Chapter 06 Making Investment Decisions with the Net Present Value Rule Answer Key
1. Important points to remember while estimating cash flows of projects are: I) only cash flow is
relevant
II) always estimate cash flows on an incremental basis
III) be consistent in the treatment of inflation
A. I only
B. I and II only
C. II, and III only
D. I,II, and III
2. Preferably, cash flows for a project are estimated as:
A. Cash flows before taxes
B. Cash flows after taxes
C. Accounting profits before taxes
D. Accounting profits after taxes
3. When a firm has the opportunity to add a project that will utilize excess factory capacity (that is currently not being
used), which costs should be used to determine if the added project should be undertaken?
A. Opportunity cost
B. Sunk cost
C. Incremental costs
D. None of the above
4. A reduction in the sales of existing products caused by the introduction of a new product is an example of:
A. incidental effects
B. opportunity cost
C. sunk cost
D. none of the above
5. For example, when Honda develops a new engine, the incidental effects might include the following:
I) demand for replacement parts
II) profitable service facilities
III) offer modified or improved versions of the engine for other uses
A. I only
B. I and II only
C. I,II, and III
D. None of the given ones
6. 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. Opportunity cost
C. Working capital
D. None of the above
7. Net Working Capital is the:
I) short-term assets
II) short term liabilities
III) long-term assets
IV) long term liabilities
A. I only
B. (I - II)
C. (III - I)
D. (III - IV)
8. Investment in net working capital is not depreciated because:
A. It is not a cash flow
B. It is recovered during or at the end of the project and is not a depreciating asset
C. It is a sunk cost
D. All of the above
9. Net Working Capital should be considered in project cash flows because:
A. Firms must invest cash in short-term assets to produce finished goods
B. They are sunk costs
C. Firms need positive NPV projects for investment
D. None of the above
10. Investment in inventories includes investment in:
I) Raw material
II) Work-in-progress
III) Finished goods
A. I only
B. I and II only
C. I, II, and III
D. III only
11. For example, in case of an electric car project, the following cash flows should be treated as incremental flows
when deciding whether to go ahead with the project except: A. The consequent reduction in sales of the company's
existing gasoline models (i.e.: incidental effects)
B. Interest payment on debt
C. The value of tools that can be transferred from the company's existing plants D. The expenditure on
new plants and equipment
12. The principal short-term assets are:
I) Cash, II) Accounts receivable, III) Inventories, and IV) Accounts Payable A. I only
B. I and IV only
C. I, II, and III
D. IV only
13. The value of a previously purchased machine 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
14. Money that a firm has already spent or committed to spend regardless of whether a project is taken is called:
A. Fixed cost
B. Opportunity cost
C. Sunk cost
D. None of the above
15. The cost that is incurred as a result of past, irrevocable decisions and is irrelevant to future decisions is called:
A. Opportunity cost
B. Sunk cost
C. Incremental cost
D. None of the above
16. For example, in the case of an electric car project, which of the following cash flows should be treated as
incremental flows when deciding whether to go ahead with the project? A. The cost of research and development
undertaken for developing the electric car in the past three years
B. The annual depreciation charge
C. Tax savings resulting from the depreciation charges
D. Dividend payments
17. In the case of freely traded resources, opportunity cost is the:
A. book value
B. market value
C. historical value
D. none of the above
18. If the discount rate is stated in nominal terms, then in order to calculate the NPV in a consistent manner
requires that project:
I) cash flows be estimated in nominal terms
II) cash flows be estimated in real terms
III) accounting income be used
A. I only
B. II only
C. III only
D. None of the above
19. If the discount rate is stated in real terms, then in order to calculate the NPV in a consistent manner
requires that project:
I) cash flows be estimated in nominal terms
II) cash flows be estimated in real terms
III) accounting income be used
A. I only
B. II only
C. III only
D. None of the above
20. 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
21. The real interest rate is 3% and the inflation rate is 5%. What is the nominal interest rate? A. 3%
B. 5%
C. 8.15%
D. 2%
1 + nominal rate = (1 + real rate) (1 + inflation rate) = (1.03)(1.05) = (1.0815) Nominal rate = 0.0815
= 8.15%
22. If the nominal interest rate is 7. 5% and the inflation rate is 4%, what is the real interest rate?
A. 4%
B. 9.5%
C. 3.4%
D. None of the above
1 + real rate = (1 + nominal rate) / (1 + inflation rate) = 1.075/1.04 = 1.0337; real rate = 3.4%
23. A cash flow received in two years is expected to be $10,816 in nominal terms. If the real rate of interest is 2% and
the inflation rate is 4%, what is the real cash flow for year-2? A. $11,236
B. $10,816
C. $10,000
D. $9,246
Real cash flow = 10,816/(1.04^2) = 10,000
24. Given the following data for Project M:
A. $51.70
B. $35.54
C. $45.21
D. None of the above
NPV = -200 + 150/1.05 + 120/(1.05^2) = 51.70
25. Given the following data for Project M:
A. $25.85
B. $17.77
C. $22.65
D. None of the above
NPV = -100 + 75/1.1 + 60/(1.1^2) = 17.77
26. The real rate of interest is 3% and the inflation is 4%. What is the nominal rate of interest?
A. 3%
B. 4%
C. 7.12%
D. 1%
1 + nominal rate = 1.03 * 1.04 = 1.0712; nominal rate = 7.12%
27. The NPV value obtained by discounting nominal cash flows using the nominal discount rate is the:
I) same as the NPV value obtained by discounting real cash flows using the real discount rate II) same as the NPV value
obtained by discounting real cash flows using the nominal discount rate
III) same as the NPV value obtained by discounting nominal cash flows using the real discount rate
A. I only
B. II only
C. III only
D. II and III only
28. Real cash flow occurring in year-2 is $60,000. If the inflation rate is 5% per year, the real rate of interest is 2%,
calculate the cash flow for the year-2.
A. $60,000
B. $55,422
C. $66,150
D. None of the above
Nominal cash flow = (60,000)(1.05)^2 = 66,150
29. Proper treatment of inflation in the NPV calculation involves:
I) Discounting nominal cash flows using the nominal discount rate
II) Discounting real cash flows using the real discount rate
III) Discounting nominal cash flows using the real discount rates
A. I only
B. II only
C. III only
D. I and II only
30. A firm has a general-purpose machine, which has a book value of $300,000 and is sold for $500,000 in the market.
If the tax rate is 35%, what is the opportunity cost of using the machine in a project?
A. $500,000
B. $430,000
C. $300,000
D. None of the above
500,000 - (500,000 - 300,000) * 0.35 = 430,000
31. Capital equipment costing $250,000 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
Annual depreciation = (250,000 - 50,000)/5 = 40,000
Book value at the end of two years = 250,000 - 80,000 = 170,000
32. A capital equipment costing $400,000 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. $120,000
B. $80,000
C. $160,000
D. $240,000
Annual depreciation = $400,000/5 = 80,000
Depreciation for 3 years = 240,000
Book value = 400,000 - 240,000 = 160,000
33. For project Z, year-5 inventories increase by $6,000, accounts receivables by $4,000 and accounts payables by
$3,000. Calculate the increase or decrease in working capital for year-5. A. Increases by $6,000
B. Decreases by $4,000
C. Increases by $7,000
D. Decreases by $7,000
Working capital: 6000 + 4000 - 3000 = 7,000
Type: Medium
34. For project A in year-2, inventories increase by $12,000 and accounts payable by $2,000. Calculate the increase or
decrease in net working capital for year-2.
A. Decreases by $14,000
B. Increases by $14,000
C. Decreases by $10,000
D. Increases by $10,000
Working capital = 12,000 - 2000 = + 10,000
35. Working capital is one of the most common causes of misunderstanding in estimating project cash flows. The
following are the most common errors:
I) forgetting about working capital entirely
II) forgetting that working capital may change during the life of the project III) forgetting that
working capital is recovered at the end of the project IV) forgetting to depreciate the working
capital
A. I and II only
B. I, II, and III only
C. II,III and IV only
D. I,II and IV only
36. If the depreciation amount is 600,000 and the marginal tax rate is 35%, then the tax shield due to depreciation is:
A. $210,000
B. $600,000
C. $390,000
D. None of the above
Tax shield effect = (600,000)(0.35) = 210,000
37. If the depreciation amount is $100,000 and the marginal tax rate is 35%, then the tax shield due to
depreciation is:
A. $35,000
B. $100,000
C. $65,000
D. None of the above
38. If the depreciable investment is $600,000 and the MACRS 5-Year class schedule is: Year-1: 20%; Year-2: 32%;
Year-3: 19.2%; Year-4: 11.5%; Year-5: 11.5% and Year-6: 5.8% Calculate the depreciation for Year-2.
A. $120,000
B. $192,000
C. $96,000
D. $115,200
Depreciation for Year-2 = (600,000)(0.32) = 192,000
39. If the depreciable investment is $1,000,000 and the MACRS 5-Year class schedule is: Year-1: 20%; Year-2: 32%;
Year-3: 19.2%; Year-4: 11.5%; Year-5: 11.5% and Year-6: 5.8% Calculate the depreciation tax shield for Year-2 using a
tax rate of 30%: A. $224,000
B. $60,000
C. $96,000
D. $300,000
Depreciation = (1,000,000)(0.32)(0.3) = 96,000
40. 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%); (t = 2: 45%); (t = 3: 15%); (t = 4: 7%). 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: (Approximately)
A. $22,463
B. $19,315
C. $16,244
D. None of the above
-200,000 + (103,800/1.12) + ((111,000 + 44,000)/(1.12^2)) = $16,244
41. 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%); (t = 2: 45%); (t = 3: 15%); (t = 4: 7%). The company's tax
situation is such that it can make use of all applicable tax shields. The opportunity cost of capital is 11%. Assume that
the asset can be sold for book value. Calculate the IRR for the project: (approximately)
A. 12.00%
B. 11.00%
C. 17.73%
D. None of the above
0 = -200,000 + (103,800/(1 + IRR)) + (155,000/((1 + IRR)^2)) = 17.73%
42. 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. $500.00
B. $1629.62
C. $365.38
D. None of the above
NPV = [((1000/1.04) - (500/1.04)) (0.7)] / 0.1 - (3000 ) = $365.38
43. A project requires an investment of $900 today. It has sales of $1,100 per year forever. Costs will be $600 the
first year and increase by 20% per year. Ignoring taxes calculate the NPV of the project at a 12% discount rate.
A. $65.00
B. $57.51
C. $100.00
D. Cannot be calculated as g > r
NPV = -900 + (1,100 - 600)/1.12 + (1,100 - (600 * 1.2))/(1.12^2) +
(1,100 - 600 (1.2^2))/(1.12)^3 + (1,100 - 600 (1.2^3))/(1.12^4) = $57.51. (The project is stopped
when costs> revenues)
44. Which of the following countries allow firms to keep two separate sets of books, one for the stockholders and one
for the tax authorities like the Internal Revenue Service? I) U.S.A., II) Japan, and III) France
A. I only
B. I and II only
C. I, II, and III only
D. None of the above
45. Germany allows firms to choose the following depreciation methods: I) Straight-line method,
and II) Declining-balance method
A. I only
B. II only
C. I and II only
D. Germany allows a totally different system
46. Two machines, A and B, which perform the same functions, have the following costs and lives.
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
D. Accept both A and B
EAC(A) = 6,000/3.35215 = 1789.89
EAC(B) = 8000/4.1604 = 1922.88
47. Two mutually exclusive projects have the following NPVs and project lives.
If the cost of capital is 15%, which project would you accept?
A. A
B. B
C. Both A and B
D. Reject both A and B
EAC(A) = 5000/2.2832 = 2189.88 (Accept the project with higher EAC) EAC(B) =
6500/3.35216 = 1939.05
48. 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
PV (A) = 600,000 + 60,000 (3.6048) = 816,286
EAC = 816,286/(3.6048) = $226,444
PV(B) = 750,000 + 30, 000 (4.5638) = 886,913
EAC = 886,913/(4.5638) = $194,336.45 (Accept the project with least annual cost)
49. You are considering the purchase of one of two machines required in your production process. Machine A has a life
of two years. Machine A costs $50 initially and then $70 per year in maintenance. Machine B has an initial cost of $90.
It requires $40 in maintenance for each year of its 3 year life. Either machine must be replaced at the end of its life.
Which is the better machine for the firm? The discount rate is 15% and the tax rate is zero. A. Machine A as EAC for
Machine A is $100.76
B. Machine B as EAC for Machine B is $79.42
C. Machine A as PV of costs for Machine A is $163.80
D. Machine B as PV of costs for Machine B is $181.33
Costs: PV(A) = 50 + 70/1.15 + 70/(1.15^2) = 163.80; EAC = 163.80/(1.6257) = 100.76 PV(B) = 90 + 40/1.15 +
40/(1.15^2) + 40/(1.15^3) = 181.33; EAC = 181.33/2.2832 = 79.42 (Accept the project with least annual cost)
50. RainMan Inc. is in the business of producing rain upon request. They must decide between two investment
projects; a new airplane for seeding rain clouds or a new weather control machine built by Dr. Nutzbaum. The
discount rate for the new airplane is 9%, while the discount rate for the weather machine is 39% (it happens to be
higher risk). Which investment should the company select and why?
A. Airplane because is has a higher NPV
B. Weather machine because is has a higher NPV
C. Airplane because is has a higher annuity
D. Weather machine because is has a higher annuity
NPV of the airplane is 63.72 and the EAA of the airplane is 36.22
NPV of the weather machine is 61.29 and the EAA of the machine is 38.08 Since they have different life spans the
weather machine has a higher EAA and should be accepted.
51. Using the technique of equivalent annual cash flows and a discount rate of 7%, what is the value of the following
project?
A. 3.06
B. 3.61
C. 10.25
D. 12.23
NPV of the project is 12.23 and the EAA of the airplane is 3.61
chapter 07 Introduction to Risk and Return Answer Key
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. Portfolio of U.S. common stocks of small firms
D. None of the above
2. Long-term U.S. government bonds have:
A. Interest rate risk
B. Default risk
C. Market risk
D. None of the above
3. What has been the average annual real rate of interest on Treasury bills over the past 107 years (from 1900 to
2006)?
A. Less than 1%
B. Between 1% and 2%
C. Between 2% and 3%
D. Greater than 3%
4. What has been the average annual nominal rate of interest on Treasury bills over the past 107 years (1900 - 2006)?
A. Less than 1%
B. Between 1% and 2%
C. Between 2% and 3%
D. Greater than 3%
5. What has been the average annual nominal rate of return on a portfolio of U.S. common stocks over the past 107
years (from 1900 to 2006)?
A. Less than 2%
B. Between 2% and 5%
C. Between 5% and 11%
D. Greater than 11%
6. One dollar invested in a portfolio of U.S. government bonds in 1900 would have grown in nominal value by the end
of year 2006 to:
A. $719
B. $66
C. $176
D. $2.80
7. One dollar invested in a portfolio of U.S. common stocks in 1900 would have grown in nominal value by the end
of year 2006 to:
A. $21,536
B. $176
C. $719
D. $6.81
8. What has been the average annual rate of return in real terms for a portfolio of U.S. common stocks between 1900 and
2006?
A. Less than 2%
B. Between 2% and 5%
C. Between 5% and 8%
D. Greater than 8%
9. Which portfolio has had the lowest average annual nominal rate of return during the 1900- 2006 periods?
A. Portfolio of U.S. Common stocks
B. Portfolio of U.S. government bonds
C. Portfolio of Treasury bills
D. None of the given answers
10. Which portfolio had the highest average annual return in real terms between 1900 and 2006?
A. Portfolio of U.S. Common stocks
B. Portfolio of U.S. government bonds
C. Portfolio of Treasury bills
D. None of the given answers
11. Standard error measures:
A. Nominal annual rate of return on a portfolio
B. Risk of a portfolio Reliability of an estimate
C. Reliability of an estimate
D. Real annual rate of return on a portfolio
12. Standard error is estimated as:
A. Average annual rate of return divided by the square root of the number of observations B. Variance divided by
the number of observations
C. Standard deviation of returns divided by the square root of the number of observations D. None of the above
13. Which portfolio has had the highest average risk premium during the period 1900-2006? A. Common stocks
B. Government bonds
C. Treasury bills
D. None of the given answers
14. If the standard deviation is 19.8% and the number of observations is 107, what is the standard error?
A. 4.23 %
B. 1.9%
C. 0.47%
D. None of the above
Standard error = 19.8/√107 = 1.9%
15. If the average annual rate of return for common stocks is 11.7%, and for treasury bills it is 4.0%, what is the market
risk premium?
A. 15.8%
B. 4.1%
C. 7.7%
D. None of the above
Average risk premium: 11.7 - 4.0 = 7.7%
16. Spill Oil Company's stocks had -8%, 11% and 24% rates of return during the last three years respectively;
calculate the average rate of return for the stock.
A. 8% per year
B. 9% per year
C. 11% per year
D. None of the above
Average rate of return = (-8 + 11 + 24)/3 = 9%
17. For log-normally distributed returns the annul compound returns is equal to: A. the arithmetic
average returns minus half the variance
B. the arithmetic average returns plus half the variance
C. the arithmetic average returns minus half the standard deviation
D. the arithmetic average returns plus half the standard deviation
18. Which of the following provides a correct measure of the opportunity cost of capital regardless of the timing
of the cash flows?
A. Arithmetic average
B. Geometric average
C. Hyperbolic mean
D. None of the above
19. Given the following data: risk-free rate = 4%, average risk premium = 7.7%. Calculate the required
rate of return:
A. 5.6%
B. 7.6%
C. 11.7%
D. None of the given answers
20. Which of the following countries had the lowest risk premium? A. U.S.A
B. Denmark
C. Italy
D. none of the above
21. Which of the following countries had the highest risk premium? A. Germany
B. Denmark
C. Italy
D. None of the above
22. Mega Corporation has the following returns for the past three years: 8%, 12% and 10%. Calculate the variance of
the return and the standard deviation of the returns. A. 64 and 8%
B. 124 and 11.1%
C. 4 and 2%
D. None of the above
Mean = (8 + 12 + 10)/3 = 10%; Variance = [(8 - 10)^2 + (12 - 10)^2 + (10 - 10)^2]/(3 - 1) = 4;
Standard deviation = 4^(1/2) = 2%
Type: Difficult
23. Macro Corporation has had the following returns for the past three years, -10%, 10%, and 30%. Calculate the
standard deviation of the returns.
A. 10%
B. 20%
C. 30%
D. None of the above
Mean = (-10 + 10 + 30)/3 = 10%;
Variance = [(-10 - 10)^2 + (10 - 10)^2 + (30 - 10)^2]/2 = 400;
Standard deviation = 20%
Type: Difficult
24. Sun Corporation has had returns of -6%, 16%, 18%, and 28% for the past four years. Calculate the standard
deviation of the returns.
A. 11.6%
B. 14.3%
C. 13.4 %
D. None of the above
(-6 + 16 + 18 + 28)/4 = 14%;
Variance = [(-6 - 14)^2 + (16 - 14)^2 + (18 - 14)^2 + (28 - 14)^2]/(4 - 1) = 205.33; Standard deviation =
180.7^(1/2) = 14.3%
25. Which portfolio had the highest standard deviation during the period between 1900 and 2006?
A. Common stocks
B. Government bonds
C. Treasury bills
D. None of the given answers
26. What has been the standard deviation of returns of common stocks during the period between 1900 and 2006?
A. 19.8%
B. 33.4%
C. 8.1%
D. 7.8%
27. The standard deviation of the UK market during the period from 2001 through 2006 was: (Approximately)
A. 12.3%
B. 14.1%
C. 9.8%
D. None of the above
28. A statistical measure of the degree to which securities' returns move together is called: A. Variance
B. Correlation Coefficient
C. Standard Deviation
D. None of the above
29. The type of the risk that can be eliminated by diversification is called:
A. Market risk
B. Unique risk
C. Interest rate risk
D. Default risk
30. The unique risk is also called the:
A. Unsystematic risk
B. Diversifiable risk
C. Firm specific risk
D. All of the above
31. Market risk is also called:
I) systematic risk, II) undiversifiable risk, III) firm specific risk.
A. I only
B. II only
C. III only
D. I and II only
32. Stock A has an expected return of 10% per year and stock B has an expected return of 20%. If 40% of the funds are
invested in stock A, and the rest in stock B, what is the expected return on the portfolio of stock A and stock B?
A. 10%
B. 20%
C. 16%
D. None of the above
0.40(10) + 0.60(20) = 16%
33. As the number of stocks in a portfolio is increased:
A. Unique risk decreases and approaches to zero
B. Market risk decreases
C. Unique risk decreases and becomes equal to market risk
D. Total risk approaches to zero
34. Stock M and Stock N have had the following returns for the past three years of -12%, 10%, 32%; and 15%,
6%, 24% respectively. Calculate the covariance between the two securities.
A. -99
B. +99
C. +250
D. None of the above
E(RM ) = (-12 + 10 + 32)/3 = 10%
E(RN) = (6 + 15 + 24)/3 = 15%
Cov(RM, RN) = [(-12 - 10)(15 - 15) + (10 - 10)(6 - 15) + (32 - 10)(24 - 15)]/(3 - 1) = 99
Type: Difficult
35. 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
E(P) = (-10 + 12 + 28)/3 = 10%; E(Q) = (8 + 13 + 24)/3 = 15%
Cov(P,Q) = [(-10 - 10)(8 - 15) + (12 - 10) (13 - 15) + (28 - 10)(24 - 15)]/2 = 149
36. 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. None of the above
(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%
37. 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. +450
D. None of the above
Cov(RC, RD) = (+1)(30)(15) = +450
38. The range of values that correlation coefficients can take can be: A. zero to +1
B. -1 to +1
C. - infinity to +infinity
D. zero to + infinity
39. 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
Corr(RA, RB) = 100/(10 * 20) = +0.5
40. For a two-stock portfolio, the maximum reduction in risk occurs when the correlation coefficient between the
two stocks is:
A. +1
B. -0.5
C. -1
D. 0
41. In the case of a portfolio of N-stocks, the formula for portfolio variance contains: A. N variance terms
B. N(N - 1)/2 variance terms
C. N2 variance terms
D. None of the above
42. In the case of a portfolio of N-stocks, the formula for portfolio variance contains: A. N covariance terms
B. N(N - 1)/2 covariance terms
C. N2 covariance terms
D. None of the above
43. The "beta" is a measure of:
A. Unique risk
B. Total risk
C. Market risk
D. None of the above
44. The beta of market portfolio is:
A. + 1.0
B. +0.5
C. 0
D. -1.0
45. For each additional 1% change in the market return, Amazon stock return on the average changes by:
A. 1.26%
B. 1.59%
C. 2.2%
D. None of the above
46. The beta of Nestle measured relative to its home market is:
A. 0.17
B. 1.54
C. 1.01
D. none of the above
47. 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. 30%
B. 20%
C. 10%
D. none of the above
Standard deviation of the portfolio = (1.5) * (20) = 30%
48. 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. 1.1
B. 1.0
C. 0.9
D. 0.6
Cov (Rs, Rm) = (0.6)(20)(30) = 360; var(Rm) = 20^2 = 400
Beta = [Cov(Rs, Rm)]/var(Rm) = 360/400 = 0.9
49. 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
Mean A = 8%; Mean M = 16%; Cov(Ra, Rm) = 138; Var(Rm) = 84;
Beta = 138/84 = 1.64
50. The annual return for three years for stock B comes out to be 0%, 10% and 26%. Annual returns for three years for
the market portfolios are +6%, 18%, 24%. Calculate the beta for the stock.
A. 0.74
B. 1.36
C. 1.0
D. None of the above
Mean B = 12%, Mean M = 16%, Cov(Ra, Rm) = 114; Va (Rm) = 84;
Beta = 114/84 = 1.36
51. 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
Cov(Rb,Rm) = (0.8)(20)(35) = 560; Beta = 560/400 = 1.4
52. The covariance between YOHO stock and the S&P 500 is .05. The standard deviation of the stock market is 20%.
What is the beta of YOHO?
A. 0.00
B. 1.00
C. 1.25
D. 1.42
Beta = .05/(.2 ⋅ .2) = 1.25
Chapter 08 Portfolio Theory and the Capital Asset Pricing Model
1. Portfolio Theory was first developed by:
A. Merton Miller
B. Richard Brealey
C. Franco Modigliani
D. Harry Markowitz
2. The distribution of returns, measured over a short interval of time, like daily returns, can be approximated by:
A. Normal distribution
B. Lognormal distribution
C. Binomial distribution
D. none of the above
3. The distribution of returns, measured over long intervals, like annual returns, can be approximated by
A. Normal distribution
B. Binomial distribution
C. Lognormal distribution
D. none of the above
4. Normal and lognormal distributions are completely specified by:
I) mean
II) standard deviation
III) third moment
A. I only
B. I and II only
C. II only
D. III only
5. Florida Company (FC) and Minnesota Company (MC) are both service companies. Their historical return for the
past three years are: FC: - 5%, 15%, 20%; MC: 8%, 8%, 20%. Calculate the mean of returns for each company.
A. FC: 12%, MC: 6%
B. FC: 10%, MC: 12%
C. FC: 20%, MC: 32%
D. None of the above
R(FC) = ( - 5 + 15 + 20)/3 = 10%; R(MC) = (8 + 8 + 20)/3 = 12%
6. Florida Company (FC) and Minnesota Company (MC) are both service companies. Their historical return for the
past three years are: FC: -5%, 15%, 20%; MC: 8%, 8%, 20%. Calculate the variances of return for FC and MC.
A. FC: 100 MC: 256
B. FC: 350 MC: 96
C. FC: 175 MC: 48
D. None of the above
Var(FC) = [( -5 - 10)^2 + (15 - 10)^2 + (20 - 10)^2]/(3 - 1) = 175
Var(MC) = [(8 - 12)^2 + (8 - 12)^2 + (20 - 12)^2]/(3 - 1) = 48
7. Florida Company (FC) and Minnesota Company (MC) are both service companies. Their historical return for the
past three years are: FC: - 5%, 15%, 20%; MC: 8%, 8%, 20%. Calculate the covariance between the returns of FC
and MC.
A. 60
B. 80
C. 40
D. None of the above
[( -5 - 10)(8 - 12) + (15 - 10)(8 - 12) + (20 - 10)(20 - 12)]/(3 - 1) = 60
Type: Medium
8. Florida Company (FC) and Minnesota Company (MC) are both service companies. Their historical return for the
past three years are: FC: - 5%, 15%, 20%; MC: 8%, 8%, 20%. Calculate the standard deviation (S.D.) of return for
FC and MC.
A. FC: 10% MC: 12%
B. FC: 18.7% MC: 9.8%
C. FC: 13.2% MC: 6.9%
D. None of the above
Standard Deviation(FC) = 175^0.5 = 13.2%;
Standard Deviation(MC) = 48 ^0.5 = 6.9%.
9. Florida Company (FC) and Minnesota Company (MC) are both service companies. Their historical return for the
past three years are: FC: - 5%, 15%, 20%; MC: 8%, 8%, 20%. Calculate the correlation coefficient between the return
of FC and MC. A. 0.0
B. -0.655
C. +0.655
D. None of the above
Correlation Coefficient = Covariance/[(S.D.(FC)) * (S.D.(MC))] = 60/(13.2 * 6.9) = +0.655
10. Florida Company (FC) and Minnesota Company (MC) are both service companies. Their historical return for the
past three years are: FC: - 5%, 15%, 20%; MC: 8%, 8%, 20%. If FC and MC are combined in a portfolio with 50% of
the funds invested in each, calculate the expected return on the portfolio.
A. 12%
B. 10%
C. 11%
D. None of the above.
Rp = (10)(0.5) + (12)(0.5) = 11%
11. Florida Company (FC) and Minnesota Company (MC) are both service companies. Their historical return for the
past three years are: FC: - 5%, 15%, 20%; MC: 8%, 8%, 20%. What is the variance of the portfolio with 50% of the
funds invested in FC and 50% in MC (approximately)?
A. 85.75
B. 111.50
C. 55.75
D. None of the above
Var(P) = (0.5^2)(175) + (0.5^2)(48) + (2)(0.5)(0.5)(60) = 85.75
12. Florida Company (FC) and Minnesota Company (MC) are both service companies. Their historical return for the
past three years are: FC: - 5%, 15%, 20%; MC: 8%, 8%, 20%. What is the standard deviation of the portfolio with 50%
of the funds invested in FC and 50% in MC? A. 10.6%
B. 14.4%
C. 9.3%
D. None of the above
S.D. = (85.75)^0.5 = 9.3%
13. Investments A and B both offer an expected rate of return of 12%. If the standard deviation of A is 20%
and that of B is 30%, then investors would:
A. Prefer A to B
B. Prefer B to A
C. Prefer a portfolio of A and B
D. Cannot answer without knowing investor's risk preferences
14. Investments B and C both have the same standard deviation of 20%. If the expected return on B is 15% and that of
C is 18%, then the investors would
A. Prefer B to C
B. Prefer C to B
C. Reject both B and C
D. None of the above
15. The efficient portfolios:
I) have only unique risk
II) provide highest returns for a given level of risk
III) provide the least risk for a given level of returns
IV) have no risk at all
A. I only
B. II and III only
C. IV only
D. II only
16. In practice, efficient portfolios are generated using:
A. regression analysis
B. quadratic programming
C. trial and error method
D. graphical method
17. By combining lending and borrowing at the risk-free rate with the efficient portfolios, we can I) extend the range
of investment possibilities
II) change an efficient set of portfolios from being curvilinear to a straight line. III) provide a higher expected
return for any level of risk except the tangential portfolio A. I only
B. I and II only
C. I, II, and III
D. none of the above
18. Suppose you invest equal amounts in a portfolio with an expected return of 16% and a standard
deviation of returns of 20% and a risk-free asset with an interest rate of 4%; calculate the expected
return on the resulting portfolio:
A. 10%
B. 4%
C. 12%
D. none of the above
Expected return = 0.5(16) + 0.5(4) = 10%
19. Suppose you invest equal amounts in a portfolio with an expected return of 16% and a standard deviation of returns
of 20% and a risk-free asset with an interest rate of 4%; calculate the standard deviation of the returns on the resulting
portfolio:
A. 8%
B. 10%
C. 20%
D. none of the above
Standard deviation = 0.5(20) = 10%
20. Suppose you borrow at the risk-free rate an amount equal to your initial wealth and invest in a portfolio with an
expected return of 16% and a standard deviation of returns of 20%. The risk-free asset has an interest rate of 4%;
calculate the expected return on the resulting portfolio:
A. 20%
B. 32%
C. 28%
D. none of the above
Expected return = 2(16) - (4) = 28%
21. Suppose you borrow at the risk-free rate an amount equal to your initial wealth and invest in a portfolio with an
expected return of 20% and a standard deviation of returns of 16%. The risk-free asset has an interest rate of 4%;
calculate standard deviation of the resulting portfolio:
A. 28%
B. 40%
C. 32%
D. none of the above
Standard Deviation = 2(20) = 40%
22. If the covariance of Stock A with Stock B is - 100, what is the covariance of Stock B with Stock A?
A. +100
B. -100
C. 1/100
D. Need additional information
23. The correlation measures the:
A. Rate of movements of the return of individual stocks
B. Direction of movement of the return of individual stocks
C. Direction of movement between the returns of two stocks
D. Stock market volatility
24. If the correlation coefficient between Stock A and Stock B is +0.6, what is the correlation between Stock B with
Stock A?
A. +0.6
B. -0.6
C. +0.4
D. -0.4
25. The correlation between the efficient portfolio and the risk-free asset is: A. +1
B. -1
C. 0
D. cannot be calculated
26. In the presence of a risk-free asset, the investor's job is to: I) invest in the market
portfolio
II) find an interior portfolio using quadratic programming III) borrow or lend at
the risk-free rate
IV) read and understand Markowitz's portfolio theory A. I and II only
B. I and III only
C. II and IV only
D. IV only
27. Sharpe ratio is defined as:
A. (rP - rf)/σP
B. (rP - rM)/σP
C. (rP - rf)/bP
D. none of the above
28. Beta of Treasury bills is:
A. +1.0
B. +0.5
C. -1.0
D. 0
29. Beta of the market portfolio is:
A. Zero
B. +0.5
C. -1.0
D. +1.0
30. The capital asset pricing model (CAPM) states that:
A. The expected risk premium on an investment is proportional to its beta B. The expected rate of return on an
investment is proportional to its beta C. The expected rate of return on an investment depends on the risk-free rate and
the market rate of return
D. The expected rate of return on an investment is dependent on the risk-free rate
31. The graphical representation of CAPM (Capital Asset Pricing Model) is called: A. Capital Market Line
B. Characteristic Line
C. Security Market Line
D. None of the above
32. Beta measure indicates:
A. The ability to diversify risk
B. The change in the rate of return on an investment for a given change in the market return C. The actual return on
an asset
D. A and C
33. The security market line (SML) is the graph of:
A. Expected rate on investment (Y-axis) vs. variance of return
B. Expected return on investment vs. standard deviation of return
C. Expected rate of return on investment vs. beta
D. A and B
34. If the beta of Microsoft is 1.13, risk-free rate is 3% and the market risk premium is 8%, calculate the expected
return for Microsoft.
A. 12.04%
B. 15.66%
C. 13.94%
D. 8.65%
E(R) = 3 + 1.13(8) = 12.04%
35. If the beta of Amazon.com is 2.2, risk-free rate is 5.5% and the market risk premium is 8%, calculate the
expected rate of return for Amazon.com stock:
A. 15.8%
B. 14.3%
C. 35.2%
D. 23.1%
Beta = 5.5 + (2.2)(8) = 23.1% 36. If the beta of Exxon Mobil is 0.65, risk-free rate is 4% and the market rate of return is
14%, calculate the expected rate of return from Exxon:
A. 12.6%
B. 10.5%
C. 13.1%
D. 6.5%
Beta = 4 + 0.65(14 - 4) = 8.7%
37. A stock with a beta of zero would be expected to:
A. Have a rate of return equal to zero
B. Have a rate of return equal to the market risk premium
C. Have a rate of return equal to the risk-free rate
D. Have a rate of return equal to the market rate of return
38. A stock with a beta of 1. 25 would be expected to:
A. Increase in returns 25% faster than the market in up markets
B. Increase in returns 25% faster than the market in down markets C. Increase in returns
125% faster than the market in up markets D. Increase in returns 125% faster than the
market in down markets
39. If the market risk premium is (rm - rf) is 8%, then according to the CAPM, the risk premium of a stock with
beta value of 1.7 must be:
A. less than 12%
B. 12%
C. greater than 12%
D. cannot be determined
40. The main shortcoming of CAPM is that it
A. ignores the return on the market portfolio
B. uses too many factors
C. requires a single risk measure of systematic risk
D. ignores risk-free rate of return
41. If a stock is overpriced it would plot:
A. Above the security market line
B. Below the security market line
C. On the security market line
D. On the Y-axis
42. If a stock is under priced it would plot:
A. Above the security market line
B. Below the security market line
C. On the security market line
D. On the Y-axis
43. Given the following data for a stock: beta = 1.5; risk-free rate = 4%; market rate of return = 12%; and Expected
rate of return on the stock = 15%. Then the stock is: A. overpriced
B. under priced
C. correctly priced
D. cannot be determined
r = 4 + (1.5) * (12 - 4) = 16%; the expected rate of return is less than the required rate of return. The stock is
overpriced.
44. Given the following data for a stock: beta = 0.5; risk-free rate = 4%; market rate of return = 12%; and Expected
rate of return on the stock = 10%. Then the stock is: A. overpriced
B. under priced
C. correctly priced
D. cannot be determined
r = 4 + (0.5) * (12 - 4) = 8%; the expected rate of return is more than the required rate of return. The stock is
under priced.
45. Given the following data for a stock: beta = 0.9; risk-free rate = 4%; market rate of return = 14%; and Expected
rate of return on the stock = 13%. Then the stock is: A. overpriced
B. under priced
C. correctly priced
D. cannot be determined
r = 4 + (0.9) * (14 - 4) = 13%; the expected rate of return is equal to the required rate of return. The stock is
correctly priced.
46. A "factor" in APT is a variable that:
A. is pure "noise"
B. correlates with risky asset returns in an unsystematic manner
C. affects the return of risky assets in a systematic manner
D. affects the return of a risky asset in a random manner
47. Given the following data for a stock: risk-free rate = 4%; factor-1 beta = 1.5; factor-2 beta = 0.5; factor-1
risk-premium = 8%; factor-2 risk-premium = 2%. Calculate the expected rate of return on the stock using the two-factor
APT model.
A. 13%
B. 17%
C. 10%
D. none of the above
r = 4 + (1.5) * (8) + (0.5) * (2) = 17%
48. The three factors in the Three-Factor Model are:
I) Market factor
II) Size factor
III) Book-to-market factor
A. I only
B. I and II only
C. I,II, and III
D. III only
49. Given the following data for the a stock: risk-free rate = 5%; beta (market) = 1.5; beta (size) = 0.3; beta
(book-to-market) = 1.1; market risk premium = 7%; size risk premium = 3.7%; and book-to-market risk premium =
5.2%. Calculate the expected return on the stock using the Fama-French three-factor model.
A. 22.3%
B. 7.8%
C. 11.5%
D. none of the above
Expected return = 5 + (1.5) * (7) + (0.3) * (3.7) + (1.1) * (5.2) = 22.3%
50. Given the following data for the a stock: risk-free rate = 5%; beta (market) = 1.4; beta (size) = 0.4; beta
(book-to-market) = -1.1; market risk premium = 7%; size risk premium = 3.7%; and book-to-market risk premium =
5.2%. Calculate the expected return on the stock using the Fama-French three-factor model.
A. 22.3%
B. 7.8%
C. 10.6%
D. none of the above
Expected return = 5 + (1.4) * (7) + (0.4) * (3.7) + ( - 1.1) * (5.2) = 10.6%
51. How does an investor earn more than the return generated by the tangency portfolio and still stay on the security
market line?
A. Borrow at the risk free rate and invest in the tangency portfolio.
B. Add high risk/return assets to the portfolio.
C. Adjust the weight of stock in the portfolio to include more high return stocks. D. It cannot be done.
52. For a company like Alcoa, what is likely to be the major factor when developing an arbitrage pricing model?
A. Asset price of stocks
B. Commodity price of aluminum
C. GDP
D. Inflation
Chapter 09 Risk and the Cost of Capital Answer Key
Multiple Choice Questions
1. The company cost of capital is the appropriate discount rate for a firm's: A. low risk projects
B. high risk projects
C. average-risk projects
D. all of the above
2. Cost of capital is the same as cost of equity for firms: A. financed entirely
by debt
B. financed by both debt and equity
C. financed entirely by equity
D. none of the above
3. The cost of capital for a project depends on:
A. The company's cost of capital
B. The use to which the capital is put, i.e. the project
C. The industry cost of capital
D. All of the above
4. Using the company cost of capital to evaluate a project is:
I) Always correct
II) Always incorrect
III) Correct for projects that are about as risky as the average of the firm's other assets A. I only
B. II only
C. III only
D. I and III only
5. If a firm uses the same company cost of capital for evaluating all projects, which of the following is likely?
I) Rejecting good low risk projects
II) Accepting poor high risk projects
III) Correctly accept projects with average risk
A. I only
B. I and II only
C. I, II, and III
D. II only
6. If firms use the company cost of capital for evaluating all of their projects, which of the following is likely?
I) Accepting poor low risk projects.
II) Rejecting good high risk projects.
III) Correctly accept projects with average risk.
A. I only
B. II only
C. III only
D. I,II and III
7. Which of the following types of projects have the highest risk? A. Speculation
ventures
B. New products
C. Expansion of existing business
D. Cost improvement, (known technology)
8. A firm might categorize its projects into:
I) Cost improvement projects
II) Expansion projects (existing business)
III) New products projects
IV) Speculative ventures
A. III only
B. I, II and III only
C. II and IV only
D. I,II,III, and IV
9. Which of the following type of projects has the lowest risk? A. Speculation
ventures
B. New products
C. Expansion of existing business
D. Cost improvement
Type: Easy
10. Which of the following type of projects has average risk? A. Speculation
ventures
B. New products
C. Expansion of existing business
D. Cost improvement
11. The market value of Charter Cruise Company's equity is $15 million, and the market value of its risk-free debt is
$5 million. If the required rate of return on the equity is 20% and that on the debt is 8%, calculate the company's cost
of capital. (Assume no taxes.) A. 20%
B. 17%
C. 14%
D. None of the above
Company cost of capital = (5/20)(8) + (15/20)(20) = 17%
12. The market value of Cable Company's equity is $60 million, and the market value of its risk-free debt is $40
million. If the required rate of return on the equity is 15% and that on the debt is 5%, calculate the company's cost of
capital. (Assume no taxes.) A. 15%
B. 10%
C. 11%
D. None of the above
Company cost of capital = (40/100)(5) + (60/100)(15) = 11%
13. The hurdle rate for capital budgeting decisions is:
A. The cost of capital
B. The cost of debt
C. The cost of equity
D. All of the above
14. The company cost of capital when debt as well as equity is used for financing is: A. cost of debt
B. cost of equity
C. the weighted average cost of capital (WACC)
D. none of the above 15. The after-tax weighted average cost of capital (WACC) is calculated using the formula: A.
WACC = (rD) (D/V) + (rE) (E/V) where: V = D + E
B. WACC = (rD) (1 - TC ) (D/V) + (rE) (E/V) where: V = D + E
C. WACC = (rD) (D/E) + (rE) (E/D)
D. none of the above
16. The market value of Charcoal Corporation's common stock is $20 million, and the market value of its risk-free debt
is $5 million. The beta of the company's common stock is 1.25, and the market risk premium is 8%. If the Treasury bill
rate is 5%, what is the company's cost of capital? (Assume no taxes.)
A. 15%
B. 14.6%
C. 13%
D. None of the above
rE = 5 + 1.25(8) = 15 ; rD = 5%
Company Cost of capital = 5 (5/25) + 15(20/25) = 1 + 12 = 13%
17. The market value of XYZ Corporation's common stock is 40 million and the market value of the risk-free debt is 60
million. The beta of the company's common stock is 0.8, and the expected market risk premium is 10%. If the Treasury
bill rate is 6%, what is the firm's cost of capital? (Assume no taxes.)
A. 9.2%
B. 14%
C. 8.1%
D. None of the above
rE = 6 + 0.8(10) = 14%; rD = 5%; Cost of capital = (0.6)(6) + (0.4) (14) = 9.2%
18. Cost of equity can be estimated using:
A. Discounted cash flow (DCF) approach
B. Capital Asset Pricing Model (CAPM)
C. Arbitrage Pricing theory (APT)
D. All of the above
19. Cost of equity can be estimated using:
A. The Fama-French three-factor model
B. Capital Asset Pricing Model (CAPM)
C. Arbitrage Pricing theory (APT)
D. All of the above
20. The historical returns data for the past three years for Company A's stock is -6%, 15%, 15% and that of the
market portfolio is 10%, 10% and 16%. Calculate the beta for Stock A. A. 1.75
B. 1.0
C. 0.57
D. None of the above
Beta: = Cov(RA, RM)/Var(RM) = 21/12 = 1.75
21. The historical returns data for the past three years for Company A's stock is -6.0%, 15%, 15% and that of the
market portfolio is 10%, 10% and 16%. If the risk-free rate of return is 4%, what is the cost of equity capital (required
rate of return of company A's common stock) using CAPM?
A. 18%
B. 14%
C. 12%
D. None of the above
rM = (10 + 10 + 16)/3 12% ; r = 4 + 1.75 (12 - 4) = 18%
22. The historical data for the past three years for the market portfolio are 10%, 10% and 16%. If the risk-free rate
of return is 4%, what is the market risk premium? A. 4%
B. 8%
C. 16%
D. None of the above
rM = (10 + 10 + 16)/3 = 12%; RPM = (12 - 4)= 8%
23. The historical returns data for the past three years for Company A's stock is -6.0%, 15%, 15% and that of the
market portfolio is 10%, 10% and 16%. According to the security market line (SML), the Stock A is:
A. Over priced
B. Under priced
C. Correctly priced
D. Need more information
(-6 + 15 + 15)/3 = 8%; (8% < 18%)
24. The historical returns data for the past three years for Stock B and the stock market portfolio are: Stock B:
24%, 0%, 24%, Market Portfolios: 10%, 12%, 20%. Calculate the expected return for Stock B and the market
portfolio.
A. Stock B 16%, Market Portfolio: 14%
B. Stock B 14%, Market Portfolio: 16%
C. Stock B 24%, Market Portfolio: 12%
D. None of the above
RB = (24 + 0 + 24)/3 = 16%; RM = (10 + 12 + 20)/3 = 14%
25. The historical returns data for the past three years for Stock B and the stock market portfolio are: Stock B:
24%, 0%, 24%, Market Portfolios: 10%, 12%, 20%. Calculate the variance of the market portfolio returns.
A. 192
B. 128
C. 28
D. None of the above
Variance = [(10 - 14)^2 + (12 - 14)^2 + (20 - 14)^2]/2 = 28
26. The historical returns data for the past three years for Stock B and the stock market portfolio are: Stock B:
24%, 0%, 24%, Market Portfolios: 10%, 12%, 20%. Calculate the covariance of returns between Stock B and the
market portfolio.
A. 24
B. 28
C. 292
D. None of the above
Cov(RB, RM) = (24 - 16)(10 - 14) + (0 - 16)(12 - 14) + (24 - 16)(20 - 14)]/2 = 24
27. The historical returns data for the past three years for Stock B and the stock market portfolio are: Stock B: 24%,
0%, 24%, Market Portfolios: 10%, 12%, 20%. Calculate the beta for Stock B.
A. 0.86
B. 1.0
C. 0.125
D. None of the above
beta(b) = 24/28 = 0.86
[Statistical functions in a calculator may be used for this estimation]
28. The historical returns data for the past three years for Stock B and the stock market portfolio are: Stock B: 24%,
0%, 24%, Market Portfolios: 10%, 12%, 20%. If the risk-free rate is 4%, calculate the market risk premium.
A. 18.1%
B. 14%
C. 10%
D. None of the above
rM = (10 + 12 + 20)/3 = 8%; Market risk premium = 14 - 4 = 10%
29. On a graph with common stock returns on the Y- axis and market returns on the X-axis, the slope of the
regression line represents the:
A. Alpha
B. Beta
C. R-squared
D. Adjusted beta
30. The historical returns data for the past three years for Stock B and the stock market portfolio are: Stock B: 24%,
0%, 24%, Market Portfolios: 10%, 12%, 20%. Calculate the required rate of return (cost of equity) for Stock B using
CAPM. (The risk-free rate of return = 4%)
A. 8.6%
B. 12.6%
C. 14.3%
D. None of the above
E(RB) = 4 + 0.86(14 - 4) = 12.6%
31. The historical returns data for the past four years for Stock C and the stock market portfolio returns are: Stock C:
10%, 30%, 20%,20%; Market Portfolio: 5%, 15%, 25%, 15%. Calculate the beta for the stock:
A. 0.86
B. 0.5
C. 1.5
D. none of the above
32. The historical returns data for the past four years for Stock C and the stock market portfolio returns are: Stock C:
10%, 30%, 20%, 20%; Market Portfolio: 5%, 15%, 25%, 15%. If the risk-free rate of return is 5%, calculate the
required rate of return on the Stock C using CAPM.
A. 5%
B. 10%
C. 15%
D. none of the above
RM = (5 + 15 + 25 + 15)/4 = 15%; RC = 5 + (0.5)(15 - 5) = 10%
33. The beta of the computer company is 1.7 and the standard error of the estimate is 0.3. What is the range of
values for beta, that has 95% chance of being right? A. 1.1 - 2.3
B. 1.4 - 2.0
C. 1.5 - 2.0
D. None of the above
Range = 1.7 +/- 2(0.3) i.e. (1.1 - 2.3)
34. Generally, the value to use for the risk-free interest rate is:
A. Short-term Treasury bill rate
B. Long-term Corporate bond rate
C. Medium-term Corporate bond rate
D. none of the above
35. A project has an expected risky cash flow of $200, in year-1. The risk-free rate is 6%, the market rate of return is
16%, and the project's beta is 1.5. Calculate the certainty equivalent cash flow for year-1.
A. $175.21
B. $164.29
C. $228.30
D. None of the above
rw = 6 + 1.5(10) = 21%; CEQ = (200 * 1.06)/1.21 = 175.21
36. A project has an expected risky cash flow of $500, in year-2. The risk-free rate is 4%, the market rate of return is
14%, and the project's beta is 1.2. Calculate the certainty equivalent cash flow for year-2.
A. $622.04
B. $164.29
C. $401.90
D. None of the above
rw = 4 + 1.2(10) = 16%; CEQ = (500 * 1.04^2)/ (1.16^2) = 401.90
37. The risk-free rate is 4%, the market rate of return is 14%, and the project's beta is 1.2. Calculate the certainty
equivalent cash flow for year-3.
A. $622.04
B. $360.33
C. $401.90
D. None of the above
rw = 4 + 1.2(10) = 16%; CEQ = (500 * 1.04^3)/ (1.16^3) = 360.33
38. The risk-free rate is 5%, the market risk premium is 8% and the project's beta is 1.25. Calculate the certainty
equivalent cash flow for
year-3.
A. $228.35
B. $197.25
C. $300
D. None of the above
rw = 5 + (1.25 * 8) = 15% CF = 300(1.05)^3/(1.15^3) = 228.35
39. The country beta for Egypt is:
A. 1.0
B. 0.14
C. 1.35
D. 0.93
40. Financial slang referring to the reduction of the cash flow from its forecasted value to its certainty equivalent is a
A. Deep discount
B. Haircut for risk
C. Arbitrage profit
D. Speculative gain
41. An example of diversifiable risk that should be ignored when analyzing project risk would include
A. Commodity price changes
B. Labor costs
C. Stock price fluctuations
D. Risk of government non-approval
42. A fudge factor might include:
A. Commodity price changes
B. Labor costs
C. Stock price fluctuations
D. Risk of government non-approval
43. What does a low standard error mean relative to beta?
A. Beta is a reliable measurement of risk
B. Beta has very little meaning
C. There is tremendous benefit to be gained from diversification
D. Nothing
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