Chapter 4 The Value of Common Stocks
Multiple Choice Questions
1. If the Vol. 100s is reported as 10,233 in the Wall Street Journal quotation, then the trading
volume for that day of trading is:
A) 10,233 shares
B) 102,330 shares
C) 1,023,300 shares
D) 10,233,000 shares
Answer: C
Type: Medium
Page: 60
Response: Trading volume = 10,233 * 100 = 1,023,300
2. The dividend yield reported as Yld. % in The Wall Street Journal quotation is calculated as
follows:
A) (dividends / hi)
B) (dividends / lo)
C) (dividends / close)
D) None of the above
Answer: C
Type: Medium
Page: 60
3. The Wall Street Journal quotation for a company has the following values: Div: 2.28, PE: 19,
Close: 75.30. Calculate the dividend pay out ratio for the company.
A) 58%
B) 12%
C) 75%
D) None of the above
Answer: A
Type: Difficult
Page: 60
Response: EPS = (75.30)/19 = 3.9631 dividend payout = 2.28/3.9631 = 0.5753= 58%
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4. If the Wall Street Journal Quotation for a company has the following values close: 26.00; Net
chg: =+1.00; then the closing price for the stock for the previous trading day was?
A) $26
B) $25
C) $27
D) None of the above.
Answer: B
Type: Medium
Page: 60
Response: Previous closing = today's closing net chg. = 26.00-1.00= $25.00
5. The value of a common stock today depends on:
A) Number of shares outstanding and the number of shareholders
B) The Wall Street analysts
C) The expected future dividends and the discount rate
D) Present value of the future earnings per share
Answer: C
Type: Easy
Page: 62
6. Super Computer Company's stock is selling for $100 per share today. It is expected that this
stock will pay a dividend of 5 dollars per share, and then be sold for $120 per share at the end of
one year. Calculate the expected rate of return for the shareholders.
A) 20%
B) 25%
C) 10%
D) 15%
Answer: B
Type: Easy
Page: 62
Response: r = (120+5-100)/100 = 25%
7. PC Company stockholders expect to receive a year-end dividend of $10 per share and then be
sold for $122 dollars per share. If the required rate of return for the stock is 20%, what is the
current value of the stock?
A) $100
B) $122
C) $132
D) $110
Answer: D
Type: Medium
Page: 62
Response: P = (122+10)/1.2 = 110
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8. Macrohard Company expects to pay a dividend of $6 per share at the end of year one, $8 per
share at the end of year two and then be sold for $136 per share. If the required rate on the stock
is 20%, what is the current value of the stock?
A) $100
B) $105
C) $110
D) $120
Answer: B
Type: Medium
Page: 62
Response: P = (6/1.2)+(8+136)/(1.2^2) = 105
9. The constant dividend growth formula P0 = D1/(r-g) assumes:
A) The dividends are growing at a constant rate g forever.
B) r > g
C) g is never negative.
D) Both A and B
Answer: D
Type: Medium
Page: 64
10. Casino Co. is expected to pay a dividend of $6 per share at the end of year one and these
dividends are expected to grow at a constant rate of 8% per year forever. If the required rate of
return on the stock is 20%, what is current value of the stock today?
A) $30
B) $50
C) $100
D) $54
Answer: B
Type: Medium
Page: 64
Response: P = (6/(0.2-0.08) = 50
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11. WorldTour Co. has just now paid a dividend of $6 per share (Do), the dividends are expected to
grow at a constant rate of 5% per year forever. If the required rate of return on the stock is 15%,
what is the current value on stock, after paying the dividend?
A) $63
B) $56
C) $40
D) $48
Answer: A
Type: Medium
Page: 64
Response: P = (6*1.05)/(0.15 0.05) = 63
12. The required rate of return or the market capitalization rate is estimated as follows:
A) Dividend yield + expected rate of growth in dividends
B) Dividend yield - expected rate of growth in dividends
C) Dividend yield / expected rate of growth in dividends
D) (Dividend yield) * (expected rate of growth in dividends)
Answer: A
Type: Difficult
Page: 65
13. Mcom Co. is expected to pay a dividend of $4 per share at the end of year one and the dividends
are expected to grow at a constant rate of 4% forever. If the current price of the stock is $25 per
share calculated the required rate of return or the market capitalization rate for the firms' stock.
A) 4%
B) 16%
C) 20%
D) None of the above.
Answer: C
Type: Medium
Page: 65
Response: r = (4/25) + 0.04 = 20%
14. Dividend growth rate for a stable firm can be estimated as:
A) Plow back rate * the return on equity (ROE)
B) Plow back rate / the return on equity (ROE)
C) Plow back rate +the return on equity (ROE)
D) Plow back rate - the return on equity (ROE)
Answer: A
Type: Difficult
Page: 66
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15. MJ Co. pays out 60% of its earnings as dividends. Its return on equity is 20%. What is the stable
dividend growth rate for the firm?
A) 3%
B) 5%
C) 8%
D) 12%
Answer: C
Type: Difficult
Page: 66
Response: g = (1 - 0.6)*20 = 8%
16. Michigan Motor Company is currently paying a dividend of $1.50 per year. The dividends are
expected to grow at a rate of 20% for the next three years and then a constant rate of 6 %
thereafter. What is the expected dividend per share in year 5?
A) $2.59
B) $2.00
C) $2.91
D) $1.50
Answer: C
Type: Medium
Page: 69
Response: D5 = (1.5) * (1.2^3) * (1.06^2) = 2.91
17. Great Lakes Co. is currently paying a dividend of $2.20 per share. The dividends are expected to
grow at 25% per year for the next four years and then grow 5% per year thereafter. Calculate the
expected dividend in year 6.
A) $5.37
B) $2.95
C) $5.92
D) $8.39
Answer: A
Type: Medium
Page: 69
Response: Div6=2.2 * (1.25^4) * (1.05^2) = 5.92
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18. Y2K Technology Corporation has just paid a dividend of $0.40 per share. The dividends are
expected to grow at 30% per year for the next two years and at 5% per year thereafter. If the
required rate of return in the stock is 15% (APR), calculate the current value of the stock.
A) $1.420
B) $6.33
C) $5.63
D) None of the above
Answer: B
Type: Difficult
Page: 69
Response: Po = [(0.4 *1.3)/1.15] + [(0.4 * 1.3^2)/(1.15^2)] + [(0.4 * 1.3^2*1.06)/((1.15^2 * (0.15
0.05))] = $6.33
19. The NetTech Co. has just paid a dividend of $1 per share. The dividends are expected to grow at
20% per year for the next three years and at the rate of 5% per year thereafter. If the required
rate of return on the stock is 15%(APR), what is the current value of the stock?
A) $18.14
B) $15.20
C) $12.51
D) None of the above
Answer: B
Type: Difficult
Page: 69
Response: P = (1.2/1.15) + (1.44/1.15^2) + (1.728/1.15^3) + (1.8144/((1.15^3) * (0.15 0.05)) =
15.20
20. Lake Co. has paid a dividend $2 per share out of earnings of $4 per share. If the book value per
share is $25, what is the expected growth rate in dividends (g)?
A) 16%
B) 12%
C) 8%
D) 4%
Answer: C
Type: Difficult
Page: 72
Response: g = (1 0.5) (4/25) = 0.08 or 8%
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21. Lake Co. has paid a dividend $2 per share out of earnings of $4 per share. If the book value per
share is $25 and is currently selling for $30 per share, calculate the required rate of return on the
stock. (Use the calculated g from the previous problem to answer this question.)
A) 7.2%
B) 15.2%
C) 14.7%
D) 16.6%
Answer: B
Type: Difficult
Page: 72
Response: g = (1 0.5)(4/25) = 0.08 or 8%; [(2*1.08)/30] + 0.08 = 15.2 %.
22. Lake Co. has paid a dividend $3 per share out of earnings of $5 per share. If the book value per
share is $40, what is the expected growth rate in dividends?
A) 12.5%
B) 8%
C) 5%
D) 3%
Answer: C
Type: Difficult
Page: 72
Response: g = (1 (5/40) = .05 or 5%;
23. Lake Co. has paid a dividend $3 per share out of earnings of $5 per share. If the book value per
share is $40 and the share value is 52.50 per share, calculate the required rate of return on the
stock. (Use the calculated 'g' from the previous problem to answer this question)
A) 11%
B) 12%
C) 5%
D) 6%
Answer: A
Type: Difficult
Page: 72
Response: g = (1 0.6) (5/40) = .05 or 5%; [(3*1.05)/52.50] + 0.05 = 0.11 = 11%.
24. The growth rate in dividends can be thought of as a sum of two parts. They are:
A) ROE and the Retention Ratio.
B) Dividend yield and growth rate in dividends
C) ROA and ROE
D) Book value per share and EPS
Answer: A
Type: Medium
Page: 72
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25. The value of the stock:
A) Increases as the dividend growth rate increases
B) Increases as the required rate of return decreases
C) Increases as the required rate of return increases
D) Both A and B
Answer: D
Type: Difficult
Page: 72
26. Company X has a P/E ratio of 10 and a stock price of $50 per share. Calculate earnings per share
of the company.
A) $5 per share
B) $10 per share
C) $0.20 per share
D) $6 per share
Answer: A
Type: Medium
Page: 74
Response: EPS = 50/10 = $5
27. Companies with higher expected growth opportunities usually sell for:
A) Lower P/E ratio
B) Higher P/E ratio
C) A price that is independent of P/E ratio
D) A price that the dependent upon the payment ratio
Answer: B
Type: Medium
Page: 74
28. Which of the following formulas regarding earnings to price ratio is true:
A) EPS/Po = r[1+(PVGO/Po]
B) EPS/Po = r[1 - (PVGO/Po)]
C) EPS/Po = [r+(PVGO/Po)]
D) EPS/Po =[r(1+(PVGO/Po)]/r
Answer: B
Type: Difficult
Page: 74
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29. Woe Co. is expected to pay a dividend or $4.00 per share out of earnings of $7.50 per share. If
the required rate of return on the stock is 15% and dividends are growing at a current rate of 10%
per year, calculate the percent value of the growth opportunity for the stock (PVGO).
A) $80
B) $50
C) $30
D) $26
Answer: C
Type: Difficult
Page: 74
Response: No growth value = 7.5/0.15 = 50; Po = 4/ (0.15-0.1) = 80; PVGO = 80-50 = 30
30. Parcel Corporation is expected to pay a dividend of $5 per share next year, and the dividends pay
out ratio is 50%. If the dividends are expected to grow at a constant rate of 8% forever and the
required rate of return on the stock is 13%, calculate the present value of the growth opportunity.
A) $23.08
B) $64.10
C) $100
D) None of the above
Answer: A
Type: Difficult
Page: 74
Response: EPS= (5/0.5)=$10; No Growth Value = 10/0.13 = 76.92; Growth Value = 5/(0.130.08) = 100; PVGO = 100-76.92 = 23.08
31. A high proportion of the value a growth stock comes from:
A) Past dividend payments
B) Past earnings
C) PVGO (Present Value of the Growth Opportunities)
D) Both A and B
Answer: C
Type: Medium
Page: 74
32. Generally high growth stocks pay:
A) High dividends
B) Low or no dividends
C) Erratic dividends
D) Both A and C
Answer: B
Type: Medium
Page: 74
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33. The following stocks are examples of growth stocks except:
A) Wal-Mart
B) Dell Computer
C) Microsoft
D) Chubb
Answer: D
Type: Medium
Page: 74
34. The following stocks are examples of income stocks except:
A) Exxon Mobil
B) Wal-Mart
C) Chubb
D) Kellogg
E) All of the above
Answer: B
Type: Easy
Page: 74
35. Which of the following stocks are growth stocks?
A) Dell Computer
B) AT&T
C) Duke Power
D) Exxon
E) None of the above
Answer: A
Type: Easy
Page: 74
36. Which of the following stocks are income stocks?
A) Duke Power
B) Dell Computer
C) Microsoft
D) Wal-Mart
E) None of the above
Answer: A
Type: Easy
Page: 74
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37. The relationship between P/E ratio and market capitalization rate can be described by the
following statements:
A) EPS/Po measures r, only if PVGO = 0
B) High P/E ratios indicate low r
C) There is no reliable association between the P/E ratio and r
D) A and C above
Answer: D
Type: Easy
Page: 75
38. Universal Air is a no growth firm and has two million shares outstanding. It is expected to earn a
constant 20 million per year on its assets. If all earnings are paid out as dividends and the cost of
capital is 10%, calculate the current price per share for the stock.
A) $200
B) $100
C) $150
D) $50
Answer: B
Type: Medium
Page: 77
Response: EPS = DPS = 20/2 = $10 per share = Po = 10/0.1 = 100
39. Which of the following statements regarding free cash flow is true?
A) Free cash flow is always positive
B) Free cash flow is always negative
C) Free cash flow is the net cash flow to the shareholders after paying for future investments
D) None of the above
Answer: C
Type: Medium
Page: 77
40. Discounted cash flow formulas work for the valuation of:
A) Stocks with constant dividend growth
B) Businesses
C) Stocks with super normal dividend growth
D) All of the above
Answer: D
Type: Medium
Page: 77
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41. The value of a business is given by:
A) PV = PV(free cash flows)
B) PV = PV(free cash flows) + PV (horizon value)
C) PV(free cash flows) – PV(horizon value)
D) None of the above
Answer: B
Type: Medium
Page: 77
42. The present value of free cash flow is $5 million and the present value of the horizon value is $10
million. Calculate the present value of the business.
A) $5 million
B) $10 million
C) $15 million
D) None of the above
Answer: C
Type: Medium
Page: 77
Response: PV(business) = 5 + 10 = 15
True/False Questions
T
F 43. The New York Stock Exchange is the only stock market in the US.
Answer: False
Type: Easy
Page: 60
T
F 44. Shareholders receive cash from the firm in the form of dividends and capital gains.
Answer: False
Type: Difficult
Page: 61
T
F 45. The return that is expected by investors from a common stock is often called its market
capitalization rate.
Answer: True
Type: Medium
Page: 61
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T
F 46. At each point in time, all securities in an equivalent-risk class are priced to offer the same
expected return.
Answer: True
Type: Difficult
Page: 62
T
F 47. The constant growth formula for stock valuation does not work for firms with negative
growth (declining) rates in dividends.
Answer: False
Type: Difficult
Page: 64
T
F 48. The market capitalization equals the dividend yield plus the growth rate in dividends for a
constant dividend growth stock.
Answer: True
Type: Medium
Page: 65
T
F 49. The value of a share of common stock is equal to the discounted stream of free cash flow
per share.
Answer: True
Type: Difficult
Page: 69
T
F 50. The value of a share of common stock is equal to the discounted stream of earnings per
share.
Answer: False
Type: Medium
Page: 69
T
F 51. There is a strong relationship between a stock's price-earnings (P/E) ratio and its
capitalization rate.
Answer: False
Type: Medium
Page: 70
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T
F 52. Discounted cash flow approach can be used to value ongoing businesses.
Answer: True
Type: Medium
Page: 76
Essay Questions
53. Explain the term "primary market."
Type: Easy
Page: 59
Answer:
When new shares of common stocks are sold in the market to raise capital, it is called a primary
market transaction. A good example of a primary market transaction is the IPO (Initial Public
Offering).
54. Explain the term "secondary market."
Type: Easy
Page: 59
Answer:
When already issued stocks are traded in the market, it is called a secondary market transaction.
Most transactions in the stock market are secondary market transactions.
55. Briefly explain the term "market capitalization rate."
Type: Medium
Page: 61
Answer:
The rate of return expected by the investors in common stocks is called the market capitalization
rate. For a constant growth stock it is the dividend yield plus the growth rate in dividends.
56. Discuss the general principle in the valuation of a common stock.
Type: Medium
Page: 62
Answer:
The value of a common stock is the present value of all the dividends received by owning the
stock discounted at the market capitalization rate. This is called the discounted cash flow (DCF)
method.
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57. Discuss the term "price-earnings (P/E) ratio."
Type: Medium
Page: 70
Answer:
The P/E ratio is a widely used financial indicator, but is also quite ambiguous. Generally, a high
P/E ratio indicates that the investors think a firm has good growth potential. The P/E ratio is
helpful in evaluating shocks. It is the ratio of current market price and earnings of a stock.
58. Discuss the problems inherent in the valuation of a business.
Type: Difficult
Page: 75
Answer:
The main problems are estimating future cash flows for the next several years, and estimating the
horizon value. The latter is quite difficult and is a significant proportion of the total estimated
value of the firm. Generally, the discounted cash flow approach is applied for the valuation.
There are other methods like using the market to book ratio and the P/E ratio.
Chapter 5 Why Net Present Value Leads to Better Investment Decisions than Other Criteria
Multiple Choice Questions
1. The following measures are used by firms when making capital budgeting decisions except:
A) Payback period
B) Internal rate of return
C) Net present value
D) P/E ratio
Answer: D
Type: Easy
Page: 91
2. Which of the following investment rules does not use the time value of the money concept?
A) The payback period
B) Internal rate of return
C) Net present value
D) All of the above use the time value concept
Answer: A
Type: Easy
Page: 93
3. Suppose a firm has a $500 million in excess cash. It could:
A) Invest the funds in projects with positive NPVs
B) Pay high dividends to the shareholders
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C) Buy another firm
D) All of the above
Answer: D
Type: Easy
Page: 93
4. Which of the following investment rules has value additivity property?
A) The payback period method
B) The internal rate of return method
C) The book rate of return method
D) Net present value method
E) All of the above have value additivity property
Answer: D
Type: Difficult
Page: 93
65
5. If the net present value of project A is +$80, and of project B is +$60, then the net present value
of the combined project is:
A) +$80
B) +$60
C) +$140
D) None of the above
Answer: C
Type: Easy
Page: 93
Response: NPV(A +B) = 80 + 60 = 140
6. If the NPV of project A is +$100, and that of project B is -$50 and that of project C is +$20, what
is the NPV of the combined project?
A) $100
B) -$50
C) $120
D) $70
Answer: D
Type: Easy
Page: 93
Response: NPV(A+B+C) = 100 + 20 = 70
7. You are given a job to make a decision on project X, which is composed of three independent
projects A, B, and C which have NPVs of +$50, -$20 and +$100, respectively. How would you
go about making the decision about whether to accept or reject the project?
A) Accept the firm's joint project as it has a positive NPV
B) Reject the joint project
C) Break up the project into its components: accept A and C and reject B
D) None of the above
Answer: C
Type: Difficult
Page: 93
8. If the NPV of project A is +$50 and that of project B is -$60, than the NPV of the combined
project is:
A) +$50
B) +$60
C) -$10
D) None of the above.
Answer: C
Type: Easy
Page: 93
Response: NPV(A+B) = 50 - 60 = 10
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9. The net present value of a project depends upon:
A) forecasted cash flows and opportunity cost of capital
B) manager's tastes and preferences
C) company's choice of accounting method
D) all of the above
Answer: A
Type: Medium
Page: 93
10. The payback period rule:
A) Varies the cut-off point with the interest rate
B) Determines a cut-off point so that all projects accepted by the NPV rule will be accepted by
the payback period rule.
C) Requires an arbitrary choice of a cut-off point
D) Both A and C
Answer: C
Type: Medium
Page: 94
11. The payback period rule accepts all projects for which the payback period is:
A) Greater than the cut-off value
B) Less than the cut-off value
C) Is positive
D) An integer
Answer: B
Type: Easy
Page: 94
12. Which of the following investment rules may not use all possible cash flows in its calculations?
A) Payback period.
B) NPV
C) IRR
D) All of the above
Answer: A
Type: Medium
Page: 95
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13. Given the following cash flows for project A: C0 = -2000, C1 = +500 , C2 = +1500 and C3 =
+5000, calculate the payback period.
A) One year
B) 2 years
C) 3 years
D) None of the above
Answer: B
Type: Medium
Page: 95
Response: 2000 = Year one cash flow + year 2 cash flow; Payback period = 2 years
14. The main advantage of the payback rule is:
A) Adjustment for uncertainty of early cash flows
B) It is simple to use
C) Does not discount cash flows
D) Both A and C
Answer: B
Type: Medium
Page: 94
15. Which of the following statements regarding the discounted payback period rule is true?
A) The discounted payback rule uses the time value of money concept.
B) The discounted payback rule is better than the NPV rule
C) The discounted payback rule considers all cash flows
D) The discounted payback rule exhibits the value additive property
Answer: A
Type: Easy
Page: 95
16. The following are disadvantages of using the payback rule except:
A) The payback rule ignores all cash flow after the cutoff date
B) The payback rule does not use the time value of money
C) The payback period is easy to calculate and use
D) The payback rule does not have the value additive property
Answer: C
Type: Medium
Page: 95
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17. Given the following cash flows for project Z: C0 = -2,000, C1 = 600, C2 = 2160 and C3 = 6000,
calculate the discounted payback period for the project at a discount rate of 20%.
A) One year
B) 2 years
C) 3 years
D) None of the above
Answer: B
Type: Difficult
Page: 96
Response: 2000 = (600/1.2) + (2160/1.2^2); The discounted payback = 2 years
18. Given the following cash flows for Project M: C0 = -2,000, C1 = +500, C2 = +1,500, C3 = +1455,
calculate the IRR for the project.
A) 10%
B) 18%
C) 28%
D) None of the above
Answer: C
Type: Difficult
Page: 96
Response: -2000 + [500/(1+IRR)] + [1500/(1+IRR)^2] + [1455/(1 + IRR)^3] = 0; IRR = 28%
19. The quickest way to calculate the IRR of a project is by:
A) Trial and error method
B) Using the graphical method
C) Using a financial calculator
D) Guessing the IRR
Answer: C
Type: Easy
Page: 97
20. If an investment project (normal project) has an IRR equal to the cost of capital , the NPV for that
project is:
A) Positive
B) Negative
C) Zero
D) Unable to be determined
Answer: C
Type: Easy
Page: 97
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21. Project Y-File has the following cash flows: C0 = +2000, C1 = -1,200, and C2 = -1,500. If the
IRR of the project is 21.65% and if the cost of capital is 15%, you would:
A) Accept the project
B) Reject the project
Answer: B
Type: Difficult
Page: 98
Response: This is a loan project therefore reject
22. Project Y-File has the following cash flows: C0 = +2000, C1 = -1,200, and C2 = -1,200. If the
IRR of the project is 13.1% and if the cost of capital is 15%, you would:
A) Accept the project
B) Reject the project
Answer: B
Type: Difficult
Page: 98
Response: This is a loan project therefore accept
23. The IRR is defined as:
A) The discount rate that makes the NPV equal to zero
B) The difference between the cost of capital and the present value of the cash flows
C) The discount rate used in the NPV method
D) The discount rate used in the discounted payback period method
Answer: A
Type: Easy
Page: 98
24. The following are some of the shortcomings of the IRR method except:
A) IRR is conceptually easy to communicate
B) Projects can have multiple IRRs
C) IRR method cannot distinguish between a borrowing project and a lending project
D) It is very cumbersome to evaluate mutually exclusive projects using the IRR method
Answer: A
Type: Difficult
Page: 99
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25. Valentine Company is considering investing in a new project. The project will need an initial
investment of $1,200,000 and will generate $600,000 (after-tax) cash flows for three years.
Calculate the IRR for the project.
A) 14.5%
B) 18.6%
C) 23.4%
D) 20.2%
Answer: C
Type: Difficult
Page: 99
Response: -1,200,000 + [600,000/(1+IRR)] + [600,000/(1+IRR)^2] + [600,000/(1+IRR)^3] = 0;
IRR = 23.4%.
26. Valentine Company is considering investing in a new project. The project will need an initial
investment of $1,200,000 and will generate $600,000 (after-tax) cash flows for three years.
Calculate the MIRR (modified internal rate of return) for the project if the cost of capital is 15%.
A) 14.5%
B) 18.6%
C) 23.4%
D) 20.2%
Answer: D
Type: Difficult
Page: 101
Response: -1,200,000 + [(600,000(1.15)^2)+ (600,000(1.15)) + 600,000]/[(1+MIRR)^3] = 0;
MIRR = 20.2%.
27. Valentine Company is considering investing in a new project. The project will need an initial
investment of $1,200,000 and will generate $600,000 (after-tax) cash flows for three years.
Calculate the NPV for the project if the cost of capital is 15%.
A) $169,935
B) $129,211
C) $600,000
D) $125,846
Answer: A
Type: Medium
Page: 102
Response: NPV = -1,200,000 + [(600,000)/(1.15)] + [(600,000/(1.15)^2] + [600,000/(1.15)^3] =
169,935
71
28. A project will have only one internal rate of return if:
A) The net present value is positive
B) The net present value is negative
C) There is a one fifth change in the cash flows
D) The cash flows decline over the life of the project
Answer: C
Type: Medium
Page: 102
29. Elephant company is investing in a giant crane. It is expected to cost 2.2 million in initial
investment and it is expected to generate an end of year cash flow of 1.0 million each year for
three years. Calculate the IRR approximately.
A) 14.6
B) 16.4
C) 22.1
D) 17.3
Answer: D
Type: Medium
Page: 101
Response: 0 = -2.2 + ((1/(1+IRR) + (1/((1+IRR)^2)) + (1/((1+IRR)^3))); IRR = 17.3 (by trial &
error)
30. Elephant company is investing in a giant crane. It is expected to cost 2.2 million in initial
investment and it is expected to generate an end of year cash flow of 1.0 million each year for
three years. Calculate the MIRR for the project if the cost of capital is 12% APR.
A) 15.3%
B) 17.3%
C) 23.8%
D) 22.1%
Answer: A
Type: Difficult
Page: 102
Response: Year 0 = -2.2, Year 3 = 3.3744; 1 + MIRR = (3.3744/2.2)^0.3333 = 15.3%
72
31. Elephant company is investing in a giant crane. It is expected to cost 2.2 million in initial
investment and it is expected to generate an end of year cash flow of 1.0 million each year for
three years. Calculate the NPV at 12% (approximately).
A) 2.4 million
B) 0.20 million
C) 0.80 million
D) 0.40 million
Answer: B
Type: Medium
Page: 102
Response: NPV = -2.2 + 1/1.12 + 1/(1.12^2) + 1/(1.12^3) = 0.2
32. Given the following cash flow for project A: C0 = -2000, C1 = +500, C2 = +1500 and C3 =
+5000, calculate the NPV of the project using a 15% discount rate.
A) $5000
B) $2857
C) $3201
D) $2352
Answer: B
Type: Medium
Page: 102
Response: NPV = -2000 + (500/1.15) + (1500 / 1.15^2) + (5000/1.15^3) = 2857
33. Profitability index is the ratio of:
A) Present value of cash flow to initial investment
B) Net present value cash flow to initial investment
C) Net present value of cash flow to IRR
D) Present value of cash flow to IRR
Answer: B
Type: Medium
Page: 106
34. Benefit-cost ratio is defined as the ratio of:
A) Present value of cash flow to initial investment
B) Net present value cash flow to initial investment
C) Net present value of cash flow to IRR
D) Present value of cash flow to IRR
Answer: A
Type: Medium
Page: 106
73
35. Profitability index is useful under:
A) Capital rationing
B) Mutually exclusive projects
C) Non-normal projects
D) None of the above
Answer: A
Type: Medium
Page: 106
36. The following table gives the available projects for a firm.
A
90
140
B
20
70
C
60
65
D
50
-10
E
150
30
F
40
32
G
20 Initial investment
10 NPV
If the firm has a limit of 210 million to invest, what is the maximum NPV the company can
obtain?
A) 200
B) 307
C) 283
D) None of the above
Answer: B
Type: Difficult
Page: 106
Response: A + B + C + F = 140 + 70 + 65 + 32 = 307
37.
A
5.0
1.5
B
4.0
-0.5
C
5.0
1.0
D
1.0
0.5
E
2.0
0.5
F
7.0
1.0
G
8.0 Initial investment
1.0 NPV
The firm has only twenty million to invest. What is the maximum NPV that the company can
obtain?
A) 3.5
B) 4.5
C) 4.0
D) None of the above
Answer: B
Type: Difficult
Page: 106
Response: A + C + D + E + F = 4.5
74
38. The profitability index can be used for ranking projects under:
A) Soft capital rationing
B) Hard capital rationing
C) Capital rationing at t = 0
D) Both A and B
Answer: C
Type: Difficult
Page: 108
True/False Questions
T
F 39. Present values have value additivity property.
Answer: True
Type: Difficult
Page: 93
T
F 40. The payback rule gives equal weight to all cash flows before the payback date and zero
weight to subsequent cash flows.
Answer: True
Type: Medium
Page: 95
T
F 41. The discounted payback rule calculates the payback period and then discounts it at the
opportunity cost of capital.
Answer: False
Type: Medium
Page: 96
T
F 42. The internal rate of return is the discount rate that makes the PV of a project equal to
zero.
Answer: False
Type: Difficult
Page: 96
75
T
F 43. The IRR rule states that firms should accept any project offering an internal rate of return
in excess of the cost of capital.
Answer: True
Type: Medium
Page: 97
T
F 44. In case of a loan project, one should accept the project if the IRR is less than the cost of
capital.
Answer: True
Type: Difficult
Page: 98
T
F 45. MIRRs have the value additivity property and IRRs do not.
Answer: False
Type: Difficult
Page: 101
T
F 46. Soft rationing may be used to control managerial behavior.
Answer: True
Type: Easy
Page: 108
Essay Questions
47. Briefly explain the value additivity property.
Type: Medium
Page: 93
Answer:
For example, the net present value (NPV) of the combined project say A and B is equal to the
NPV(A) and NPV(B). This property holds good for the present values also. This property is not
shared by IRR. IRR of the combined project is not the sum of the individual IRRs. The value
additivity property is very useful when making decisions about numerous projects.
76
48. Discuss some of the advantages of using the payback method.
Type: Easy
Page: 95
Answer:
It tells you how quickly you can recover your investment. The main advantage is that it is easy to
calculate and use.
49. Discuss some of the disadvantages of the payback rule.
Type: Easy
Page: 95
Answer:
The disadvantages are that it does not take the time value of money into account and also does not
use all the cash flow. It has limited applications such as small projects.
50. What are some of the advantages of using the IRR method?
Type: Medium
Page: 97
Answer:
The main advantage of IRR is that it is easy to communicate.
51. What are some of the disadvantages of using the IRR method?
Type: Difficult
Page: 98
Answer:
There are several disadvantages to IRR method. It is difficult to intuitively explain the concept of
internal rate of return. It is not useful in evaluating complex projects, mutually exclusive projects
and dependent projects. For projects with high IRRs, reinvestment rate assumption implicit in the
method may be unrealistic. It is also more complicated to calculate. You can also get multiple
rates of return in case of complex projects. One way to eliminate this problem is by using the
modified internal rate of return method. Also, IRR cannot distinguish between borrowing and
lending projects
52. In what way is the modified internal rate of return (MIRR) method better than the IRR method?
Type: Medium
Page: 101
Answer:
With the modified internal rate of return method, cash flows form the project are explicitly
reinvested at the cost of capital, thus eliminating the reinvestment rate assumption problem. This
eliminates the multiple IRR problems inherent in complex projects. Also reinvesting the cash
flows from the project at the cost of capital is more realistic.
77
78
53. Briefly discuss capital rationing.
Type: Medium
Page: 106
Answer:
There are two types of capital rationing; soft rationing imposed by the company and hard
rationing imposed by the capital markets. Capital rationing results in the firm foregoing some
positive NPV projects thereby reducing a firm's value.
54. Briefly explain how linear programming is useful for solving capital rationing problems.
Type: Difficult
Page: 107
Answer:
Linear programming can be used for solving complex capital rationing problems. In this method
NPV function, which is a linear function of all feasible projects, is maximized subject to
constraints of available capital. Many times linear programming solutions tell us to take
"fractional" projects to maximize NPV. This might be possible for certain projects only. A
modified form of linear programming called "integer programming" can be used if only whole
projects are to be accepted.
55. Briefly explain the term "soft rationing"
Type: Medium
Page: 108
Answer:
Soft rationing is used by management to help in financial control. Soft rationing is imposed by
the management on a temporary basis and not by capital markets.
Chapter 6 Making Investment Decisions with the Net Present Value Rule
Multiple Choice Questions
1. Preferably, cash flows for a project are estimated as:
A) Cash flows before taxes
B) Cash flows after taxes
C) Earnings before taxes
D) Earnings after taxes
Answer: B
Type: Medium
Page: 119
2. Important points to remember while estimating cash flows of projects are:
A) only cash flow is relevant
79
B)
C)
D)
E)
always estimate cash flows on an incremental basis
be consistent in the treatment of inflation
all of the above
none of the above
Answer: D
Type: Easy
Page: 120
3. Net Working Capital is the:
A) Difference between short-term assets and short term liabilities
B) Difference between long-term assets and long term liabilities
C) Difference between long-term assets and short term liabilities
D) None of the above
Answer: A
Type: Medium
Page: 121
4. Net Working Capital should be considered in project cash flows because:
A) They are sunk costs
B) Firms must invest cash in short-term assets to produce finished goods
C) Firms need positive NPV projects for investment
D) None of the above
Answer: B
Type: Medium
Page: 121
5. Investment in net working capital is not depreciated because:
A) it is not a cash flow
B) it is a sunk cost
C) it is recovered during or at the end of the project and is not a depreciating asset
D) all of the above
Answer: C
Type: Medium
Page: 121
6. The principal short-term assets are:
A) Cash
B) Accounts receivable
C) Inventories
D) All of the above
Answer: D
80
Type: Easy
Page: 121
7. Investment in inventories includes investment in:
A) Raw material
B) Work-in-progress
C) Finished goods
D) All of the above
Answer: D
Type: Easy
Page: 121
8. The cost of a resource that may be relevant to an investment decision even when no cash changes
hand is called a (an):
A) sunk cost
B) working capital
C) opportunity cost
D) none of the above
Answer: C
Type: Medium
Page: 121
81
9. The following cash flows should be treated as incremental flows when deciding whether to go
ahead with an electric car except:
A) The consequent deduction in sales of the company's existing gasoline models
B) The expenditure on new plants and equipment
C) The value of tools that can be transferred from the company's existing plants
D) Interest payment on debt
Answer: D
Type: Medium
Page: 121
10. Which of the following cash flows should be treated as incremental flows when deciding whether
to go ahead with an electric car?
A) The cost of research and development undertaken for developing the electric car in the past
three years
B) The annual depreciation charge
C) The reduction in taxes resulting from the depreciation charges
D) Dividend payments
Answer: C
Type: Difficult
Page: 121
11. Money that a firm has already spent or committed to spend regardless of whether a project is
taken is called:
A) Sunk cost
B) Opportunity cost
C) Fixed cost
D) None of the above
Answer: A
Type: Medium
Page: 121
12. The value of a previously purchased machine expected to be used by a proposed project is an
example of:
A) Sunk cost
B) Opportunity cost
C) Fixed cost
D) None of the above
Answer: B
Type: Medium
Page: 121
82
13. A firm owns a building with a book value of $150,000 and a market value of $250,000. If the
building is utilized for a project, then the opportunity cost ignoring taxes is:
A) $100,000
B) $150,000
C) $250,000
D) None of the above
Answer: C
Type: Medium
Page: 121
14. A firm has a general purpose machine which has a book value of $400,000 and is sold for
$600,000 in the market. If the tax rate is 30%, what is the opportunity cost of using the machine
in a project?
A) $500,000
B) $600,000
C) $540,000
D) None of the above
Answer: C
Type: Difficult
Page: 121
Response: 600,000 (600,000 400,000) * 0.30 = 540,000
15. A reduction in the sales of existing products caused by the introduction of a new product is an
example of:
A) sunk cost
B) opportunity cost
C) incidental effects
D) none of the above
Answer: C
Type: Easy
Page: 121
16. The real rate of interest is 2% and the inflation is 5%. What is the nominal rate of interest?
A) 3%
B) 4%
C) 7.1%
D) 1%
Answer: C
Type: Easy
Page: 123
Response: 1 + nominal rate = 1.02* 1.05 = 1.071; nominal rate = 7.1%
83
17. A cash flow received in two years is expected to be $11,236. If the real rate of interest is 4% and
the inflation rate is 6%, what is the real cash flow for year-2?
A) $11,236
B) $10,388
C) $10,000
D) $9,246
Answer: C
Type: Medium
Page: 123
Response: Real cash flow = 11236/(1.06^2) = 10,000
18. The real interest rate is 2% and the inflation rate is 4%. What is the nominal interest rate?
A) 3%
B) 4%
C) 6.08%
D) 2%
Answer: C
Type: Easy
Page: 123
Response: 1 + nominal rate = (1 + real rate) (1 + inflation rate) = (1.02)(1.04) =(1.0608) = 6.08%
19. If the nominal interest rate is 6.5% and the inflation rate is 3%, what is the real interest rate?
A) 3.4%
B) 9.5%
C) 4%
D) None of the above
Answer: A
Type: Easy
Page: 123
Response: 1 + real rate = (1 + nominal rate) / (1 + inflation rate) = 1.065/1.03 =1.034; real rate =
3.4%
20. Proper treatment of inflation in the NPV calculation involves:
A) Discounting nominal cash flows using the nominal discount rate
B) Discounting real cash flows using the real discount rate
C) Discounting nominal cash flows using the real discount rates
D) A and B
Answer: D
Type: Medium
Page: 123
84
21. Real cash flow occurring in year-2 is 50,000. If the inflation rate is 10% per year, calculate
nominal cash flow for year-2.
A) 60,500
B) 50,000
C) 55,000
D) None of the above
Answer: A
Type: Medium
Page: 123
Response: Nominal cash flow = (50,000)(1.1)^2 = 60,500
22. The NPV value obtained by discounting nominal cash flows using the nominal discount rate is:
A) The same as the NPV value obtained by discounting real cash flows using the real discount
rate
B) The same as the NPV value obtained by discounting real cash flows using the nominal
discount rate
C) The same as the NPV value obtained by discounting nominal cash flows using the real
discount rate
D) None of the above
Answer: A
Type: Medium
Page: 123
23. A capital equipment costing $100,000 today has no (zero) salvage value at the end of 5 years. If
straight-line depreciation is used, what is the book value of the equipment at the end of three
years?
A) $110,000
B) $80,000
C) $60,000
D) $40,000
Answer: D
Type: Medium
Page: 124
Response:
Annual depreciation = $100,000/5 = 20,000
Depreciation for 3 years = 60,000
Book value = 100,000 60,000 = 40,000
85
24. Capital equipment costing $200,000 today has 50,000 salvage value at the end of 5 years. If the
straight line depreciation method is used, what is the book value of the equipment at the end of
two years?
A) $200,000
B) $170,000
C) $140,000
D) $50,000
Answer: C
Type: Medium
Page: 124
Response:
Annual depreciation = (200,000 50,000)/5 = 30,000
Book value at the end of two years = 200,000 60,000 = 140,000
25. For project A in year - 2, inventories increase by $10,000 and accounts payable by $4,000.
Calculate the increase or decrease in net working capital for year-2.
A) Increases by $14,000
B) Decreases by $14,000
C) Increases by $6,000
D) Decreases by $6,000
E) None of the above
Answer: C
Type: Medium
Page: 124
Response: Working capital = 10,000 4000 = 6,000
26. For project X, year - 5 inventories increase by $5,000, accounts receivables by $3,000 and
accounts payables by $2,000. Calculate the increase or decrease in working capital for year-5.
A) Increases by $6,000
B) Decreases by $6,000
C) Increases by $8,000
D) Decreases by $7,000
Answer: A
Type: Medium
Page: 124
Response: Working capital: 5000 + 3000 2000 = 6,000
86
27. If the depreciation amount is $100,000 and the marginal tax rate is 30%, then the tax shield due to
depreciation is:
A) $333,333
B) $100,000
C) $30,000
D) None of the above
Answer: C
Type: Easy
Page: 127
Response: Tax shield effect = (100,000)(.3) = 30,000
28. If the depreciation amount is 600,000 and the marginal tax rate is 30%, then the tax shield due to
depreciation is:
A) $180,000
B) $600,000
C) $210,000
D) None of the above
Answer: A
Type: Easy
Page: 127
Response: Tax shield effect = (600,000)(0.30) = 180,000
Use the following to answer questions 29-30:
You own 100 acres of timberland, with young timber worth $20,000 if logged today. This represents 500
cords of wood at $40 per cord. After logging, the land can be sold today for $10,000 ($100 per acre).
The opportunity cost of capital is 10%. You have made the following estimates:
(i) The price of a cord of wood will increase by 5% per year.
(ii) The price of land will increase by 3% per year.
(iii) The yearly growth rate of the cords of wood on your land are: years 1-2: 15%; years 3-4: 10%; years
5-8: 5%; years thereafter: 2%.
29. The present value of the optimal decision is approximately:
A) $30,000
B) $32,800
C) $34,250
D) $33,830
Answer: C
Type: Difficult
Page: 129
Response: PV = [500(1.15^2)(1.1^2)(40)(1.05^4) + (10,000)(1.03^4)]/(1.1^4) = 34,250
87
30. The optimal decision is to sell after:
A) 8 years
B) 5 years
C) 4 years
D) 3 years
Answer: C
Type: Difficult
Page: 129
31. You have been asked to evaluate a project with infinite life. Sales and costs are projected to be
$1000 and $500 respectively. There is no depreciation and the tax rate is 30%. The real required
rate of return is 10%. The inflation rate is 4% and is expected to be 4% forever. Sales and costs
will increase at the rate of inflation. If the project costs $3000, what is the NPV?
A) $365.38
B) $1629.62
C) $500.00
D) None of the above
Answer: A
Type: Difficult
Page: 129
Response: [((1000/1.04) (500/1.04)) (0.7)] / 0.1 - 3000 = $365.38
32. A project costs $100 today. It has sales of $100 per year forever. Costs will be $50 the first year
and increase by 19% per year. Ignoring taxes calculate the NPV of the project at the discount rate
of 10%.
A) $11.62
B) $65.00
C) $100.00
D) Cannot be calculated as g > r
Answer: A
Type: Difficult
Page: 129
Response: NPV = -100 + (100-50)/1.1 + (100 (50 * 1.19))/(1.1^2) + (100 50 (1.19^2))/(1.1)^3 +
(100 50 (1.19^3))/(1.1^4) = -100+111.62 = $11.62
88
33. A project requires an initial investment of $200,000 and is expected to produce a cash flow before
taxes of 120,000 per year for two years. [i.e. cash flows will occur at t = 1 and t = 2]. The
corporate tax rate is 30%. The assets will be depreciated using MACRS – 3 year schedule: t=1,
33.33%; t = 2: 44.45%; t = 3: 14.81%; t = 4: 7.4%. The company's tax situation is such that it can
make use of all applicable tax shields. The opportunity cost of capital is 12%. Assume that the
asset can be sold for book value. Calculate the NPV of the project at the end of two years.
(approximately)
A) $16,510
B) $19,571
C) $47,035
D) None of the above
Answer: A
Type: Difficult
Page: 129
Response: -200,000 + (104,000/1.12) + ((110,670+44,440)/(1.12^2)) = $16,510
34. The IRR for the project in the previous question is: (approximately)
A) 12%
B) 10%
C) 17.8%
D) None of the above
Answer: D
Type: Difficult
Page: 129
Response: 0 = -200,000 + (104,000/(1+IRR)) + (155,000/((1+IRR)^2)) = 17.8%
35. OM Construction Company must choose between two types of cranes. Crane A costs $600,000,
will last for 5 years, and will require $60,000 in maintenance each year. Crane B costs $750,000
and will last for seven years and will require $30,000 in maintenance each year. Maintenance
costs for cranes A and B are incurred at the end of each year. The appropriate discount rate is
12% per year. Which machine should OM Construction purchase?
A) Crane A as EAC is $226,444
B) Crane B as EAC is $194,336
C) Crane A as the PV is $816,286
D) Cannot be calculated as the revenues for the project are not given
Answer: B
Type: Difficult
Page: 131
Response:
PV (A) = 600000 + 60000 (3.6048) = 816,286
EAC = $ 226,444
PV(B) = 750000 + 30000 (4.5638) = 886,913
EAC = 194,336.45
89
36. The projects have the following NPVs and project lives.
Project
Project A
Project B
NPV
$5,000
$7,000
Life
4 years
7 years
If the cost of capital is 12%, which project would you accept?
A) A
B) B
C) Both A and B
D) Reject both A and B
Answer: B
Type: Difficult
Page: 133
Response:
EAC(A) = 5000/3.037349 = 1646.17
EAC(B) = 7000/4.563750 = 1533.82
37. Two machines, A and B, which perform the same functions, have the following costs and lives.
T
y
p
e P
V
C
o
s
t
sL
i
f
e
M
a
c
h
i
n
e
A $
6
0
0
0 5
M
a
c
h
i
n
e
B $
8
0
0
0 7
Which machine would you choose? The two machines are mutually exclusive and the cost of
capital is 15%.
A) Machine A as the EAC is $1789.89
B) Machine B as the EAC is $1922.88
C) Don't buy either machine
Answer: A
Type: Difficult
Page: 133
Response:
EAC(A) = 6,000/3.35215 = 1789.89
EAC(B) = 8000/4.1604 = 1922.88
True/False Questions
T
F 38. When calculating cash flows, it is important to consider all incidental effects.
Answer: True
Type: Easy
Page: 120
90
T
F 39. Sunk costs are unaffected by the decision to accept or reject and should be ignored.
Answer: True
Type: Easy
Page: 121
T
F 40. Opportunity costs should not be included as they are missed opportunities.
Answer: False
Type: Medium
Page: 121
T
F 41. By undertaking the analysis in real terms, the financial manager avoids having to forecast
inflation.
Answer: False
Type: Medium
Page: 122
T
F 42. Do not forget to include interest and dividend payments when calculating the project's
cash flow.
Answer: False
Type: Medium
Page: 122
T
F 43. Depreciation acts as a tax shield in reducing the taxes.
Answer: True
Type: Medium
Page: 128
T
F 44. An investment should be postponed as long as the opportunity cost of capital is less than
the growth rate of the value of the project.
Answer: True
Type: Medium
Page: 130
91
T
F 45. The rule for comparing machines with different lines is to select the machine with the
lowest equivalent annual cost (EAC).
Answer: True
Type: Medium
Page: 132
T
F 46. You should replace a machine when the EAC of continuing to operate it exceeds the
EAC of the next machine.
Answer: True
Type: Difficult
Page: 133
T
F 47. You should always replace all old machines with new ones.
Answer: False
Type: Medium
Page: 136
Short Answer Questions
48. Define the term cash flow for a project.
Answer: Cash flow for a project is the net income plus depreciation.
Type: Easy
Page: 120
49. What are some of the important points to remember while estimating the cash flows of a project?
Answer:
 Estimate after-tax cash flows on an incremental basis.
 Include all incidental effects.
 Include working capital requirements
 Include opportunity costs.
 Do not include sunk costs
 Take inflation into consideration in a consistent manner
Type: Medium
Page: 123
92
50. Briefly discuss how taxes are taken into consideration in other countries like Japan.
Answer: In Japan and all of the European Community countries, it is not possible to separate tax
accounts reported to the government and those reported to shareholders. They must be the same.
Type: Medium
Page: 129
51. What are some of the additional factors that have to be considered while estimating cash flows in
other countries and currencies:
Answer:
 Currency of the cash flow should be relevant to the project
 Use an appropriate inflation rate for the project
 Use the relevant tax rate for the project
 Use the appropriate discount rate for the project
Type: Medium
Page: 130
52. How do you compare projects with different lives?
Answer: Projects with different lives are compared assuming that the projects are repeated to
infinity, called replacement chains. The replacement chains are analyzed using equivalent annual
costs (EAC) or adjusted NPVs (adjusted for differences in project lives)
Type: Medium
Page: 135
53. Briefly explain how the decision to replace an existing machine is made?
Answer: The decision to replace an existing machine is done for economic or technological
reasons or for both. For this equivalent annuity approach is used. As long as the benefits exceed
equivalent annual costs replacing old machine with a new one will be a sound decision.
Type: Difficult
Page: 135
54. Briefly explain the term " project interactions"
Answer: Project interactions can happen in many ways. Mutually exclusive projects and
dependent projects are simple examples. Project interactions occur when taking a project affects
the cash flows of other projects.
Type: Medium
Page: 137
93
55. Explain the idea behind the optimal timing of investment.
Answer: In many situations a project may be more valuable if undertaken in the future. Thus
waiting may be an option in many situations. These have to be analyzed before undertaking a
project.
Type: Medium
Page: 137
56. Briefly explain how peak demand can be met economically.
Answer: Many projects involve dealing with fluctuating demand. Keeping inventory of finished
goods is one way of handling this problem. Many times it is economical to use old (less efficient)
machines to take care of peak demand if it occurs for a short period of time. Investing in new
equipment to meet peak loads may not be economical. In some instances, the option of not
replacing all the old machines with new machines should also be considered.
Type: Medium
Page: 138
Chapter 7 Introduction to Risk, Return, and the Opportunity Cost of Capital
Multiple Choice Questions
1. Which of the following portfolios have the least risk?
A) A portfolio of Treasury bills
B) A portfolio of long term United States Government bonds
C) Standard and Poor's composite index
D) Portfolio of common stocks of small firms
Answer: A
Type: Easy
Page: 153
2. What has been the average nominal rate of interest on Treasury bills over the past seventy-five
years?
A) Less than 1%
B) Between 1% and 2%
C) Between 2% and 3%
D) Between 3% and 4%
Answer: D
Type: Easy
Page: 155
3. What has been the average real rate of interest on Treasury bills over the past seventy-five years?
A) Less than 1%
94
B) Between 1% and 2%
C) Between 2% and 3%
D) Between 3% and 4%
Answer: A
Type: Easy
Page: 155
4. Standard and Poor's 500 Index is a:
A) Portfolio of common stocks
B) Portfolio of corporate bonds
C) Portfolio of government bonds
D) A and B above
Answer: A
Type: Medium
Page: 155
95
5. Long-term government bonds have:
A) Interest rate risk
B) Default risk
C) Market risk
D) None of the above
Answer: A
Type: Medium
Page: 155
6. One dollar invested in the S&P index in 1926 would have grown in nominal value by the end of
year 2000 to:
A) $6402.2
B) $2586.5
C) $64.1
D) $16.6
Answer: B
Type: Medium
Page: 155
7. One dollar invested in the S&P index in 1926 would have grown in real value by the end of year
2000 to:
A) $659.6
B) $266.5
C) $6.6
D) $5.0
Answer: B
Type: Medium
Page: 155
8. What has been the average risk premium on common stocks between 1926 and 2000?
A) 13.4%
B) 9.1%
C) 2.2%
D) 1.9%
Answer: B
Type: Medium
Page: 155
96
9. What has been the average annual rate of return (normal value) for small common stocks between
1926 and 2000?
A) 17.3%
B) 13.0%
C) 6.0%
D) 3.9%
Answer: A
Type: Medium
Page: 155
10. Which portfolio had the highest average annual (real) return between 1926 and 2000?
A) Small firm common stocks
B) Common stocks
C) Government bonds
D) Treasury bills
Answer: A
Type: Medium
Page: 155
11. Which portfolio has had the lowest average annual nominal rate of return during the 1926-2000
period?
A) Small firm common stocks
B) Common stocks
C) Government bonds
D) Treasury bills
Answer: D
Type: Medium
Page: 155
12. What has been the average risk premium on small-firm common stocks between 1926 and 2000?
A) More than 10%
B) Between 8% and 10%
C) Between 2% and 5%
D) Less than 2%
Answer: A
Type: Medium
Page: 155
97
13. Which portfolio has had the highest average risk premium during the period 1926-2000?
A) Small firm common stocks
B) Common stocks
C) Government bonds
D) Treasury bills
Answer: A
Type: Medium
Page: 155
14. Standard error measures:
A) Nominal annual rate of return on a portfolio
B) Risk of a portfolio
C) Reliability of an estimate
D) Real annual rate of return on a portfolio
Answer: C
Type: Difficult
Page: 156
15. Standard error is estimated as:
A) Average annual rate of return divided by the square root of the number of observations
B) Standard deviation of returns divided by the square root of the number of observations
C) Variance divided by the number of observations
D) None of the above
Answer: B
Type: Medium
Page: 156
16. If the standard deviation is 13.4% and the number of observations is 10, what is the standard
error?
A) 4.23 %
B) 2.4%
C) 0.47%
D) None of the above
Answer: A
Type: Difficult
Page: 156
Response: Standard error = 13.4v10 = 4.23%
98
17. Spill Oil Company's stocks had -8%, 12% and 26% rates of return during the last three years
respectively; calculate the average rate of return for the stock.
A) 10% per year
B) 8% per year
C) 12% per year
D) None of the above
Answer: A
Type: Easy
Page: 156
Response: Average rate of return = (-8 + 12 + 26) / 3 = 10%
18. If the average annual rate of return for common stocks is 13%, and treasury bills is 3.8%, what is
the average market risk premium?
A) 13%
B) 3.8%
C) 9.2%
D) None of the above
Answer: C
Type: Easy
Page: 156
Response: Average risk premium: 13 3.8 = 9.2%
19. The discount rate for safe projects is the:
A) Market rate of return
B) Risk-free rate
C) Market risk premium
D) None of the above
Answer: B
Type: Easy
Page: 157
20. The discount rate for a project with a risk the same as the market risk is the:
A) Market rate of return
B) Risk-free rate
C) Market risk premium
D) None of the above
Answer: A
Type: Easy
Page: 157
99
21. Mega Corporation has the following returns for the past three years: 8%, 16% and 24%.
Calculate the variance of the return and the standard deviation of the returns.
A) 64 and 8%
B) 128 and 11.3%
C) 43 and 6.5%
D) None of the above
Answer: A
Type: Difficult
Page: 161
Response: Mean = (8+6+24)/3 = 16%; Variance = [(8-16)^2 + (16-16)^2 + (24-16)^2]/(3-1) = 64;
Standard deviation = 64^(1/2) = 8%
22. Macro Corporation has had the following returns for the past three years, -20%, 10%, 40%.
Calculate the standard deviation of the returns.
A) 10%
B) 30%
C) 60%
D) None of the above
Answer: B
Type: Difficult
Page: 161
Response: Mean = (-20+10+40)/3 = 10%; Variance = [(-20-10)^2 + (10-10)^2 + (40-10)^2] /2 =
900;
Standard deviation = 30%
23. Micro Corporation has had returns of –5%, 15% and 20% for the past three years. Calculate the
standard deviation of the returns.
A) 10%
B) 22.9%
C) 30%
D) None of the above
Answer: B
Type: Difficult
Page: 161
Response: (-5 +15+20)/3 = 10%; Variance = [(-5-10)^2 + (15-10)^2 + (20-10)^2]/(3-1) = 525;
Standard deviation = 525^(1/2) = 22.9%
100
24. What has been the standard deviation of returns of common stocks during the period between
1926 and 2000?
A) 20.2%
B) 33.4%
C) 8.7%
D) 9.4%
Answer: A
Type: Medium
Page: 164
25. Which portfolio had the highest standard deviation during the period between 1926 and 2000?
A) Small firm common stocks
B) Common stocks
C) Government bonds
D) Treasury bills
Answer: A
Type: Easy
Page: 164
26. The standard deviation of the UK market during the period from 1996 through 2001 was:
A) 24.1%
B) 20.7%
C) 14.5%
D) None of the above
Answer: C
Type: Medium
Page: 166
27. The portion of the risk that can be eliminated by diversification is called:
A) Unique risk
B) Market risk
C) Interest rate risk
D) Default risk
Answer: A
Type: Medium
Page: 168
101
28. The unique risk is also called the:
A) Unsystematic risk
B) Diversifiable risk
C) Firm specific risk
D) Residual risk
E) All of the above
Answer: E
Type: Easy
Page: 168
29. Stock A has an expected return of 10% per year and stock B has an expected return of 20%. If
55% of the funds are invested in stock B, what is the expected return on the portfolio of stock A
and stock B?
A) 10%
B) 20%
C) 15.5%
D) None of the above
Answer: C
Type: Easy
Page: 169
Response: 0.55(10) + 0.45(20) = 15.5%
30. As the number of stocks in a portfolio is increased:
A) Unique risk decreases and approaches to zero
B) Market risk decrease
C) Unique risk decreases and becomes equal to market risk
D) total risk approaches to zero
Answer: A
Type: Medium
Page: 169
102
31. Stock X has a standard deviation of return of 10%. Stock Y has a standard deviation of return of
20%. The correlation coefficient between stocks is 0.5. If you invest 60% of the funds in stock X
and 40% in stock Y, what is the standard deviation of a portfolio?
A) 10%
B) 20%
C) 12.2%
D) 22%
E) None of the above
Answer: C
Type: Difficult
Page: 171
Response: (0.6^2)(10^2) + (0.4^2) (20^2) + (2)(0.6)(0.4)(0.5)(10)(20) = 148 ; Standard deviation
= (148^0.5) = 12.2%
32. Stock M and Stock N have had returns for the past three years of –12%. 10%, 32% and 6%, 15%,
24% respectively. Calculate the covariance between the two securities.
A) +198
B) –198
C) +132
D) None of the above
Answer: A
Type: Difficult
Page: 171
Response:
(-12 +10 + 32)/3 = 10%
(6+15+24)/3 = 15%
Cov(RM, RN) = [(-12-10)(6-15) + (10-10)(15-15)+(32-10)(24-15)]/(3-1) = 198
33. Stock P and stock Q have had annual returns of -10%, 12%, 28% and 8%, 13%, 24%
respectively. Calculate the covariance of return between the securities.
A) 149
B) –149
C) 100
D) None of the above
Answer: A
Type: Difficult
Page: 171
Response:
Mean (P) = (-10 + 12 + 28)/3 = 10% Mean (Q) = (8+13+24)/3 = 15%
Cov(P,Q) = [(-10-10)(8-15)+ (12-10) (13-15) + (28-10)(24-15)]/2 = 149
103
34. If the covariance between stock A and stock B is 100, the standard deviation of stock A is 10%
and that of stock B is 20%, calculate the correlation coefficient between the two securities.
A) +0.5
B) +1.0
C) –0.5
D) None of the above
Answer: A
Type: Medium
Page: 171
Response: Corr(RA, RB) = 100/(10 * 20) = +0.5
35. If the correlation coefficient between stock C and stock D is +1.0% and the standard deviation of
return for stock C is 15% and that for stock D is 30%, calculate the covariance between stock C
and stock D.
A) +45
B) +450
C) –45
D) None of the above
Answer: B
Type: Medium
Page: 171
Response: Cov(RC, RD) = (+1)(30)(15) = +450
36. The range of values that correlation coefficients can take can be:
A) –1 to +1
B) zero to +1
C) –infinity to +infinity
D) zero to +infinity
Answer: A
Type: Medium
Page: 171
37. For a two-stock portfolio, the maximum reduction in risk occurs when the correlation coefficient
between the two stocks is:
A) +1
B) 0
C) –0.5
D) –1
Answer: D
Type: Medium
Page: 171
104
38. The "beta" is a measure of:
A) Unique risk
B) Market risk
C) Total risk
D) None of the above
Answer: B
Type: Medium
Page: 173
39. The variance or standard deviation is a measure of:
A) Total risk
B) Unique risk
C) Market risk
D) None of the above
Answer: A
Type: Medium
Page: 173
40. The beta of market portfolio is:
A) 0
B) +0.5
C) +1.0
D) –1.0
Answer: C
Type: Easy
Page: 177
41. The beta of a risk-free portfolio is:
A) 0
B) +0.5
C) +1.0
D) –1.0
Answer: A
Type: Easy
Page: 177
105
42. If the standard deviation of returns of the market is 20% and the beta of a well-diversified
portfolio is 1.5, calculate the standard deviation of the portfolio:
A) 10%
B) 20%
C) 30%
D) 40%
E) none of the above
Answer: C
Type: Medium
Page: 177
Response: Standard deviation of the portfolio = (1.5)*(20) = 30%
43. The correlation coefficient between stock A and the market portfolio is +0.6. The standard
deviation of return of the stock is 30% and that of the market portfolio is 20%. Calculate the beta
of the stock.
A) 0.9
B) 1.0
C) 1.1
D) 0.6
Answer: A
Type: Difficult
Page: 177
Response:
Cov (Rs, Rm) = (0.6)(20)(30) = 360 var(Rm)= 20^2 = 400
Beta = (Cov(Rs, Rm)) / var(Rm)= 360/400 = 0.9
44. The correlation coefficient between stock B and the market portfolio is 0.8. The standard
deviation of the stock B is 35% and that of the market is 20%. Calculate the beta of the stock.
A) 1.0
B) 1.4
C) 0.8
D) 0.7
Answer: B
Type: Difficult
Page: 177
Response: Cov(Rb Rm)= (0.8)(20)(35) = 560 Beta = 560/400 = 1.4
106
45. Historical nominal return for stock A is –8%, +10% and +22%. The nominal return for the
market portfolio is +6%, +18% and 24%. Calculate the beta for stock A.
A) 1.64
B) 0.61
C) 1.0
D) None of the above
Answer: A
Type: Difficult
Page: 177
Response: Mean A = 8%, Mean M=16%, Cov(Ra, Rm) = 138 Var (Rm) = 84 Beta=138/84=1.64
46. The three year annual return for stock B comes out to be 0%, 10% and 26%. Three year annual
returns for the market portfolios are +6%, 18%, 24%. Calculate the beta for the stock.
A) 1.36
B) 0.74
C) 0
D) None of the above
Answer: A
Type: Difficult
Page: 177
Response: Mean B = 12%, Mean M=16%, Cov(Ra, Rm) = 114 Var (Rm) = 84 Beta=114/84=1.36
True/False Questions
T
F 47. Treasury bills have provided the lowest average return between 1926-1997.
Answer: True
Type: Easy
Page: 155
T
F 48. Risk premium is the difference between the security return and the Treasury bill return.
Answer: True
Type: Easy
Page: 155
T
F 49. The standard statistical measures of spread are variance and standard deviation.
Answer: True
Type: Easy
Page: 160
107
T
F 50. Diversification reduces risk because prices of different securities do not move exactly
together.
Answer: True
Type: Easy
Page: 167
T
F 51. The risk that cannot be eliminated by diversification is called market risk.
Answer: True
Type: Medium
Page: 168
T
F 52. The risk that cannot be eliminated by diversification is called unique risk.
Answer: False
Type: Medium
Page: 168
T
F 53. The average beta of all stocks is zero.
Answer: False
Type: Medium
Page: 175
T
F 54. A portfolio with a beta of zero offers an expected return of zero.
Answer: False
Type: Medium
Page: 177
T
F 55. Beta of a well-diversified portfolio is equal to the value weighted average beta of the
securities included in the portfolio.
Answer: True
Type: Medium
Page: 177
108
Short Answer Questions
56. Define the term risk premium.
Answer: The difference between the security return and the risk free rate, such as a Treasury bill
return, is called the risk premium. This denotes the additional return on the security because of
additional risk.
Type: Medium
Page: 155
57. Briefly explain the term "variance" of the returns.
Answer: Variance is a standard statistical measure of spread. The variance is the expected
squared deviation from the expected return. From a finance point of view this measures the total
risk of a security: higher the variance, higher the risk. This is also called the measure of total risk.
Type: Medium
Page: 161
58. Briefly explain how diversification reduces risk.
Answer: Diversification reduces risk because prices of different securities do not move exactly
together. When you form portfolios using a large number of stacks the variability of the portfolio
is much less than average variability of individual stocks.
Type: Medium
Page: 168
59. In the formula for calculating the variance of N- asset portfolio, how many covariance and
variance terms are there?
Answer: In the formula for calculating the variance of N-asset portfolio, there are [N(N-1)]/2
covariance terms and N variance terms
Type: Easy
Page: 178
60. Discuss the importance of "beta" as a measure of risk.
Answer: "Beta" is a measure of market risk. It is also called relative measure of risk as it
measures risk relative to the market risk. Beta is useful as a measure of risk in the context of
well-diversified portfolios. It measures the risk contribution of a single security to the portfolio
risk.
Type: Medium
Page: 173
109
61. Briefly explain how "beta" of a stock is estimated.
Answer: "Beta" of a stock can be estimated graphically by plotting the market returns on the xaxis and the corresponding stock returns on the y-axis. The slope of the resulting linear graph is
the "beta" estimate for the stock. [i = Cov(Ri, Rm )/Var(Rm )]
Type: Medium
Page: 173
62. What is the statistical definition of "beta"?
Answer: Statistically, beta is defined as the ratio of covariance between stock returns and the
market returns, and the variance of the market returns. [[i = Cov(Ri, Rm )/Var(Rm )]
Type: Medium
Page: 175
63. Briefly explain the difference between beta as a measure of risk and variance as a measure of risk.
Answer: Variance measures the total risk of a security and is a measure of stand-alone risk. Total
risk has both unique risk and market risk. In a well-diversified portfolio, unique risks tend to
cancel each other out and only the market risk is remaining. Beta is a measure of market risk and
is useful in the context of a well-diversified portfolio. Beta measures the sensitivity of the
security returns to changes in market returns. Market portfolio has a beta of one and is
considered the average risk.
Type: Medium
Page: 176
64. Briefly explain how individual securities affect portfolio risk.
Answer: The risk of a well-diversified portfolio depends on the market risk of the securities
included in the portfolio. Portfolio beta is the weighted average of individual security betas
included in the portfolio.
Type: Medium
Page: 176
110
65. What is the beta of a portfolio with a large number of randomly selected stocks?
Answer: The beta of a portfolio with a large number of randomly selected stocks is equal to one.
The standard deviation of such a portfolio is equal to the standard deviation of the market.
Type: Medium
Page: 177
66. How can individual investors diversify?
Answer: One of the simplest ways for individual investor to diversify is to buy shares in a mutual
fund that holds a diversified portfolio.
Type: Medium
Page: 178
111