assignment ordering exercise 14.03

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14.3E: Exercises

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Practice Makes Perfect

Factor Trinomials of the Form \(x^2+bx+c\)

In the following exercises, factor each trinomial of the form \(x^2+bx+c\).

1. \(p^2+11p+30\)

\((p+5)(p+6)\)

2. \(w^2+10w+21\)

3. \(n^2+19n+48\)

\((n+3)(n+16)\)

4. \(b^2+14b+48\)

5. \(a^2+25a+100\)

\((a+5)(a+20)\)

6. \(u^2+101u+100\)

7. \(x^2−8x+12\)

\((x−2)(x−6)\)

8. \(q^2−13q+36\)

9. \(y^2−18y+45\)

\((y−3)(y−15)\)

10. \(m^2−13m+30\)

11. \(x^2−8x+7\)

\((x−1)(x−7)\)

12. \(y^2−5y+6\)

13. \(5p−6+p^2\)

\((p−1)(p+6)\)

14. \(6n−7+n^2\)

15. \(8−6x+x^2\)

\((x−4)(x−2)\)

16. \(7x+x^2+6\)

17. \(x^2−12−11x\)

\((x−12)(x+1)\)

18. \(−11−10x+x^2\)

In the following exercises, factor each trinomial of the form \(x^2+bxy+cy^2\).

19. \(x^2−2xy−80y^2\)

\((x+8y)(x−10y)\)

20. \(p^2−8pq−65q^2\)

21. \(m^2−64mn−65n^2\)

\((m+n)(m−65n)\)

22. \(p^2−2pq−35q^2\)

23. \(a^2+5ab−24b^2\)

\((a+8b)(a−3b)\)

24. \(r^2+3rs−28s^2\)

25. \(x^2−3xy−14y^2\)

26. \(u^2−8uv−24v^2\)

27. \(m^2−5mn+30n^2\)

28. \(c^2−7cd+18d^2\)

Factor Trinomials of the Form \(ax^2+bx+c\) Using Trial and Error

In the following exercises, factor completely using trial and error.

29. \(p^3−8p^2−20p\)

\(p(p−10)(p+2)\)

30. \(q^3−5q^2−24q\)

31. \(3m^3−21m^2+30m\)

\(3m(m−5)(m−2)\)

32. \(11n^3−55n^2+44n\)

33. \(5x^4+10x^3−75x^2\)

\(5x^2(x−3)(x+5)\)

34. \(6y^4+12y^3−48y^2\)

35. \(2t^2+7t+5\)

\((2t+5)(t+1)\)

36. \(5y^2+16y+11\)

37. \(11x^2+34x+3\)

\((11x+1)(x+3)\)

38. \(7b^2+50b+7\)

39. \(4w^2−5w+1\)

\((4w−1)(w−1)\)

40. \(5x^2−17x+6\)

41. \(4q^2−7q−2\)

\((4q+1)(q−2)\)

42. \(10y^2−53y−111\)

43. \(6p^2−19pq+10q^2\)

\((2p−5q)(3p−2q)\)

44. \(21m^2−29mn+10n^2\)

45. \(4a^2+17ab−15b^2\)

\((4a−3b)(a+5b)\)

46. \(6u^2+5uv−14v^2\)

47. \(−16x^2−32x−16\)

\(−16(x+1)(x+1)\)

48. \(−81a^2+153a+18\)

49. \(−30q^3−140q^2−80q\)

\( - 10q(3q+2)(q+4)\)

50. \(−5y^3−30y^2+35y\)

Factor Trinomials of the Form \(ax^2+bx+c\) using the ‘ac’ Method

In the following exercises, factor using the ‘ac’ method.

51. \(5n^2+21n+4\)

\((5n+1)(n+4)\)

52. \(8w^2+25w+3\)

53. \(4k^2−16k+15\)

\((2k−3)(2k−5)\)

54. \(5s^2−9s+4\)

55. \(6y^2+y−15\)

\((3y+5)(2y−3)\)

56. \(6p^2+p−22\)

57. \(2n^2−27n−45\)

\((2n+3)(n−15)\)

58. \(12z^2−41z−11\)

59. \(60y^2+290y−50\)

\(10(6y−1)(y+5)\)

60. \(6u^2−46u−16\)

61. \(48z^3−102z^2−45z\)

\(3z(8z+3)(2z−5)\)

62. \(90n^3+42n^2−216n\)

63. \(16s^2+40s+24\)

\(8(2s+3)(s+1)\)

64. \(24p^2+160p+96\)

65. \(48y^2+12y−36\)

\(12(4y−3)(y+1)\)

66. \(30x^2+105x−60\)

Factor Using Substitution

In the following exercises, factor using substitution.

67. \(x^4−x^2−12\)

\((x^2+3)(x^2−4)\)

68. \(x^4+2x^2−8\)

69. \(x^4−3x^2−28\)

\((x^2−7)(x^2+4)\)

70. \(x^4−13x^2−30\)

71. \((x−3)^2−5(x−3)−36\)

72. \((x−2)^2−3(x−2)−54\)

73. \((3y−2)^2−(3y−2)−2\)

\((3y−4)(3y−1)\)

74. \((5y−1)^2−3(5y−1)−18\)

Mixed Practice

In the following exercises, factor each expression using any method.

75. \(u^2−12u+36\)

\((u−6)(u−6)\)

76. \(x^2−14x−32\)

77. \(r^2−20rs+64s^2\)

\((r−4s)(r−16s)\)

78. \(q^2−29qr−96r^2\)

79. \(12y^2−29y+14\)

\((4y−7)(3y−2)\)

80. \(12x^2+36y−24z\)

81. \(6n^2+5n−4\)

\((2n−1)(3n+4)\)

82. \(3q^2+6q+2\)

83. \(13z^2+39z−26\)

\(13(z^2+3z−2)\)

84. \(5r^2+25r+30\)

85. \(3p^2+21p\)

\(3p(p+7)\)

86. \(7x^2−21x\)

87. \(6r^2+30r+36\)

\(6(r+2)(r+3)\)

88. \(18m^2+15m+3\)

89. \(24n^2+20n+4\)

\(4(2n+1)(3n+1)\)

90. \(4a^2+5a+2\)

91. \(x^4−4x^2−12\)

\((x^2+2)(x^2−6)\)

92. \(x^4−7x^2−8\)

93. \((x+3)^2−9(x+3)−36\)

\((x−9)(x+6)\)

94. \((x+2)^2−25(x+2)−54\)

Writing Exercises

95. Many trinomials of the form \(x^2+bx+c\) factor into the product of two binomials \((x+m)(x+n)\). Explain how you find the values of \(m\) and \(n\).

Answers will vary.

96. Tommy factored \(x^2−x−20\) as \((x+5)(x−4)\). Sara factored it as \((x+4)(x−5)\). Ernesto factored it as \((x−5)(x−4)\). Who is correct? Explain why the other two are wrong.

97. List, in order, all the steps you take when using the “\(ac\)” method to factor a trinomial of the form \(ax^2+bx+c\).

98. How is the “\(ac\)” method similar to the “undo FOIL” method? How is it different?

a. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

b. After reviewing this checklist, what will you do to become confident for all objectives?

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14.E: Regression (Exercises)

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• Page ID 2650

• Rice University

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General Questions

What is the equation for a regression line? What does each term in the line refer to? (relevant section)

The formula for a regression equation based on a sample size of \(25\) observations is \(Y' = 2X + 9\).

• What would be the predicted score for a person scoring \(6\) on \(X\)?
• If someone's predicted score was \(14\), what was this person's score on \(X\)? (relevant section)

What criterion is used for deciding which regression line fits best? (relevant section)

What does the standard error of the estimate measure? What is the formula for the standard error of the estimate? (relevant section)

• In a regression analysis, the sum of squares for the predicted scores is \(100\) and the sum of squares error is \(200\), what is \(R^2\)?
• In a different regression analysis, \(40\%\) of the variance was explained. The sum of squares total is \(1000\). What is the sum of squares of the predicted values? (relevant section)

For the \(X,Y\) data below, compute:

• \(r\) and determine if it is significantly different from zero.
• the slope of the regression line and test if it differs significantly from zero.
• the \(95\%\) confidence interval for the slope.

(relevant section)

What assumptions are needed to calculate the various inferential statistics of linear regression? (relevant section)

The correlation between years of education and salary in a sample of \(20\) people from a certain company is \(0.4\). Is this correlation statistically significant at the \(0.05\) level? (relevant section)

A sample of \(X\) and \(Y\) scores is taken, and a regression line is used to predict \(Y\) from \(X\). If \(SSY' = 300\), \(SSE = 500\), and \(N = 50\), what is: (relevant section relevant section)

• the standard error of the estimate?

Using linear regression, find the predicted post-test score for someone with a score of \(43\) on the pre-test. (relevant section)

The equation for a regression line predicting the number of hours of TV watched by children (\(Y\)) from the number of hours of TV watched by their parents (\(X\)) is \(Y' = 4 + 1.2X\). The sample size is \(12\).

• If the standard error of \(b\) is \(0.4\), is the slope statistically significant at the \(0.05\) level? (relevant section)
• If the mean of \(X\) is \(8\), what is the mean of \(Y\)? (relevant section)

Based on the table below, compute the regression line that predicts \(Y\) from \(X\). (relevant section)

Does \(A\) or \(B\) have a larger standard error of the estimate? (relevant section)

True/false: If the slope of a simple linear regression line is statistically significant, then the correlation will also always be significant. (relevant section)

True/false: If the slope of the relationship between \(X\) and \(Y\) is larger for \(\text{Population 1}\) than for \(\text{Population 2}\), the correlation will necessarily be larger in \(\text{Population 1}\) than in \(\text{Population 1}\). Why or why not? (relevant section)

True/false: If the correlation is \(0.8\), then \(40\%\) of the variance is explained. (relevant section)

True/false: If the actual \(Y\) score was \(31\), but the predicted score was \(28\), then the error of prediction is \(3\). (relevant section)

Questions from Case Studies

The following question is from the Angry Moods (AM) case study.

(AM#23) Find the regression line for predicting Anger-Out from Control-Out.

• What is the slope?
• What is the intercept?
• Is the relationship at least approximately linear?
• Test to see if the slope is significantly different from \(0\).
• What is the standard error of the estimate?

(relevant section, relevant section, relevant section)

The following question is from the SAT and GPA (SG) case study.

(SG#3) Find the regression line for predicting the overall university GPA from the high school GPA.

• What is the \(y\)-intercept?
• If someone had a \(2.2\) GPA in high school, what is the best estimate of his or her college GPA?
• If someone had a \(4.0\) GPA in high school, what is the best estimate of his or her college GPA?

The following questions are from the Driving (D) case study.

(D#5) What is the correlation between age and how often the person chooses to drive in inclement weather? Is this correlation statistically significant at the \(0.01\) level? Are older people more or less likely to report that they drive in inclement weather? (relevant section, relevant section )

(D#8) What is the correlation between how often a person chooses to drive in inclement weather and the percentage of accidents the person believes occur in inclement weather? Is this correlation significantly different from \(0\)? (relevant section, relevant section )

(D#10) Use linear regression to predict how often someone rides public transportation in inclement weather from what percentage of accidents that person thinks occur in inclement weather. (Pubtran by Accident)

• Create a scatter plot of this data and add a regression line.
• Test if the slope is significantly different from \(0\).
• Comment on possible assumption violations for the test of the slope.

Selected Answers

• \(b = 1.91\)

\(a = 19.2\)

\(r = 0.43\)

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14.11: Exercises

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• Page ID 18885

• Allen B. Downey
• Olin College via Green Tea Press

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The code for this chapter is in the ch06 directory of ThinkJavaCode . See [ Section 0.4 ] for instructions on how to download the repository. Before you start the exercises, we recommend that you compile and run the examples.

If you have not already read Appendix A.7, now might be a good time. It describes JUnit, a tool for efficiently testing value methods.

Exercise \(\PageIndex{1}\)

If you have a question about whether something is legal, and what happens if it is not, a good way to find out is to ask the compiler. Answer the following questions by trying them out.

• What happens if you invoke a value method and don’t do anything with the result; that is, if you don’t assign it to a variable or use it as part of a larger expression?
• What happens if you use a void method as part of an expression? For example, try System.out.println("boo!") + 7;

Exercise \(\PageIndex{2}\)

Write a method named isDivisible that takes two integers, n and m , and that returns true if n is divisible by m , and false otherwise.

Exercise \(\PageIndex{3}\)

If you are given three sticks, you may or may not be able to arrange them in a triangle. For example, if one of the sticks is 12 inches long and the other two are one inch long, you will not be able to get the short sticks to meet in the middle. For any three lengths, there is a simple test to see if it is possible to form a triangle:

If any of the three lengths is greater than the sum of the other two, you cannot form a triangle.

Write a method named isTriangle that takes three integers as arguments and returns either true or false , depending on whether you can or cannot form a triangle from sticks with the given lengths. The point of this exercise is to use conditional statements to write a value method

Exercise \(\PageIndex{4}\)

Many computations can be expressed more concisely using the “multadd” operation, which takes three operands and computes a * b + c . Some processors even provide a hardware implementation of this operation for floating-point numbers.

• Create a new program called Multadd.java .
• Write a method called multadd that takes three doubles as parameters and that returns a * b + c .
• Write a main method that tests multadd by invoking it with a few simple parameters, like 1.0, 2.0, 3.0 .
• Also in main , use multadd to compute the following values: \[\begin{align*} & \sin(\frac{\pi}{4}) + \frac{\cos(\frac{\pi}{4})}{2} \\[5pt] & \log{10} + \log{20} \end{align*} \]
• Write a method called expSum that takes a double as a parameter and that uses multadd to calculate: \[ xe^{-x} + \sqrt{1-e^{-x}} \nonumber \]

In the last part of this exercise, you need to write a method that invokes another method you wrote. Whenever you do that, it is a good idea to test the first method carefully before working on the second. Otherwise, you might find yourself debugging two methods at the same time, which can be difficult.

One of the purposes of this exercise is to practice pattern-matching: the ability to recognize a specific problem as an instance of a general category of problems.

The method for raising e to a power is Math.exp .

Exercise \(\PageIndex{5}\)

What is the output of the following program?

Exercise \(\PageIndex{6}\)

In this exercise, you will use a stack diagram to understand the execution of the following recursive program.

• Draw a stack diagram showing the state of the program just before the last invocation of prod completes.
• What is the output of this program? (Try to answer this question on paper first, then run the code to check your answer.)
• Explain in a few words what prod does (without getting into the details of how it works).
• Rewrite prod without the temporary variables recurse and result . Hint: You only need one line for the else branch.

Exercise \(\PageIndex{7}\)

Write a recursive method named oddSum that takes a positive odd integer n and returns the sum of odd integers from 1 to n. Start with a base case, and use temporary variables to debug your solution. You might find it helpful to print the value of n each time oddSum is invoked.

Exercise \(\PageIndex{8}\)

The goal of this exercise is to translate a recursive definition into a Java method. The Ackermann function is defined for non-negative integers as follows:

\[ A(m,n) = \begin{cases} n+1 & \mbox{if } m = 0 \\ A(m-1,1) & \mbox{if } m > 0 \mbox{ and } n = 0 \\ A(m-1, A(m, n-1)) & \mbox{if } m > 0 \mbox{ and } n > 0 \end{cases} \nonumber \]

Write a method called ack that takes two int s as parameters and that computes and returns the value of the Ackermann function.

Test your implementation of Ackermann by invoking it from main and displaying the return value. Note the return value gets very big very quickly. You should try it only for small values of m and n (not bigger than 3).

Write a recursive method called power that takes a double x and an integer n and returns x n .

A recursive definition of this operation is x n = x · x n −1 . Also, remember that anything raised to the zeroth power is 1.

You can make this method more efficient, when n is even, using x n = ( x n /2 ) 2 .

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14.5: Exercises- Unit 14

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Short-Answer Questions, Exercises, and Problems: Corporations: Paid-in Capital, Retained Earnings, Dividends and Treasury Stock

Short-Answer Questions

➢ What are dividends in arrears, and how should they be disclosed in the financial statements?

➢ A corporation has 1,000 shares of 8 per cent, $ 200 par value, cumulative, preferred stock outstanding. Dividends on this stock have not been declared for three years. Is the corporation legally liable to its preferred stockholders for these dividends? How should this fact be shown in the balance sheet, if at all?

➢ What are the two main elements of stockholders’ equity in a corporation? Explain the difference between them.

➢ Name several sources of paid-in capital. Would it suffice to maintain one account called Paid-In Capital for all sources of paid-in capital? Why or why not?

➢ Does accounting for treasury stock resemble accounting for an asset? Is treasury stock an asset? If not, where is it properly shown on a balance sheet?

➢ What are some possible reasons for a corporation to reacquire its own capital stock as treasury stock?

➢ What is the purpose underlying the statutes that provide for restriction of retained earnings in the amount of the cost of treasury stock? Are such statutes for the benefit of stockholders, management, or creditors?

➢ What is the effect of each of the following on the total stockholders’ equity of a corporation: (a) declaration of a cash dividend, (b) payment of a cash dividend already declared, (c) declaration of a stock dividend, and (d) issuance of a stock dividend already declared?

➢ The following dates are associated with a cash dividend of $ 80,000: July 15, July 31, and August 15. Identify each of the three dates, and give the journal entry required on each date, if any.

➢ How should a declared but unpaid cash dividend be shown on the balance sheet? How should a declared but unissued stock dividend be shown?

➢ On May 8, the board of directors of Park Corporation declared a dividend, payable on June 5, to stockholders of record on May 17. On May 10, James sold his capital stock in Park Corporation directly to Benton for $ 20,000, endorsing his stock certificate and giving it to Benton. Benton placed the stock certificate in her safe. On May 30, Benton sent the certificate to the transfer agent of Park Corporation for transfer. Who received the dividend? Why?

➢ What are the possible reasons for a corporation to declare a stock dividend?

➢ Why is a dividend consisting of the distribution of additional shares of the common stock of the declaring corporation not considered income to the recipient stockholders?

➢ What is the difference between a small stock dividend and a large stock dividend?

➢ What is the purpose of a retained earnings appropriation?

➢ What is a statement of stockholders’ equity?

➢ Describe a discontinued operation.

➢ What are extraordinary items? Where and how are they reported?

➢ Give an example of a change in accounting principle. How are the effects of changes in accounting principle reported?

➢ What are prior period adjustments? Where and how are they reported?

➢ Why are stockholders and potential investors interested in the amount of a corporation’s EPS? What does the EPS amount reveal that total earnings do not.

Exercise A Winters Corporation has outstanding 1,000 shares of noncumulative preferred stock and 2,000 shares of common stock. The preferred stock is entitled to an annual dividend of $ 100 per share before dividends are declared on common stock. What are the total dividends received by each class of stock if Winters Corporation distributes $ 280,000 in dividends in 2010?

Exercise B Zeff Corporation has 2,000 shares outstanding of cumulative preferred stock and 6,000 shares of common stock. The preferred stock is entitled to an annual dividend of $ 18 per share before dividends are declared on common stock. No preferred dividends were paid for last year and the current year. What are the total dividends received by each class of stock if Zeff Corporation distributes $ 108,000 in dividends?

Exercise A The 2009 December 31, trial balance of Yamey Corporation had the following account balances:

Present in proper form the stockholders’ equity section of the balance sheet.

Exercise B Fogg Company has issued all of its authorized 5,000 shares of $ 400 par value common stock. On 2009 February 1, the board of directors declared a dividend of $ 12 per share payable on 2009 March 15, to stockholders of record on 2009 March 1. Give the necessary journal entries.

Exercise C The stockholders’ equity section of Jay Company’s balance sheet on 2009 December 31, shows 100,000 shares of authorized and issued $ 20 stated value common stock, of which 9,000 shares are held in the treasury. On this date, the board of directors declared a cash dividend of $ 2 per share payable on 2010 January 21, to stockholders of record on January 10. Give dated journal entries for these.

Exercise D Kevin Company has outstanding 75,000 shares of common stock without par or stated value, which were issued at an average price of $ 80 per share, and retained earnings of $ 3,200,000. The current market price of the common stock is $ 120 per share. Total authorized stock consists of 500,000 shares.

• Give the required entry to record the declaration of a 10 per cent stock dividend.
• If, alternatively, the company declared a 30 per cent stock dividend, what additional information would you need before making a journal entry to record the dividend?

Exercise E Grant Corporation’s stockholders’ equity consisted of 60,000 authorized shares of $ 30 par value common stock, of which 30,000 shares had been issued at par, and retained earnings of $ 750,000. The company then split its stock, two for one, by changing the par value of the old shares and issuing new $ 15 par shares.

• Give the required journal entry to record the stock split.
• Suppose instead that the company declared and later issued a 10 per cent stock dividend. Give the required journal entries, assuming that the market value on the date of declaration was $ 40 per share.

Exercise F The balance sheet of Willis Company contains the following:

Appropriation per loan agreement $ 900,000

• Give the journal entry made to create this account.
• Explain the reason for the appropriation’s existence and its manner of presentation in the balance sheet.

Exercise E Li & Tu, Inc., needed land for a plant site. It issued 100 shares of $ 480 par value common stock to the incorporators of their corporation in exchange for land, which cost $ 56,000 one year ago. Experienced appraisers recently valued the land at $ 72,000. What journal entry would be appropriate to record the acquisition of the land?

Exercise H Evan Company received 200 shares of its $ 200 stated value common stock on 2009 December 1, as a donation from a stockholder. On 2009 December 15, it reissued the stock for $ 62,400 cash. Give the journal entry or entries necessary for these transactions.

Exercise I Vista Company has revenues of $ 80 million, expenses of $ 64 million, a tax-deductible earthquake loss (its first such loss) of $ 4 million, and a tax-deductible loss of $ 6 million resulting from the voluntary early extinguishment (retirement) of debt. The assumed income tax rate is 40 per cent. The company’s beginning-of-the-year retained earnings were $ 30 million, and a dividend of $ 2 million was declared.

• Prepare an income statement for the year.
• Prepare a statement of retained earnings for the year.

Exercise J Conner Company had retained earnings of $ 56,000 as of 2009 January 1. In 2009, Conner Company had sales of $ 160,000, cost of goods sold of $ 96,000, and other operating expenses, excluding taxes, of $ 32,000. In 2009, Conner Company discovered that it had, in error, depreciated land over the last three years resulting in a balance in the accumulated depreciation account of $ 40,000. The assumed tax rate for Conner Company is 40 per cent. Present in proper form a statement of retained earnings for the year ended 2009 December 31.

Exercise K The following information relates to Perry Corporation for the year ended 2009 December 31:

Calculate EPS for the year ended 2009 December 31. Present the information in the same format used in the corporation’s income statement.

Exercise L Dean Company had an average number of shares of common stock outstanding of 200,000 in 2009 and 215,000 in 2010. Net income for these two years was as follows:

• Calculate EPS for the years ended 2009 December 31, and 2010.
• What might the resulting figures tell a stockholder or a potential investor?

Problem A The outstanding capital stock of Robbins Corporation consisted of 3,000 shares of 10 per cent preferred stock, $ 250 par value, and 30,000 shares of no-par common stock with a stated value of $ 250. The preferred was issued at $ 412, the common at $ 480 per share. On 2005 January 1, the retained earnings of the company were $ 250,000. During the succeeding five years, net income was as follows:

No dividends were in arrears as of 2005 January 1, and during the five years 2005-2009, the board of directors declared dividends in each year equal to net income of the year.

Prepare a schedule showing the dividends declared each year on each class of stock assuming the preferred stock is:

• Cumulative.
• Noncumulative.

Problem B The only stockholders’ equity items of Jody Company at 2009 June 30, are:

On 2009 August 4, a 4 per cent cash dividend was declared, payable on September 3. On November 16, a 10 per cent stock dividend was declared. The shares were issued on December 1. The market value of the common stock was $ 360 per share on November 16 and $ 354 per share on December 1.

Prepare journal entries for these dividend transactions.

Problem C Following are selected transactions of White Corporation:

Dec. 31 The board of directors authorized the appropriation of $ 50,000 of retained earnings to provide for the future acquisition of a new plant site and the construction of a new building. (On the last day of the next six years, the same action was taken. You need not make entries for these six years.)

Jan. 2 Purchased a new plant site for cash, $ 100,000.

Mar. 29 Entered into a contract for construction of a new building, payment to be made within 30 days following completion.

Feb. 10 Following final inspection and approval of the new building, Dyer Construction Company was paid in full, $ 500,000.

Mar. 10 The board of directors authorized release of the retained earnings appropriated for the plant site and building.

Apr. 2 A 5 per cent stock dividend on the 100,000 shares of $ 50 par value common stock outstanding was declared. The market price on this date was $ 55 per share.

Prepare journal entries for all of these transactions.

Problem D Following are selected data of Kane Corporation at 2009 December 31:

Prepare a statement of retained earnings for the year ended 2009 December 31.

Problem E The stockholders’ equity of Sayers Company at 2009 January 1, is as follows:

During 2009, the following transactions occurred in the order listed:

• Issued 10,000 shares of stock for $ 368,000.
• Declared a 4 per cent stock dividend when the market price was $ 48 per share.
• Sold 1,000 shares of treasury stock for $ 43,200.
• Issued stock certificates for the stock dividend declared in transaction 2.
• Bought 2,000 shares of treasury stock for $ 67,200.
• Increased the appropriation by $ 43,200 per loan agreement.

Prepare journal entries as necessary for these transactions.

Problem F The stockholders’ equity of Briar Company on 2008 December 31, consisted of 1,000 authorized, issued, and outstanding shares of $ 72 cumulative preferred stock, stated value $ 240 per share, which were originally issued at $ 1,192 per share; 100,000 shares authorized, issued, and outstanding of no-par, $ 160 stated value common stock, which were originally issued at $ 160; and retained earnings of $ 1,120,000. Following are selected transactions and other data relating to 2009. No previous treasury stock transactions had occurred.

• The company reacquired 2,000 shares of its common stock at $ 336.
• One thousand of the treasury shares were reissued at $ 288.
• Stockholders donated 1,000 shares of common stock to the company. These shares were immediately reissued at $ 256 to provide working capital.
• The first quarter’s dividend of $ 18 per share was declared and paid on the preferred stock. No other dividends were declared or paid during 2009.

The company suffered a net loss of $ 224,000 for the year 2009.

• Prepare journal entries for the preceding numbered transactions.
• Prepare the stockholders’ equity section of the 2009 December 31, balance sheet.

Problem G The following stockholders’ equity section is from Bell Company’s 2008 October 31, balance sheet:

During the ensuing fiscal year, Bell Company entered into the following transactions:

• The appropriation of $ 12,000 of retained earnings had been authorized in October 2008 because of the likelihood of an unfavorable court decision in a pending lawsuit. The suit was brought by a customer seeking damages for the company’s alleged breach of a contract to supply the customer with certain products at stated prices in 2007. The suit was concluded on 2009 March 6, with a court order directing the company to pay $ 10,500 in damages. These damages were not deductible in determining the income tax liability. The board ordered the damages paid and the appropriation closed. The loss does not qualify as an extraordinary item.
• The company acquired 1,000 shares of its own common stock at $ 9 in May 2009. On June 30, it reissued 500 of these shares at $ 7.20.
• Dividends declared and paid during the year were 6 per cent on preferred stock and 18 cents per share on common stock. Both dividends were declared on September 1 and paid on 2009 September 30.

For the fiscal year, the company had net income after income taxes of $ 11,400, excluding the loss of the lawsuit.

• Prepare a statement of retained earnings for the year ended 2009 October 31.
• Prepare the stockholders’ equity section of the 2009 October 31, balance sheet.

Problem H Selected data for Brinks Company for 2009 are given below:

Assume the applicable federal income tax rate is 40 per cent. All of the items of expense, revenue, and loss are included in the computation of taxable income. The earthquake loss resulted from the first earthquake experienced at the company’s location. In addition, the company discovered that in 2008 it had erroneously charged to expense the $ 160,000 cost of a tract of land purchased that year and had made the same error on its tax return for 2008.

• Prepare an income statement for the year ended 2009 December 31.

Alternate problems

Alternate problem A On 2005 January 1, the retained earnings of Quigley Company were $ 432,000. Net income for the succeeding five years was as follows:

The outstanding capital stock of the corporation consisted of 2,000 shares of preferred stock with a par value of $ 480 per share that pays a dividend of $ 19.20 per year and 8,000 shares of no-par common stock with a stated value of $ 240 per share. No dividends were in arrears as of 2005 January 1.

Prepare schedules showing how the net income for these five years was distributed to the two classes of stock if in each of the years the entire current net income was distributed as dividends and the preferred stock was:

Alternate problem B The stockholders’ equity section of Carson Company’s 2008 December 31, balance sheet follows:

On 2009 July 15, the board of directors declared a cash dividend of $ 12 per share, which was paid on 2009 August 1. On 2009 December 1, the board declared a stock dividend of 10 per cent, and the shares were issued on 2009 December 15. Market value of the stock was $ 144 on December 1 and $ 168 on December 15.

Alternate problem C The ledger of Falcone Company includes the following account balances on 2009 September 30:

During October 2009, the company took action to:

• Increase the appropriation for contingencies by $ 60,000.
• Decrease the appropriation for plant expansion by $ 160,000.
• Establish an appropriation per loan agreement, with an annual increase of $ 48,000.
• Declare a cash dividend of $ 140,000.

Prepare the journal entries to record these transactions of Falcone Company.

Alternate problem D Following are selected transactions of Taylor Corporation:

Dec. 31 By action of the board of directors, $ 450,000 of retained earnings was appropriated to provide for future expansion of the company’s main building. (On the last day of each of the next four years, the same action was taken. You need not make entries for these years.)

Jan. 3 Obtained, at a cost of $ 4,500, a building permit to construct a new wing on the main plant building.

July 30 Paid $ 1,800,000 to Starke Construction Company for completion of the new wing.

Aug. 4 The board of directors authorized the release of the sum appropriated for expansion of the plant building.

4 The board of directors declared a 10 per cent common stock dividend on the 25,000 shares of $ 500 par value common stock outstanding. The market price on this date was $ 660 per share.

Prepare journal entries to record all of these transactions.

Alternate problem E The following information relates to Dahl Corporation for the year 2009:

Alternate problem F The stockholders’ equity of Acorn Company as of 2008 December 31, consisted of 20,000 shares of authorized, issued, and outstanding $ 50 par value common stock, paid-in capital in excess of par of $ 240,000, and retained earnings of $ 400,000. Following are selected transactions for 2009:

May 1 Acquired 3,000 shares of its own common stock at $ 100 per share.

June 1 Reissued 500 shares at $ 120.

30 Reissued 700 shares at $ 90.

Oct. 1 Declared a cash dividend of $ 5 per share.

31 Paid the cash dividend declared on October 1.

Net income for the year was $ 80,000. No other transactions affecting retained earnings occurred during the year.

• Prepare general journal entries for these transactions.

Alternate problem G The stockholders’ equity section of Sager Company’s 2008 December 31, balance sheet follows:

Following are selected transactions that occurred in 2009:

Jan. 13 Cash was received for 550 shares of previously unissued common stock at $ 13.20.

Feb. 4 A plot of land was accepted as payment in full for 500 shares of common stock, and the stock was issued. Closing market price of the common stock on this date was $ 12 per share.

Mar. 24 All of the treasury stock was reissued at $ 14.40 per share.

June 23 The regular semiannual dividend on the preferred stock was declared.

30 The preferred dividend was paid.

July 3 A 10 per cent stock dividend was declared on the common stock. Market price on this date was $ 16.80.

18 The stock dividend shares were issued.

Oct. 4 The company reacquired 105 shares of its common stock at $ 14.40.

Dec. 18 The regular semiannual dividend on the preferred stock and a $ 0.24 per share dividend on the common stock were declared.

31 Both dividends were paid.

31 An additional appropriation of retained earnings of $ 3,000 for plant expansion was authorized.

• Prepare journal entries to record the 2009 transactions.
• Prepare a statement of retained earnings for the year 2009, assuming net income for the year was $ 25,800.

Alternate problem H Selected data of Ace Company for the year ended 2009 December 31, are:

Assume the applicable federal income tax rate is 40 per cent. All of the preceding items of expense, revenue, and loss are included in the computation of taxable income. The litigation loss resulted from a court award of damages for patent infringement on a product that the company produced and sold in 2005 and 2006, but was discontinued in 2006. In addition, the company discovered that in 2005 it had erroneously charged to expense the $ 250,000 cost of a tract of land purchased that year and had made the same error on its tax return for 2008. Retained earnings as of 2009 January 1, were $ 5,600,000. Assume there were 10,000 shares of common stock and 5,000 shares of preferred stock outstanding for the entire year.

Prepare an income statement and a statement of retained earnings for 2009.

Beyond the numbers—Critical thinking

Business decision case A The stockholders’ equity section of the Bates Corporation’s balance sheet for 2009 June 30, follows:

On 2009 July 1, the corporation’s directors declared a 10 per cent stock dividend distributable on August 2 to stockholders of record on July 16. On 2009 November 1, the directors voted a $ 2.40 per share annual cash dividend payable on December 2 to stockholders of record on November 16. For four years prior to 2009, the corporation had paid an annual cash dividend of $ 2.52.

As of 2009 July 1, Bob Jones owned 8,000 shares of Bates Corporation’s common stock, which he had purchased four years earlier. The market value of his stock was $ 48 per share on 2009 July 1, and $ 43.64 per share on 2009 July 16.

• What amount of cash dividends will Jones receive in 2009? How does this amount differ from the amount of cash dividends Jones received in the previous four years?
• Jones has asked you, his CPA, to explain why the price of the stock dropped from $ 48 to $ 43.64 on 2009 July 16. Write a memo to Jones explaining your answer.
• Do you think Jones is better off as a result of the stock dividend and the $ 2.40 cash dividend than he would have been if he had just received the $ 2.52 cash dividend? Write a memo to Jones explaining your answer.

Business decision case B The following journal entries are for Keel Corporation:

The management of Keel Corporation has asked you, a CPA, to analyze these journal entries and decide whether each is correct. The explanations are all correct. Wherever a journal entry is incorrect, prepare the journal entry that should have been made.

Annual report analysis C The following questions are based on the Coca-Cola Company’s 2006 annual report. To view the report, go to the Coca-Cola web site at www.cocacola.com. After you activate the web site, click on The Coca-Cola Company. Go to investors and a menu will drop down that has financials as an option with Financial Statements (select this) to its right. Click on Balance Sheet and then open it to find the total cost of treasury shares. Then go to Selected Financial Data and open it to find the number of common shares outstanding.

• Based on the information in the balance sheet and the note, determine the number of common shares outstanding; and the total cost of treasury stock shares on hand at the end of 2006.
• In writing, discuss what reasons Coca-Cola might have to acquire treasury stock.
• Find Coca-Cola’s basic EPS for 2006 listed in its Income Statement. If the common stock’s market price at 2006 December 31, was $ 30, what was the price-earnings ratio?

Ethics case–Writing experience D Based on the ethics case, answer the following questions concerning Ace Chemical Company in writing:

• Is this transaction fair to the creditors?
• Why would the officers not merely declare a $ 4 million cash dividend? Is the proposed treasury stock transaction fair to the other stockholders?
• If you were one of the officers, would you feel comfortable in going ahead with this proposed treasury stock transaction?

Group project E In teams of two to three students, go to the library to find articles evaluating accounting software packages. Use a periodicals index such as the Accounting and Tax Index or the Business Periodicals Index to locate these articles. Compare the cost and features of three accounting software packages. As a team, prepare a memorandum to the manager of a small retail business. Compare and contrast the three accounting software packages so the manager might decide which package to purchase. In the memorandum, cite the sources used in gathering the data and properly reference any direct quotes or paraphrasing. The heading of the memorandum should contain the date, to whom it is written, from whom, and the subject matter.

Group project F With a small group of students, go to the library and locate Statement of Financial Accounting Standards No. 4 , “Reporting Gains and Losses from Extinguishing of Debt”, published by the Financial Accounting Standards Board. Write a report to your instructor giving the highlights of the standard. Why are these gains and losses treated as extraordinary items? Why did the Board act on this topic? Why did one member of the Board dissent?

Group project G With one or two other students, locate the annual reports of three companies and study their statements of stockholders’ equity. Determine why the number of common shares outstanding changed (if at all) during the current year. For instance, the number of outstanding shares may have increased due to new issuances, exercise of stock options, conversion of preferred stock, exercise of warrants, stock dividends, and other causes. The number of shares outstanding may have decreased because of repurchases of stock (treasury stock transactions). Write a report to your instructor presenting your findings. Also be prepared to make a short presentation to your class.

Using the Internet—A view of the real world

Visit the following website for the General Electric Company:

http://www.ge.com

Pursue choices on the screen until you locate the consolidated statement of changes in stockholders’ equity. You will probably go down some “false paths” to get to this financial statement, but you can get there. This experience is all part of learning to use the Internet. Trace the changes that have occurred in the last three years in the dividends and other transactions with stockholders. Check out the notes to the financial statements for further information. Write a memo to your instructor summarizing your findings.

Visit the following website for 3M:

Pursue choices on the screen until you locate the Financial Section. You will probably go down some “false paths” to get to this information, but you can get there. This experience is all part of learning to use the Internet. Trace the changes that have occurred in the stockholders’ equity section for the most recent two years. Identify the causes of the changes. Check out the notes to the financial statements for further information. Write a memo to your instructor summarizing your findings.

• [1] Stockholders might agree to rescind (cancel) a dividend already declared if the company is in difficult financial circumstances and needs to retain cash to pay bills or acquire assets to continue operations.
• [2] If a corporation reduces the par value of its stock without issuing more shares, say, from $ 100 to $ 60 per share, then $ 40 per share must be removed from the appropriate capital stock account and credited to Paid-In Capital Recapitalization. Further discussion of this process, called recapitalization, is beyond the scope of this text.
• [3] Another acceptable method of accounting for treasury stock transactions is the par value method. We leave further discussion of the par value method to intermediate accounting texts.
• [4] The method illustrated here is called the memo method. Other acceptable methods of accounting for donated stock are the cost method and par value method. Intermediate accounting texts discuss these latter two methods.
• [5] FASB, Statement of Financial Accounting Standards No. 96 , “Accounting for Income Taxes” (Stamford. Conn., 1987). Copyright © by the Financial Accounting Standards Board, High Ridge Park, Stamford, Connecticut 06905, U.S.A.