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A. Prove that the cyclic group of order 3 is a group by doing the following:
1. State each step of your proof.
2. Provide written justification for each step of your proof.

Prove that the cyclic group of order 3 is isomorphic to Z3 under addition by doing the following:
1. State each step of your proof.
2. Provide written justification for each step of your proof.

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1. A class of 26 music students includes 12 who play piano, 15 who play guitar, and 4 who play both piano and guitar. How many students in the class play neither piano nor guitar?
2. Write the resulting set using the listing method:
a. {3, 21, 6, 12} { – 3, – 21, – 6, – 12}
b.
{4, 6, 8, 11} { – 4, – 6, 8, – 11}
3. Maximize objective profit function (use following grid if desired) subject to:

By inspection, the corner points of the feasible region are (0, 0), (0, 4), (7, 0) and (4, 3).

Evaluating the profit at each corner point:

P(0, 0) = 2(0) + 3(0) = 0
P(0, 4) = 2(0) + 3(4) = 12
P(7, 0) = 2(7) + 3(0) = 14
P(4, 3) = 2(4) + 3(3) = 17

4. A city council voted to conduct a study on inner-city community problems using sociologists and research assistants from UMUC. Allocation of time and costs per week are given in the following table:

Labor hours – Sociologist Labor hours – research assistant MINIMUM labor hours needed per week
Fieldwork 10 30 180
Research center 20 10 160
Costs per week $500 $300

a. How many sociologists and how many research assistants should be hired to MINIMIZE the cost and meet the weekly labor-hour requirement?
What is the MINIMUM weekly cost?
5. A college offers 2 introductory courses in history, 3 in science, 2 in philosophy, 4 in mathematics, and 3 in English. If a freshman takes one course in each area during her first semester, how many course selections are possible?
6. If , complete the following table:

A  A’ Totals B

40
30
70

B’
40
90
130

Totals
80
120
200
7. A couple is planning to have 4 children. They could be all girls, all boys, or some of each. How many groupings are possible? Solve using the multiplication principle of counting.

Since there are 2 options for each child, the number of groupings (considering the order
as significant) is:
8. Evaluate the expression:

9. Because of declining profits, corporate headquarters at Belchfire Motor Industries has decided to keep only 5 of its 8 existing auto assembly plants open after summer 2015. How many groupings of the five plants to remain open are possible? (Hint: Does order matter?)

10. Apocalyptic Biomedical Company must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief marketing officer. There are 13 qualified candidates. How many different ways can the 4 officers be appointed? (Hint: Does order matter?)

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1. (TCO 8) It is the end of the accounting period, and your boss asks you to help determine the inventory balance to place in the company’s balance sheet. Explain which physical quantities of inventory you will include, and which you will exclude.

2. (TCO 8) Fulbright Corp. uses the periodic inventory system. During its first year of operation, Fulbright made the following purchases (listed in chronological order of acquisition):

• 40 units at $100
• 70 units at $80
• 170 units at $60

Sales for the year totaled 270 units, leaving 10 units on hand at the end of the year. What is the ending inventory using the average cost method (rounded)?

3. (TCO 4) You are reviewing the December 31, 2012 financial statements of Ellie’s Antiques that is considering an initial public offering of its shares. The following items come to your attention:

a. Included in long-term investments are 10-year U.S. Treasury bonds that mature March 31, 2013. The bonds were purchased November 20, 2012.
b. The property, plant, and equipment account is stated at cost, except that it includes a parcel of land purchased for investment purposes at a cost of $40,000. Because of rising land prices, the value of the land has been written up to $60,000. The company has an independent appraisal that attests to this amount.
c. The accounts receivable account includes $20,000 due in 3 years from officers and employees and a 2-year, 8% note for $25,000 due from a customer. The loan enabled the customer to buy equipment needed to process materials purchased from Ellie’s Antiques.

Please discuss how the above items should be classified and accounted for.

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Question 1 of 20
A firm’s earnings per share increased from $10 to $12, dividends increased from $4.00 to $4.80, and the share price increased from $80 to $90. Given this information, it follows that ________.
A. the stock experienced a drop in the P/E ratio
B. the firm had a decrease in dividend payout ratio
C. the firm increased the number of shares outstanding
D. the required rate of return decreased
E. none of the above
Question 2 of 20
Old Style Corporation produces goods that are very mature in their product life cycles. Old Style Corporation is expected to have per share FCFE in year 1 of $1.00, per share FCFE of $0.90 in year 2, and per share FCFE of $0.85 in year 3. After year 3, per share FCFE is expected to decline at a rate of 2% per year. An appropriate required rate of return for the stock is 8%. The stock should be worth ______.
A. $127.63
B. $10.57
C. $20.00
D. $22.22
E. $8.98
Question 3 of 20
Each of two stocks, C and D, are expected to pay a dividend of $3 in the upcoming year. The expected growth rate of dividends is 9% for both stocks. You require a rate of return of 10% on stock C and a return of 13% on stock D. The intrinsic value of stock C _____.
A. will be greater than the intrinsic value of stock D
B. will be the same as the intrinsic value of stock D
C. will be less than the intrinsic value of stock D
D. cannot be calculated without knowing the market rate of return
E. none of the above is true.
Question 4 of 20
The most appropriate discount rate to use when applying a FCFF valuation model is the ___________.
A. required rate of return on equity
B. WACC
C. risk-free rate
D. A or C depending on the debt level of the firm
E. none of the above
Question 5 of 20
The most appropriate discount rate to use when applying a FCFE valuation model is the ___________.
A. required rate of return on equity
B. WACC
C. risk-free rate
D. A or C depending on the debt level of the firm
E. none of the above
Question 6 of 20
Consider the free cash flow approach to stock valuation. Utica Manufacturing Company is expected to have before-tax cash flow from operations of $500,000 in the coming year. The firm’s corporate tax rate is 30%. It is expected that $200,000 of operating cash flow will be invested in new fixed assets. Depreciation for the year will be $100,000. After the coming year, cash flows are expected to grow at 6% per year. The appropriate market capitalization rate for unleveraged cash flow is 15% per year. The firm has no outstanding debt. The total value of the equity of Utica Manufacturing Company should be
A. $1,000,000
B. $2,000,000
C. $3,000,000
D. $4,000,000
E. none of the above
Question 7 of 20
Mature Products Corporation produces goods that are very mature in their product life cycles. Mature Products Corporation is expected to pay a dividend in year 1 of $2.00, a dividend of $1.50 in year 2, and a dividend of $1.00 in year 3. After year 3, dividends are expected to decline at a rate of 1% per year. An appropriate required rate of return for the stock is 10%. The stock should be worth ______.
A. $9.00
B. $10.57
C. $20.00
D. $22.22
E. none of the above
Question 8 of 20
Old Quartz Gold Mining Company is expected to pay a dividend of $8 in the coming year. Dividends are expected to decline at the rate of 2% per year. The risk-free rate of return is 6% and the expected return on the market portfolio is 14%. The stock of Old Quartz Gold Mining Company has a beta of -0.25. The intrinsic value of the stock is ______.

A. $80.00
B. $133.33
C. $200.00
D. $400.00
E. none of the above
Question 9 of 20
Paper Express Company has a balance sheet which lists $85 million in assets, $40 million in liabilities and $45 million in common shareholders’ equity. It has 1,400,000 common shares outstanding. The replacement cost of the assets is $115 million. The market share price is $90.
What is Paper Express’s book value per share?
A. $1.68
B. $2.60
C. $32.14
D. $60.71
E. none of the above
Question 10 of 20
Assume that Bolton Company will pay a $2.00 dividend per share next year, an increase from the current dividend of $1.50 per share that was just paid. After that, the dividend is expected to increase at a constant rate of 5%. If you require a 12% return on the stock, the value of the stock is ________.
A. $28.57
B. $28.79
C. $30.00
D. $31.78
E. none of the above
Question 11 of 20
Return on total assets is the product of _______.
A. interest rates and pre-tax profits
B. the debt-equity ratio and P/E ratio
C. the after-tax profit margin and the asset turnover ratio
D. sales and fixed assets
E. none of the above
Question 12 of 20
A firm has a lower asset turnover ratio than the industry average, which implies The financial statements of Snapit Company are given below.
A. the firm has a lower P/E ratio than other firms in the industry.
B. the firm is less likely to avoid insolvency in the short run than other firms in the industry.
C. the firm is less profitable than other firms in the industry.
D. the firm is utilizing assets less efficiently than other firms in the industry.
E. the firm has lower spending on new fixed assets than other firms in the industry.
Question 13 of 20
The financial statements of the Snapit Company are given below
Snapit Company
Income Statement (2009)
Sales $4,000,000
Cost of Goods Sold 3,040,000
Gross Profit 960,000
Selling and Admin expenses 430,000
Operating Profit 530,000
Interest expense 160,000
Income before tax 370,000
Tax expense 148,000
Net Income $222,000
Balance Sheet
2009 2008
Cash $60,000 $50,000
Accounts Receivable 550,000 500,000
Inventory 690,000 620,000
Total Current Assets 1,300,000 1,170,000
Fixed Assets 1,300,000 1,230,000
Total Assets 2,600,000 2,400,000
Accounts Payable 270,000 250,000
Bank Loan 580,000 500,000
Total current liabilities 850,000 750,000
Bonds Payable 900,000 1,000,000
Total Liabilities 1,750,000 1,750,000
Common stock (25,000 shares) 250,000 250,000
Retained Earnings 600,000 400,000
Total Liabilities and Equity $2,600,000 $2,400,000
Note: Common shares are trading at $100 each
Refer to the financial statements of Snapit Company. The firm’s times interest earned ratio for 2009 is __________.
A. 2.26
B. 3.16
C. 3.84
D. 3.31
E. none of the above
Question 14 of 20
Which of the following are issues when dealing with the financial statements of international firms? I) Many countries allow firms to set aside larger contingency reserves than the amounts allowed for U.S. firms. II) Many firms outside the U.S. use accelerated depreciation methods for reporting purposes, whereas most U.S. firms use straight-line depreciation for reporting purposes. III) Intangibles such as goodwill may be amortized over different periods or may be expensed rather than capitalized. IV) There is no way to reconcile the financial statements of non-U. S. firms to GAAP. The financial statements of Black Barn Company are given below
A. I and II
B. II and IV
C. I, II, and III
D. I, III, and IV
E. I, II, III, and IV
Question 15 of 20
The financial statements of the Black Barn Company are given below
Black Barn Company
Income Statement (2009)
Sales $8,000,000
Cost of Goods Sold 5,260,000
Gross Profit 2,740,000
Selling and Admin expenses 1,500,000
Operating Profit 1,240,000
Interest expense 140,000
Income before tax 1,100,000
Tax expense 440,000
Net Income $660,000
Balance Sheet
2009 2008
Cash $200,000 $50,000
Accounts Receivable 1,200,000 950,000
Inventory 1,840,000 1,500,000
Total Current Assets 3,240,000 2,500,000
Fixed Assets 3,200,000 3,000,000
Total Assets $6,440,000 $5,500,000
Accounts Payable 800,000 720,000
Bank Loan 600,000 100,000
Total current liabilities 1,400,000 820,000
Bonds Payable 900,000 1,000,000
Total Liabilities 2,300,000 1,820,000
Common stock (130,000 shares) 300,000 300,000
Retained Earnings 3,840,000 3,380,000
Total Liabilities and Equity $6,440,000 $5,500,000
Note: Common shares are trading at $40 each
Refer to the financial statements of Black Barn Company. The firm’s times interest earned ratio for 2009 is _____.
A. 8.86
B. 7.17
C. 9.66
D. 6.86
E. none of the above
Question 16 of 20
Fundamental analysis uses __________.
A. earnings and dividends prospects
B. relative strength
C. price momentum
D. A and B
E. A and C
Question 17 of 20
One problem with comparing financial ratios prepared by different reporting agencies is
A. some agencies receive financial information later than others.
B. agencies vary in their policies as to what is included in specific calculations.
C. some agencies are careless in their reporting.
D. some firms are more conservative in their accounting practices.
E. none of the above.
Question 18 of 20
Common size financial statements make it easier to compare firms ____________.
A. of different sizes
B. in different industries
C. with different degree of leverage
D. that use different inventory valuation methods (FIFO vs. LIFO)
E. none of the above
Question 19 of 20
A firm’s current ratio is above the industry average; however, the firm’s quick ratio is below the industry average. These ratios suggest that the firm _________.
A. has relatively more total current assets and even more inventory than other firms in the industry
B. is very efficient at managing inventories
C. has liquidity that is superior to the average firm in the industry
D. is near technical insolvency
E. none of the above
Question 20 of 20
The financial statements of the Black Barn Company are given below
Black Barn Company
Income Statement (2009)
Sales $8,000,000
Cost of Goods Sold 5,260,000
Gross Profit 2,740,000
Selling and Admin expenses 1,500,000
Operating Profit 1,240,000
Interest expense 140,000
Income before tax 1,100,000
Tax expense 440,000
Net Income $660,000
Balance Sheet
2009 2008
Cash $200,000 $50,000
Accounts Receivable 1,200,000 950,000
Inventory 1,840,000 1,500,000
Total Current Assets 3,240,000 2,500,000
Fixed Assets 3,200,000 3,000,000
Total Assets $6,440,000 $5,500,000
Accounts Payable 800,000 720,000
Bank Loan 600,000 100,000
Total current liabilities 1,400,000 820,000
Bonds Payable 900,000 1,000,000
Total Liabilities 2,300,000 1,820,000
Common stock (130,000 shares) 300,000 300,000
Retained Earnings 3,840,000 3,380,000
Total Liabilities and Equity $6,440,000 $5,500,000
Note: Common shares are trading at $40 each
Refer to the financial statements of Black Barn Company. The firm’s asset turnover ratio for 2009 is _____.
A. 1.79
B. 1.63
C. 1.34
D. 2.58
E. none of the above