lowest reporting level under IFRS and at the smallest cash-generating unit level under ASPE.
D)Goodwill impairment testing is done at the smallest cash-generating unit level under IFRS and at the lowest reporting level under ASPE.

Question 23

On December 31, 20X2, Pipe Ltd. purchased 100% of the outstanding common shares of Fitter Ltd. for $10.5 million in cash. On that date, the shareholders' equity of Fitter totalled $8 million and consisted of $1 million in no par common shares and $7 million in retained earnings. Both companies use the straight-line method to calculate depreciation and amortization. Goodwill, if any arises as a result of this business combination, is written down if there is an impairment in its value. Pipe follows IFRS.
For the year ending December 31, 20X6, the income statements for Pipe and Fitter were as follows:
$\begin{array}{lll}&\text {Pipe }&\text {Fitter}\\\text { Sales and other revenue } & \underline{\$ 22,500,000 }& \underline{\$ 9,800,000} \\\text { Cost of goods sold } & 16,000,000 & 5,000,000 \\\text { Depreciation expense } & 2,500,000 & 2,000,000 \\\text { Other expenses } & \underline{1,800,000} & \underline{1,200,000} \\\text { Total expenses } & \underline{20,300,000} & \underline{8,200,000} \\\text {Net income}& \underline{\$ 2,200,000 }& \underline{1,600,000}\end{array}$ At December 31, 20X6, the condensed balance sheets for the two companies were as follows:
$$\begin{array} { l l l } & \text { Pipe } & \text { Fitter } \\\text { Total assets } &\underline{ \$ 31,000,000 }& \underline{\$ 13,500,000}\end{array}$$ $$\begin{array} { l l l } \text { Liabilities } & \$ 5,000,000 & \$ 1,200,000 \\\text { No par common stock } & 12,100,000 & 1,000,000 \\\text { Retained earnings } & \underline { 13,900,000 } & \underline { 11,300,000 } \\\text { Total liabilities andshareholders' equity } & \underline { \$ 31,000,000} & \underline { \$ 13,500,000}\end{array}$$ OTHER INFORMATION:
1. On December 31, 20X2, Fitter had a building with a fair value that was $500,000 greater than its carrying value. The building had an estimated remaining useful life of 20 years.
2. On December 31, 20X2, Fitter had trademark that was not reported on its balance sheet but had a fair value that was $200,000. The trademark is amortized over 10 years.
3. During 20X6, Fitter sold merchandise to Pipe for $100,000, a price that included a gross profit of $40,000. During 20X6, 20% of this merchandise was resold by Pipe and the other 80% remains in its December 31, 20X6, inventories. On December 31, 20X5, the inventories of Pipe contained merchandise purchased from Fitter on which Fitter had recognized a gross profit in the amount of $50,000.
4. During 20X6, it was determined that the goodwill arising at the date of acquisition was impaired and that an impairment loss of $70,000 should be recorded. No impairment had been charged in earlier years.
5. During 20X6, Pipe declared and paid dividends of $300,000, while Fitter declared and paid dividends of $100,000.
6. Pipe accounts for its investment in Fitter using the cost method.
The retained earnings of Pipe as at December 31, 20X5, equalled $12,000,000. On that date, Fitter had retained earnings of $9,800,000. Fitter has not issued any common stock since its acquisition by Pipe.
Required:
Prepare, in good form, a consolidated statement of comprehensive income for the year ended December 31, 20X6.

Question 24

On December 31, 20X5, Space Co. purchased 100% of the outstanding common shares of Shuttle Ltd. for $1,200,000 in shares and $200,000 in cash. The statements of financial position of Space and Shuttle immediately before the acquisition and issuance of the notes payable were as follows (in 000s):
$\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text {Space}\quad\quad\quad\quad\text {Shuttle}$
$\begin{array}{lllll}&\text { Book } & \text { Fair } & \text { Book } & \text { Fair } \\&\text { Value } & \text { Value } & \text { Value } & \text { Value } \\\text { Cash } & \$ 360 & \$ 360 & \$ 200 & \$ 200 \\\text { Accounts receivable } & 520 & 500 & 380 & 340 \\\text { Inventory } & 800 & 880 & 400 & \\\text { Property, plant, and equipment } & \underline{1,820} & 2,000 & \underline{1,420} & 1,520 \\& \$ 3,500 & & \$ 2,400 &\end{array}$ $\begin{array}{lllll}\text { Accounts payable } & \$ 380 & \$ 380 & \$ 260 & \$ 260 \\\text { Long-term liabilities } & 1,200 & 1,200 & 1000 & 1000 \\\text { Common shares } & 500 & & 600 & \\\text { Retained earnings } & \underline{1,420} & & \underline{540} & \\& \underline{\$ 3.500} & & \underline{ \$ 2.400} &\end{array}$ The difference in the carrying value and the fair value of the property, plant, and equipment for Shuttle relates to its office building. This building was originally purchased by Shuttle in January 20X1 and is being depreciated over 30 years.
During 20X6, the year following the acquisition, the following occurred:
1. Shuttle borrowed $350,000 from Space on June 1, 20X6, and was charged interest at 10% per annum, which it paid on a monthly basis. There were no repayments of principal made during the remaining of the year.
2. Throughout the year, Shuttle purchased merchandise of $800,000 from Space. Space's gross margin is 30% of selling price. At December 31, 20X6, Shuttle still owed Space $250,000 on this merchandise; 75% of this merchandise was resold by Shuttle prior to December 31, 20X6.
3. Shuttle paid dividends of $250,000 at the end of 20X6 and Space paid dividends of $500,000.
During 20X7, the following occurred:
1. Shuttle paid $150,000 on the loan payable to Space on May 30, 20X7.
2. Throughout the year, Shuttle purchased merchandise of $1,000,000 from Space. Space's gross margin is 30% of selling price. At December 31, 20X6, Shuttle still owed Space $150,000 on this merchandise; 85% of this merchandise was resold by Shuttle prior to December 31, 20X7.
3. Shuttle paid dividends of $250,000 at the end of 20X7 and Space paid dividends of $500,000. Required:
Space has decided to record its investment in Shuttle using the equity method. Determine the balance in the Investment in Shuttle account at December 31, 20X7, using the equity method.
Prepare the statement of financial position and the statement of comprehensive income for the year ended December 31, 20X7, for Space, assuming it accounts for its investment in Shuttle using the equity method.

Question 25

On January 1, 20X3, Dwayne Ltd. formed Carlos Co., a 100% owned subsidiary. During 20X6, Dwayne sold Carlos $100,000 in goods. The unrealized profit in Carlos's inventories was $20,000 at December 31, 20X5, and $25,000 at December 31, 20X6.

-Ignoring income taxes, what accounts should Dwayne debit and credit by $25,000 in preparing its consolidated financial statements for the year ended December 31, 20X6, to reflect the unrealized profit in Carlos's ending inventory? $\begin{array} { l l } { \text { Debit } } &&&&&&& { \text { Credit } } \\\end{array}$

A) $\begin{array} { l l } \text {Cost of sales } &&& \text { Inventory } \\\end{array}$
B) $\begin{array} { l l }\text { Inventcry } &&&& \text { Cost of Sales } \\\end{array}$
C) $\begin{array} { l l } \text {Retained earnings } & \text { Cost of sales } \\\end{array}$
D) $\begin{array} { l l } \text {Cost of sales } &&& \text { Tetained earnings }\end{array}$

Question 26

Which of the following consolidation adjustments will be required for a subsidiary that was acquired as a going concern, but will not be applicable for a parent-founded subsidiary?

A)Amortization of fair value increments on plant and equipment
B)Unrealized profits in ending inventory
C)Unrealized profits in beginning inventory
D)Future income tax on unrealized profits

Question 27

On December 31, 20X5, Space Co. purchased 100% of the outstanding common shares of Shuttle Ltd. for $1,200,000 in shares and $200,000 in cash. The statements of financial position of Space and Shuttle immediately before the acquisition and issuance of the notes payable were as follows (in 000s):
$\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text {Space}\quad\quad\quad\quad\text {Shuttle}$
$\begin{array}{lllll}&\text { Book } & \text { Fair } & \text { Book } & \text { Fair } \\&\text { Value } & \text { Value } & \text { Value } & \text { Value } \\\text { Cash } & \$ 360 & \$ 360 & \$ 200 & \$ 200 \\\text { Accounts receivable } & 520 & 500 & 380 & 340 \\\text { Inventory } & 800 & 880 & 400 & \\\text { Property, plant, and equipment } & \underline{1,820} & 2,000 & \underline{1,420} & 1,520 \\& \underline{\$ 3,500} & &\underline{ \$ 2,400 }&\end{array}$ $\begin{array}{lllll}\text { Accounts payable } & \$ 380 & \$ 380 & \$ 260 & \$ 260 \\\text { Long-term liabilities } & 1,200 & 1,200 & 1000 & 1000 \\\text { Common shares } & 500 & & 600 & \\\text { Retained earnings } & \underline{1,420} & & \underline{540} & \\& \underline{\$ 3.500 }& & \underline{ \$ 2.400} &\end{array}$ The difference in the carrying value and the fair value of the capital assets for Shuttle relates to its office building. This building was originally purchased by Shuttle in January 20X1 and is being depreciated over 30 years.
During 20X6, the year following the acquisition, the following occurred:
1. Shuttle borrowed $350,000 from Space on June 1, 20X6, and was charged interest at 10% per annum, which it paid on a monthly basis. There were no repayments of principal made during the remaining of the year.
2. Throughout the year, Shuttle purchased merchandise of $800,000 from Space. Space's gross margin is 30% of selling price. At December 31, 20X6, Shuttle still owed Space $250,000 on this merchandise; 75% of this merchandise was resold by Shuttle prior to December 31, 20X6.
3. Shuttle paid dividends of $250,000 at the end of 20X6 and Space paid dividends of $500,000.
During 20X7, the following occurred:
1. Shuttle paid $150,000 on the loan payable to Space on May 30, 20X7.
2. Throughout the year, Shuttle purchased merchandise of $1,000,000 from Space. Space's gross margin is 30% of selling price. At December 31, 20X6, Shuttle still owed Space $150,000 on this merchandise; 85% of this merchandise was resold by Shuttle prior to December 31, 20X7.
3. Shuttle paid dividends of $250,000 at the end of 20X7 and Space paid dividends of $500,000. $$\begin{array} { l } \begin{array} { l } \text { Statements of Changes in Equity - Retained Earnings Section } \\\text { Year Ended December 31, 20X7 } \\\text { (in thousands of \$'s) }\end{array} \\\begin{array} { | l | r | r | } \hline & \text { Space \$} & \text { Shuttle \$} \\\hline \text { Retained earnings, December 31, 20X6 } & 1,775 & 695 \\\hline \text { Net income } & 990 & 490 \\\hline \text { Dividends declared } & ( 500 ) & ( 250 ) \\\hline \text { Retained earnings, December 31, 20X7 } & \underline { 2,265 } & 935 \\\hline\end{array}\end{array}$$ Required:
Prepare the consolidated statement of comprehensive income for the year ended December 31, 20X7, for Space.s) } \end{array} \\ \begin{array} { | l | r | r | } \hline & \text { Space \$} & \text { Shuttle \$} \\ \hline \text { Retained earnings, December 31, 20X6 } & 1,775 & 695 \\ \hline \text { Net income } & 990 & 490 \\ \hline \text { Dividends declared } & ( 500 ) & ( 250 ) \\ \hline \text { Retained earnings, December 31, 20X7 } & \underline { 2,265 } & 935 \\ \hline \end{array} \end{array} Required: Prepare the consolidated statement of comprehensive income for the year ended December 31, 20X7, for Space. " class="answers-bank-image d-block" loading="lazy" > 11ea84f2_a85b_0257_9a63_4171128d30b3_TB3071_00 $$\begin{array} { l } \begin{array} { l } \text { Statements of Changes in Equity - Retained Earnings Section } \\\text { Year Ended December 31, 20X7 } \\\text { (in thousands of \$'s) }\end{array} \\\begin{array} { | l | r | r | } \hline & \text { Space \$} & \text { Shuttle \$} \\\hline \text { Retained earnings, December 31, 20X6 } & 1,775 & 695 \\\hline \text { Net income } & 990 & 490 \\\hline \text { Dividends declared } & ( 500 ) & ( 250 ) \\\hline \text { Retained earnings, December 31, 20X7 } & \underline { 2,265 } & 935 \\\hline\end{array}\end{array}$$ Required:
Prepare the consolidated statement of comprehensive income for the year ended December 31, 20X7, for Space.s) } \end{array} \\ \begin{array} { | l | r | r | } \hline & \text { Space \$} & \text { Shuttle \$} \\ \hline \text { Retained earnings, December 31, 20X6 } & 1,775 & 695 \\ \hline \text { Net income } & 990 & 490 \\ \hline \text { Dividends declared } & ( 500 ) & ( 250 ) \\ \hline \text { Retained earnings, December 31, 20X7 } & \underline { 2,265 } & 935 \\ \hline \end{array} \end{array} Required: Prepare the consolidated statement of comprehensive income for the year ended December 31, 20X7, for Space. " class="answers-bank-image d-block" loading="lazy" > $$\begin{array} { l } \begin{array} { l } \text { Statements of Changes in Equity - Retained Earnings Section } \\\text { Year Ended December 31, 20X7 } \\\text { (in thousands of \$'s) }\end{array} \\\begin{array} { | l | r | r | } \hline & \text { Space \$} & \text { Shuttle \$} \\\hline \text { Retained earnings, December 31, 20X6 } & 1,775 & 695 \\\hline \text { Net income } & 990 & 490 \\\hline \text { Dividends declared } & ( 500 ) & ( 250 ) \\\hline \text { Retained earnings, December 31, 20X7 } & \underline { 2,265 } & 935 \\\hline\end{array}\end{array}$$ Required:
Prepare the consolidated statement of comprehensive income for the year ended December 31, 20X7, for Space.s) } \end{array} \\ \begin{array} { | l | r | r | } \hline & \text { Space \$} & \text { Shuttle \$} \\ \hline \text { Retained earnings, December 31, 20X6 } & 1,775 & 695 \\ \hline \text { Net income } & 990 & 490 \\ \hline \text { Dividends declared } & ( 500 ) & ( 250 ) \\ \hline \text { Retained earnings, December 31, 20X7 } & \underline { 2,265 } & 935 \\ \hline \end{array} \end{array} Required: Prepare the consolidated statement of comprehensive income for the year ended December 31, 20X7, for Space. " class="answers-bank-image d-block" loading="lazy" > 11ea84f2_a85b_0257_9a63_4171128d30b3_TB3071_00 $$\begin{array} { l } \begin{array} { l } \text { Statements of Changes in Equity - Retained Earnings Section } \\\text { Year Ended December 31, 20X7 } \\\text { (in thousands of \$'s) }\end{array} \\\begin{array} { | l | r | r | } \hline & \text { Space \$} & \text { Shuttle \$} \\\hline \text { Retained earnings, December 31, 20X6 } & 1,775 & 695 \\\hline \text { Net income } & 990 & 490 \\\hline \text { Dividends declared } & ( 500 ) & ( 250 ) \\\hline \text { Retained earnings, December 31, 20X7 } & \underline { 2,265 } & 935 \\\hline\end{array}\end{array}$$ Required:
Prepare the consolidated statement of comprehensive income for the year ended December 31, 20X7, for Space.

Question 28

On December 31, 20X5, Space Co. purchased 100% of the outstanding common shares of Shuttle Ltd. for $1,200,000 in shares and $200,000 in cash. The statements of financial position of Space and Shuttle immediately before the acquisition and issuance of the notes payable were as follows (in 000s):
$\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text {Space}\quad\quad\quad\quad\text {Shuttle}$
$\begin{array}{lllll}&\text { Book } & \text { Fair } & \text { Book } & \text { Fair } \\&\text { Value } & \text { Value } & \text { Value } & \text { Value } \\\text { Cash } & \$ 360 & \$ 360 & \$ 200 & \$ 200 \\\text { Accounts receivable } & 520 & 500 & 380 & 340 \\\text { Inventory } & 800 & 880 & 400 & \\\text { Property, plant, and equipment } & \underline{1,820} & 2,000 & \underline{1,420} & 1,520 \\&\underline{ \$ 3,500 }& &\underline{ \$ 2,400 }&\end{array}$ $\begin{array}{lllll}\text { Accounts payable } & \$ 380 & \$ 380 & \$ 260 & \$ 260 \\\text { Long-term liabilities } & 1,200 & 1,200 & 1000 & 1000 \\\text { Common shares } & 500 & & 600 & \\\text { Retained earnings } & \underline{1,420} & & \underline{540} & \\& \underline{\$ 3.500 }& & \underline{ \$ 2.400} &\end{array}$ The difference in the carrying value and the fair value of the capital assets for Shuttle relates to its office building. This building was originally purchased by Shuttle in January 20X1 and is being depreciated over 30 years.
During 20X6, the year following the acquisition, the following occurred:
1. Shuttle borrowed $350,000 from Space on June 1, 20X6, and was charged interest at 10% per annum, which it paid on a monthly basis. There were no repayments of principal made during the remainder of the year.
2. Throughout the year, Space purchased merchandise of $800,000 from Shuttle. Shuttle's gross margin is 35% of selling price. At December 31, 20X6, Shuttle still owed Space $250,000 on this merchandise; 60% of this merchandise was resold by Space prior to December 31, 20X6.
3. Shuttle paid dividends of $250,000 at the end of 20X6 and Space paid dividends of $500,000.
During 20X7, the following occurred:
1. Shuttle paid $150,000 on the loan payable to Space on May 30, 20X7.
2. Throughout the year, Space purchased merchandise of $900,000 from Space. Space's gross margin is 35% of selling price. At December 31, 20X6, Shuttle still owed Space $350,000 on this merchandise; 80% of this merchandise was resold by Shuttle prior to December 31, 20X7.
3. The goodwill was tested and found to be impaired, resulting in an impairment loss of $120,000.
4. Shuttle paid dividends of $250,000 at the end of 20X7 and Space paid dividends of $500,000. Required:
Calculate the consolidated retained earnings for Space as at December 31, 20X7.
Prepare the consolidated statement of financial position for the year ended December 31, 20X7, for Space.

Question 29

On December 31, 20X1, Dad Ltd. purchased 100% of the outstanding common shares of Sad Ltd. for $9.5 million in cash. On that date, the shareholders' equity of Sad totalled $8 million and consisted of $1 million in no par common shares and $7 million in retained earnings. Both companies use the straight-line method to calculate depreciation. Goodwill, if any arises as a result of this business combination, is written down when there is impairment. Both Dad and Sad report under accounting standards for private enterprises.
For the year ending December 31, 20X6, the statements of earnings for Dad and Sad were as follows:
$\begin{array}{lll}&\text { Dad}&\text { Sad}\\\text { Sales and other revenue } & \underline{\$ 22,500,000} & \underline{\$ 9,800,000} \\\text { Cost of goods sold } & 16,000,000 & 5,000,000 \\\text { Amortization expense } & 2,500,000 & 2,000,000 \\\text { Other expenses (including taxes) } & \underline{1,800,000} & \underline{1,200,000} \\\text { Total expenses (including taxes) } & \underline{20,300,000} & \underline{8,200,000} \\\text { Net income } &\underline{ \$ 2,200,000} &\underline{ \$ 1,600,000}\end{array}$ At December 31, 20X6, the condensed statements of financial position for the two companies were as follows:
$\begin{array}{lll}& \text { Dad } & \text { Sad } \\\text { Total assets } & \$ 31,000,000 & \$ 13,500,000\end{array}$ $$\begin{array} { l l l } \text { Liabilities } & \$ 5,000,000 & \$ 1,200,000 \\\text { No par common shares } & 12,100,000 & 1,000,000 \\\text { Retained earnings } & \underline { 13,900,000 } & \underline { 11,300,000 } \\\text { Total liabilities andshareholders' equity } &\underline {\$ 1,000,000} &\underline { \$ 13,500,000}\end{array}$$
OTHER INFORMATION:
1. On December 31, 20X1, Sad had a building with a fair value that was $300,000 greater than its carrying value. The building had an estimated remaining useful life of 20 years.
2. On December 31, 20X1, Sad had inventory with a fair value that was $200,000 less than its carrying value. This inventory was sold in 20X3.
3. During 20X6, Dad sold merchandise to Sad for $100,000, a price that includes a gross profit of $40,000. During 20X6, 40% of this merchandise was resold by Sad to third parties and the other 60% remains in its December 31, 20X6, inventories. On December 31, 20X5, the inventories of Sad contained merchandise purchased from Dad on which Dad had recognized a gross profit in the amount of $20,000.
4. During 20X6, Dad declared and paid dividends of $300,000 while Sad declared and paid dividends of $100,000.
5. Dad accounts for its investment in Sad using the cost method.
6. The retained earnings of Dad as at December 31, 20X5, was $12,000,000. On that date, Sad had retained earnings of $9,800,000. Sad has not issued any common shares since its acquisition by Dad.
7. There were no specific events or circumstances between 20X2 and 20X6 to indicate any impairment of goodwill.
Required:
Calculate consolidated net income for the year ending December 31, 20X6. Prepare the consolidated statement of comprehensive income for the year ended December 31, 20X6.

Question 30

DIY Ltd. owns 20 subsidiary companies. Most of the subsidiaries are hardware stores operating in rural areas. One of the subsidiaries has been having financial difficulties and has finally decided to cease operations. Which of the following statements about DIY's consolidated financial statements is true?

A)DIY should report this as a discontinued operation.
B)DIY should report any losses from this as part of its normal operating activities.
C)Whether DIY treats this as a discontinued operation depends on if it used the cost method or the equity method to record the subsidiary.
D)DIY is not required to disclose anything about this closure.

Question 31

On December 31, 20X1, Dad Ltd. purchased 100% of the outstanding common shares of Sad Ltd. for $9.5 million in cash. On that date, the shareholders' equity of Sad totalled $8 million and consisted of $1 million in no par common shares and $7 million in retained earnings. Both companies use the straight-line method to calculate depreciation. Goodwill, if any arises as a result of this business combination, is written down if there is a permanent impairment in its value. Dad records the investment in Sad using the cost method.
For the year ending December 31, 20X6, the statements of comprehensive income for Dad and Sad were as follows:
$\begin{array}{lll}&\text { Dad}&\text { Sad}\\\text { Sales and other revenue } & \underline{\$ 22,500,000} & \underline{\$ 9,800,000} \\\text { Cost of goods sold } & 16,000,000 & 5,000,000 \\\text { Amortization expense } & 2,500,000 & 2,000,000 \\\text { Other expenses (including taxes) } & \underline{1,800,000} & \underline{1,200,000} \\\text { Net income } &\underline{ \$ 2,200,000} &\underline{ \$ 1,600,000}\end{array}$ At December 31, 20X6, the condensed statements of financial position for the two companies were as follows:
$\begin{array}{lll}& \text { Dad } & \text { Sad } \\\text { Total assets } & \$ 31,000,000 & \$ 13,500,000\end{array}$
$$\begin{array} { l l l } \text { Liabilities } & \$ 5,000,000 & \$ 1,200,000 \\\text { No par common shares } & 12,100,000 & 1,000,000 \\\text { Retained earnings } & \underline { 13,900,000 } & \underline { 11,300,000 } \\\text { Total liabilities andshareholders' equity } & \underline { \$ 1,000,000 } & \underline { \$ 13,500,000}\end{array}$$ OTHER INFORMATION:
1. On December 31, 20X1, Sad had a building with a fair value that was $300,000 greater than its carrying value. The building had an estimated remaining useful life of 20 years.
2. On December 31, 20X1, Sad had inventory with a fair value that was $200,000 less than its carrying value. This inventory was sold in 20X3.
3. During 20X6, Dad sold merchandise to Sad for $100,000, a price that includes a gross profit of $40,000. During 20X6, 40% of this merchandise was resold by Sad to third parties and the other 60% remains in its December 31, 20X6, inventories. On December 31, 20X5, the inventories of Sad contained merchandise purchased from Dad on which Dad had recognized a gross profit in the amount of $20,000.
4. During 20X6, Dad declared and paid dividends of $300,000, while Sad declared and paid dividends of $100,000.
5. Dad accounts for its investment in Sad using the cost method.
6. The retained earnings of Dad as at December 31, 20X5, was $12,000,000. On that date, Sad had retained earnings of $9,800,000. Sad has not issued any common shares since its acquisition by Dad.
7. There were no specific events or circumstances between 20X2 and 20X6 to indicate any impairment of goodwill.
The retained earnings of Dad as at December 31, 20X5, equalled $12,000,000. On that date, Sad had retained earnings of $9,800,000. Sad has not issued any common shares since its acquisition by Dad.
Required:
Calculate the consolidated retained earnings at December 31, 20X6. Prepare a condensed statement of financial position as at December 31, 20X6.

Question 32

What does "one-line consolidation" refer to?

A)Cost method
B)Equity method
C)Direct method of consolidation
D)Worksheet method of consolidation

Question 33

In consolidating parent-founded subsidiaries, what account is used to offset the parent company's "Investment in Subsidiary" account?

A)Retained earnings
B)Goodwill
C)Paid-in-capital accounts
D)No offset is necessary

Question 34

In 20X1, a parent company sold a tract of land to its wholly owned subsidiary for $100,000, resulting in a $30,000 loss. The subsidiary's plans for the land did not materialize and it still owned the land at the end of 20X4. At the end of 20X4, what consolidating journal entry should be made with respect to the loss associated with the sale of land?

A) $$\begin{array} { | l | l | } \hline \text { DR Loss on the sale of land } & 30,000 \\\hline \text { CR Land } & 30,000 \\\hline\end{array}$$
B) $$\begin{array} { | l | l | } \hline \text { DR Land } & 30,000 \\\hline \text { CR Loss on the sale of land } & 30,000 \\\hline\end{array}$$
C) $$\begin{array} { | l | l | } \hline \text { DR Retained earnings } & 30,000 \\\hline \text { CR Land } & 30,000 \\\hline\end{array}$$
D) $$\begin{array} { | l | l | } \hline \text { DR Land } & 30,000 \\\hline \text { CR Retained earnings } & 30,000 \\\hline\end{array}$$

Question 35

Franklin Ltd., a subsidiary of Frayer Ltd., sold $500,000 of goods to its parent company in 20X1. At the end of 20X1, some of the goods were not sold and there was $90,000 of unrealized profit associated with these goods. The goods were sold in 20X2. At the end of 20X2, which of the following consolidating entries should be made with respect to the unrealized profits?

A) $$\begin{array} { | c | c | } \hline \text { DR Cost of sales } & 90,000 \\\hline \text { CR Inventory } & 90,000 \\\hline\end{array}$$
B) $$\begin{array} { | l | c | } \hline \text { DR Cost of sales } & 90,000 \\\hline \text { CR Retained earnings } & 90,000 \\\hline\end{array}$$
C) $$\begin{array} { | c | c | } \hline \text { DR Retained earnings } & 90,000 \\\hline \text { CR Cost of sales } & 90,000 \\\hline\end{array}$$
D)An entry is not required as the goods have been sold to external parties.

Question 36

On September 1, 20X5, CanAir Limited decided to buy 100% of the shares outstanding of SkyAir Inc. for $900,000. CanAir will pay for this acquisition by using cash of $500,000 and issuing share capital for the remaining amount. The balances showing on the statement of financial position for the two companies at August 31, 20X5, are as follows: After a review of the financial assets and liabilities, CanAir determines that some of the assets of SkyAir have fair values different from their carrying values. These items are listed below:
• Land has a fair value of 225,000.
• The building has a fair value of $1,090,000. (The company does not own any equipment.)The remaining useful life of the building is 20 years.
• Internet domain name has a fair value is $55,000. The domain name is estimated to have a useful life of five years.
• Customer lists have a fair value is $35,000. It is estimated that the customer lists will have a useful life of seven years.
During the 20X9 fiscal year, the following events occurred:
1. On March 1, 20X9, SkyAir sold land to CanAir for $390,000, which had a carrying value of $275,000. CanAir paid for this with $90,000 cash and a note payable for the difference. This note pays interest at 10%, which is paid monthly.
2. CanAir provided management expertise to SkyAir and charged management fees of $890,000.
3. CanAir sold supplies (included in CanAir sales)to SkyAir for $200,000. CanAir charged SkyAir an amount that was 25% above cost. SkyAir still has supplies on hand of $70,000.
4. In 20X8, SkyAir provided seat space on flights to CanAir for a value of $500,000. This amount was included in sales for SkyAir. Profit margin on these sales is 40%. At the end of August, 20X8, CanAir still had an amount of $200,000 in these prepaid seats that had not yet been used. (CanAir includes this in inventory.) Required:
Prepare the consolidated statement of comprehensive income for the year ended August 31, 20X9.

Question 37

On September 1, 20X5, CanAir Limited decided to buy 100% of the shares outstanding of SkyAir Inc. for $500,000. Can Air will pay for this acquisition by using cash of $500,000. The balances showing on the statement of financial position for the two companies at August 31, 20X5, are as follows: After a review of the financial assets and liabilities, CanAir determines that some of the assets of SkyAir have fair values different from their carrying values. These items are listed below:
• The building has a fair value of $1,090,000. The remaining useful life of the building is 20 years.
• Internet domain name has a fair value is $55,000. The domain name is estimated to have a useful life of five years.
• Brand name has a fair value is $65,000 and an indefinite life.
During the 20X9 fiscal year, the following events occurred:
1. On March 1, 20X9, SkyAir sold land to CanAir for $390,000, which had a carrying value of $275,000. CanAir paid for this with $90,000 cash and a note payable for the difference. This note pays interest at 10%, which is paid monthly.
2. CanAir provided management expertise to SkyAir and charged management fees of $890,000.
3. CanAir sold supplies (included in CanAir sales)to SkyAir for $200,000. CanAir charged SkyAir an amount that was 25% above cost. SkyAir still has supplies on hand of $20,000.
4. In 20X8, SkyAir provided seat space on flights to Can Air for a value of $300,000. This amount was included in sales for SkyAir. Profit margin on these sales is 30%. At the end of August, 20X8, CanAir still had an amount of $150,000 in these prepaid seats that had not yet been used. (CanAir includes this in inventory.) Required:
CanAir would like to report this investment in SkyAir using the equity method.
Determine the income from this equity investment for the year.
Determine the balance in the Investment in SkyAir account if the company used the equity method.

Question 38

On December 31, 20X2, Pipe Ltd. purchased 100% of the outstanding common shares of Fitter Ltd. for $10.5 million in cash. On that date, the shareholders' equity of Fitter totalled $8 million and consisted of $1 million in no par common shares and $7 million in retained earnings. Both companies use the straight-line method to calculate depreciation and amortization. Goodwill, if any arises as a result of this business combination, is written down if there is a permanent impairment in its value.
For the year ending December 31, 20X6, the income statements for Pipe and Fitter were as follows:
$\begin{array}{lll}&\text {Pipe }&\text {Fitter}\\\text { Sales and other revenue } & \underline{\$ 22,500,000 }& \underline{\$ 9,800,000} \\\text { Cost of goods sold } & 16,000,000 & 5,000,000 \\\text { Depreciation expense } & 2,500,000 & 2,000,000 \\\text { Other expenses } & \underline{1,800,000} & \underline{1,200,000} \\\text {Net income}& \underline{\$ 2,200,000 }& \underline{1,600,000}\end{array}$ At December 31, 20X6, the condensed balance sheets for the two companies were as follows:
$$\begin{array} { l l l } & \text { Pipe } & \text { Fitter } \\\text { Total assets } & \$ 31,000,000 & \$ 13,500,000\end{array}$$ $$\begin{array} { l l l } \text { Liabilities } & \$ 5,000,000 & \$ 1,200,000 \\\text { No par common stock } & 12,100,000 & 1,000,000 \\\text { Retained earnings } & \underline { 13,900,000 } & \underline { 11,300,000 } \\\text { Total liabilities and shareholders' equity } & \underline {\$ 13,000,000 }& \underline { \$ 13,500,000}\end{array}$$ OTHER INFORMATION:
1. On December 31, 20X2, Fitter had a building with a fair value that was $500,000 greater than its carrying value. The building had an estimated remaining useful life of 20 years.
2. On December 31, 20X2, Fitter had trademark that was not reported on its balance sheet, but had a fair value that was $200,000. The trademark is amortized over 10 years.
3. During 20X6, Fitter sold merchandise to Pipe for $100,000, a price that included a gross profit of $40,000. During 20X6, 20% of this merchandise was resold by Pipe and the other 80% remains in its December 31, 20X6, inventories. On December 31, 20X5, the inventories of Pipe contained merchandise purchased from Fitter on which Fitter had recognized a gross profit in the amount of $50,000.
4. During 20X6, it was determined that the goodwill arising at the date of acquisition was impaired and that an impairment loss of $70,000 should be recorded. No impairment had been charged in earlier years.
5. During 20X6, Pipe declared and paid dividends of $300,000, while Fitter declared and paid dividends of $100,000.
6. Pipe accounts for its investment in Fitter using the cost method.
The retained earnings of Pipe as at December 31, 20X5, equalled $12,000,000. On that date, Fitter had retained earnings of $9,800,000. Fitter has not issued any common stock since its acquisition by Pipe.
Required:
Calculate the consolidated retained earnings at December 31, 20X5, and December 31, 20X6. Calculate the consolidated net earnings for 20X6. Prepare the consolidated statement of changes equity-partial statement showing the change in retained earnings for December 31, 20X6, for Pipe. Prepare the condensed consolidated statement of financial position for Pipe as at December 31, 20X6.

Question 39

In consolidating a wholly owned parent-founded subsidiary, which of the following adjustments or eliminations is not required?

A)Eliminating any unrealized profits or losses
B)Eliminating intercompany payables and receivables
C)Adjusting for intercompany transactions
D)Adjusting for goodwill impairment

Question 40

On January 1, 20X3, Dwayne Ltd. formed Carlos Co., a 100% owned subsidiary. During 20X6, Dwayne sold Carlos $100,000 in goods. The unrealized profit in Carlos's inventories was $20,000 at December 31, 20X5, and $25,000 at December 31, 20X6.

-Ignoring income taxes, what accounts should Dwayne debit and credit by $20,000 in preparing its consolidated financial statements for the year ended December 31, 20X6, to reflect the unrealized profit in Carlos's beginning inventory? $\begin{array} { l l } { \text { Debit } } &&&&&&& { \text { Credit } } \\\end{array}$

A) $\begin{array} { l l } \text {Cost of sales } &&& \text { Inventory } \\\end{array}$
B) $\begin{array} { l l }\text { Inventcry } &&&& \text { Cost of Sales } \\\end{array}$
C) $\begin{array} { l l } \text {Retained earnings } & \text { Cost of sales } \\\end{array}$
D) $\begin{array} { l l } \text {Cost of sales } &&& \text { Tetained earnings }\end{array}$