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COURSE REVIEW HOMEWORK

( MULTIPLE CHOICE. Choose the one alternative that best answers the question. )

1. Which of the following appears to be the most appropriate goal for corporate management?

A) Maximizing the company's market share.

B) Minimizing the company's liabilities.

C) Maximizing the current profits of the company.

D) Maximizing market value of the company's shares.

2. Corporate managers are expected to make corporate decisions that are in the best interest of:

A) top corporate management.

B) the corporation's board of directors.

C) the corporation's shareholders.

D) all corporate employees.

3. Which one of the following can best be characterized as an agency problem?

A) Having a higher than industry average rate of defects on the firm's products.

B) Differing opinions among directors as to the merits of paying a higher dividend.

C) Management dispute over which accounting firm to use.

D) Differing incentives between managers and owners.

4. A primary market would be utilized when:

A) shares of common stock are exchanged.

B) a commission must be paid on the transaction.

C) securities are initially issued.

D) investors buy or sell existing securities.

5. The primary distinction between securities sold in the primary and secondary markets is:

A) the riskiness of the securities.

B) whether the securities are new or already exist.

C) the price of the securities.

D) the profitability of the issuing corporation.

6. Assume the total expense for your current year in college equals $20,000. How much would your parents have needed to invest 21 years ago in an account paying 8% compounded annually to cover this amount?

A) $1,728.08

B) $2,952.46

C) $3,973.12

D) $1,600.00

7. Approximately how much must you have saved by retirement if you want to withdraw $100,000 for 25 years if your account earns 9% annually and the first withdrawal occurs one year after retiring?

A) $982,258

B) $887,320

C) $1,128,433

D) $925,667

8. You just won the lottery. You will receive $50,000 per year for 10 years with the first payment being made 5 years from today. If the discount rate is 7%, what is the present value of your winnings?

A) $277,152.33

B) $310,547.48

C) $250,385.83

D) $291,662.95

9. A struggling college student only has $5,000 in her bank account. What interest rate must she earn on her account if she wants to accumulate $1 million in 35 years by adding $10,000 annually?

A) 5.34%

B) 7.85%

C) 9.67%

D) 6.42%

10. Cleveland signed a contract that will provide four annual cash inflows of $41,000, $11,000, $35,000, and $56,000 respectively with the first payment of $41,000 occurring three years from today. What is the contract worth today at a discount rate of 6%?

A) $106,559

B) $108,769

C) $199,999

D) $112,555

11. You want your 10-year-old child to have a million dollars in the future. Today you deposit $25,000 in an account that earns 8.5%. The money will be distributed to your child when the total reaches $1 million. How old will your child be when the money is distributed?

A) 59

B) 55

C) 45

D) 61

12. You just bought a new car. You paid $5,000 down at time zero. You will then make payments of $500 per month for the next 48 months. At the end of 48 months you will make a balloon payment of

$10,000. Based on this payment schedule and an interest rate of 6%, what is the value (present value) of your car today?

A) $51,338.12

B) $37,987.54

C) $34,161.14

D) $29,481.27

13. The present value of an ordinary annuity is $1600 when valued at 10%. How much would the value change if this was an annuity due?

A) $1,440

B) $178

C) $82

D) $160

14. Using a discount rate of 8%, how much more is a perpetuity of $800 worth than a 30-year annuity of the same amount?

A) $994

B) $876

C) $723

D) $919

15. What is the expected real rate of interest for an account that offers a 12% nominal rate of return when the rate of inflation is 6% annually?

A) 5.00%

B) 9.46%

C) 6.00%

D) 5.66%

16. If the effective annual rate of interest is known to be 16.08% on a debt that has quarterly payments, what is the annual percentage rate?

A) 15.19%

B) 16.02%

C) 14.50%

D) 12.02%

17. What is the effective annual interest rate on a 9% APR automobile loan that has monthly payments? A) 9.00%

B) 8.65%

C) 9.38%

D) 9.81%

18. The coupon rate of a bond equals:

A) the annual interest divided by the current market price.

B) its yield to maturity.

C) the yield to maturity when the bond sells at a discount.

D) a defined percentage of its face value.

19. When an investor purchases a $1,000 par value bond that was quoted at 97.162, the investor:

A) receives $971.62 upon the maturity date of the bond.

B) pays 97.162% of face value for the bond.

C) pays $10,971.62 for a $10,000 face value bond.

D) receives 97.162% of the stated coupon payments.

20. Assume a bond is currently selling at par value. What will happen in the future if the yield on the bond is lower than the coupon rate?

A) The coupon rate of the bond will increase.

B) The coupon payments will be adjusted to the new discount rate.

C) The par value of the bond will decrease.

D) The price of the bond will increase.

21. How much should you pay for a $1,000 bond with a 10% coupon, annual payments, and 5 years to maturity if the interest rate is 12%?

A) $927.90

B) $981.40

C) $1,000.00

D) $1,075.82

22. A bond has a coupon rate of 8%, pays interest annually, sells for $962, and matures in 3 years. What is its yield to maturity?

A) 9.52%

B) 4.78%

C) 12.17%

D) 5.48%

23. What is the coupon rate for an annual coupon bond with 3 years to maturity, a price of $1,026, and a yield to maturity of 7.5%?

A) 9.25%

B) 6.67%

C) 8.50%

D) 7.42%

24. When a fixed-rate bond has its rating upgraded from B to A, then:

A) the bond's current yield increases.

B) the bond's price increases.

C) the bond's face value decreases.

D) the bond's coupon rate increases.

25. If a project's expected rate of return exceeds its opportunity cost of capital, one would expect:

A) the NPV to be zero.

B) the project to have a positive NPV.

C) the profitability index to be negative.

D) the opportunity cost of capital to be too low.

26. What is the NPV of a project that costs $100,000 and returns $50,000 annually for 3 years if the opportunity cost of capital is 14%?

A) $33,749

B) $14,473

C) $13,398

D) $16,082

27. The ratio of net present value to initial investment is known as the:

A) net present value.

B) profitability index.

C) internal rate of return.

D) payback period.

28. What is the profitability index for a project costing $40,000 and returning $15,000 annually for 4 years at an opportunity cost of capital of 12%?

A) 0.861

B) 0.500

C) 0.139

D) 0.320

29. A polisher costs $10,000 and will cost $20,000 a year to operate and maintain. If the discount rate is 10% and the polisher will last for 5 years, what is the equivalent annual cost?

A) $17,163

B) $22,638

C) $19,411

D) $22,188

30. What is the equivalent annual cost for a project that requires a $40,000 investment at time zero, and a

$10,000 annual expense during each of the next 4 years, if the opportunity cost of capital is 12%? A) $21,356

B) $25,237

C) $23,169

D) $20,000

31. When is it appropriate to include sunk costs in the evaluation of a project?

A) If they are considered to be overhead costs.

B) If they improve the project's NPV.

C) Whenever they are relatively large.

D) Never.

32. Investments in working capital:

A) do not matter because the cash is generally recovered when the project ends.

B) reduce project NPV.

C) increase NPV because they make the project more valuable.

D) are simply accounting entries and do not affect NPV.

33. What is the net effect on a firm's cash flow of a $100,000 increase in accounts receivable, $250,000 increase in inventory and $75,000 increase in accounts payable?

A) -$275,000

B) -$425,000

C) -$225,000

D) $75,000

34. In what manner does depreciation expense affect investment projects?

A) It reduces taxes by the amount of the depreciation expense.

B) It reduces taxable income by the amount of the depreciation expense.

C) It reduces cash flows by the amount of the depreciation expense.

D) It increases cash flows by the amount of the depreciation expense.

35. Cookie Castle [CKC] issued $1,000,000 of debt with a cost of debt of 8%. If CKC has a 25% tax rate and intends to maintain the debt continuously, what is the present value of the perpetual debt tax shield? A) $250,000

B) $170,000

C) $320,000

D) $20,000

36. When a depreciable asset is ultimately sold, the after-tax cash flow from the sale is:

A) not used in capital budgeting.

B) reduced by the book value of the asset.

C) the total sales price minus tax.

D) the same as the after-tax accounting amount.

37. Seven years ago, you purchased a new packaging machine for $90,000 and depreciated it straight-line over a 10-year life. Today, you sold the machine for $35,000. If your tax rate is 25%, what is the after- tax cash flow from the sale of the machine?

A) $33,000

B) $26,250

C) $24,819

D) $8,000

38. What is the annual depreciation tax shield for a $100,000 annual depreciation expense if the tax rate is 21%?

A) $79,000

B) $15,500

C) $21,000

D) $25,000

39. A firm invests $10 million in a new stamping machine. It depreciates the machine straight-line over 5 years. The tax rate is 21% and the discount rate is 8%. What is the PV of the depreciation tax shield? A) $3,000,000

B) $634,978

C) $2,579,497

D) $1,676,938

40. What is the NPV of an 8-year project that costs $200,000, has annual revenues of $75,000 and cash expenses of $25,000? Assume the investment is depreciated straight-line over 8 years, the corporate tax rate is 21%, and the discount rate is 13%.

A) $13,411

B) $14,182

C) $15,560

D) $14,745

41. Suppose marginal tax rates are 18% for income below $50,000, 22% from $50,000 to $60,000, and 25% for income above $60,000. What is the average tax rate for an individual that earned $72,000? A) 19.72%

B) 21.67%

C) 20.28%

D) 18.76%

42. A stock's beta measures the:

A) sensitivity of the stock's returns to those of the market portfolio.

B) market risk premium on the stock.

C) difference between the return on the stock and the return on the market portfolio.

D) average return on the stock.

43. When using CAPM to find required rates of return, why is diversifiable risk ignored?

A) Only systematic risk is rewarded.

B) There is no method for quantifying diversifiable risk.

C) Beta includes a component to compensate for diversifiable risk.

D) Diversifiable risk is compensated by the market risk premium.

44. The 4-week T Bill rate is 2% and the market risk premium is 8%. If you have a portfolio consisting of 50% of the risk-free asset and 50% in the market, what is the expected return on your portfolio?

A) 2%

B) 4%

C) 5%

D) 6%

45. What is the beta of a 3-stock portfolio consisting of $10,000 of Stock A with a beta of 0.90, $8,000 of Stock B with a beta of 1.05, and $2,000 of Stock C with a beta of 1.70?

A) 1.00

B) 1.04

C) 1.17

D) 1.22

46. A project has a beta of 1.24, the risk-free rate is 3.8%, and the market rate of return is 9.2%. What is the project's expected rate of return?

A) 11.41%

B) 15.21%

C) 10.50%

D) 14.61%

47. The project cost of capital is:

A) not necessarily related to the company cost of capital.

B) greater than the company cost of capital because the project has specific risk.

C) less than the company cost of capital.

D) equal to the company cost of capital.

48. TJ Maxx (beta 0.67) is evaluating a project in the airline industry (beta 1.70). If the risk-free rate is 1.9% and the market risk premium is 11%, what is the required rate of return on this project?

A) 20.60%

B) 17.37%

C) 9.27%

D) 8.00%

49. A company's nominal pre-tax cost of debt is represented by the:

A) yield to maturity on outstanding bonds.

B) coupon rate of current bonds.

C) return calculated by CAPM.

D) company's beta.

50. A firm has 12,500 shares of stock outstanding that sell for $42 each. The book value of equity is

$400,000. The firm has also issued $250,000 face value of debt that is currently quoted at 101.2. What value should be used as the weight of equity when computing WACC?

A) 72.09%

B) 61.54%

C) 67.48%

D) 69.74%

51. If a firm with no current liabilities has a long-term debt to equity ratio of 1, then:

A) The firm has a total debt ratio of 0.5.

B) The firm has more equity than debt.

C) The firm has no diversifiable risk.

D) The firm has a high cost of equity.

52. Debt provides a tax shield for the company because:

A) the amount of debt reduces taxable income.

B) the amount of interest reduces the total taxes payable.

C) the amount of interest reduces taxable income.

D) the amount of debt reduces the total taxes payable.

53. Dell Technologies [DELL] has 700 million shares of common stock outstanding which currently sell at

$55 per share. It also has $10 billion in book value debt currently quoted at 101. What value should be used as the weight on debt when computing DELL's WACC?

A) 79.22%

B) 19.41%

C) 28.63%

D) 20.78%

54. Wayfair [W] has 90 million shares of common stock outstanding which currently sell at $86 per share. W has a beta of 1.85. If the risk-free rate is 1.8% and the expected return on the market is 12.2%, what is W's cost of equity?

A) 21.04%

B) 24.37%

C) 22.57%

D) 25.90%

55. Dick's Sporting Goods [DKS] has 110 million shares of common stock outstanding which currently sell at $39 per share. DKS also has 1.3 million outstanding bonds that mature in 14 years. The bonds have a face value of $1,000, pay an annual coupon of 9% and currently sell at 110. DKS has a beta of 0.59 and a tax rate of 21%. If the risk-free rate is 1.85% and the market risk premium is 12%, what is DKS's WACC?

A) 8.24%

B) 7.05%

C) 5.71%

D) 6.98%

Answer Key

1. D

2. C

3. D

4. C

5. B

6. C

7. A

8. C

9. A

10. B

11. B

12. C

13. D

14. A

15. D

16. A

17. C

18. D

19. B

20. D

21. A

22. A

23. C

24. B

25. B

26. D

27. B

28. C

29. B

30. C

31. D

32. B

33. A

34. B

35. A

36. C

37. A

38. C

39. D

40. D

41. A

42. A

43. A

44. D

45. B

46. C

47. A

48. A

49. A

50. C

51. A

52. C

53. D

54. A

55. A

COURSE REVIEW HOMEWORK SOLUTIONS

Question 06

	N I/Y PV PMT FV
INPUTS	21	8		0	20,000
CPT			−𝟑𝟑, 𝟗𝟗𝟗𝟗𝟑𝟑. 𝟏𝟏𝟏𝟏

Question 07

	N I/Y PV PMT FV
INPUTS	25	9		100,000	0
CPT			−𝟗𝟗𝟗𝟗𝟏𝟏, 𝟏𝟏𝟐𝟐𝟗𝟗

Question 08

0	0	50,000		7	250,385.83
	5	10

Question 09

	N I/Y PV PMT FV
INPUTS	35		−5,000	−10,000	1,000,000
CPT		5.34

Question 10

0	0	41,000	11,000	35,000	56,000	6	108,769
	2	1	1	1	1
Tip: To push inflow 1 out to year 3, enter 2 cash flows of zero amount in C01

Question 11

	N I/Y PV PMT FV
INPUTS		8.5	−25,000	0	1,000,000
CPT	45.22
Add N to the age of the child today. 45.22 + 10 = 𝟐𝟐𝟐𝟐. 𝟏𝟏𝟏𝟏

Question 12

−$5,000	−$500	−$10,500		6 ÷ 12 = 0.5	−𝟑𝟑𝟑𝟑, 𝟏𝟏𝟏𝟏𝟏𝟏. 𝟏𝟏𝟑𝟑
	47	1
Note: This is a simple PV question when using the CF worksheet. You could also calculate each payment separately using TVM and then sum their PV’s.

( 𝑃𝑃 𝑃𝑃 𝐴𝐴𝐴 𝐴 = 𝑃𝑃 𝐴 𝐴 ( 1 + 𝑟 𝑟 ) = $1 , 600 ( 1 . 10 ) = $1 , 760 $1,760 − $1,600 = $ 𝟏𝟏𝟏𝟏𝟏𝟏 A shortcut to find the difference is to multiply 𝑃𝑃𝑃𝑃 𝐴𝐴 × 𝑟𝑟 = $1,600 × 0.10 = $160 )Question 13

Question 14

𝑃𝑃𝑃𝑃𝑃𝑃 $800 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 = 𝑟𝑟 = 0.08 = $10,000
	N I/Y PV PMT FV
INPUTS	30	8		800	0
CPT			−9,006.23
Difference: $10,000 − 9,006.23 = 𝟗𝟗𝟗𝟗𝟑𝟑. 𝟗𝟗𝟗𝟗

( 1.06 1.12 − 1 = − 1 = 0.0566 = 𝟐𝟐 . 𝟏𝟏𝟏𝟏 % 1 + 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑟𝑟𝑟𝑟 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 1 + 𝑛 𝑛 𝑛𝑛 𝑖𝑖 𝑟𝑟𝑟𝑟𝑟 𝑟 𝑛 𝑛 𝑛𝑛𝑛 𝑛 𝑟𝑟𝑟 𝑟 𝑟𝑟 𝑟𝑟 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 = )Question 15

Question 16

𝐸𝐸𝐸𝐸𝐸𝐸 = 16.08 𝑛𝑛 = 4 𝐸𝐸𝑃𝑃𝐸𝐸 = 𝟏𝟏𝟐𝟐. 𝟏𝟏𝟗𝟗 Use “ICONV” function:
	16.08			4				15.19

Question 17

𝐸𝐸𝑃𝑃𝐸𝐸 = 9 𝑛𝑛 = 12 𝐸𝐸𝐸𝐸𝐸𝐸 = 𝟗𝟗. 𝟑𝟑𝟗𝟗 Use “ICONV” function:
	9			12				9.38

Question 21

	N I/Y PV PMT FV
INPUTS	5	12		100	1,000
CPT			−𝟗𝟗𝟏𝟏𝟗𝟗. 𝟗𝟗𝟏𝟏
You need to find the coupon payment PMT: 𝑃𝑃𝑃𝑃𝑃𝑃 = 𝑖𝑖𝑟𝑟𝑓𝑓𝑟𝑟 𝑣𝑣𝑟𝑟𝑟𝑟𝑣𝑣𝑟𝑟 × 𝑓𝑓𝑛𝑛𝑣𝑣𝑐𝑐𝑛𝑛𝑛𝑛 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 = $1,000 × 0.10 = $100

Question 22

	N I/Y PV PMT FV
INPUTS	3		−962	80	1,000
CPT		𝟗𝟗. 𝟐𝟐𝟏𝟏
Unless specifically told otherwise, assume the face value of a bond is $1,000. To find coupon payment (𝑖𝑖𝑟𝑟𝑓𝑓𝑟𝑟 𝑣𝑣𝑟𝑟𝑟𝑟𝑣𝑣𝑟𝑟 × 𝑓𝑓𝑛𝑛𝑣𝑣𝑐𝑐𝑛𝑛𝑛𝑛 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟)

Question 23

	N I/Y PV PMT FV
INPUTS	3	7.5	−1,026		1,000
CPT				85
Unless specifically told otherwise, assume the face value of a bond is $1,000. Solve for PMT then divide it by the face value: 𝑓𝑓𝑛𝑛𝑣𝑣𝑐𝑐𝑛𝑛𝑛𝑛 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 = 85 ÷ 1,000 = 0.10 = 𝟗𝟗. 𝟐𝟐%

Question 26

−100,000	50,000	3	14	16,082

Question 28

−40,000	15,000	4	12	5,560.24
𝑃𝑃𝑃𝑃 = 5,560.24 ÷ 40,000 = 𝟏𝟏. 𝟏𝟏𝟑𝟑𝟗𝟗

Question 29

−10,000	−20,000	5	10	−85,815.74
Find NPV of costs, then use TVM Worksheet to find the equivalent annual annuity.
	N I/Y PV PMT FV
INPUTS	5	10	−85,815.74		0
CPT				𝟏𝟏𝟏𝟏, 𝟏𝟏𝟑𝟑𝟗𝟗

Question 30

−40,000	−10,000	4	12	−70,373.49
Find NPV of costs, then use TVM Worksheet to find the equivalent annual annuity.
	N I/Y PV PMT FV
INPUTS	4	12	−70,373.49		0
CPT				𝟏𝟏𝟑𝟑, 𝟏𝟏𝟏𝟏𝟗𝟗. 𝟑𝟑𝟗𝟗

( Investments in WC decrease cash flows, while reductions in WC increase cash flows. WC Reductions include current liabilities, e.g., Accounts Payable WC Investments include current assets, e.g., Accounts Receivable, Inventory 𝐶 𝐶 𝐶𝐶 = 𝑊𝑊𝐶𝐶 𝐸𝐸 𝑟 𝑟 𝑅 𝑅 𝑣𝑣 𝑓𝑓𝑟 𝑟 𝑛 𝑛 𝑛 𝑛 𝑛𝑛 𝑅𝑅 – 𝑊𝑊𝐶𝐶 𝑃 𝑃 𝑛𝑛 𝑣𝑣𝑟𝑟𝑅 𝑅 𝑛 𝑛 𝑟𝑟𝑛 𝑛 𝑟𝑟 𝑅𝑅 𝐶𝐶𝐶𝐶 = $75,000 − $100,000 − $250,000 = − $ 𝟏𝟏𝟗𝟗𝟐𝟐 , 𝟏𝟏𝟏𝟏𝟏𝟏 )Question 33

( PV of Perpetual Debt Tax Shield = 𝑅𝑅𝑟𝑟𝑑𝑑𝑟𝑟 × 𝑟𝑟𝑟𝑟𝑡𝑡 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 = $1,000,000 × 0.25 = $ 𝟏𝟏𝟐𝟐𝟏𝟏 , 𝟏𝟏𝟏𝟏𝟏𝟏 )Question 35

( A ft e r – t a x c a sh f l o w = 𝑅𝑅𝑟𝑟 𝑟 𝑟 𝑟 𝑟 𝑛𝑛𝑛 𝑛 𝑠𝑠 𝑐 𝑐 𝑟𝑟𝑛 𝑛 𝑓 𝑓 𝑟𝑟 − ( 𝑠𝑠 𝑟 𝑟 𝑛𝑛𝑛 𝑛 𝑛𝑛𝑛 𝑛 𝑅 𝑅 𝑟𝑟𝑟𝑟𝑟 𝑟 × 𝑟𝑟 𝑟 𝑟 𝑡𝑡 𝑟𝑟𝑟 𝑟 𝑟𝑟 𝑟 𝑟 ) 𝑅 𝑅 𝑟 𝑟 𝑐 𝑐 𝑟 𝑟 𝑟 𝑟 𝑓 𝑓 𝑛 𝑛 𝑟𝑟𝑟 𝑟 𝑛 𝑛 𝑛𝑛𝑛 𝑛 = $90 , 000 ÷ 10 = $9 , 000 𝑑𝑑 𝑛𝑛𝑛𝑛 𝑏𝑏 𝑣 𝑣 𝑟𝑟𝑟 𝑟 𝑣𝑣 𝑟𝑟 = ( 𝑛𝑛𝑟 𝑟 𝑛 𝑛 𝑠𝑠 𝑛 𝑛 𝑛𝑛 𝑟𝑟𝑟 𝑟 𝑓 𝑓 𝑛 𝑛 𝑅𝑅𝑟 𝑟 − 𝑟𝑟𝑓𝑓 𝑓 𝑓 𝑣𝑣 𝑛𝑛 𝑣𝑣 𝑟𝑟𝑟𝑟𝑟 𝑟 𝑟 𝑟 𝑅𝑅 𝑅 𝑅 𝑟 𝑟 𝑐𝑐𝑟 𝑟 𝑟 𝑟 𝑓 𝑓 𝑛𝑛𝑟 𝑟 𝑟𝑟 𝑛𝑛𝑛𝑛 𝑛 𝑛 ) = $90 , 000 − ( 7 × 9 , 000 ) = $27 , 000 𝑠𝑠 𝑟 𝑟 𝑛𝑛𝑛 𝑛 𝑛𝑛𝑛 𝑛 𝑅𝑅𝑟𝑟 𝑟 𝑟 𝑟𝑟 = ( 𝑅 𝑅 𝑟 𝑟 𝑟𝑟𝑟𝑟𝑛 𝑛 𝑛 𝑛 𝑠𝑠 𝑐𝑐𝑟 𝑟 𝑛𝑛𝑓𝑓 𝑟𝑟 − 𝑑𝑑 𝑛𝑛𝑛𝑛 𝑏𝑏 𝑣 𝑣 𝑟𝑟𝑟𝑟 𝑣 𝑣 𝑟 𝑟 ) = $3 5 , 000 − $27 , 000 = $8 , 000 𝑟𝑟𝑖 𝑖 𝑟𝑟 𝑟 𝑟 𝑟 𝑟 - 𝑟𝑟 𝑟 𝑟 𝑡𝑡 𝑓 𝑓 𝑟𝑟𝑅 𝑅 ℎ 𝑖𝑖 𝑟𝑟𝑛𝑛 𝑓𝑓 = $35 , 000 − ( $ 8 , 000 × 0 . 25 ) = $ 𝟑𝟑𝟑𝟑 , 𝟏𝟏𝟏𝟏𝟏𝟏 )Question 37

( D e p r e c i a tio n T a x S h i e l d = ( 𝑅 𝑅 𝑟 𝑟 𝑐 𝑐 𝑟 𝑟 𝑟 𝑟 𝑓 𝑓 𝑛 𝑛 𝑟𝑟𝑟 𝑟 𝑛 𝑛 𝑛𝑛𝑛 𝑛 × 𝑟𝑟 𝑟 𝑟 𝑡𝑡 𝑟𝑟𝑟 𝑟 𝑟𝑟 𝑟 𝑟 ) = $100 , 000 × 0 . 21 = $ 𝟏𝟏𝟏𝟏 , 𝟏𝟏𝟏𝟏𝟏𝟏 )Question 38

Question 39

Annual Depreciation = (𝑛𝑛𝑛𝑛𝑛𝑛𝑟𝑟𝑛𝑛𝑟𝑟𝑟𝑟 𝑛𝑛𝑛𝑛𝑣𝑣𝑟𝑟𝑅𝑅𝑟𝑟𝑛𝑛𝑟𝑟𝑛𝑛𝑟𝑟 ÷ 𝑦𝑦𝑟𝑟𝑟𝑟𝑟𝑟𝑅𝑅) = $10,000,000 ÷ 5 = $2,000,000 Annual Depreciation Tax Shield = (𝑅𝑅𝑟𝑟𝑐𝑐𝑟𝑟𝑟𝑟𝑓𝑓𝑛𝑛𝑟𝑟𝑟𝑟𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑟𝑟𝑟𝑟𝑡𝑡 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟) = $2,000,000 × 0.21 = $420,000 Then use TVM Worksheet to find PV of Depreciation Tax Shield.
	N I/Y PV PMT FV
INPUTS	5	8		420,000	0
CPT			−𝟏𝟏, 𝟏𝟏𝟗𝟗𝟏𝟏, 𝟗𝟗𝟑𝟑𝟗𝟗

Question 40

Depreciation = (𝑛𝑛𝑛𝑛𝑛𝑛𝑟𝑟𝑛𝑛𝑟𝑟𝑟𝑟 𝑛𝑛𝑛𝑛𝑣𝑣𝑟𝑟𝑅𝑅𝑟𝑟𝑛𝑛𝑟𝑟𝑛𝑛𝑟𝑟 ÷ 𝑦𝑦𝑟𝑟𝑟𝑟𝑟𝑟𝑅𝑅) = $200,000 ÷ 8 = $25,000 Operating CF: Revenue $75,000 Expenses -$25,000 Depreciation -$25,000 Pre-Tax Profit $25,000 Tax @ 21% -$5,250 Net Income $19,750 Add Depreciation $25,000 Operating CF $44,750
−200,000	44,750	8	13	14,745

( Calculating marginal tax rates is a simple weighted average: $50,000 × 0.18 = $9,000 $10,000 × 0.22 = 2,200 (72,000 − 60,000) × 0.25 = 3,000 Average Tax Rate = ( $9,000 + $2,200 + $3,000 ) ÷ $72,000 = 0.1972 = 𝟏𝟏𝟗𝟗 . 𝟗𝟗𝟏𝟏 % )Question 41

( 𝑟𝑟𝑟 𝑟 𝑟𝑟 𝑣𝑣 𝑟 𝑟 𝑛𝑛 𝑛𝑛𝑛 𝑛 𝑟𝑟 ℎ 𝑟𝑟 𝑛 𝑛 𝑟 𝑟 𝑟𝑟𝑏 𝑏 𝑟 𝑟 𝑟𝑟 = ( 𝑛 𝑛 𝑟 𝑟 𝑟𝑟𝑏 𝑏 𝑟 𝑟 𝑟𝑟 𝑟 𝑟 𝑛 𝑛 𝑅 𝑅 𝑏𝑏 𝑐 𝑐 𝑟 𝑟 𝑟 𝑟 𝑛𝑛𝑛 𝑛 𝑣𝑣 𝑛𝑛 + 𝑟 𝑟 𝑛𝑛𝑅𝑅𝑏 𝑏 - 𝑖𝑖 𝑟𝑟𝑟 𝑟 𝑟𝑟 𝑟𝑟𝑟 𝑟 𝑟𝑟 𝑟 𝑟 ) = 8% + 2% = 10% 𝑟𝑟𝑟 𝑟 𝑟𝑟 𝑣𝑣 𝑟 𝑟 𝑛𝑛 𝑛𝑛𝑛 𝑛 𝑟𝑟 ℎ 𝑟𝑟 𝑐 𝑐 𝑛𝑛𝑟 𝑟 𝑟𝑟 𝑖𝑖 𝑛𝑛𝑟𝑟𝑛 𝑛 𝑛𝑛 = ( 0 . 5 × 2% ) + ( 0 . 5 × 10% ) = 𝟏𝟏 % )Question 44

( 𝑃 𝑃 𝑛𝑛𝑟 𝑟 𝑟𝑟 𝑖𝑖 𝑛𝑛𝑟𝑟𝑛 𝑛 𝑛𝑛 𝑃𝑃 𝑟𝑟𝑟𝑟𝑣 𝑣 𝑟𝑟 = $10 , 000 + $8 , 000 + $2 , 000 = $2 0 , 000 𝑊𝑊 𝑟 𝑟 𝑛𝑛𝑠 𝑠 ℎ 𝑟𝑟 𝑛𝑛𝑖 𝑖 𝑆𝑆 𝑟𝑟 𝑛𝑛𝑓𝑓 𝑏𝑏 𝐸𝐸 = $10 , 000 ÷ $2 0 , 000 = 0 . 50 𝑊𝑊 𝑟 𝑟 𝑛𝑛𝑠 𝑠 ℎ 𝑟𝑟 𝑛𝑛𝑖 𝑖 𝑆𝑆 𝑟𝑟 𝑛𝑛𝑓𝑓 𝑏𝑏 𝐵𝐵 = $ 8 , 000 ÷ $2 0 , 000 = 0 . 40 𝑊𝑊 𝑟 𝑟 𝑛𝑛𝑠 𝑠 ℎ 𝑟𝑟 𝑛𝑛𝑖 𝑖 𝑆𝑆 𝑟𝑟 𝑛𝑛𝑓𝑓 𝑏𝑏 𝐶𝐶 = $2 , 000 ÷ $20 , 000 = 0 . 10 𝛽𝛽 𝑃𝑃 = ( 0.50 × 0.90 ) + ( 0.40 × 1.05 ) + ( 0.10 × 1.70 ) = 𝟏𝟏 . 𝟏𝟏𝟑𝟑 )Question 45

( 𝑏𝑏 𝑃𝑃 = 𝑟𝑟 𝑓𝑓 + 𝛽𝛽 𝑃𝑃 � 𝑏𝑏 𝑀𝑀 − 𝑟𝑟 𝑓𝑓 � 𝑏𝑏 𝑃𝑃 = 3.8 + 1.24 ( 9.2 − 3.8 ) = 𝟏𝟏𝟏𝟏 . 𝟐𝟐𝟏𝟏 % )Question 46

( Use the project beta if its risk is different than that of the company. 𝑏𝑏 𝑃𝑃 = 𝑟𝑟 𝑓𝑓 + 𝛽𝛽 𝑃𝑃 ( 𝑃𝑃𝐸𝐸𝑃𝑃 ) 𝑏𝑏 𝑃𝑃 = 1.9 + 1.70 ( 11 ) = 𝟏𝟏𝟏𝟏 . 𝟏𝟏𝟏𝟏 % )Question 48

( 𝑃𝑃 $525 𝑃𝑃𝑃𝑃 𝑃𝑃 𝑓𝑓 𝑃𝑃 = = $778 = 0.6748 = 𝟏𝟏𝟗𝟗 . 𝟑𝟑𝟗𝟗 % 𝑃𝑃𝑃𝑃 𝑃𝑃 = $42 × 12,500 = $525,000 𝑃𝑃𝑃𝑃 𝐴𝐴 = $250,000 × 1.012 = $253,000 𝑃𝑃 = 𝑃𝑃𝑃𝑃 𝑃𝑃 + 𝑃𝑃𝑃𝑃 𝐴𝐴 = $525,000 + $253,000 = $778,000 )Question 50

( 𝑃𝑃 $10,100 𝑃𝑃𝑃𝑃 𝐴𝐴 𝑓𝑓 𝐴𝐴 = = $48,600 = 0.2078 = 𝟏𝟏𝟏𝟏 . 𝟗𝟗𝟗𝟗 % (In Millions) 𝑃𝑃𝑃𝑃 𝑃𝑃 = $55 × 700 = $38,500 𝑃𝑃𝑃𝑃 𝐴𝐴 = $10,000 × 1.01 = $10,100 𝑃𝑃 = 𝑃𝑃𝑃𝑃 𝑃𝑃 + 𝑃𝑃𝑃𝑃 𝐴𝐴 = $38,500 + $10,100 = $48,600 ) Question 53

( 𝑏𝑏 𝑊𝑊 = 𝑟𝑟 𝑓𝑓 + 𝛽𝛽 𝑊𝑊 � 𝑏𝑏 𝑀𝑀 − 𝑟𝑟 𝑓𝑓 � 𝑏𝑏 𝑊𝑊 = 1.8 + 1.85 ( 12.2 − 1.8 ) = 𝟏𝟏𝟏𝟏 . 𝟏𝟏𝟑𝟑 % )Question 54

Question 55

(In Millions) 𝑃𝑃𝑃𝑃𝑃𝑃 = $39 × 110 = $4,290 𝑃𝑃𝑃𝑃𝐴𝐴 = $1100 × 1.3 = $1,430 𝑃𝑃 = 𝑃𝑃𝑃𝑃𝑃𝑃 + 𝑃𝑃𝑃𝑃𝐴𝐴 = $4,290 + $1,430 = $5,720 𝑃𝑃𝑃𝑃𝑃𝑃 $4,290 𝑓𝑓𝑃𝑃 = 𝑃𝑃 = $5,720 = 0.75 = 75% 𝑓𝑓𝐴𝐴 = 1 − 0.75 = 0.25 = 25% 𝑟𝑟𝑃𝑃 = 𝑟𝑟𝑓𝑓 + 𝛽𝛽(𝑃𝑃𝐸𝐸𝑃𝑃) = 1.85 + 0.59(12) = 8.93%
𝑟𝑟𝐴𝐴	N I/Y PV PMT FV
INPUTS	14		-1,100	90	1,000
CPT		7.8
𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶 = (𝑓𝑓𝑃𝑃 × 𝑟𝑟𝑃𝑃 ) + [𝑓𝑓𝐴𝐴 × 𝑟𝑟𝐴𝐴 × (1 − 𝑟𝑟)] 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶 = (0.75 × .0893) + [0.25 × 0.078 × (1 − 0.21)] = 0.0824 = 𝟗𝟗. 𝟏𝟏𝟑𝟑%