Table of Contents
CHAPTER 1 ..............................................................................................................................5
GOALS AND GOVERNANCE OF THE FIRM .....................................................................5
1.1
Finance / Financial market: ........................................................................................5
1.2
Organizational structure of a corporation: ................................................................5
1.3
Sole proprietorship: ....................................................................................................6
1.4
Limited partnership vs General partnership: ............................................................6
1.5
Goals of the firm: ........................................................................................................6
1.6
Agency problems:........................................................................................................6
1.7
Real assets vs financial assets: ....................................................................................7
1.8
Investing decisions vs Financing decisions: ................................................................7
1.9
Tangible assets vs Intangible assets: ...........................................................................7
1.10 Capital structure: ........................................................................................................7
1.11 Stakeholders: ...............................................................................................................7
CHAPTER 2 ..............................................................................................................................8
HOW TO CALCULATE PRESENT VALUE? .......................................................................8
2.1
LÝ THUYẾT:..............................................................................................................8
2.2
Dạng bài “Single payment cashflow” – Chỉ có 𝑪𝟎 và 𝑪𝒏 ..........................................9
2.3
Dạng bài “Multiple payment cashflows” – Có 𝑪𝟎, 𝑪𝟏, 𝑪𝟐, …., 𝑪𝒏......................... 10
2.4
Dạng bài “Net present value”: .................................................................................. 11
2.5
Dạng bài “Annuity” .................................................................................................. 13
2.6
Dạng bài “Perpetuity” .............................................................................................. 15
2.7
Dạng bài “Growth Annuity” .................................................................................... 16
2.8
Dạng bài “Growth Perpetuity”................................................................................. 17
2.9
Dạng bài “Discount Factor” ..................................................................................... 17
2.10 Dạng APR (Annual Percentage Rate) ...................................................................... 18
2.11 Dạng EAR.................................................................................................................. 19
CHAPTER 3 ............................................................................................................................ 20
VALUING BONDS ................................................................................................................. 20
LÝ THUYẾT: ...................................................................................................................... 20
3.1
Dạng bài tính “Price” của bond: .............................................................................. 21
3.2
Dạng bài tính “Coupon payment” của bond:........................................................... 22
GV: TS. Ngô Nguyễn Quỳnh Như
3.3
Dạng bài tính “Coupon rate” của bond: .................................................................. 22
3.4
Dạng bài tính “YTM” của bond: .............................................................................. 22
3.5
Dạng bài tính “Duration” của bond: ........................................................................ 23
3.6
Dạng bài tính “Volatility” của bond: ....................................................................... 24
CHAPTER 4 ............................................................................................................................ 26
THE VALUE OF COMMON STOCKS ................................................................................ 26
LÝ THUYẾT: ...................................................................................................................... 26
4.1
Dạng bài tính “Market Capitalization”: .................................................................. 26
4.2
Dạng bài tính “P/E, EPS”: ........................................................................................ 26
4.3
Dạng bài tính “dividend payout ratio” vs “plowback ratio”: ................................. 27
4.4
Dạng bài tính “Price” của stock: .............................................................................. 27
4.5
Dạng bài tính “Rate of return” (r%): ...................................................................... 30
4.6
Dạng bài tính “dividend growth rate” (g%): ........................................................... 30
4.7
Dạng bài tính “Dividend in year n”: ........................................................................ 31
CHAPTER 5 ............................................................................................................................ 32
INTRODUCTION TO RISK AND RETURN ....................................................................... 32
LÝ THUYẾT: ...................................................................................................................... 32
5.1
Dạng bài 1 stock, n year ............................................................................................ 32
5.2
Dạng bài 1 stock, in different economy .................................................................... 33
5.3
Dạng bài tính Covariance, Correlation coefficient, n year ...................................... 34
5.4
Dạng bài tính Covariance, Correlation coefficient, in different economies ............ 36
5.5
Dạng bài tính “Portfolio weight” .............................................................................. 38
5.6
Dạng bài 1 portfolio including 2 stocks .................................................................... 39
5.7
Dạng bài tính Beta of a stock .................................................................................... 41
5.8
Dạng bài tính “Market risk premium” .................................................................... 42
CHAPTER 6 ............................................................................................................................ 44
PORTFOLIO THEORY AND THE CAPM .......................................................................... 44
Key terms cần nhớ:.............................................................................................................. 44
6.1
Dạng bài “Investment decision”: .............................................................................. 46
6.2
Expected return of a single stock with data of beta, rf, rm – rf .............................. 46
6.3
Beta of a portfolio...................................................................................................... 47
CHAPTER 7 ............................................................................................................................ 48
GV: TS. Ngô Nguyễn Quỳnh Như
RISK AND THE COST OF CAPITAL .................................................................................. 48
Key terms cần nhớ:.............................................................................................................. 48
7.1
Market risk premium ............................................................................................... 48
7.2
Expected rate of return / Expected rate of return / Discount rate, CAPM ............. 49
7.3
Cost of capital............................................................................................................ 49
7.4
WACC ....................................................................................................................... 50
7.5
WACC and NPV ....................................................................................................... 52
7.6
Certainty equivalent cash flow ................................................................................. 53
CHAPTER 8 ............................................................................................................................ 55
FINANCIAL ANALYSIS ....................................................................................................... 55
Key terms cần nhớ:.............................................................................................................. 55
Financial statements ............................................................................................................ 55
Income of a company ........................................................................................................... 56
8.1
Measuring performance............................................................................................ 56
8.2
Measuring Profitability............................................................................................. 57
8.3
Measuring Efficiency ................................................................................................ 58
8.4
Measuring Leverage.................................................................................................. 59
8.5
Measuring Liquidity: ................................................................................................ 60
8.6
Measuring Investment .............................................................................................. 61
8.7
Dạng tổng hợp ........................................................................................................... 62
CHAPTER 9 ............................................................................................................................ 64
WORKING CAPITAL MANAGEMENT ............................................................................. 64
Key terms cần nhớ:.............................................................................................................. 64
9.1
Inventory Management............................................................................................. 64
9.2
Receivables Management .......................................................................................... 66
9.3
Payables Management .............................................................................................. 68
9.4
Cash Management..................................................................................................... 68
CHAPTER 10 .......................................................................................................................... 71
FINANCIAL PLANNING ...................................................................................................... 71
Key terms cần nhớ:.............................................................................................................. 71
10.1 Sources of cash .......................................................................................................... 71
10.2 Uses of cash................................................................................................................ 73
GV: TS. Ngô Nguyễn Quỳnh Như
10.3 Cash budgeting.......................................................................................................... 73
CHAPTER 11 .......................................................................................................................... 78
PAYOUT POLICY ................................................................................................................. 78
Key terms cần nhớ:.............................................................................................................. 78
11.1 Dạng Stock price ....................................................................................................... 79
11.2 Dạng Value of dividend............................................................................................. 79
11.3 Dạng Stock outstanding / Split stocks ...................................................................... 80
GV: TS. Ngô Nguyễn Quỳnh Như
CHAPTER 1
GOALS AND GOVERNANCE OF THE FIRM
Chiến lược làm bài tổng quát:
1.1
-
Nhận dạng từ khóa
-
Loại trừ đáp án sai từ trên xuống dưới
-
Target: Làm 1 câu trong vòng 20 giây
Finance / Financial market:
1. Finance, generally, deals with: I) Money; II) Markets; III) People.
2. Functions of financial markets: I) Source of financing; II) Provide liquidity; III) Reduce risk;
IV) Source of information.
1.2
Organizational structure of a corporation:
1. Generally, a corporation is owned by the shareholders.
2. Shareholders of a corporation could be: I) Individuals; II) Pension Funds; III) Insurance
Companies.
3. Corporations, potentially, have infinite life because of the separation of ownership and
management. Limited liability is an important feature of corporations.
4. Organizational structure of a corporation: The chief executive officer (CEO), chief financial
officer (CFO) report to the board of directors.
5. Managers' actions are monitored by the board of directors, Commercial banks that have loaned
funds to the firm, The Wall Street analysts.
6. Common function of the firm's chief financial officer (CFO): Hiring controller, hiring
treasurer, investing capital, paying dividends. The Chief Financial Officer (CFO) of a
corporation oversees: Treasurer's functions & Controller's functions.
7. The treasurer and the controller of a corporation generally report to the CFO. The key
difference between the duties of the controller and those of the treasurer is the separation of
cash control from accounting records.
8. Treasurer: directly responsible for financial planning and capital expenditures. The treasurer is
usually responsible the following functions of a corporation: Investor relationships, Cash
management, raising new capital.
9. Controller usually oversees the following functions of a corporation: Preparation of financial
statements, Internal accounting, Taxes.
GV: TS. Ngô Nguyễn Quỳnh Như
10. Articles of incorporation is a corporate document that sets forth the intended life of the firm.
The articles of incorporation set forth the number of shares of stock that can be issued. The
articles of incorporation establish the rights of the shareholders.
1.3
Sole proprietorship:
1. Sole proprietorship is the easiest type of business to form. Sole proprietorships are limited to
the business owner's life. The owner of a sole proprietorship may be forced to sell his/her
personal assets to pay company debts.
1.4
Limited partnership vs General partnership:
1. A limited partnership generally permits limited partners to sell their ownership interest without
the partnership terminating. In a limited partnership, each limited partner's liability is limited
to the amount he/she invested.
2. The primary advantage of being a limited partner rather than a general partner is liability for
firm debts limited to the capital invested. A general partner has more management
responsibility than a limited partner.
3. The division of profits and losses among the members of a partnership is formalized in the
partnership agreement.
4. Disadvantages of a general partnership:
1.5
•
Limited life of the firm
•
Personal liability for firm debt
•
Lack of ability to transfer partnership interest
Goals of the firm:
1. The financial goal of a corporation is to: Maximize value of the corporation to the stockholders.
2. The primary goal of financial management is to maximize the current value per share of the
existing stock.
1.6
Agency problems:
1. Agency problem refers to a conflict of interest between the stockholders and managers of a
corporation. Conflicts of interest between shareholders and managers of a firm result in:
Principal-agent problem, Increased agency costs, Managers owning the firm.
2. Agency costs refer to the costs of any conflicts of interest between stockholders and
management. Agency costs: Costs associated with the conflicts of interest between the
bondholders and the shareholders of a corporation.
GV: TS. Ngô Nguyễn Quỳnh Như
3. Agency costs are incurred by a corporation because:
•
managers may not attempt to maximize the value of the firm to shareholders
•
shareholders incur monitoring cost
•
separation of ownership and management
4. If the corporation is not performing well, shareholders can:
1.7
•
Replace the board of directors in an election
•
Force the board of directors to change the management team
•
Sell their shares of stock in the corporation
Real assets vs financial assets:
1. Real assets: Machinery, Office buildings, Warehouse.
2. Financial assets: Common stock, Bank loan, Preferred stock.
1.8
Investing decisions vs Financing decisions:
1. Investment decision / capital budgeting decision: The purchase of real assets; Deciding
whether or not to open a new store. A firm's investment decision is also called the capital
budgeting decision – The process of planning and managing a firm's long-term investments.
2. Financing decision: The sale of financial assets.
1.9
Tangible assets vs Intangible assets:
1. Tangible assets: Machinery; Office buildings; Warehouse; Factories; Offices.
2. Intangible assets: Trademarks; Patents; Technical expertise.
1.10
Capital structure:
1. Capital structure refers to decisions related to long-term debt and equity financing.
2. The mixture of debt and equity, used to finance a corporation is also known as Capital structure.
1.11
Stakeholders:
1. A stakeholder is any person or entity other than a stockholder or creditor who potentially has
a claim on the cash flows of a firm. Example: Employee, Customer; Community; Supplier.
2. The following groups are some of the claimants to a firm's income stream: I) Shareholders; II)
Bondholders; III) Employees; IV) Management and V) Government.
GV: TS. Ngô Nguyễn Quỳnh Như
CHAPTER 2
HOW TO CALCULATE PRESENT VALUE?
Chiến lược làm bài tổng quát
-
Phân tích đề thuộc dạng nào
-
Viết công thức ra nháp + Áp dụng công thức chính xác
-
Làm bài chỉ cần bước thế số và ra đáp án.
-
Dùng dấu “,” cho phần ngàn, dấu “.” cho phần thập phân.
-
Làm tròn 2 số sau phần thập phân
-
Target: Làm 1 câu trong vòng 20 giây
2.1
LÝ THUYẾT:
1.
Present Value is defined as future cash flows discounted to the present at an appropriate
discount rate
2.
If the present value of the cash flow X is $240, and the present value cash flow Y $160,
then the present value of the combined cash flow is:
 $400
3.
The rate of return is also called: I) discount rate; II) hurdle rate; III) opportunity cost of
capital.
4.
The present value formula for one period cash flow is: PV = C1/(1 + r)
5.
An annuity is defined as equal cash flows at equal intervals of time for a specified period
of time
6.
Example of annuity: If you receive $1,000 payment at the end each year for the next five
years
7.
You are considering investing in a retirement fund that requires you to deposit $5,000 per
year, and you want to know how much the fund will be worth when you retire. What
financial technique should you use to calculate this value?
 Future value of an annuity
8.
According to the net present value rule, an investment in a project should be made if the
Net present value is positive.
9.
NPV rule and the rate of return rule: Accept a project if its NPV > 0, Reject a project if the
NPV < 0, Accept a project if its rate of return > opportunity cost of capital
GV: TS. Ngô Nguyễn Quỳnh Như
10.
The net present value formula for one period is: NPV = C0 + [C1/(1 + r)]; NPV = PV
required investment.
11.
The managers of a firm can maximize stockholder wealth by:
 Taking all projects with positive NPVs
12.
A perpetuity is defined as Equal cash flows at equal intervals of time forever. Example:
consols
13.
The concept of compound interest is most appropriately described as: Interest earned on
interest
14.
The opportunity cost of capital for a risky project is the expected rate of return on a
portfolio of securities of similar risks as the project
Dạng bài “Single payment cashflow” – Chỉ có 𝑪𝟎 và 𝑪𝒏
2.2
Chến lược làm bài:
-
Nhận dạng câu hỏi có cụm “The present value + of + FUTURE VALUE”
-
Dùng công thức:
𝑃𝑉 =
𝑃𝑉 =
𝐶𝑛
(1 + 𝑟 ) 𝑛
𝐶𝑛
𝑟 𝑛×𝑚
(1 + 𝑚)
1. What is the present value of $1,000 expected in two years from today at a discount rate of 8%?
2. What is the present value of $121,000 expected to be received one year from today at an interest
rate (discount rate) of 10% per year?
3. What is the present value of $100,000 expected to be received at the end of one year at a
discount rate of 25% per year?
4. Find the future value of an investment of $100,000 made today for five years and paying 12%
percent for the following compounding periods:
a) Quarterly
b) Monthly
c) Daily
5. Ms. Nhu is looking to invest some money, so that she has $55,000 at the end of three years.
Which investment should she make given the following choices:
a) 8.2% compounded daily
GV: TS. Ngô Nguyễn Quỳnh Như
b) 8.9% compounded monthly
c) 9.2% compounded quarterly
6. Find the future value of an investment of $22,500 made today for the following rates and
periods:
a) 6.25% compounded semiannually for 12 years
b) 7.63% compounded quarterly for 6 years
c) 8.9% compounded monthly for 10 years
d) 10% compounded daily for 3 years
7. Ms. Nhu needs to decide whether to accept a bonus of $1,820 today or wait two years and
receive $2,100 then. She can invest at 16 percent. What should she do?
8. Ms. Nhu saves $70,250 and she needs some money at the end of five years. Which investment
should she make given the following choices:
a) 16.25% compounded quarterly
b) 16.5% compounded semi-annually
9. You have won a prize of 52 million VNĐ to be paid exactly after 3 years. You were offered
45 million VNĐ today as a consideration for his agreement to sell the right to receive the prize.
The market interest rate is 12% and the interest is compounded on quarterly basis. Whether the
offer should be accepted or not?
Dạng bài “Multiple payment cashflows” – Có 𝑪𝟎 , 𝑪𝟏 , 𝑪𝟐 , …., 𝑪𝒏
2.3
Chiến lược làm bài:
-
Nhận dạng câu hỏi có following cash flows (dòng tiền cho từng năm)
-
Dùng công thức:
𝑃𝑉 =
𝐶1
𝐶2
𝐶𝑛
+
+⋯+
1
2
(1 + 𝑟 )
(1 + 𝑟 )
(1 + 𝑟 )𝑛
𝐹𝑉𝑛 = 𝐶0 × (1 + 𝑟)𝑛 + 𝐶1 × (1 + 𝑟)𝑛−1 + ⋯ + 𝐶𝑛−1 × (1 + 𝑟) + 𝐶𝑛
1. What is the present value of the following cash flow at a discount rate of 12%?
Year -1
Year - 2
Year - 3
$100,000
$150,000
$200,000
GV: TS. Ngô Nguyễn Quỳnh Như
2. At an interest rate of 10%, which of the following cash flows has highest present value?
Option
Year 1
Year 2
Year 3
A
500
300
100
B
100
300
500
C
300
300
300
3. What is the present value of the following cash flow at a discount rate of 9%?
Year
1
2
CF ($)
-100,000
300,000
4. A project is expected to produce cash flows of $6,000, $8,000, and $9,000 over the next three
years, respectively. After three years, the project will be discontinued. What is this project
worth today at a discount rate of 20 percent?
5. What is the future value of the following cash flow at the end of five years with the discount
rate of 10%?
Year
0
1
2
3
4
5
CF
$250,000
0
$120,000
$80,000
$50,000
$25,000
Dạng bài “Net present value”:
2.4
Chiến lược làm bài:
-
Nhận dạng câu hỏi có kêu tính NPV của dự án.
-
Vận dụng NPV rule: chấp nhận dự án khi NPV > 0, từ chối dự án khi NPV âm.
-
Dùng công thức:
𝑁𝑃𝑉 = 𝐶0 +
𝐶1
𝐶2
𝐶𝑛
+
+
⋯
+
(1 + 𝑟)1 (1 + 𝑟)2
(1 + 𝑟 )𝑛
(𝐶𝑜 < 0)
1. An initial investment of $400,000 will produce an end of year cash flow of $480,000. What is
the NPV of the project at a discount rate of 20%?
2. If the present value of a cash flow generated by an initial investment of $200,000 is $250,000.
What is the NPV of the project?
3. What is the net present value of the following cash flow at a discount rate of 11%?
Year
0
1
2
CF ($)
-120,000
300,000
-100,000
GV: TS. Ngô Nguyễn Quỳnh Như
4. A project is expected to produce cash flows of $5,000, $8,000, and $16,000 over the next three
years, respectively. After three years, the project will be discontinued. What is the Net Present
Value of project at a discount rate of 15 percent if initial investment cost is $25,000?
5. A project is expected to produce cash flows of $5,000, $8,000, and $16,000 over the next three
years, respectively. After three years, the project will be discontinued. What is the Net Present
Value of project at a discount rate of 15 percent if initial investment cost is $15,000?
6. Vinamilk wants to purchase an equipment for $320,000. It will produce the following net cash
flows:
Year
Net Cash Flows
1
$130,000
2
280,000
3
110,000
Assume that the cost of capital is 10%. What is the net present value?
7. What is the net present value (NPV) of the following cash flows at a discount rate of 9%?
Year
0
1
2
3
CF ($)
-250,000
100,000
150,000
200,000
8. A project requires an initial investment of $21,600 and will produce cash inflows of $4,900,
$14,200, and $8,700 over the next three years, respectively. What is the project's NPV at a
required return of 14 percent? The project will be accepted or not? Why?
9. What is the net present value of the following cash flow at a discount rate of 12%?
Year
0
1
2
3
4
5
CF
($150,000)
$50,000
$30,000
$75,000
$10,000
($75,000)
10. VinGroup wants to purchase an equipment for $420,000. It will produce the following net cash
flows:
Year
Net Cash Flows ($)
1
160,000
2
-260,000
3
200,000
4
210,000
Assume that the cost of capital is 10%. What is the net present value? Should VinGroup accept
this project? Why?
GV: TS. Ngô Nguyễn Quỳnh Như
11. What is the net present value of the following cash flow at a discount rate of 12%?
Year
0
1
2
3
4
5
CF
-120,000
35,000
35,000
35,000
35,000
-10,000
Dạng bài “Annuity”
2.5
Chiến lược làm bài:
-
Nhận dạng câu hỏi có từ “annuity”: đều hàng năm, xác định được số năm đều
-
1 số ví dụ khác về annuity:
-
•
Sau khi về hưu, mỗi năm sẽ nhận 75,000$ trong vòng 25 năm.
•
Mỗi năm trả nợ với 1 khoản tiền bằng nhau, trong vòng 20 năm.
•
Mỗi năm đóng tiền học là 12,500$ trong vòng 6 năm.
•
Cho thuê xe trong vòng 5 năm, mỗi tháng nhận được $250.
•
Nhà máy hoạt động tạo ra dòng tiền đều $150,000 mỗi năm, trong vòng 8 năm.
Lưu ý: Dòng tiền đều bắt đầu phát sinh từ lúc nào. Nếu là cuối năm 1 thì dùng công thức
tính PV bình thường. Nếu là đầu năm 1 (today) thì dùng công thức là đang tính C(-1),
rồi nhân lại cho (1+r) để ra PV.
-
Dùng công thức:
1 − (1 + 𝑟)−𝑛
]
𝑃𝑉 = 𝐶 × [
𝑟
(1 + 𝑟 )𝑛 − 1
]
𝐹𝑉 = 𝐶 × [
𝑟
1. What is the present value of $1000 per year annuity for five years at an interest rate of 12%?
2. What is the present value of $1000 per year annuity at a discount rate of 12% for 8 years?
3. What is the present value of $5000 per year annuity at a discount rate of 10% for 6 years?
4. After retirement, you expect to live for 25 years. You would like to have $75,000 income each
year. How much should you have saved in the retirement to receive this income, if the interest
is 9% per year (assume that the payments start one year after the retirement)?
5. After retirement, you expect to live for 25 years. You would like to have $75,000 income each
year. How much should you have saved in the retirement to receive this income, if the interest
is 9% per year (assume that the payments start on the day of retirement)?
6. Mr. Trump is expected to retire in 25 years and he wishes accumulate $750,000 in his
retirement fund by that time. If the interest rate is 10% per year, how much should Mr. Trump
GV: TS. Ngô Nguyễn Quỳnh Như
into the retirement fund each year in order to achieve this goal? Assume that the payments are
made at the end of each year.
7. After retirement, you expect to live for 20 years. You would like to have $7,000 income each
year. How much should you have saved in the retirement to receive this income, if the interest
is 10% per year (assume that the payments start on the day of retirement)?
8. After retirement, you would like to have $80,000 income each year for 20 years. How much
should you have saved in the retirement to receive this income, if the interest is 3.0% per year
(Assume that the payments start one year after the retirement)
9. Mr. Trump is expected to retire in 30 years and he wishes accumulate $1,000,000 in his
retirement fund by that time. If the interest rate is 12% per year, how much should Mr. Trump
put into the retirement fund each year in order to achieve this goal?
10. Mr. Trump expects to retire in 30 years and would like to accumulate $1 million in the pension
fund. If the annual interest rate is 12% per year, how much should Mr. Trump put into the
pension fund each month in order to achieve his goal? Assume that Mr. Trump will deposit the
same amount each month into his pension fund and also use monthly compounding.
11. You have to pay $12,500 a year in school fees at the end of each of the next six years. If the
interest rate is 8%, how much do you need to set aside today to cover these bills? You have
invested $70,476 at 8%. After paying the above school fees, how much would remain at the
end of the six years?
12. Mr. Sugar has taken a $250,000 mortgage on his house at an interest rate of 6% per year. If
the mortgage calls for twenty equal annual payments, what is the amount of each payment?
13. Ms. Trang has just taken out a $150,000 mortgage at an interest rate of 6% per year. If the
mortgage calls for equal monthly payments for twenty years, what is the amount of each
payment? (Assume monthly compounding or discounting.)
14. You borrow $150,000 to buy a house. The mortgage rate is 8.5 percent and the loan period is
30 years. Payments are made monthly. If you pay for the house according to the loan
agreement, how much total interest will you pay?
15. The discount rate is 10 percent for five years, compounded quarterly. What is the difference in
the present value of these two sets of the following payments?
Case 1: you receive $200 on the first of each quarter.
Case 2: you receive $200 on the last day of each quarter.
GV: TS. Ngô Nguyễn Quỳnh Như
16. You agree to lease a car for 5 years at $250 per month. You are not required to pay any money
up front or at the end of your agreement. If your opportunity cost of capital is 0.3% per month,
what is the cost of the lease?
17. A factory costs $750,000. You reckon that it will produce an inflow after operating costs of
$150,000 a year for 8 years. If the opportunity cost of capital is 14%, what is the net present
value of the factory? What will the factory be worth at the end of five years?
18. I order to save money for travelling to Europe, I have to deposit 30 million VNĐ at the end of
each year, during 3 years. Help me to calculate the total money I get in my account at the end
of year 3, if the interest rate is 8%, compounding semi-annually?
19. Khanh is planning for retirement. He expects to retire 28 years from now, at which time he
wishes to have accumulated $2,500,000 in his retirement fund (money at that time). If the
interest rate is 3% per year, how much should Khanh put into his retirement fund at the end of
each year in order to achieve his goal?
Dạng bài “Perpetuity”
2.6
Chiến lược làm bài:
-
Nhận dạng câu hỏi có từ “perpetuity”
-
1 số ví dụ khác về perpetuity:
•
Sau khi về hưu, mỗi năm sẽ nhận 80,000$ cho đến vĩnh viễn.
•
Trong thực tế, trái phiếu consols của Anh, là có trả trái tức (coupon) đều cho
đến vĩnh viễn.
-
Lưu ý: Dòng tiền đều vĩnh viên bắt đầu phát sinh từ lúc nào. Nếu là cuối năm 1 thì dùng
công thức tính C0 bình thường. Nếu là đầu năm 1 (today) thì dùng công thức là đang
tính C(-1), rồi nhân lại cho (1+r) để ra C0. Nếu là cuối năm 4 thì dung công thức để tính
C3, rồi chiết khấu 3 năm về để tính C0.
-
Dùng công thức:
𝐶0 =
𝐶1
𝑟
1. What is the present value of $10,000 per year perpetuity at an interest rate of 10%?
2. You would like to have enough money saved to receive $80,000 per year perpetuity after
retirement so that you and your family can lead a good life. How much would you need to save
GV: TS. Ngô Nguyễn Quỳnh Như
in your retirement fund to achieve this goal (assume that the perpetuity payments start one year
from the date of your retirement. The interest rate is 8%)?
3. You would like to have enough money saved to receive $100,000 per year perpetuity after
retirement so that you and your family can lead a good life. How much would you need to save
in your retirement fund to achieve this goal (assume that the perpetuity payments start one year
from the date of your retirement. The interest rate is 12.5%)?
4. You would like to have enough money saved to receive a $50,000 per year perpetuity after
retirement so that you and your family can lead a good life. How much would you need to save
in your retirement fund to achieve this goal (assume that the perpetuity payments start on the
day of retirement. The interest rate is 8%)?
5. You would like to have enough money saved to receive an $80,000 per year perpetuity after
retirement so that you and your family can lead a good life. How much would you need to save
in your retirement fund to achieve this goal (assume that the perpetuity payments start on the
day of retirement. The interest rate is 10%)?
6. What is the present value of cash flows of $5,000 start at the end of year 4 in perpetuity?
Assuming a rate of return of 10%?
7. Calculate the present value of cash flows of $9,500 start at the end of year 5 in perpetuity.
Assuming a rate of return of 8.25%?
Dạng bài “Growth Annuity”
2.7
Chiến lược làm bài:
-
Nhận dạng câu hỏi có từ “growing annuity”
-
1 số ví dụ khác về growing annuity:
•
Sau khi về hưu, năm đầu nhận đc 60,000$, các năm sau mỗi năm số tiền nhận
được tăng trưởng với tốc độ g = 4%, nhận tiền như vậy trong vòng 25 năm.
-
Dùng công thức:
𝐶0 =
𝐶1
1+𝑔 𝑛
× [1 − (
) ]
𝑟−𝑔
1+𝑟
1. You would like to have enough money saved to receive a growing annuity for 25 years,
growing at a rate of 4% per year, the first payment being $60,000 after retirement, so that you
and your family can lead a good life. How much would you need to save in your retirement
GV: TS. Ngô Nguyễn Quỳnh Như
fund to achieve this goal? (Assume that the growing annuity payments start one year from the
date of your retirement. The interest rate is 12%)?
2. You would like to have enough money saved to receive a growing annuity for 20 years,
growing at a rate of 5% per year, the first payment being $50,000 after retirement. That way,
you hope that you and your family can lead a good life after retirement. How much would you
need to save in your retirement fund to achieve this goal. (Assume that the growing annuity
payments start one year from the date of your retirement. The interest rate is 10%)?
Dạng bài “Growth Perpetuity”
2.8
Chiến lược làm bài:
-
Nhận dạng câu hỏi có từ “perpetuity” và có cho growth rate (g%)
-
1 số ví dụ khác về growing perpetuity:
•
Cuối năm 1 nhận đc 1,000$, cuối các năm kế tiếp nhận được số tiền tăng trưởng
với tốc độ tăng trưởng g%, cho đến vĩnh viễn.
•
Cuối năm 4 nhận được 5,000$, cuối năm thứ 5 cho đến vĩnh viễn, mỗi năm số
tiền nhận được tăng trưởng với tốc độ g%.
-
Lưu ý: Phải xác định được dòng tiền đầu tiên phát sinh tại thời điểm nào. Nếu tại thời
điểm cuối năm 1 thì dùng công thức tính C0 bình thường. Nếu là đầu năm 1 (today) thì
dùng công thức là đang tính C(-1), rồi nhân lại cho (1+r) để ra C0. Nếu là cuối năm 4 thì
dùng công thức để tính C3, rồi chiết khấu 3 năm về để tính C0.
-
Dùng công thức:
𝐶0 =
𝐶1
𝑟−𝑔
1. What is the present value of cash flows of $5,000 start at the end of year 4 in perpetuity,
assuming a rate of return of 10% and a constant growth rate of 4%?
2. Calculate the present value of cash flows of $9,500 start at the end of year 5 in perpetuity.
Assuming a rate of return of 8.25% and a constant growth rate of 3.5%?
Dạng bài “Discount Factor”
2.9
Chiến lược làm bài:
-
Nhận dạng câu hỏi kêu tính cái gì?
𝑛 − 𝑦𝑒𝑎𝑟 𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡 𝑓𝑎𝑐𝑡𝑜𝑟 =
GV: TS. Ngô Nguyễn Quỳnh Như
1
(1 + 𝑟 )𝑛
𝑃𝑉 = 𝐹𝑉 × (𝑛 − 𝑦𝑒𝑎𝑟 𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡 𝑓𝑎𝑐𝑡𝑜𝑟)
1 − (1 + 𝑟)−𝑛
𝑃𝑟𝑒𝑠𝑒𝑛𝑡 𝑉𝑎𝑙𝑢𝑒 𝐴𝑛𝑛𝑢𝑖𝑡𝑦 𝐹𝑎𝑐𝑡𝑜𝑟 =
𝑟
(1 + 𝑟 )𝑛 − 1
𝐹𝑢𝑡𝑢𝑟𝑒 𝑉𝑎𝑙𝑢𝑒 𝐴𝑛𝑛𝑢𝑖𝑡𝑦 𝐹𝑎𝑐𝑡𝑜𝑟 =
𝑟
1. If the interest rate is 12%, what is the 2-year discount factor?
2. One-year discount factor at a discount rate of 25% per year is:
3. The one-year discount factor at an interest rate of 100% per year is:
4. If the one-year discount factor is 0.8333, what is the discount rate (interest rate) per year?
5. If the present value of $480 to be paid at the end of one year is $400, what is the one-year
discount factor?
6. If the present value of $250 expected to be received one year from today is $200, what is the
discount rate?
7. If the one-year discount factor is 0.90, what is the present value of $120 to be received one
year from today?
8. If the present value of $600 expected to be received one year from today is $400, what is the
one-year discount rate?
9. What is the present value annuity factor at a discount rate of 11% for 8 years?
10. What is the present value annuity factor at an interest rate of 9% for 6 years?
11. If the present value annuity factor at 8% APR for 10 years is 6.71, what is the equivalent future
value annuity factor?
2.10
Dạng APR (Annual Percentage Rate)
Chiến lược làm bài:
-
Nhận dạng bài cho APR
-
Xem kêu tính FV bằng tính lãi suất đơn hay lãi suất kép (lãi chồng lại)
-
Nếu apply lãi suất đơn thì:
𝐹𝑉𝑛 = 𝑃𝑉 × (1 + 𝐴𝑃𝑅 × 𝑛)
-
Nếu apply lãi suất kép thì:
𝐹𝑉𝑛 = 𝑃𝑉 × (1 + 𝐴𝑃𝑅)𝑛
1. If you invest $100 at 12% APR for three years, how much would you have at the end of 3 years
using simple interest?
GV: TS. Ngô Nguyễn Quỳnh Như
2. If you invest $100 at 12% APR for three years, how much would you have at the end of 3 years
using compound interest?
2.11
Dạng EAR
Chiến lược làm bài:
-
Nhận dạng bài:
•
Cho EAR, kêu tính Nominal rate:
1
𝑁𝑜𝑚𝑖𝑛𝑎𝑙 𝑟𝑎𝑡𝑒 = [(1 + 𝐸𝐴𝑅)𝑚 − 1] × 𝑚
•
Cho Nominal rate compounded m, kêu tính EAR:
𝐸𝐴𝑅 = (1 +
•
𝑁𝑜𝑚𝑖𝑛𝑎𝑙 𝑟𝑎𝑡𝑒 𝑚
) −1
𝑚
Cho Nominal rate compounded continuously, kêu tính EAR:
𝐸𝐴𝑅 = 𝑒 𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝑟𝑎𝑡𝑒 − 1
•
Cho Nominal rate per m (VD: 1% / tháng), kêu tính APR: Nominal rate × m
1. An investment at 10.47% effective rate compounded monthly is equal to a nominal (annual)
rate of:
 Nominal rate = [(1.1047)^(1/12) - 1] * 12 = 0.1 = 10%
2. An investment at 12% nominal rate compounded monthly is equal to an annual rate of:
 12.68%
3. An investment at 10% nominal rate compounded continuously is equal to an equivalent annual
rate of:
 (e^(0.1)) - 1 = 0.10517 = 10.517%
4. Given a monthly rate of 1%, what is the Effective Annual Rate (EAR)? What is the Annual
Percentage Rate (APR)?
 EAR = (1+1%)^12 – 1 = 12.68%
 APR = 1%*12 = 12%
GV: TS. Ngô Nguyễn Quỳnh Như
CHAPTER 3
VALUING BONDS
LÝ THUYẾT:
1. Face value = market value: par value bond
YTM < Coupon rate: premium bond
YTM > Coupon rate: discount bond
2. Example of par value bond: A bond with a 5 percent coupon that pays interest semiannually
and is priced at par will have a market price of $1,000 and interest payments in the amount of
$25 each.
3. The following entities issue bonds to raise long-term loans:
•
The federal government;
•
State and local governments
•
Companies.
4. If a bond is paying interest semi-annually, then interest is paid every six months. If a bond is
paying interest annually, then interest is paid once a year.
5. Relationship between bond prices and interest rates:
•
There is an inverse relationship between bond prices and interest rates.
•
The price of long-term bonds fluctuates more than the price of short-term bonds for a
given change in interest rates. (Assuming that the coupon rate is the same for both)
6. Volatility of a bond is given by:
I)
Duration/ (1 + yield)
II)
Slope of the curve relating the bond price to the interest rate
7. The term structure of interest rates can be described as the relationship between spot interest
rates and maturity of a bond.
8. Interest rate risk increases with increases in time to maturity and decreases in coupon rates.
9. Interest rates or rates of return on investments that have been adjusted for the effects of inflation
are called real rates.
GV: TS. Ngô Nguyễn Quỳnh Như
Dạng bài tính “Price” của bond:
3.1
Chiến lược làm bài:
-
Cho Face value và coupon rate => Tính ngay fixed coupon
-
Gạch bỏ coupon rate để tránh nhầm với YTM
-
Lưu ý: Đọc kỹ coi coupon trả 1 năm 2 lần (semi-annually) hay 1 năm 1 lần. Nếu coupon
trả 1 năm 1 lần thì dung CT Price bình thường. Nếu coupon trả 1 năm 2 lần thì r/2, n*2,
C/2
-
Dùng công thức:
𝑃𝑉 = 𝐶 × [
1 − (1 + 𝑟)−𝑛
𝐹𝑎𝑐𝑒 𝑣𝑎𝑙𝑢𝑒
]+
(1 + 𝑟 )𝑛
𝑟
1. A government bond has a coupon rate of 5%, face value of euros 100 and maturing in five
years. The interest payments are made annually. Calculate the price of the bond (in euros) if
the yield to maturity is 3.5%.
2. A 3-year bond with 10% coupon rate and $1000 face value yields 8% APR. Assuming annual
coupon payment, calculate the price of the bond.
3. A three-year bond has 8.0% coupon rate and face value of $1000. If the yield to maturity on
the bond is 10%, calculate the price of the bond assuming that the bond makes semi-annual
coupon interest payments.
4. Antonio's offers a 10-year bond that has a coupon rate of 5 percent and semiannual payments.
The face value is $1,000 and the yield to maturity is 12.6 percent. What is the current value of
this bond?
5. A treasury bond matures in 17 years, pays interest semiannually, and carries a coupon rate of
3.5 percent. How much are you willing to pay for a $1,000 face value bond if you desire a rate
of return of 4.25 percent?
6. A 20-year zero coupon bond has a $1,000 face value, a required rate of return of 5 percent, and
semiannually compounding. What is this bond worth today?
7. The $1,000 face value ABC bond has a coupon rate of 6%, with interest paid semi-annually,
and matures in 5 years. If the bond is priced to yield 8%, what is the bond’s value today?
GV: TS. Ngô Nguyễn Quỳnh Như
Dạng bài tính “Coupon payment” của bond:
3.2
Chiến lược làm bài:
-
Cho Face value và coupon rate => Tính ngay fixed coupon
-
Lưu ý: Đọc kỹ coi coupon trả 1 năm 2 lần (semi-annually) hay 1 năm 1 lần. Nếu coupon
trả 1 năm 1 lần thì dung CT Price bình thường. Nếu coupon trả 1 năm 2 lần thì r/2, n*2,
C/2
-
Dùng công thức:
Annually: C = Face value x coupon rate
Semi-annually: C = Face value x coupon rate / 2
1. A 5-year treasury bond with a coupon rate of 8% has a face value of $1000. What is the
semi-annual interest payment?
Dạng bài tính “Coupon rate” của bond:
3.3
Chiến lược làm bài:
-
Viết công thức tính Price của bond ra.
-
Lưu ý: Đọc kỹ coi coupon trả 1 năm 2 lần (semi-annually) hay 1 năm 1 lần. Nếu coupon
trả 1 năm 1 lần thì dung CT Price bình thường. Nếu coupon trả 1 năm 2 lần thì r/2, n*2,
C/2
-
Đề bài cho n, r, Face value, Po => Tính ra được Coupon payment => Tính ra được
coupon rate.
-
Dùng công thức:
Coupon rate = Coupon payment / Face value
1. Your firm offers a 20-year, semiannual coupon bond with a yield to maturity of 8.35 percent,
a face value of $1,000, and a market price of $1,054. What is the coupon rate?
Dạng bài tính “YTM” của bond:
3.4
Chiến lược làm bài:
-
Viết công thức tính Price của bond ra.
-
Cho Face value và coupon rate => Tính ngay fixed coupon
-
Gạch bỏ coupon rate để tránh nhầm với YTM
-
Lưu ý: Đọc kỹ coi coupon trả 1 năm 2 lần (semi-annually) hay 1 năm 1 lần. Nếu coupon
trả 1 năm 1 lần thì dung CT Price bình thường. Nếu coupon trả 1 năm 2 lần thì r/2, n*2,
C/2
GV: TS. Ngô Nguyễn Quỳnh Như
-
Đề bài cho n, coupon, Face value, Po => Tính ra được YTM. Nên dùng hàm số trong
máy tính để bấm cho nhanh.
-
Trường hợp tính Current yield = coupon trả cho 1 năm / Market price of bond
1. A government bond issued in Germany has a coupon rate of 5%, face value of euros 100 and
maturing in five years. The interest payments are made annually. Calculate the yield to
maturity of the bond (in euros) if the price of the bond is 106 euros.
2. A four-year bond has an 8% coupon rate and a face value of $1000. If the current price of the
bond is $878.31, calculate the yield to maturity of the bond (assuming annual interest
payments).
3. A 5-year bond with 10% coupon rate and $1000 face value is selling for $1123. Calculate the
yield to maturity on the bond assuming annual interest payments.
4. The bonds issued by North & South bear a coupon rate of 7.5 percent, payable semiannually.
The bonds mature in 6.5 years, sell at par, and have a $1,000 face value. What is the yield to
maturity?
5. A General Co. bond has a coupon rate of 7 percent and pays interest annually. The face value
is $1,000 and the current market price is $1,020.50. The bond matures in 20 years. What is the
yield to maturity?
6. Webster's has a 12-year bond issue outstanding that pays a coupon rate of 6.5 percent. The
bond is currently priced at $938.76 and has a par value of $1,000. Interest is paid semiannually.
What is the yield to maturity?
7. The Doolittle bonds have a face value of $1,000, a current market price of $1,048.50, a coupon
rate of 4.6 percent, compounded semiannually. What is the current yield on these bonds?
Dạng bài tính “Duration” của bond:
3.5
Chiến lược làm bài:
-
Tính Price của bond ra.
-
Tính PV(C1) – PV(Cn)
-
Dùng công thức Duration:
𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛 =
-
1 × 𝑃𝑉 (𝐶1 ) + 2 × 𝑃𝑉 (𝐶2 ) + ⋯ + 𝑛 × 𝑃𝑉(𝐶𝑛 )
𝑃𝑉
Lưu ý: Khi làm câu trắc nghiệm tính Duration với số năm nhiều thì bấm máy dung
sigma. Khi làm tự luận tính Duration thì cần trình bày rõ từng bước PV, PV(C1), …
GV: TS. Ngô Nguyễn Quỳnh Như
1. A bond with a face value of $1,000 has coupon rate of 7%, yield to maturity of 10%, and
twenty years to maturity. The bond's duration is:
2. A bond with a face value of $1,000, coupon rate of 0%, yield to maturity of 9%, and ten years
to maturity. This bond's duration is:
3. Consider a bond with a face value of $1,000, a coupon rate of 6%, a yield to maturity of 8%,
and ten years to maturity. This bond's duration is:
4. Consider a bond with a face value of $1,000, a coupon rate of 6%, a yield to maturity of 4%,
and five years to maturity. What is bond's duration?
5. Consider a bond with a face value of $1,000, a coupon rate of 6.75%, a yield to maturity of
9.5%, and five years to maturity. What is bond's Macaulay duration?
Dạng bài tính “Volatility” của bond:
3.6
Chiến lược làm bài:
-
Tính Duration.
-
Tính Modified duration:
𝑀𝑜𝑑𝑖𝑓𝑖𝑒𝑑 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛 =
-
𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛
1 + 𝑌𝑇𝑀
Dùng công thức Volatility:
∆(𝑃𝑟𝑖𝑐𝑒) = −𝑀𝑜𝑑𝑖𝑓𝑖𝑒𝑑 𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛 × ∆(𝑌𝑇𝑀)
1. A bond with duration of 10 years has yield to maturity of 10%. This bond's volatility is:
2. A bond with duration of 5.7 years has yield to maturity of 9%. The bond's volatility is:
3. If a bond's volatility is 10% and the interest rate goes down by 0.75% (points) then the price
of the bond:
4. If a bond's volatility is 5% and the interest rate changes by 0.5% (points) then the price of the
bond:
5. A 12-year, 5 percent coupon bond with a face value of $1,000 pays interest semiannually. What
is the percentage change in the price of this bond if the market yield rises to 6 percent from its
current level of 4.5 percent?
6. A 15-year, 4 percent coupon bond with a face value of $1,000 pays interest semiannually.
Assume the bond currently sells at par. What will the percentage change in the price of this
bond be if market rates increase by 10 percent?
GV: TS. Ngô Nguyễn Quỳnh Như
7. Given a 5-year annual coupon bond with a face value of $1000, coupon rate of 8.5% and a
yield to maturity of 7%.
a. Calculate the Macaulay duration of this bond
b. If yield to maturity decreases from 7% to 5.2%, calculate the price of bond after yield
to maturity changes
8. Given a 5-year annual coupon bond with a face value of $1000, coupon rate of 9% and a yield
to maturity of 12%.
a. Calculate the Macaulay duration of this bond
b. If yield to maturity decreases from 12% to 9.2%, calculate the price of bond after yield
to maturity changes
GV: TS. Ngô Nguyễn Quỳnh Như
CHAPTER 4
THE VALUE OF COMMON STOCKS
LÝ THUYẾT:
1. The market in which new securities are originally sold to investors is called the primary market.
2. The value of a common stock today depends on: The expected future dividends and the
discount rate.
3. An agent who arranges security transactions among investors without maintaining an inventory
is called a: broker.
4. The underlying assumption of the dividend growth model is that a stock is worth: the present
value of the future income provided by that stock.
5. If the Wall Street Journal Quotation for a company has the following values close: 55.14; Net
chg: = + 1.04; then the closing price for the stock for the previous trading day was?
 $54.10
6. The constant dividend growth formula P0 = Div1/(r - g) assumes:
I) the dividends are growing at a constant rate g forever.
II) r > g
7. Dividend growth rate for a stable firm can be estimated as: Plow back rate * the return on
equity (ROE)
Dạng bài tính “Market Capitalization”:
4.1
Chiến lược làm bài:
-
Dùng công thức:
𝑀𝑎𝑟𝑘𝑒𝑡 𝑐𝑎𝑝𝑖𝑡𝑎𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛 = 𝑁𝑜 𝑜𝑓 𝑠𝑡𝑜𝑐𝑘𝑠 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 × 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑚𝑎𝑟𝑘𝑒𝑡 𝑝𝑟𝑖𝑐𝑒 𝑝𝑒𝑟 𝑠𝑡𝑜𝑐𝑘
1. Assume General Electric (GE) has about 10.3 billion shares outstanding and the stock price is
$37.10. Also assume the P/E ratio is about 18.3. Calculate the market capitalization for GE.
(Approximately)
Dạng bài tính “P/E, EPS”:
4.2
Chiến lược làm bài:
-
Dùng công thức:
𝑃/𝐸 =
GV: TS. Ngô Nguyễn Quỳnh Như
𝑃𝑟𝑖𝑐𝑒
𝐸𝑃𝑆
1. Company X has a P/E ratio of 10 and a stock price of $50 per share. Calculate earnings per
share of the company.
Dạng bài tính “dividend payout ratio” vs “plowback ratio”:
4.3
Chiến lược làm bài:
-
Cho P/E và Price => Tính EPS
-
Dùng công thức:
𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑝𝑎𝑦𝑜𝑢𝑡 𝑟𝑎𝑡𝑖𝑜 =
𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒
𝐸𝑎𝑟𝑛𝑖𝑛𝑔 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒
1. The Wall Street Journal quotation for a company has the following values: Div: $1.12, PE:
18.3, Close: $37.22. Calculate the dividend payout ratio for the company (Approximately).
Dạng bài tính “Price” của stock:
4.4
Chiến lược làm bài:
-
Bản chất là đem các dòng cổ tức chiết khấu về hiện tại, và chiết khấu giá cổ phiếu
dự đoán tại năm (n) về hiện tại.
-
Lưu ý: Các dòng cổ tức thuộc dạng nào Annuity, Perpetuity, Growth Perpeptuity
-
Dùng công thức:
𝑃0 =
𝐷1
𝐷2
𝐷𝑛 + 𝑃𝑛
+
+⋯+
2
(1 + 𝑟 ) (1 + 𝑟 )
(1 + 𝑟 )𝑛
1. A company has decided to issue preferred stock with an annual dividend of $4 a share. Similar
stocks are currently yielding 11 percent. What price should the firm expect to receive for each
new share issued?
2. A company’s stockholders expect to receive a year-end dividend of $5 per share and then be
sold for $115 dollars per share. If the required rate of return for the stock is 20%, what is the
current value of the stock?
3. A company expects to pay a dividend of $2 per share at the end of year-1, $3 per share at the
end of year-2 and then be sold for $32 per share. If the required rate on the stock is 15%, what
is the current value of the stock?
4. A company is expected to pay a dividend of $3 per share at the end of year-1 (D1) and these
dividends are expected to grow at a constant rate of 6% per year forever. If the required rate of
return on the stock is 18%, what is current value of the stock today?
GV: TS. Ngô Nguyễn Quỳnh Như
5. A company has just now paid a dividend of $2.83 per share (D0); the dividends are expected
to grow at a constant rate of 6% per year forever. If the required rate of return on the stock is
16%, what is the current value on stock?
6. A company has just paid a dividend of $1 per share. The dividends are expected to grow at
25% 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 18%(APR), what is the current value of the stock?
7. A company has just paid a dividend of $0.50 per share. The dividends are expected to grow at
24% per year for the next two years and at 8% per year thereafter. If the required rate of return
in the stock is 16% (APR), calculate the current value of the stock.
8. A company just announced its next annual dividend will be $1.50 a share with future dividends
increasing by 1.8 percent annually. How much will one share of this stock be worth five years
from now if the required return is 15.5 percent?
9. A company has just paid an annual dividend of $1 a share. The firm plans to increase its
dividend by 20 percent a year for the next four years and then decrease the growth rate to 5
percent annually. If the required rate of return is 10.25 percent, what is one share of this stock
worth today?
10. A company last paid a $1.50 per share annual dividend. The company is planning on paying
$3, $5, $7.50, and $10 a share over the next four years, respectively. After that the dividend
will be a constant $2.50 per share per year. What is the current price of this stock if the rate of
return is 14 percent?
11. A company is going to pay $1, $2.50, and $5 a share over the next three years, respectively.
After that, the company plans to pay annual dividends of $1.25 per share indefinitely. If your
required return is 13 percent, how much are you willing to pay for one share today?
12. A company pays no dividend at the present time. In Years 2 and 3, the firm will pay annual
dividends of $3 a share. After that, it will pay a constant $1 a share dividend indefinitely. What
is this stock worth at a required return of 15 percent?
13. A company last annual dividend was $2 a share. The company plans to lower the dividend by
$.50 each year for the next three years. In Year 5, it will pay a final liquidating dividend of $22
a share. If the required return is 16 percent, what is the current per share value of this stock?
GV: TS. Ngô Nguyễn Quỳnh Như
14. A company paid its first annual dividend yesterday in the amount of $.28 a share. The company
plans to double each annual dividend payment for the next three years. After that, it will pay a
constant $1.50 per share dividend indefinitely. What is one share of this stock worth today if
the market rate of return on similar securities is 11.5 percent?
15. Last week, A company paid its annual dividend of $1.20 a share. The company has been
reducing its dividends by 6 percent each year. What is one share of stock worth at a required
return of 14 percent?
16. A company is expecting a period of intense growth, so it has decided to retain more of its
earnings to help finance that growth. As a result, it is going to reduce its annual dividend by
20 percent a year for the next three years. After that it will maintain a constant dividend of
$1.60 a share. Last year, the annual dividend was $2.60 a share. What is the market value of
this stock if the required rate of return is 13 percent?
17. A company plans to pay an annual dividend of $.75 next year, increase the dividend by 12
percent for the following three years, and then increase the dividend by 2 percent annually
thereafter. The required rate of return is 12.5 percent. What is this stock worth per share today?
18. A company has just paid a dividend of $.50 a share. The dividends are expected to increase by
20 percent a year for the next two years and then increase by 3 percent annually thereafter.
What is the current value of a share if the appropriate discount rate is 12 percent?
19. A company just announced its next annual dividend will be $1.50 a share with future dividends
increasing by 1.8 percent annually. How much will one share of this stock be worth five years
from now if the required return is 15.5 percent?
20. A company will pay an annual dividend of $2.10 a share on its common stock next year. Last
week, the company paid a dividend of $2 a share. The company adheres to a constant rate of
growth dividend policy. What will one share of this stock be worth ten years from now if the
applicable discount rate is 9 percent?
21. Suppose a company is expected to increase dividends by 20% in one year and by 15% in two
years. After that, dividends will increase at a rate of 5% per year indefinitely. If the last
dividend was $1 and the required return is 20%, what is the price of the stock?
22. A company has just paid a dividend of $3.12 and is expected to grow at a constant rate of 5
percent. The required rate of return is 23 percent. What is the current price of the stock?
GV: TS. Ngô Nguyễn Quỳnh Như
23. A company expects to pay a dividend of $1 per share at the end of year 1; $2 per share at the
end of year 2; and $3 per share at the end of year 3. After three years, the dividends are expected
to grow at a constant rate of 8% per year. If the required rate of return demanded by investors
is 12%, what is the current price of your company stock?
24. You expect your company to pay the following dividend pattern for three years as follows:
D1 = $1.7
D2 = $1.2
D3=$3
a. After three years, you sell your shares for $32 per share. If the required rate of return
demanded by investors is 15%, what is the current price of your company stock?
b. Assume that after three years, you won’t sell your shares and the dividends are expected to
grow at a constant rate of 9% per year. If the required rate of return demanded by investors
is 15%, what is the current price of your company stock?
c. If your stock was selling on the market for $35. Should you hold or sell the stock?
Dạng bài tính “Rate of return” (r%):
4.5
Chiến lược làm bài:
-
Ghi Công thức tính Price
-
Thường là dùng công thức đặc biệt.
1. A company's stock is selling for $100 per share today. It is expected that this stock will pay a
dividend of 6 dollars per share, and then be sold for $114 per share at the end of one year.
Calculate the expected rate of return for the shareholders.
2. A company just announced that its next annual dividend will be $1.42 a share and that all future
dividends are expected to increase by 2.5 percent annually. What is the market rate of return if
this stock is currently selling for $14.11 a share?
3. A company is expected to pay a dividend of $2 per share at the end of year -1(D1) and the
dividends are expected to grow at a constant rate of 4% forever. If the current price of the stock
is $20 per share calculate the expected return or the cost of equity capital for the firm.
Dạng bài tính “dividend growth rate” (g%):
4.6
Chiến lược làm bài:
-
Dùng công thức:
𝑔 = 𝑝𝑙𝑜𝑤𝑏𝑎𝑐𝑘 𝑟𝑎𝑡𝑒 × 𝑅𝑂𝐸
1. A company pays out 60% of its earnings as dividends. Its return on equity is 15%. What is the
stable dividend growth rate for the firm?
GV: TS. Ngô Nguyễn Quỳnh Như
Dạng bài tính “Dividend in year n”:
4.7
Chiến lược làm bài:
-
Tính Dividend từng năm. Lưu ý tốc độ g khác nhau.
-
Di = D(i-1) * (1 + g)
1. A company is currently paying a dividend of $2.00 per share. The dividends are expected to
grow at 20% per year for the next four years and then grow 6% per year thereafter. Calculate
the expected dividend in year 5.
2. A company is currently paying a dividend of $1.40 per year. The dividends are expected to
grow at a rate of 18% for the next three years and then a constant rate of 5% thereafter. What
is the expected dividend per share in year 5?
3. A company has just paid an annual dividend of $.24 a share and plans on increasing this amount
by 2 percent annually. What is the expected dividend for Year 6?
GV: TS. Ngô Nguyễn Quỳnh Như
CHAPTER 5
INTRODUCTION TO RISK AND RETURN
LÝ THUYẾT:
1. A portfolio of Treasury bills has the least risk.
2. Variance is the average squared difference between the actual return and the average return.
3. The standard deviation for a set of stock returns can be calculated as the positive square root
of the variance.
4. Long-term U.S. government bonds have interest rate risk.
5. Standard error measures the reliability of an estimate. Standard error is estimated as standard
deviation of returns divided by the square root of the number of observations.
6. The range of values that correlation coefficients can take can be -1 to +1.
7. The type of the risk that can be eliminated by diversification is called: Unique risk. The unique
risk is also called the: Unsystematic risk, Diversifiable risk, Firm specific risk.
8. The "beta" is a measure of Market risk. The beta of market portfolio is + 1.0. Market risk is
also called: systematic risk, undiversifiable risk.
9. As the number of stocks in a portfolio is increased: Unique risk decreases and approaches to
zero.
5.1
Dạng bài 1 stock, n year
Chiến lược làm bài:
-
Nhận diện đạng bài cho r thực tế của 1 stock qua từng năm. Dùng công thức:
-
Expected rate of return:
𝐄𝐱𝐩𝐞𝐜𝐭𝐞𝐝 𝐫𝐚𝐭𝐞 𝐨𝐟 𝐫𝐞𝐭𝐮𝐫𝐧 = 𝒓̅ =
-
𝒓𝟏 + 𝒓𝟐 + … + 𝒓𝒏
𝒏
Risk:
𝐕𝐚𝐫𝐢𝐚𝐧𝐜𝐞 = 𝛔𝟐 =
[(𝒓𝟏 − 𝒓̅)𝟐 + (𝒓𝟐 − 𝒓̅)𝟐 + ⋯ . +(𝒓𝒏 − 𝒓̅)𝟐 ]
𝐧−𝟏
𝐒𝐭𝐚𝐧𝐝𝐚𝐫𝐝 𝐃𝐞𝐯𝐢𝐚𝐭𝐢𝐨𝐧 = 𝝈
-
Lưu ý: Đơn vị tính rate of return và standard deviation là %
1. 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.
2. A stock had returns of 12 percent, 6 percent, 14 percent, and -3 percent annually for the past
four years. What is the mean and standard deviation of these returns?
GV: TS. Ngô Nguyễn Quỳnh Như
3. A stock had returns of 14 percent, 3 percent, 9 percent, and -12 percent annually for the past
four years. What is the mean and variance of these returns?
4. A stock had annual returns of 8 percent, -2 percent, 4 percent, and 20 percent over the past four
years. What is the standard deviation of these returns?
5. A stock had returns of 19 percent, 12 percent, -29 percent, 35 percent, and 4 percent annually
for the past five years. Based on these returns, what is the standard deviation of these returns?
6. A stock returned 13 percent, 18 percent, -16 percent and -1 percent annually for the past four
years. Based on this information, what is the 99.74 percent probability range for any one given
year?
7. 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.
8. Macro Corporation has had the following returns for the past three years, -10%, 10%, and 30%.
Calculate the standard deviation of the returns.
9. Sun Corporation has had returns of -6%, 16%, 18%, and 28% for the past four years. Calculate
the standard deviation of the returns.
10. Florida Company (FC) and Minnesota Company (MC) are both service companies. Their
historical returns for the past three years are: FC: - 5%, 15%, 20%; MC: 8%, 8%, 20%.
Calculate the mean of returns, the variances and SD of return for each company.
5.2
Dạng bài 1 stock, in different economy
Chiến lược làm bài:
-
Nhận diện dạng bài cho r thực tế của 1 stock tương ứng với từng tình trạng nền kinh tế.
Đồng thời cho xác suất xảy ra từng tình trạng nền kinh tế. Dùng công thức:
-
Expected rate of return:
𝐄𝐱𝐩𝐞𝐜𝐭𝐞𝐝 𝐫𝐚𝐭𝐞 𝐨𝐟 𝐫𝐞𝐭𝐮𝐫𝐧 = 𝒓̅ = 𝒘𝟏 𝒓𝟏 + 𝒘𝟐 𝒓𝟐 + ⋯ + 𝒘𝒊 𝒓𝒊
-
Risk:
𝐕𝐚𝐫𝐢𝐚𝐧𝐜𝐞 = 𝛔𝟐 = 𝒘𝟏 (𝒓𝟏 − 𝒓̅)𝟐 + 𝒘𝟐 (𝒓𝟐 − 𝒓)𝟐 + ⋯ . +𝒘𝒊 (𝒓𝐢 − 𝒓̅)𝟐
𝐒𝐭𝐚𝐧𝐝𝐚𝐫𝐝 𝐃𝐞𝐯𝐢𝐚𝐭𝐢𝐨𝐧 = 𝝈
-
Lưu ý: Đơn vị tính rate of return và standard deviation là %
1. You recently purchased a stock that is expected to earn 15 percent in a booming economy, 9
percent in a normal economy and lose 5 percent in a recessionary economy. There is a 15
GV: TS. Ngô Nguyễn Quỳnh Như
percent probability of a boom, a 75 percent chance of a normal economy, and a 10 percent
chance of a recession. What is your expected rate of return on this stock?
2. The Inferior Goods Co. stock is expected to earn 22 percent in a booming, 7 percent in a normal
economy, and lose 14 percent in a recession economy. The probability of a boom is 20 percent
while the probability of a normal economy is 55 percent. What is the expected rate of return
on this stock?
3. The rate of return on the common stock of Flowers by Flo is expected to be 15 percent in a
boom economy, 7 percent in a normal economy, and only 3 percent in a recessionary economy.
The probabilities of these economic states are 20 percent for a boom, 70 percent for a normal
economy, and 10 percent for a recession. What is the variance of the returns on this stock?
4. KNF stock is quite cyclical. In a boom economy, the stock is expected to return 30 percent in
comparison to 12 percent in a normal economy and a negative 17 percent in a recessionary
period. The probability of a recession is 25%. There is a 15% chance of a boom economy.
What is the standard deviation of the returns this stock?
5.3
Dạng bài tính Covariance, Correlation coefficient, n year
Chiến lược làm bài:
-
Nhận diện đạng bài cho r thực tế của stock X, Y lần lượt qua n năm. Dùng công thức:
-
Covariance:
𝐂𝐨𝐯𝐚𝐫𝐢𝐚𝐧𝐜𝐞 (𝒓𝐀 , 𝒓𝐁 ) = 𝛔𝐀𝐁 =
-
∑[(𝐫𝐀𝐭 − 𝒓̅𝐀 ) × (𝒓𝐁𝐭 − 𝒓̅𝐁 )]
𝐧−𝟏
Correlation coefficient:
𝐂𝐨𝐫𝐫𝐞𝐥𝐚𝐭𝐢𝐨𝐧(𝒓𝐀 , 𝒓𝑩 ) = 𝛒𝐀𝐁 (đọ𝐜 𝐥à 𝐫ô) =
𝛔𝐀𝐁
𝛔𝐀 × 𝛔𝐁
-
Lưu ý: Covariance và Correlation Coefficient không có đơn vị
-
Ý nghĩa của Cov và Corr:
•
Covariance (Hiệp phương sai) đo lường 2 biến ngẫu nhiên quan hệ với nhau như thế nào.
•
Covariance measures the interrelationship between two securities.
•
Cov > 0: cho thấy một mối quan hệ cùng chiều của 2 tỷ suất sinh lợi sẽ cho. Tức là khi
tỷ suất sinh lợi của cp X thấp hơn mức trung bình thì tỷ suất sinh lợi của cp Y cũng sẽ
thấp hơn mức trung bình của nó.
GV: TS. Ngô Nguyễn Quỳnh Như
•
Cov < 0: cho thấy một mối quan hệ ngược chiều của 2 tỷ suất sinh lợi sẽ cho. Tức là khi
tỷ suất sinh lợi của cp X thấp hơn mức trung bình thì tỷ suất sinh lợi của cp Y cũng sẽ
cao hơn mức trung bình của nó.
o Cov = 0: cho thấy 2 chứng khoán không có tương quan.
•
Correlation coefficient (Hệ số tương quan) đo lường hai biến ngẫu nhiên quan hệ với
nhau như thế nào. Hệ số tương quan (Corr) luôn nằm giữa [-1,1].
•
The correlation measures the direction of movement between the returns of two stocks.
If the correlation coefficient between Stock A and Stock B is +0.6, the correlation
between Stock B with Stock A will be +0.6.
•
Corr (𝒓𝐀 , 𝒓𝑩 ) = 1: Tỷ suất sinh lợi của chứng khoán A và chứng khoán B cùng cao hơn
tỷ suất sinh lợi trung bình trong cùng 1 thời điểm. Ngược lại, tỷ suất sinh lợi của chứng
khoán A và chứng khoán B cùng thấp hơn tỷ suất sinh lợi trung bình trong cùng 1 thời
điểm.
•
Corr (𝒓𝐀 , 𝒓𝑩 ) = -1: Tỷ suất sinh lợi chứng khoán A cao hơn mức tỷ suất sinh lợi trung
bình khi tỷ suất sinh lợi B thấp hơn tỷ suất sinh lợi trung bình và ngược lại.
•
Corr (𝒓𝐀 , 𝒓𝑩 ) = 0: Tỷ suất sinh lợi của chứng khoán A hoàn toàn không tương quan đến
tỷ suất sinh lợi chứng khoán B.
1. 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.
2. 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.
3. 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.
4. If the covariance between stock A and stock B is 0.01, the standard deviation of stock A is
10% and that of stock B is 20%, calculate the correlation coefficient between the two securities.
5. For a two-stock portfolio, the maximum reduction in risk occurs when the correlation
coefficient between the two stocks is:……
6. The variance of Stock A is .003969, the variance of Stock B is .007056, and the covariance
between the two is .0026. What is the correlation coefficient?
GV: TS. Ngô Nguyễn Quỳnh Như
7. The variance of Stock A is .015376, the variance of Stock B is .028561, and the covariance
between the two is .0024. What is the correlation coefficient?
8. Florida Company (FC) and Minnesota Company (MC) are both service companies. Their
historical returns for the past three years are: FC: - 5%, 15%, 20%; MC: 8%, 8%, 20%.
Calculate the covariance between the returns of FC and MC.
9. 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.
5.4
Dạng bài tính Covariance, Correlation coefficient, in different economies
Chiến lược làm bài:
-
Nhận diện đạng bài cho r thực tế của stock X, Y lần lượt qua từng tình trạng nền kinh tế
khác nhau. Đồng thời cho xác suất xảy ra từng tình trạng nền kinh tế. Dùng công thức:
-
Covariance:
𝐂𝐨𝐯𝐚𝐫𝐢𝐚𝐧𝐜𝐞 (𝒓𝐀 , 𝒓𝐁 ) = 𝛔𝐀𝐁 = ∑[𝒘𝒊 × (𝐫𝐀𝐭 − 𝒓̅𝐀 ) × (𝒓𝐁𝐭 − 𝒓̅𝐁 )]
-
Correlation coefficient:
𝐂𝐨𝐫𝐫𝐞𝐥𝐚𝐭𝐢𝐨𝐧(𝒓𝐀 , 𝒓𝑩 ) = 𝛒𝐀𝐁 (đọ𝐜 𝐥à 𝐫ô) =
𝛔𝐀𝐁
𝛔𝐀 × 𝛔𝐁
-
Lưu ý: Covariance và Correlation Coefficient không có đơn vị
-
Ý nghĩa của Cov và Corr:
•
Covariance (Hiệp phương sai) đo lường 2 biến ngẫu nhiên quan hệ với nhau như thế nào.
•
Covariance measures the interrelationship between two securities.
•
Cov > 0: cho thấy một mối quan hệ cùng chiều của 2 tỷ suất sinh lợi sẽ cho. Tức là khi
tỷ suất sinh lợi của cp X thấp hơn mức trung bình thì tỷ suất sinh lợi của cp Y cũng sẽ
thấp hơn mức trung bình của nó.
•
Cov < 0: cho thấy một mối quan hệ ngược chiều của 2 tỷ suất sinh lợi sẽ cho. Tức là khi
tỷ suất sinh lợi của cp X thấp hơn mức trung bình thì tỷ suất sinh lợi của cp Y cũng sẽ
cao hơn mức trung bình của nó.
o Cov = 0: cho thấy 2 chứng khoán không có tương quan.
•
Correlation coefficient (Hệ số tương quan) đo lường hai biến ngẫu nhiên quan hệ với
nhau như thế nào. Hệ số tương quan (Corr) luôn nằm giữa [-1,1].
GV: TS. Ngô Nguyễn Quỳnh Như
•
The correlation measures the direction of movement between the returns of two stocks.
If the correlation coefficient between Stock A and Stock B is +0.6, the correlation
between Stock B with Stock A will be +0.6.
•
Corr (𝒓𝐀 , 𝒓𝑩 ) = 1: Tỷ suất sinh lợi của chứng khoán A và chứng khoán B cùng cao hơn
tỷ suất sinh lợi trung bình trong cùng 1 thời điểm. Ngược lại, tỷ suất sinh lợi của chứng
khoán A và chứng khoán B cùng thấp hơn tỷ suất sinh lợi trung bình trong cùng 1 thời
điểm.
•
Corr (𝒓𝐀 , 𝒓𝑩 ) = -1: Tỷ suất sinh lợi chứng khoán A cao hơn mức tỷ suất sinh lợi trung
bình khi tỷ suất sinh lợi B thấp hơn tỷ suất sinh lợi trung bình và ngược lại.
•
Corr (𝒓𝐀 , 𝒓𝑩 ) = 0: Tỷ suất sinh lợi của chứng khoán A hoàn toàn không tương quan đến
tỷ suất sinh lợi chứng khoán B.
1. A portfolio consists of 40 percent of Stock S and 60 percent of Stock T. Stock S will return
13 percent if the economy booms and 8 percent if it is normal. Stock T will return 6 percent
in a boom and 10 percent in a normal economy. The probability of a boom is 50 percent.
What is the covariance and correlation coefficient between 2 stocks?
2. The economy has a 14 percent chance of booming. Otherwise, the economy will be normal.
Stock G will return 15 percent in a boom and 8 percent in a normal economy. Stock H will
return 9 percent in a boom and 6 percent in a normal economy. What is the covariance and
correlation coefficient between 2 stocks?
3. Stock Q will return 18 percent in a boom and 9 percent in a normal economy. Stock R will
return 9 percent in a boom and 5 percent in a normal economy. There is a 75 percent
probability the economy will be normal. What is the covariance and correlation coefficient
between 2 stocks?
4. Stock A will return 15 percent in a normal economy and lose 14 percent in a recession.
Stock B deals with inferior goods and will return 7 percent in a normal economy and 18
percent in a recession. There is a 20 percent chance of a recession occurring. What is the
covariance and correlation coefficient between 2 stocks?
5. There is a 5 percent probability the economy will boom, an 85 percent probability it will
be normal, and a 10 percent probability it will be recessionary. For these economic states,
Stock A has deviations from its expected returns of .06, .01, and -.08, respectively. Stock
GV: TS. Ngô Nguyễn Quỳnh Như
B has deviations from its expected returns of .06, .00, and -.05, for the three economic
states, respectively. What is the covariance of the two stocks?
6. There is a 10 percent probability the economy will boom, a 65 percent probability it will
be normal, and a 25 percent probability it will be recessionary. For these economic states,
Stock A has deviations from its expected returns of .07, .02, and -.12, respectively. Stock
B has deviations from its expected returns of .05, .01, and -.04, for the three economic
states, respectively. What is the covariance of the two stocks?
Dạng bài tính “Portfolio weight”
5.5
Chiến lược làm bài:
-
1 portfolio có 2 chứng khoán (A, B), cho 𝑟̅𝑝 , kêu tính 𝑤𝐴 , 𝑤𝐵 . Dùng công thức:
𝑟̅𝑝 = 𝑤𝐴 𝑟̅𝐴 + (100% − 𝑤𝐴 ) × 𝑟̅𝐵
-
Cho số lượng cổ phiếu và giá cổ phiếu, kêu tính 𝑤𝑖 . Dùng công thức:
𝑤𝑖 =
-
𝑆ố 𝑙ượ𝑛𝑔 𝑐𝑝 𝑖 × 𝐺𝑖á 1 𝑐ổ 𝑝ℎ𝑖ế𝑢 𝑖
𝑇ổ𝑛𝑔 𝑠ố 𝑡𝑖ề𝑛 đầ𝑢 𝑡ư 𝑡𝑟𝑜𝑛𝑔 𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜
Lưu ý: 𝒘𝒊 đơn vị %.
1. You have a 2-stock portfolio with an expected return of 10.6 percent. Stock A has an expected
return of 12 percent while Stock B is expected to return 8 percent. What is the portfolio weight
of Stock A?
2. A portfolio consists of 600 shares of Stock A, 100 shares of Stock B, 200 shares of Stock C,
and 500 shares of Stock D. The prices of these stocks are $27, $22, $38, and $16 for Stocks A
through D, respectively. What is the portfolio weight of stock C?
GV: TS. Ngô Nguyễn Quỳnh Như
5.6
Dạng bài 1 portfolio including 2 stocks
Chiến lược làm bài:
-
Nhận diện dạng bài cho 1 portfolio có nhiều loại tài sản tài chính chiếm tỷ trọng 𝑤𝑖 .
Dùng công thức:
-
Expected rate of return of a portfolio including 2 stocks A and B:
̅̅̅
𝒓𝒑 = 𝒘𝑨 𝒓𝑨 + 𝒘𝑩 𝒓𝑩
-
Risk of a portfolio including 2 stocks A and B:
𝝈𝟐𝒑 = 𝐰𝐀 𝟐 𝛔𝐀 𝟐 + 𝟐𝐰𝐀 𝐰𝐁 𝛔𝐀𝐁 + 𝐰𝐁 𝟐 𝛔𝐁 𝟐
Hoặc
𝝈𝟐𝒑 = 𝐰𝐀 𝟐 𝛔𝐀 𝟐 + 𝟐𝐰𝐀 𝐰𝐁 𝛒𝐀𝐁 𝝈𝑨 𝝈𝑩 + 𝐰𝐁 𝟐 𝛔𝐁 𝟐
𝐒𝐭𝐚𝐧𝐝𝐚𝐫𝐝 𝐃𝐞𝐯𝐢𝐚𝐭𝐢𝐨𝐧 = 𝝈𝒑
-
-
Trong đó:
•
wA , wB : tỷ trọng đầu tư của ck A, B trong danh mục
•
σA 2 , σB 2 : phương sai của 𝑟A , 𝑟𝐵
•
σAB : Hiệp phương sai của 𝑟A , 𝑟𝐵
•
ρAB : Hệ số tương quan của 𝑟A , 𝑟𝐵
Lưu ý: Đơn vị tính rate of return và standard deviation là %
1. A portfolio consists of $10,500 of Stock A, $21,600 of Stock B, and $27,000 of Stock C. The
expected returns on Stocks A, B, and C are 7 percent, 11 percent and 5 percent, respectively.
What is the overall portfolio expected rate of return?
2. 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?
3. 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?
GV: TS. Ngô Nguyễn Quỳnh Như
4. The table below shows the one-year return distribution for stock A and stock B.
Stock A
Stock B
Return
Probability
Return
Probability
-10%
50%
-15%
10%
20%
50%
15%
30%
10%
60%
Notes: you invest 40% in Stock A and 60% in Stock B, correlation coefficient of 2 stocks = -1.
a. Calculate expected return of two stocks?
b. Calculate the standard deviation of two stocks?
c. Calculate expected return of portfolio?
d. Calculate the standard deviation of portfolio?
5. SCS and HVN are both service companies. Their historical returns for the past three years are:
SCS: - 5%, 17%, 25%; HVN: 3%, 18%, 30%. What are the expected return and the standard
deviation of portfolio with 30% of the funds invested in SCS and 70% in HVN
(approximately)? Knowing that cov (SCS, HVN) = 0.01891.
6. A portfolio consists of $12,000 of stock K and $23,000 of stock L. Stock K will return 14
percent in a booming economy and 5 percent in a normal economy. Stock L will return 10
percent in a booming economy and 6 percent in a normal economy. The probability of the
economy booming is 22 percent. What is the expected rate of return on the portfolio if the
economy is normal?
7. A portfolio is expected to return 15 percent in a booming economy, 12 percent in a normal
economy, and lose 9 percent if the economy falls into a recession. The probability of a boom
is 25 percent while the probability of a recession is 15 percent. What is the overall portfolio
expected return?
8. A portfolio consists of 40 percent of Stock S and 60 percent of Stock T. Stock S will return 13
percent if the economy booms and 8 percent if it is normal. Stock T will return 6 percent in a
boom and 10 percent in a normal economy. The probability of a boom is 50 percent. What is
the portfolio variance?
9. The economy has a 14 percent chance of booming. Otherwise, the economy will be normal.
Stock G will return 15 percent in a boom and 8 percent in a normal economy. Stock H will
GV: TS. Ngô Nguyễn Quỳnh Như
return 9 percent in a boom and 6 percent in a normal economy. What is the variance of a
portfolio consisting of $2,500 of stock G and $7,500 of stock H?
10. Stock Q will return 18 percent in a boom and 9 percent in a normal economy. Stock R will
return 9 percent in a boom and 5 percent in a normal economy. There is a 75 percent probability
the economy will be normal. What is the standard deviation of a portfolio that is invested 40
percent in stock Q and 60 percent in stock R?
11. Stock A will return 15 percent in a normal economy and lose 14 percent in a recession. Stock
B deals with inferior goods and will return 7 percent in a normal economy and 18 percent in a
recession. There is a 20 percent chance of a recession occurring. What is the standard deviation
of a portfolio that is equally weighted between the two stocks?
12. Florida Company (FC) and Minnesota Company (MC) are both service companies. Their
historical returns 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.
13. A portfolio is equally weighted. Security One has a standard deviation of 10 percent. Security
Two has a standard deviation of 8 percent. The securities have a covariance of .4254. What is
the portfolio variance?
14. A portfolio consists of two stocks with Stock A having a weight of 64 percent. Stock A has a
standard deviation of 21.22 percent. Stock B has a standard deviation of 16.44 percent. The
stocks have a covariance of -.027. What is the portfolio variance?
5.7
Dạng bài tính Beta of a stock
Chiến lược làm bài:
-
Nếu gọi r là tỷ suất sinh lợi thực tế của chứng khoán (i), r̅ là tỷ suất sinh lợi trung bình
của chứng khoán (i) thì sự khác nhau giữa TSSL thực tế và TSSL trung bình là thể hiện
rủi ro của chứng khoán đó:
𝐫 = 𝐫̅ + 𝐮 = 𝐫̅ + 𝐦 + 𝛆
-
-
Trong đó:
•
m: systematic risk, market risk, undiversifiable risk (rủi ro hệ thống)
•
ε: unsystematic risk, unique risk, diversifiable risk (rủi ro phi hệ thống)
Rủi ro phi hệ thống có thể bị triệt tiêu trong 1 danh mục đa dạng hóa tốt, nhưng rủi ro hệ
thống thì không. Do đó, một nhà đầu tư đa dạng hóa sẽ chỉ phải quan tâm sẽ chỉ quan
GV: TS. Ngô Nguyễn Quỳnh Như
tâm đến rủi ro hệ thống và bỏ qua rủi ro phi hệ thống của tất cả chứng khoán có trong
danh mục.
-
Nhưng có cách nào đo lường rủi ro hệ thống của một chứng khoán. Có, thước đo tốt nhất
chính là beta. Beta là thước đo rủi ro tốt nhất của 1 chứng khoán riêng lẻ từ góc độ của
1 NĐT đa dạng hóa.
-
Dùng công thức:
𝛃𝐢 =
-
𝛔𝐢𝐦
𝝈𝒎 𝟐
Trong đó:
•
σim : Hiệp phương sai của 𝑟𝑖 , 𝑟𝑚 .
•
𝜎𝑚 2 : Phương sai của 𝑟𝑚 .
1. 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.
2. 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.
3. A stock has an expected return of 14.21 percent. The return on the market is 11.8 percent and
the risk-free rate of return is 3.2 percent. What is the beta of this stock?
4. 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.
5. Calculate Beta of Treasury bills
6. Calculate Beta of the market portfolio
Dạng bài tính “Market risk premium”
5.8
Chiến lược làm bài:
-
Dùng công thức tính “Phần bù rủi ro thị trường”:
𝒎𝒂𝒓𝒌𝒆𝒕 𝒓𝒊𝒔𝒌 𝒑𝒓𝒆𝒎𝒊𝒖𝒎 = 𝒓𝒎 − 𝒓𝒇
-
Trong đó:
•
𝑟𝑓 : tỷ suất sinh lời phi rủi ro (là tỷ suất sinh lời của T-Bills)
•
𝑟𝑚 : tỷ suất sinh lời của thị trường
1. Assume the market portfolio of common stocks earned 14.1 percent in one year while U.S.
Treasury bills earned 4.4 percent and inflation averaged 4.6 percent. What was the market risk
premium?
GV: TS. Ngô Nguyễn Quỳnh Như
2. 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?
3. Given the following data: risk-free rate = 4%, average risk premium = 7.7%. Calculate the
required rate of return of the market.
GV: TS. Ngô Nguyễn Quỳnh Như
CHAPTER 6
PORTFOLIO THEORY AND THE CAPM
Key terms cần nhớ:
1. Expected return of a single stock, n-year / in different economies
2. Variance and Standard Deviation of return of a stock. Standard deviation measures total risk.
3. CFO dựa trên return (mean %) và total risk (SD %) để ra quyết định tài chính. Nguyên tắc ra
quyết định tài chính đó là: Giữa 2 khoản đầu tư có cùng TSSL (mean %) thì chọn khoản đầu
tư có RR thấp hơn (SD %), và ngược lại.
4. Đo lường mối quan hệ cùng chiều hay nghịch chiều giữa 2 khoản đầu tư thì dùng Covariance
(Hiệp phương sai) và Correlation Coefficient (Hệ số tương quan). Covariance measures the
interrelationship between two securities. The correlation measures the direction of
movement between the returns of two stocks. If the correlation coefficient between Stock A
and Stock B is +0.6, the correlation between Stock B with Stock A will be +0.6.
5. If a stock portfolio is well diversified, then the portfolio variance may be less than the variance
of the least risky stock in the portfolio.
6. The standard deviation of a portfolio will tend to increase when the portfolio concentration in
a single cyclical industry increase.
7. Assume two securities are negatively correlated. If these two securities are combined into an
equally weighted portfolio, the portfolio standard deviation must be less than the weighted
average of the standard deviations of the individual securities.
8. Một stock sẽ chịu 2 loại rủi ro: unique risk (RR riêng biệt) và market risk (RR thị trường).
Unique risk
Another name
Diversifiable
Market risk
risk,
Unsystematic Non-diversifiable risk, Systematic
risk
Example
risk
A well-managed firm reduces its A well-respected chairman of the
work force and automates several Federal Reserve suddenly resigns,
jobs.
A poorly managed firm suddenly
goes out of business due to lack of
sales.
GV: TS. Ngô Nguyễn Quỳnh Như
Inflation rises unexpectedly.
A key employee of a firm suddenly
resigns and accepts employment
with a key competitor.
Features
Unsystematic risk can be effectively Systematic risk is measured by beta.
eliminated
through
portfolio
diversification.
Well-diversified
portfolios
have
negligible unsystematic risks.
9. Giảm RR riêng biệt bằng cách diversification (đa dạng hóa) danh mục đầu tư. The principle
of diversification tells us that spreading an investment across many diverse assets will lower
a portfolio's level of risk.
10. A portfolio is being effectively diversified can be indicated by a decrease in the portfolio
standard deviation.
11. The efficient portfolios provide highest returns for a given level of risk, provide the least risk
for a given level of returns.
12. Expected return of a portfolio.
•
When computing the expected return on a portfolio of stocks, the portfolio weights are
based on the market value of the total shares held in each stock.
•
The expected return on a portfolio is limited by the returns on the individual securities
within the portfolio.
13. Variance and Standard Deviation of return of a portfolio.
14. Beta measure indicates the change in the rate of return on an investment for a given change
in the market return.
Example: Beta of Treasury bills is 0. Beta of the market portfolio is +1.0
A stock with a beta of 1. 25 would be expected to increase in returns 25% faster than the market
in up markets.
15. Mô hình định giá tài sản vốn (CAPM) => một cách khác để tính TSSL của vốn đầu tư. The
capital asset pricing model (CAPM) states that the expected risk premium on an investment
is proportional to its beta.
16. The market risk premium is computed by subtracting the risk-free rate of return from the
market rate of return.
GV: TS. Ngô Nguyễn Quỳnh Như
Dạng bài “Investment decision”:
6.1
1. 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 ……………..
2. 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 ……………
Expected return of a single stock with data of beta, rf, rm – rf
6.2
Chiến lược làm bài:
-
Nhận diện dạng bài có cho beta, risk-free rate, market rate.
-
Dùng công thức:
𝑀𝑎𝑟𝑘𝑒𝑡 𝑟𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 = 𝑟𝑚 − 𝑟𝑓
𝑟𝐶𝐴𝑃𝑀 = 𝑟𝑓 + 𝛽 × (𝑟𝑚 − 𝑟𝑓 )
-
Trong đó:
•
𝑟𝑓 : risk-free rate / T-Bill rate
•
𝑟𝑚 : market rate / interest rate
-
Muốn đánh giá xem 1 stock có đang được đánh giá thấp hoặc cao hay không thì so sánh:
•
𝑟𝐶𝐴𝑃𝑀 = 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑟𝑒𝑡𝑢𝑟𝑛: correctly priced
•
𝑟𝐶𝐴𝑃𝑀 > 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑟𝑒𝑡𝑢𝑟𝑛: overpriced
•
𝑟𝐶𝐴𝑃𝑀 < 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑟𝑒𝑡𝑢𝑟𝑛: underpriced
1. The market has an expected rate of return of 12.8 percent. The long-term government bond is
expected to yield 4.5 percent and the U.S. Treasury bill is expected to yield 3.4 percent. The
inflation rate is 3.1 percent. What is the market risk premium?
2. 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.
3. 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:
4. 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:
5. The risk-free rate of return is 3.3 percent and the market risk premium is 7.5 percent. What is
the expected rate of return on a stock with a beta of 1.62?
6. PPO stock has a beta of 1.12 and an expected return of 12.64 percent. The risk-free rate of
return is 3.85 percent. What is the expected return on the market?
GV: TS. Ngô Nguyễn Quỳnh Như
7. The expected return on HiLo stock is 12.04 percent while the expected return on the market is
10.52 percent. The beta of HiLo is 1.28. What is the risk-free rate of return?
8. The stock of Martin Industries has a beta of 1.02. The risk-free rate of return is 3.7 percent and
the market risk premium is 6.85 percent. What is the expected rate of return on Martin
Industries stock?
9. Stock A has a beta of .92 and an expected return of 9.04 percent. Stock B has a beta of 1.04
and an expected return of 9.51 percent. Stock C has a beta of 1.36 and an expected return of
11.68 percent. The risk-free rate is 3 percent and the market risk premium is 6.5 percent. Which
of these stocks are underpriced?
10. Which one of the following stocks, if any, is correctly priced according to CAPM if the riskfree rate of return is 6.5 percent and the market rate of return is 10.5 percent? Stock A with a
beta of .85 and an expected return of 9.22 percent; Stock B with a beta of 1.08 and an expected
return of 11.90 percent; Stock C with a beta of 1.69 and an expected return of 15.38 percent;
Stock D with a beta of 1.45 and an expected return of 12.30 percent.
11. 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: ………..
12. 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: ………..
13. 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: ………..
6.3
Beta of a portfolio
Chiến lược làm bài:
-
Nhận diện dạng bài có cho beta của từng stock, kêu tính beta của portfolio.
-
Dùng công thức:
𝑛
𝛽𝑝 = ∑ 𝑤𝑖 × 𝛽𝑖
1
1. A portfolio is comprised of 30 percent of stock X, 55 percent of stock Y, and 15 percent of
stock Z. Stock X has a beta of .87, stock Y has a beta of 1.48, and stock Z has a beta of 1.04.
What is the portfolio beta?
GV: TS. Ngô Nguyễn Quỳnh Như
CHAPTER 7
RISK AND THE COST OF CAPITAL
Key terms cần nhớ:
1. Market risk premium = 𝑟𝑚 − 𝑟𝑓
2. Generally, the value to use for the risk-free interest rate is short-term Treasury bill rate.
3. Cost of capital is the same as cost of equity for firms financed entirely by equity.
4. The cost of capital for a project depends on the use to which the capital is put, i.e. the project.
5. The hurdle rate for capital budgeting decisions is the cost of capital.
6. Weighted average cost of capital (WACC): is the company cost of capital when debt as well
as equity is used for financing.
7. The after-tax weighted average cost of capital (WACC) is calculated using the formula:
𝑊𝐴𝐶𝐶 = 𝑟𝐷 × (1 − 𝑇𝑐 ) ×
𝐷
𝐸
+ 𝑟𝐸 ×
𝑉
𝑉
where: V = D + E
8. Using the company cost of capital to evaluate a project is correct for projects that are about as
risky as the average of the firm's other assets.
9. Cost of equity can be estimated using: Discounted cash flow (DCF) approach, Capital Asset
Pricing Model (CAPM), Arbitrage Pricing theory (APT), The Fama-French three-factor model
7.1
Market risk premium
Chiến lược làm bài:
-
Nhận diện dạng bài có cho 𝑟𝑚 và 𝑟𝑓
-
Áp dụng công thức:
Market risk premium = 𝑟𝑚 − 𝑟𝑓
1. 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.
2. 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?
GV: TS. Ngô Nguyễn Quỳnh Như
7.2
Expected rate of return / Expected rate of return / Discount rate, CAPM
Chiến lược làm bài:
-
Nhận diện dạng bài có cho beta, risk-free rate, market rate.
-
Dùng công thức:
𝑀𝑎𝑟𝑘𝑒𝑡 𝑟𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 = 𝑟𝑚 − 𝑟𝑓
𝑟𝐶𝐴𝑃𝑀 = 𝑟𝑓 + 𝛽 × (𝑟𝑚 − 𝑟𝑓 )
-
Trong đó:
•
𝑟𝑓 : risk-free rate / T-Bill rate
•
𝑟𝑚 : market rate / interest rate
1. 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.
2. An all-equity firm has a beta of .98. The firm is evaluating a project that will increase the
output of the firm's existing product. The market risk premium is 7.3 percent and the risk-free
rate is 3.4 percent. What discount rate should be assigned to this expansion project?
3. 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%)
4. 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?
5. 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 riskfree rate of return is 5%, calculate the required rate of return on the Stock C using CAPM.
7.3
Cost of capital
Chiến lược làm bài:
-
Nhận diện dạng bài có cho nguồn vốn cty từ equity và từ debt, cho tỷ suất sinh lời đòi
hỏi trên equity và cho chi phí sử dụng nợ.
-
Dùng công thức:
GV: TS. Ngô Nguyễn Quỳnh Như
𝑀𝑎𝑟𝑘𝑒𝑡 𝑟𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 = 𝑟𝑚 − 𝑟𝑓
𝑟𝐶𝐴𝑃𝑀 = 𝑟𝑓 + 𝛽 × (𝑟𝑚 − 𝑟𝑓 )
𝐶𝑂𝐶 =
-
𝐸
𝐷
× 𝑟𝐸 + × 𝑟𝐷
𝑉
𝑉
Lưu ý: COC đơn vị là %.
•
risk-free debt: debt có chi phí vay bằng 𝑟𝑓 .
•
pretax cost of debt: còn được gọi là 𝑟𝐷 .
•
COC còn có tên gọi khác là pretax cost of capital.
1. 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.)
2. The market value of Cable Company's equity is $60 million, and the market value of its riskfree 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.)
3. 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.)
4. 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.)
7.4
WACC
Chiến lược làm bài:
-
Nhận diện dạng bài có cho nguồn vốn cty từ equity và từ debt, cho tỷ suất sinh lời đòi
hỏi trên equity và cho chi phí sử dụng nợ, cho thuế suất thuế TNDN.
-
Dùng công thức:
𝑀𝑎𝑟𝑘𝑒𝑡 𝑟𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 = 𝑟𝑚 − 𝑟𝑓
𝑟𝐶𝐴𝑃𝑀 = 𝑟𝑓 + 𝛽 × (𝑟𝑚 − 𝑟𝑓 )
𝑊𝐴𝐶𝐶 =
GV: TS. Ngô Nguyễn Quỳnh Như
𝐸
𝐷
× 𝑟𝐸 + × 𝑟𝐷 × (1 − 𝑇)
𝑉
𝑉
-
Lưu ý: WACC đơn vị là %.
•
risk-free debt: debt có chi phí vay bằng 𝑟𝑓 .
•
pretax cost of debt: còn được gọi là 𝑟𝐷 .
•
WACC còn có tên gọi khác là after-tax cost of capital / discount rate.
1. A firm has a beta of 1.3 and a debt-to-equity ratio of .4. The market rate of return is 11.6
percent, the tax rate is 32 percent, and the risk-free rate is 3.3 percent. The pretax cost of debt
is 7.2 percent. What is the firm's WACC?
2. Taylor's has a beta of .78 and a debt-to-equity ratio of .2. The market rate of return is 10.6
percent, the tax rate is 34 percent, and the risk-free rate is 1.4 percent. The pretax cost of debt
is 6.1 percent. What is the firm's WACC?
3. A company is 40% financed by risk-free debt. The interest rate is 10%, the expected market
risk premium is 8%, and the beta of the company’s common stock is .5. What is the company
cost of capital (COC)? What is the after-tax WACC, assuming that the company pays tax at a
20% rate?
4. A company's target debt-to-equity ratio is .6, its cost of equity is 11.8 percent, and its beta is
1.2. The after-tax cost of debt is 6.4 percent, the tax rate is 34 percent, and the risk-free rate is
3.2 percent. What discount rate should be assigned to a new project the firm is considering if
the project's beta is estimated at 0.87?
5. A project has an internal rate of return of 11.76 percent and a beta of 1.22. The market rate of
return is 9.8 percent, the tax rate is 35 percent, and the risk-free rate is 3.4 percent. Should this
project be accepted according to the CAPM if the firm is all-equity financed? Why or why not?
6. A company currently has a debt-to-equity ratio of .45, its cost of equity is 13.6 percent, and its
beta is 1.49. The pretax cost of debt is 7.8 percent, the tax rate is 35 percent, and the risk-free
rate is 3.1 percent. The firm's target debt-to-equity ratio is 0.5. What discount rate should be
assigned to a new project the firm is considering if the project is equally as risky as the overall
firm and will be financed solely with debt?
GV: TS. Ngô Nguyễn Quỳnh Như
7.5
WACC and NPV
Chiến lược làm bài:
-
Nhận diện dạng bài có cho nguồn vốn tài trợ cho 1 dự án đến từ equity và từ debt, cho
tỷ suất sinh lời đòi hỏi trên equity và cho chi phí sử dụng nợ, cho thuế suất thuế TNDN.
Cho dòng tiền đầu tư lúc đầu và dòng tiền vào từ dự án cho những năm sau. Thẩm định
dự án xem có nên đầu tư hay không.
-
Dùng công thức:
𝐸
𝐷
× 𝑟𝐸 + × 𝑟𝐷 × (1 − 𝑇)
𝑉
𝑉
𝐶1
𝐶2
𝐶𝑛
𝑁𝑃𝑉 = −𝐶0 +
+
+ ⋯+
2
1 + 𝑊𝐴𝐶𝐶 (1 + 𝑊𝐴𝐶𝐶 )
(1 + 𝑊𝐴𝐶𝐶)𝑛
𝑊𝐴𝐶𝐶 =
-
Lưu ý: WACC đơn vị là %.
•
risk-free debt: debt có chi phí vay bằng 𝑟𝑓 .
•
pretax cost of debt: còn được gọi là 𝑟𝐷 .
•
After-tax cost of debt: còn được gọi là 𝑟𝐷 × (1 − 𝑇).
•
WACC còn có tên gọi khác là after-tax cost of capital.
1. A levered firm has a target capital structure of 30 percent debt and 70 percent equity. The
after-tax cost of debt is 6.5 percent, the tax rate is 34 percent, and the cost of equity is 12.3
percent. The firm is considering a project that is equally as risky as the overall firm. The project
has an initial cash outflow of $1.1 million and annual cash inflows of $480,000 at the end of
each year for three years. What is the NPV of the project?
2. A company has a target capital structure of 40 percent debt and 60 percent equity. The aftertax cost of debt is 7.5 percent, the tax rate is 34 percent, and the cost of equity is 15.1 percent.
The firm is considering a project that is equally as risky as the overall firm. The project has an
initial cash outflow of $1.2 million and annual cash inflows of $450,000 at the end of each
year for three years. What is the NPV of the project?
3. A company has a target capital structure of 45 percent debt and 55 percent equity. The pretax
cost of debt is 6.5 percent, the tax rate is 34 percent, and the cost of equity is 13.7 percent. The
firm is considering a project that is equally as risky as the overall firm. The project has an
initial cash outflow of $1.8 million and annual cash inflows of $550,000 at the end of each
year for four years. What is the NPV of the project?
GV: TS. Ngô Nguyễn Quỳnh Như
4. A company has a target capital structure of 60 percent debt and 40 percent equity. The pretax
cost of debt is 12.5 percent, the tax rate is 20 percent, and the cost of equity is 9.7 percent. The
firm is considering a project that is equally as risky as the overall firm. The project has an
initial cash outflow of $1.5 million and annual cash inflows of $350,000 at the end of each
year for five years. What is the NPV of the project?
5. A company is 40% financed by risk-free debt and 60 percent equity. The treasury bill rate is
4%, the expected market rate of return is 12%, and the beta of the company’s common stock
is 1.5. Tax rate is 20%. The firm is considering a project that is equally as risky as the overall
firm. The project has an initial cash outflow of $2.8 million and annual cash inflows of
$650,000 at the end of each year for four years. What is the NPV of the project?
6. A company has a capital structure of 35 percent debt and 65 percent equity. The pretax cost
of debt is 12.0 percent, the tax rate is 34 percent, and the cost of equity is 17.5 percent. The
firm is considering a project that is equally as risky as the overall firm. The project has an
initial cash outflow of $2.5 million and annual cash inflows of $1.150,000 at the end of each
year for three years. What is the NPV of the project?
7. Estimate WACC, tax rate is 20%
The amount of
Sources of fund
each source of
Figures
fund
Long term debt from bank
$1,000,000
The bank charges HGM the interest rate
of 12%.
Consider to issue 10% coupon bond with
Bond
$1,500,000
a face value of $1,000, price of bond is
$1,115, and 8 years to maturity.
If the risk-free rate is 4%, the expected
Stock
$2,000,000
market rate of return is 8%, and the
company’s stock beta is 1.62.
7.6
Certainty equivalent cash flow
1. 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.
GV: TS. Ngô Nguyễn Quỳnh Như
2. A project has an expected risky cash flow of $500, in year-3. 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.
3. A project has an expected risky cash flow of $500, in year-3. 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.
GV: TS. Ngô Nguyễn Quỳnh Như
CHAPTER 8
FINANCIAL ANALYSIS
Key terms cần nhớ:
1. The following groups are stakeholders of a public company: Shareholders, The government,
Suppliers, Employees, Bondholders, Management.
2. Assets are listed on the balance sheet in order of decreasing liquidity.
3. The following are known as current assets: Cash, Marketable securities, Receivables,
Inventories.
4. The difference between Total Assets of a firm and its Total Liabilities is called “Net worth”.
5. Inventory consists of raw material, work in process, and finished goods.
6. The difference between Current Assets of a firm and its Current Liabilities is called “Net
working capital”.
Net working capital (NWC) = Current assets – Current liabilities
7. Market value ratios indicate how highly is the firm valued by the investors.
8. Efficiency ratios indicate how productively is the firm utilizing its assets.
9. Profitability ratios indicate how profitable is the firm.
10. An example of liquidity ratios: Quick ratio
11. An example of leverage ratios: Debt-Equity ratio
12. When a firm improves (lowers) its days in inventories, it generally releases cash locked up in
inventory.
13. When a firm improves (lowers) its average collection period, it generally releases cash locked
up in accounts receivables.
14. Return on assets would be most useful in comparing the operating profitability of two firms in
different industries.
Financial statements
Balance Sheet
Asset = Liabilities + Shareholders’ Equity
Income Statement
Net Income = (Total Revenue + Gains) – (Total Expenses + Losses)
Cash Flows
Cash from operating activities
Cash from investing activities
Cash from financing activities
GV: TS. Ngô Nguyễn Quỳnh Như
Disclosure of noncash activities is sometimes included when
prepared under the generally accepted accounting principles, or
GAAP
Income of a company
Có nhiều quan điểm về lợi nhuận của 1 công ty:
•
Net income = (EBIT – Interest expense) x (1 – T)
•
EBIT = Total revenues – costs – depreciation
•
Or EBIT = Earnings after tax + Corporate income Tax + Interest expense = Earning
before tax + Interest expense
•
EBITDA = EBIT + Depreciation + Amortization
•
NOPAT = After-tax interest + Net income
8.1
Measuring performance
Chiến lược làm bài:
-
Dùng công thức:
𝑀𝑎𝑟𝑘𝑒𝑡 𝑐𝑎𝑝𝑖𝑡𝑎𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛 = 𝑁𝑜 𝑜𝑓 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 𝑠ℎ𝑎𝑟𝑒𝑠 × 𝑀𝑎𝑟𝑘𝑒𝑡 𝑝𝑟𝑖𝑐𝑒/𝑠ℎ𝑎𝑟𝑒
𝑀𝑎𝑟𝑘𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 𝑎𝑑𝑑𝑒𝑑 (𝑀𝑉𝐴) = 𝑀𝑎𝑟𝑘𝑒𝑡 𝑐𝑎𝑝𝑖𝑡𝑎𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛 − 𝐵𝑜𝑜𝑘 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑒𝑞𝑢𝑖𝑡𝑦
𝑀𝑎𝑟𝑘𝑒𝑡 − 𝑡𝑜 − 𝐵𝑜𝑜𝑘 𝑅𝑎𝑡𝑖𝑜 =
𝑀𝑎𝑟𝑘𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑒𝑞𝑢𝑖𝑡𝑦
𝐵𝑜𝑜𝑘 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑒𝑞𝑢𝑖𝑡𝑦
𝐸𝑐𝑜𝑛𝑜𝑚𝑖𝑐 𝑉𝑎𝑙𝑢𝑒 𝐴𝑑𝑑𝑒𝑑 (𝐸𝑉𝐴) = 𝑁𝑂𝑃𝐴𝑇 − 𝑊𝐴𝐶𝐶 × 𝑇𝑜𝑡𝑎𝑙 𝐶𝑎𝑝𝑖𝑡𝑎𝑙
-
Lưu ý:
•
Market capitalization: còn được gọi là Market Value of Equity
•
Book value of equity: được lấy trên Balance Sheet, khoản mục Equity.
•
Economic Value Added (EVA): còn được gọi là Residual Income.
1. Given a book value per share of $10 and a market value of $24, what is the market
capitalization of a firm with 2,000,000 outstanding shares?
2. Given a book value per share of $5 and a market value of $12, what is the market value added
of a firm with 2,000,000 outstanding shares?
GV: TS. Ngô Nguyễn Quỳnh Như
8.2
Measuring Profitability
Chiến lược làm bài:
-
Return on capital (ROC): Đo lường tổng khả năng sinh lợi trong hoạt động của doanh
nghiệp từ tất cả các nguồn tài trợ
𝑅𝑂𝐶 =
-
𝑁𝑒𝑡 𝑖𝑛𝑐𝑜𝑚𝑒
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑡𝑜𝑡𝑎𝑙 𝑐𝑎𝑝𝑖𝑡𝑎𝑙
Return on equity (ROE): Đo lường khả năng sinh lơị đối với cổ phần nói chung, bao
gồm cả cổ phần ưu đãi.
𝑅𝑂𝐸 =
-
𝑁𝑒𝑡 𝑖𝑛𝑐𝑜𝑚𝑒
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑡𝑜𝑡𝑎𝑙 𝑒𝑞𝑢𝑖𝑡𝑦
Return on assets (ROA): Đo lường hiệu quả hoạt động của công ty mà không quan tâm
đến cấu trúc tài chính
𝑅𝑂𝐴 =
-
𝑁𝑒𝑡 𝑖𝑛𝑐𝑜𝑚𝑒
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑡𝑜𝑡𝑎𝑙 𝑎𝑠𝑠𝑒𝑡𝑠
Profit Margin: Chỉ số này cho biết mỗi đồng doanh thu thu về tạo ra được bao nhiêu
đồng thu nhập.
Profit Margin =
-
Net Income
Sales
Operating Profit Margin: Hệ số biên lợi nhuận hoạt động cho biết một đồng doanh thu
có thể tạo ra bao nhiêu đồng lợi nhuận trước thuế và lãi vay.
Operating Profit Margin =
-
After tax interest + Net Income
Sales
DuPont System: để làm thay đổi chỉ số ROE doanh nghiệp có thể tác động một trong
ba yếu tố cấu thành sau: Tỷ suất lợi nhuận ròng, Vòng quay tài sản, Đòn bẩy tài chính.
ROA và ROE có mối tương quan với nhau thông qua mô hình phân tích Dupont.
ROE =
Net profit Sales Assets
×
×
Sales
Assets Equity
= Net Profit Margin × Asset turnover × Financial Leverage
ROA =
Sales Net Income + Interest
×
= Asset turnover × Operating Profit Margin
Assets
Sales
ROE = ROA × Financial Leverage
1. Given the following data: EBIT = 400; Tax = 100; Sales = 3000; Average Total Assets = 1500,
calculate net profit margin?
GV: TS. Ngô Nguyễn Quỳnh Như
2. Given the following data: EBIT = 400; Tax = 100; Sales = 3000; Average Total Assets = 1500,
calculate the ROA?
3. Given the following data: EBIT = 400; NI = 100; Average Equity = 1000, calculate the ROE?
8.3
Measuring Efficiency
Chiến lược làm bài:
-
Asset turnover: Đo lường khả năng doanh nghiệp tạo ra doanh thu từ việc đầu tư vào
tổng tài sản. Chỉ số này bằng 3 có nghĩa là : với mỗi đô la được đầu tư vào trong tổng tài
sản, thì công ty sẽ tạo ra được 3 đô la doanh thu. Các doanh nghiệp trong ngành thâm
dụng vốn thường có chỉ số vòng quay tổng tài sản thấp hơn so với các doanh nghiệp
khác.
Asset turnover =
-
Sales
Average total assets
Inventory turnover: Trong 1 năm, hàng được lấy ra khỏi kho và mua lại hàng mới bỏ
lại trong kho hết bao nhiêu lần?
Inventory turnover =
-
Cost of goods sold
Average inventory
Average days in inventory: Số ngày trung bình để công ty bán hết hàng trong kho
Average days in inventory =
-
365
Inventory turnover
Receivables turnover: Trong 1 năm, cty đã cho khách hàng thiếu nợ và thu hồi được
các khoản phải thu bao nhiêu lần?
Receivables turnover =
-
Sales
Average receivables
Average collection period: Số ngày trung bình để công ty thu hồi nợ từ khách hàng
Average collection period =
-
Payables turnover: Trong 1 năm, cty đã trả nợ cho nhà cung ứng hết bao nhiêu lần
Payables turnover =
-
365
Receivables Turnover
COGS
Average payables
Average payment period: Số ngày trung bình để công ty trả nợ cho nhà cung ứng
Average payment period =
GV: TS. Ngô Nguyễn Quỳnh Như
365
Payables Turnover
1. Given the following data: Sales = 3200; Cost of goods sold = 1600; Average total assets =
1600; Average inventory = 200, calculate the asset turnover ratio?
2. Given the following data: Sales = 3200; Cost of goods sold = 1600; Average total assets =
1600; Average inventory = 200. Calculate Inventory turnover and the days in inventory?
3. A company has sales of $1,150,000 and cost of goods sold of $830,000. The firm had a
beginning inventory of $65,000 and an ending inventory of $72,000. Calculate Inventory
turnover. What is the length of the inventory period?
4. Given the following data: Sales = 3200; Cost of goods sold = 1600; Average receivables =
200. Calculate the receivable turnover and the average collection period?
5. A company has average accounts receivable of $33,700, average inventory of $54,200, sales
of $364,200, and cost of goods sold of $193,400. How long does it take the firm to sell its
inventory and collect payment on the sale?
8.4
Measuring Leverage
Chiến lược làm bài:
-
Long term debt ratio: Phản ánh tình hình nợ dài hạn của doanh nghiệp. (D/V)
𝐿𝑜𝑛𝑔 𝑡𝑒𝑟𝑚 𝑑𝑒𝑏𝑡 𝑟𝑎𝑡𝑖𝑜 =
-
𝐿𝑜𝑛𝑔 𝑡𝑒𝑟𝑚 𝑑𝑒𝑏𝑡
𝐿𝑜𝑛𝑔 𝑡𝑒𝑟𝑚 𝑑𝑒𝑏𝑡 + 𝐸𝑞𝑢𝑖𝑡𝑦
Debt-equity ratio: Phản ánh mức độ tài trợ bằng vốn vay một cách thường xuyên (qua
đó thấy được rủi ro về mặt tài chính mà công ty phải chịu) qua việc loại bỏ các khoản nợ
ngắn hạn (tín dụng thương mại phi lãi suất và những khoản phải trả ngắn hạn). (D/E)
𝐷𝑒𝑏𝑡 − 𝑒𝑞𝑢𝑖𝑡𝑦 𝑟𝑎𝑡𝑖𝑜 =
-
𝐿𝑜𝑛𝑔 𝑡𝑒𝑟𝑚 𝑑𝑒𝑏𝑡
𝐸𝑞𝑢𝑖𝑡𝑦
Total debt ratio: Đây là một loại tỉ lệ đòn bẩy xác định tổng số nợ liên quan đến tài sản,
cho phép so sánh mức đòn bẩy được sử dụng giữa các công ty khác nhau.
𝑇𝑜𝑡𝑎𝑙 𝑑𝑒𝑏𝑡 𝑟𝑎𝑡𝑖𝑜 =
-
𝑇𝑜𝑡𝑎𝑙 𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠
𝑇𝑜𝑡𝑎𝑙 𝑎𝑠𝑠𝑒𝑡𝑠
Times interest earned: Hệ số khả năng thanh toán lãi vay cho biết mức độ lợi nhuận
đảm bảo khả năng trả lãi như thế nào.
𝑇𝑖𝑚𝑒𝑠 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑒𝑎𝑟𝑛𝑒𝑑 =
𝐸𝐵𝐼𝑇𝐷𝐴
𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑝𝑎𝑦𝑚𝑒𝑛𝑡𝑠
1. Given the following data: EBIT = 100; Depreciation = 40; Interest = 20; Dividends = 10;
calculate the Times Interest Earned (TIE) ratio.
GV: TS. Ngô Nguyễn Quỳnh Như
2. If the debt ratio is 0.5 what is the debt-equity ratio?
3. Given the following data: Long-term debt = 100; Value of leases = 20; Book value of equity =
80; Market value of equity = 100, calculate long-term debt ratio.
4. Given the following data: Long-term debt = 100; Value of leases = 20; Book value of equity =
80; Market value of equity = 100, calculate the debt-equity ratio.
8.5
Measuring Liquidity:
Chiến lược làm bài:
-
Net working capital: Chỉ số này xác định xem một công ty có thể đáp ứng các nghĩa vụ
nợ hiện tại với tài sản hiện tại của mình không; và thiếu hoặc thừa bao nhiêu.
𝑁𝑒𝑡 𝑤𝑜𝑟𝑘𝑖𝑛𝑔 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 = 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑎𝑠𝑠𝑒𝑡𝑠 − 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐿𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠
-
Net working capital to total assets ratio: Biểu thị tỷ trọng tài sản hiện tại ròng hoặc
vốn lưu động của một công ty chiếm bao nhiêu phần trăm trên tổng tài sản của công ty
đó.
𝑁𝑊𝐶 𝑡𝑜 𝑡𝑜𝑡𝑎𝑙 𝑎𝑠𝑠𝑒𝑡𝑠 𝑟𝑎𝑡𝑖𝑜 =
-
𝑁𝑒𝑡 𝑤𝑜𝑟𝑘𝑖𝑛𝑔 𝑐𝑎𝑝𝑖𝑡𝑎𝑙
𝑇𝑜𝑡𝑎𝑙 𝑎𝑠𝑠𝑒𝑡𝑠
Current ratio: Hệ số này đánh giá khả năng mà một công ty có thể thanh toán các nghĩa
vụ nợ ngắn hạn bằng cách sử dụng các tài sản hiện tại (tiền mặt, chứng khoán ngắn hạn,
các khoản phải thu hiện tại, hàng tồn kho và các khoản trả trước).
𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑟𝑎𝑡𝑖𝑜 =
-
𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑎𝑠𝑠𝑒𝑡𝑠
𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠
Quick ratio: Hệ số này (còn được gọi là chỉ số Acid Test) đo lường khả năng một công
ty có thể thanh toán các nghĩa vụ ngắn hạn bằng cách sử dụng các loại tài sản hiện tại
hoặc "tài sản nhanh" (tiền mặt, chứng khoán ngắn hạn và các khoản phải thu hiện tại).
𝑄𝑢𝑖𝑐𝑘 𝑟𝑎𝑡𝑖𝑜 =
-
𝐶𝑎𝑠ℎ + 𝑀𝑎𝑟𝑘𝑒𝑡𝑎𝑏𝑙𝑒 𝑠𝑒𝑐𝑢𝑟𝑖𝑡𝑖𝑒𝑠 + 𝑅𝑒𝑐𝑒𝑖𝑣𝑎𝑏𝑙𝑒𝑠
𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠
Cash ratio: Chỉ số này đo lường khả năng một công ty có thể trả các khoản nợ hiện tại
của mình bằng cách sử dụng tiền mặt và chứng khoán ngắn hạn. Chứng khoán ngắn
hạn là công cụ nợ ngắn hạn tốt, giống như tiền mặt.
𝐶𝑎𝑠ℎ 𝑟𝑎𝑡𝑖𝑜 =
-
Lưu ý:
GV: TS. Ngô Nguyễn Quỳnh Như
𝐶𝑎𝑠ℎ + 𝑀𝑎𝑟𝑘𝑒𝑡𝑎𝑏𝑙𝑒 𝑠𝑒𝑐𝑢𝑟𝑖𝑡𝑖𝑒𝑠
𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠
•
Current ratio, Quick ratio, Cash ratio: Tử số và mẫu số dư cuối năm trên Balance
Sheet.
1. Given the following data: Total current assets = $852; Total current liabilities = $406; Longterm debt = $442, calculate the net working capital.
2. Given the following data: Current assets = 500; Current liabilities = 250; Inventory = 200;
Account receivables = 200; calculate the current ratio.
3. Given the following data: Current assets = 500; Current liabilities = 250; Inventory = 200;
Account receivables = 200; calculate the quick ratio.
4. Given the following data: Current assets = 500; Current liabilities = 250; Inventory = 200;
Account receivables = 200; calculate the cash ratio? Assume that the firm has no marketable
securities.
5. Given the following data: Current assets = 700; Current liabilities = 350; Inventory = 250;
Account receivables = 200; calculate the quick ratio.
8.6
Measuring Investment
Chiến lược làm bài:
-
P/E ratio: Chỉ số P/E thể hiện mức giá mà bạn sẵn sàng bỏ ra cho một đồng lợi nhuận
thu được từ cổ phiếu. Hoặc nhà đầu tư sẵn sàng trả giá bao nhiêu cho cổ phiếu của 1
doanh nghiệp dựa trên lợi nhuận (thu nhập) của doanh nghiệp đó.
𝑃/𝐸 =
𝐸𝑃𝑆 =
-
𝑃𝑟𝑖𝑐𝑒
𝐸𝑎𝑟𝑛𝑖𝑛𝑔 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒
𝑁𝑒𝑡 𝑖𝑛𝑐𝑜𝑚𝑒 − 𝑃𝑟𝑒𝑓𝑒𝑟𝑟𝑒𝑑 𝑠ℎ𝑎𝑟𝑒𝑠
𝑁𝑜 𝑜𝑓 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 𝑐𝑜𝑚𝑚𝑜𝑛 𝑠𝑡𝑜𝑐𝑘𝑠
Dividend yield: là cổ tức mà một công ty trả trong một thời kỳ kế toán, thường là 1 năm,
được tính bằng cách lấy cổ tức của mỗi cổ phần chia cho giá trị hiện hành trên thị trường
của cổ phiếu.
𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑦𝑖𝑒𝑙𝑑 =
-
𝑇𝑜𝑡𝑎𝑙 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑝𝑎𝑖𝑑 𝑝𝑒𝑟 𝑦𝑒𝑎𝑟
𝑃𝑟𝑖𝑐𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒
Payout ratio: Tỷ lệ trả cổ tức là tỷ trọng của tổng lợi nhuận được phân phối dưới dạng
cổ tức, phần còn lại được gọi là lợi nhuận giữ lại.
𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑝𝑎𝑦𝑜𝑢𝑡 =
GV: TS. Ngô Nguyễn Quỳnh Như
𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑝𝑎𝑖𝑑 𝑝𝑒𝑟 𝑦𝑒𝑎𝑟
𝑁𝑒𝑡 𝑖𝑛𝑐𝑜𝑚𝑒
1. Given the following data: Earnings per share = $6; Dividends per share = $3; Price per share
= $60, calculate the P/E ratio?
2. Given the following data: Earnings per share = $5; Dividends per share = $3; Price per share
= $50. calculate the dividend yield?
3. Given the following data: Earnings per share = $5; Dividends per share = $3; Price per share
= $50. Calculate the payout ratio?
8.7
Dạng tổng hợp
Look up the financial statement of Company ABC:
Balance Sheet at 31/12/2020
Assets
31/12/2020
31/12/2019
Cash and marketable securities
661
530
Account receivable
166
247
8,209
7,611
Other current assets
215
298
Total current assets
9,251
8,686
Property, plant, and equipment
31,477
28,836
Less accumulated depreciation
8,755
7,475
Net tangible fixed assets
22,722
21,361
Long term investments
253
509
Other long-term assets
460
313
32,686
30,869
31/12/2020
31/12/2019
Debt due for repayment
1,021
1,104
Accounts payable
4,543
4,137
Other current liabilities
2,458
2,510
Current assets
Inventories
Fixed assets
Tangible fixed assets
Total assets
Liabilities and Shareholders' Equity
Current liabilities
GV: TS. Ngô Nguyễn Quỳnh Như
Total current liabilities
8,022
7,751
Long term debt
5,039
5,576
Deferred income taxes
660
670
Other long-term liabilities
910
774
14,631
14,771
735
729
Retained earnings and capital surplus
17,320
15,369
Total shareholders' equity
18,055
16,098
Total liabilities and shareholders' equity
32,686
30,869
Total liabilities
Common Stock and other paid-in-capital
Income Statement during the year
From 1/1/2020 to 31/12/2020
Net sales
48,230
Cost of goods sold
31,729
Selling, general, and administrative expenses
11,158
Depreciation
1,539
Earnings before interest and taxes (EBIT)
Interest expense
?
298
Earnings before taxes (EBT)
?
Tax (20%)
?
Net Income
?
Dividends (30%)
?
Addition to retained earnings (70%)
?
a. Fill in the blank (?) of Income statement.
b. Calculate the following financial ratios in 2020:
• Return on asset (ROA), return on equity (ROE), Return on capital (ROC), Profit Margin,
Operating Profit Margin
• Asset Turnover, Cash cycle of operation (Average Days in Inventory, Average collection
period, Average payment period)
• Current ratio, quick ratio, cash ratio
GV: TS. Ngô Nguyễn Quỳnh Như
CHAPTER 9
WORKING CAPITAL MANAGEMENT
Key terms cần nhớ:
1. The following are the types of inventories: raw material, work in process, finished goods.
2. The costs of holding inventory are carrying cost and order cost.
3. The economic order quantity (EOQ) is calculated using:
2 × 𝑠𝑎𝑙𝑒𝑠 × 𝑐𝑜𝑠𝑡 𝑝𝑒𝑟 𝑜𝑟𝑑𝑒𝑟
𝐸𝑂𝑄 = √
𝑐𝑎𝑟𝑦𝑖𝑛𝑔 𝑐𝑜𝑠𝑡
4. In the EOQ inventory model, the optimal order size is achieved when carrying costs = order
costs.
5. When credit is granted to another firm this gives rise to an Accounts receivable.
6. Account receivables include Trade credit and Consumer credit.
7. Examples of transactions involve credit: 2/30, net 60 or 2/10 EOM, net 60.
8. If a firm grants credit with terms of 3/10 net 30, the creditor receives a discount of 3% when
payment is made in less than 10 days after the sale.
9. The net credit period for a company with terms of 3/10 net 60 is 50 days.
10. The most important source of short-term financing is bank loan.
11. A large firm may hold substantial cash balances because these balances are required by the
bank in the form of compensating balances.
12. The market for short-term investments is called money market.
9.1
Inventory Management
Chiến lược làm bài:
-
Để quản trị hàng tồn kho, ngoài các chỉ số như Inventory Turnover, Days in inventory, thì
công ty có thể quản trị thông qua tính toán số lượng tối ưu hàng tồn kho – nghĩa là ở mức số
lượng đó thì chi phí liên quan đến hàng tồn kho là thấp nhất.
-
Nhận diện dạng bài có chữ “optimal” (tối ưu).
-
Dùng công thức:
2 × 𝑠𝑎𝑙𝑒𝑠 × 𝑐𝑜𝑠𝑡 𝑝𝑒𝑟 𝑜𝑟𝑑𝑒𝑟
𝐸𝑂𝑄 = √
𝑐𝑎𝑟𝑦𝑖𝑛𝑔 𝑐𝑜𝑠𝑡
-
Trong đó:
GV: TS. Ngô Nguyễn Quỳnh Như
•
EOQ: Số lượng đặt hàng tối ưu để chi phí liên quan đến hàng tồn kho là thấp nhất
•
Sales: Số đơn vị sản phẩm dự kiến sẽ bán trong năm (units)
•
Cost per order: Chi phí cố định cho 1 đơn đặt hàng ($ / đơn)
•
Carrying cost: Chi phí lưu kho cho 1 sản phẩm ($ / unit)
1. A company uses 400,000 tons of stone per year. The carrying costs are $100/ton. The cost per
order is $500. Calculate the economic order quantity per order.
2. A company uses 400,000 tons of stone per year. The carrying costs are $100/ton. The cost per
order is $500. Calculate the optimal number of orders per year.
3. A company uses 400,000 tons of stone per year. The carrying costs are $100/ton. The cost per
order is $500. Calculate the optimal annual order costs.
4. A company uses 400,000 tons of stone per year. The carrying costs are $100/ton. The cost per
order is $500. Calculate the optimal carrying costs.
5. A company uses 400,000 tons of stone per year. The carrying costs are $100/ton. The cost per
order is $500. Calculate the total costs of optimal inventory.
6. A company uses 400,000 tons of stone per year. The carrying costs are $100/ton. The cost per
order is $500. Calculate the economic order quantity per order, the optimal number of orders
per year, the optimal annual order costs, the optimal carrying costs and the total costs of optimal
inventory.
7. A company uses 1,200,000 tons of stone per year. The carrying costs are $75/ton. The cost per
order is $480. Calculate the economic order quantity per order, the optimal number of orders
per year, the optimal annual order costs, the optimal carrying costs and the total costs of optimal
inventory.
8. A company expects to sell 2,430 printers next year. Annual carrying cost is $50 per printer,
and ordering cost is $30. The company operates 360 days a year. Calculate the EOQ, number
of times per year the company reorder, the total annual cost if the EOQ quantity is ordered, the
length of an order cycle.
9. A firm has sales of $860,000 and cost of goods sold of $490,000. The firm had a beginning
inventory of $98,000 and an ending inventory of $112,000. What is the length of the inventory
period?
GV: TS. Ngô Nguyễn Quỳnh Như
10. A firm has sales of $498,000 and cost of goods sold of $221,000. At the beginning of the year,
inventory was $36,400. At the end of the year, the inventory balance was $31,800. What is the
inventory turnover rate?
11. A firm has sales of $710,000. The cost of goods sold is equal to 57 percent of sales. The firm
has average inventory of $23,940. How many days on average does it take the firm to sell its
inventory?
9.2
Receivables Management
Chiến lược làm bài:
-
Để quản trị các khoản phải thu, ngoài các chỉ số như Receivales Turnover, Collection period
thì công ty có thể quản trị thông qua Terms of sales và Break-even analysis.
-
Nhận diện dạng bài có “term of sale” (chính sách bán hàng), hỏi Effective annual rate hoặc
implied interest rate hoặc cost of forgoing the discount.
-
Dùng công thức:
365
𝑒𝑥𝑡𝑟𝑎 𝑑𝑎𝑦𝑠 𝑐𝑟𝑒𝑑𝑖𝑡
𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡
𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑎𝑛𝑛𝑢𝑎𝑙 𝑟𝑎𝑡𝑒 (𝐸𝐴𝑅) = (1 +
)
−1
𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡𝑒𝑑 𝑝𝑟𝑖𝑐𝑒
-
Nhận diện dạng bài có “credit”, “possibility” (xác suất khách hàng trả tiền mua hàng), hỏi
kêu tính “Break-even p” hoặc “Expected profit from new customer”.
-
Dùng công thức:
𝐵𝑟𝑒𝑎𝑘 − 𝑒𝑣𝑒𝑛 𝑝 =
𝐶𝑜𝑠𝑡
𝑅𝑒𝑣𝑒𝑛𝑢𝑒
1. A company has sales of $626,000. The cost of goods sold is equal to 68 percent of sales. The
beginning accounts receivable balance is $75,534 and the ending accounts receivable balance
is $76,209. How long on average does it take the firm to collect its receivables?
2. Supposing you purchase goods on terms of 1/10, net 30. Taking compounding into account,
what annual rate of interest is implied by the cash discount? (Assume a year has 365 days, sale
is $100)
3. Suppose you purchase goods on terms of 3/10, net 60. Taking compounding into account, what
annual rate of interest is implied by the cash discount? (Assume a year has 365 days, sale is
$100.)
GV: TS. Ngô Nguyễn Quỳnh Như
4. Suppose you purchase goods on terms of 2/10, net 50. Taking compounding into account, what
annual rate of interest is implied by the cash discount? (Assume a year has 365 days, sale is
$100.)
5. A supplier offers you credit terms of 1.5/10, net 30. What is the cost of forgoing the discount
on a $1,200 purchase?
6. A supplier offers you credit terms of 2/15, net 45. What is the cost of forgoing the discount on
a $218,400 purchase?
7. Ms. Nhu has ordered goods with a value of $800. The production cost is $600. Under what
conditions should you extend credit if there is no possibility of repeat orders?
8. Ms. Nhu has ordered goods with a value of $2000. The production cost is $1800. Under what
conditions should you extend credit if there is no possibility of repeat orders?
9. Ms. Nhu has ordered goods with a value of $1200. The production cost is $800. Under what
conditions should you extend credit if there is no possibility of repeat orders?
10. The default rate of a firm' new customers has been running at 10%. The average sale for each
new customer amounts to $800, generating a profit of $100 and a 40% chance of a repeat order
next year. The default rate on repeat orders is only 2%. If the interest rate is 9%, what is the
expected profit from each new customer?
11. The default rate of a firm 's new customers has been running at 20%. The average sale for each
new customer amounts to $500, generating a profit of $200 and a 30% chance of a repeat order
next year. The default rate on repeat orders is only 5%. If the interest rate is 6%, what is the
expected profit from each new customer?
12. A firm is currently experiencing a bad debt ratio of 4%. Terry is convinced that, with looser
credit controls, this ratio will increase to 8%; however, she expects sales to increase by 10%
as a result. The cost of goods sold is 80% of the selling price. Per $100 of current sales, what
is a firm 's expected profit under the proposed credit standards?
13. A firm is currently experiencing a bad debt ratio of 6%. The manager convinced that, with
tighter credit controls, he can reduce this ratio to 2%; however, he expects sales to drop by 8%
as a result. The cost of goods sold is 75% of the selling price. Per $100 of current sales, what
is the manager's expected profit under the proposed credit standards?
GV: TS. Ngô Nguyễn Quỳnh Như
9.3
Payables Management
Chiến lược làm bài:
-
Để quản trị các khoản phải trả, chúng ta có thể dùng chỉ số về Payables Turnover và Payment
period.
-
Dùng công thức:
𝑃𝑎𝑦𝑎𝑏𝑙𝑒𝑠 𝑇𝑢𝑛𝑟𝑜𝑣𝑒𝑟 =
𝐶𝑂𝐺𝑆
𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝑝𝑎𝑦𝑎𝑏𝑙𝑒𝑠 𝑏𝑎𝑙𝑎𝑛𝑐𝑒
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑃𝑎𝑦𝑚𝑒𝑛𝑡 𝑃𝑒𝑟𝑖𝑜𝑑 =
365
𝑃𝑎𝑦𝑎𝑏𝑙𝑒𝑠 𝑇𝑢𝑟𝑛𝑜𝑣𝑒𝑟
1. A firm has sales of $642,000 and beginning accounts payable of $56,400. The cost of goods
sold is equivalent to 68 percent of sales. How long does it take Down Towner to pay its
suppliers?
2. A firm had a beginning accounts payable balance of $56,900 and an ending accounts payable
balance of $62,800. Sales for the period were $675,000 and costs of goods sold were $448,000.
What is the payables turnover?
9.4
Cash Management
Chiến lược làm bài:
-
Nhận diện dạng bài hỏi “Operating cycle”, “Cash cycle”, “Cash Balance”
-
Dùng công thức:
𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑐𝑦𝑐𝑙𝑒 = 𝑁𝑜 𝑜𝑓 𝑑𝑎𝑦𝑠 𝑖𝑛 𝑖𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦 + 𝑁𝑜 𝑜𝑓 𝑐𝑜𝑙𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝑝𝑒𝑟𝑖𝑜𝑑
𝐶𝑎𝑠ℎ 𝑐𝑦𝑐𝑙𝑒 = 𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑐𝑦𝑐𝑙𝑒 − 𝑁𝑜 𝑜𝑓 𝑝𝑎𝑦𝑚𝑒𝑛𝑡 𝑝𝑒𝑟𝑖𝑜𝑑
𝐶𝑎𝑠ℎ 𝑐𝑦𝑐𝑙𝑒 = 𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑐𝑦𝑐𝑙𝑒 − 𝑁𝑜 𝑜𝑓 𝑝𝑎𝑦𝑚𝑒𝑛𝑡 𝑝𝑒𝑟𝑖𝑜𝑑
𝐶𝑎𝑠ℎ 𝑏𝑎𝑙𝑎𝑛𝑐𝑒 𝑎𝑡 𝑡ℎ𝑒 𝑒𝑛𝑑 𝑜𝑓 𝑝𝑒𝑟𝑖𝑜𝑑
= 𝐶𝑎𝑠ℎ 𝑏𝑎𝑙𝑎𝑛𝑐𝑒 𝑎𝑡 𝑡ℎ𝑒 𝑏𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝑜𝑓 𝑝𝑒𝑟𝑖𝑜𝑑
+ 𝐶𝑜𝑙𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝑏𝑦 𝑐𝑎𝑠ℎ 𝑑𝑢𝑟𝑖𝑛𝑔 𝑡ℎ𝑒 𝑝𝑒𝑟𝑖𝑜𝑑
− 𝑃𝑎𝑦𝑚𝑒𝑛𝑡 𝑏𝑦 𝑐𝑎𝑠ℎ 𝑑𝑢𝑟𝑖𝑛𝑔 𝑡ℎ𝑒 𝑝𝑒𝑟𝑖𝑜𝑑
1. A firm has an inventory turnover rate of 16, a receivables turnover rate of 21, and a payables
turnover rate of 11. How long is the operating cycle?
2. A company sells its inventory in 87 days on average. Its average customer charges their
purchases on a credit card and payment are received in 10 days. A company takes 56 days on
GV: TS. Ngô Nguyễn Quỳnh Như
average to pay for its purchases. Given this information, what is the length of D&M's cash
cycle?
3. A company has an inventory turnover rate of 13, an accounts payable period of 44 days, and
an accounts receivable period of 35 days. What is the length of the cash cycle?
4. A company has an inventory turnover of 16 and an accounts receivable turnover of 10. The
accounts payable period is 51 days. What is the length of the cash cycle?
5. A company currently has an operating cycle of 76 days. The firm is analyzing some operational
changes that are expected to decrease the accounts receivable period by 3 days and decrease
the inventory period by 8 days. The accounts payable turnover rate is expected to increase from
7 to 9 times per year. If all of these changes are adopted, what will the firm's new operating
cycle be?
6. A company has an inventory period of 33 days, an accounts payable period of 41 days and an
accounts receivable period of 27 days. Management is considering offering a 5 percent
discount if its credit customers pay for their purchases within 10 days. If the new discount is
offered the accounts receivable period is expected to decline by 13 days. If the new discount
is offered, the cash cycle will change from _____ days to _____ days.
7. A firm currently has a 36-day cash cycle. Assume the firm changes its operations such that it
decreases its receivables period by 3 days, increases its inventory period by 2 days, and
decreases its payables period by 3 days. What will the length of the cash cycle be after these
changes?
8. For its most recent year a company had Sales (all on credit) of $830,000 and Cost of Goods
Sold of $525,000. At the beginning of the year its Accounts Receivable were $80,000, its
Accounts Payable were $125,000 and its Inventory was $100,000. At the end of the year its
Accounts Receivable were $86,000, its Accounts Payable were $105,000 and its Inventory was
$110,000. Calculate cash cycle operations.
9. As of the beginning of the quarter, a firm has a cash balance of $250. During the quarter the
firm pays its suppliers $310 and collects $420 from customers. It also pays an interest payment
of $30 and a tax bill of $170. In addition, the firm borrows $135. What is the cash balance at
the end of the quarter?
10. On April 1st, a firm had a beginning cash balance of $200. March sales were $460 and April
sales were $510. During April the firm had cash expenses of $150 and payments on accounts
GV: TS. Ngô Nguyễn Quỳnh Như
payable of $210. The accounts receivable period is 30 days. What is the firm's beginning cash
balance on May 1st?
11. A firm had a Quarter 2 beginning cash balance of $430. Sales for Quarters 1 through 3 are
estimated at $600, $800, and $900, respectively. The cost of goods sold is equal to 70 percent
of sales. Goods are purchased one quarter prior to the month of sale. The accounts payable
period is 30 days and the accounts receivable period is 15 days. The firm had quarterly cash
expenses of $180. What was the cash balance at the end of Quarter 2? Assume a 360-day year.
GV: TS. Ngô Nguyễn Quỳnh Như
CHAPTER 10
FINANCIAL PLANNING
Key terms cần nhớ:
1. Short-term financial decisions involve short lived assets, short lived liabilities and are easily
reversed.
2. The main difference between short-term and long-term finance is the timing of short-term cash
flow being within a year or less.
3. Cumulative capital requirement can be met by long-term financing and short-term financing.
4. The sustainable growth rate is equal to Plowback ratio x Returns on equity.
5. Example of one of the least liquid assets: Long-term assets.
6. The order of liquidity: Marketable securities – Receivables – Inventories - Long-term assets.
7. Net working capital is defined as the difference between current assets and current liabilities.
8. The general formula for calculating the "Ending accounts receivable (AR)”:
Ending (AR) = beginning (AR) + sales - collections
9. The cash cycle is represented by the following sequence:
Cash, raw materials, finished goods, and receivables, cash
10. The first step in the preparation of cash budget is sales forecast.
11. Cash inflow in cash budgeting comes mainly from collection on accounts receivable.
12. A large part of cash outflow in cash budgeting is due to payments on accounts payable.
10.1
Sources of cash
Chiến lược làm bài:
-
Nhận dạng bài kêu tính “forcasted collections on AR in ….” hoặc “Ending AR”
-
Áp dụng công thức:
Collection của tháng x = Collection từ sales trong tháng x + Collection từ AR của tháng
trước
Ending (AR) = beginning (AR) + sales – collections
-
Trường hợp đề cho Ending (AR) của tháng i, nhưng ko cho sales của tháng i thì mặc định
luôn Ending (AR) của tháng i sẽ được collect vào tháng (i + 1).
1. A company has forecast sales in the first 3 months of the year as follows (figures in millions):
January, $60; February, $80; March, $100. 60% of sales are usually paid for in the month that
GV: TS. Ngô Nguyễn Quỳnh Như
they take place and 40% in the following month. Receivables at the end of December were $24
million. What are the forecasted collections on accounts receivable in March?
2. A company has forecast sales in the first 3 months of the year as follows (figures in millions):
January, $90; February, $20; March, $30. 70% of sales are usually paid for in the month that
they take place and 30% in the following month. Receivables at the end of December were $20
million. What are the forecasted collections on accounts receivable in March?
3. A company has forecast sales in the first 3 months of the year as follows (figures in millions):
January, $80; February, $60; March, $40. 70% of sales are usually paid for in the month that
they take place, 20% in the following month, and the final 10% in the next month. Receivables
at the end of December were $23 million. What are the forecasted collections on accounts
receivable in March?
4. A company has forecast sales in the first 3 months of the year as follows (figures in millions):
January, $200; February, $140; March, $100. 50% of sales are usually paid for in the month
that they take place, 30% in the following month, and the final 20% in the next month.
Receivables at the end of December were $100 million. What are the forecasted collections on
accounts receivable in March?
5. A company has forecast sales in the first 3 months of the year as follows (figures in millions):
February, $120; March, $135; April, $90. 65% of sales are usually paid for in the month that
they take place and 35% in the following month. Receivables at the end of January were $45
million.
a. What are the forecasted collections on accounts receivable in April?
b. What are the receivable at the end of April?
6. A company has forecast sales in the first 3 months of the year as follows (figures in millions):
January, $120; February, $135; March, $90. 60% of sales are usually paid for in the month that
they take place and 40% in the following month. Receivables at the end of December were $75
million.
a. What are the forecasted collections on accounts receivable in March?
b. What are the receivable at the end of March?
7. A company has forecast sales in the first 3 months of the year as follows (figures in millions):
January, $90; February, $20; March, $30. 60% of sales are usually paid for in the month that
GV: TS. Ngô Nguyễn Quỳnh Như
they take place and 40% in the following month. Receivables at the end of December were $25
million.
a. What are the forecasted collections on accounts receivable in March?
b. What are the receivable at the end of March?
10.2
Uses of cash
Chiến lược làm bài:
-
Nhận diện dạng bài kêu tính “Uses of cash in ….”
-
Áp dụng công thức:
Payment của tháng x = Payment từ purchases trong tháng x + Payment từ AP của
tháng trước
1. Calculate payment in February and March by cash of a company with following information:
February
March
1. Purchases of materials
+ For cash
40
40
+ For credit
10
20
10
10
3. Taxes, interest, …
5
5
4. Capital investment
20
0
2. Other expenses
10.3
Cash budgeting
Chiến lược làm bài:
-
Nhận dạng bài kêu tính “cumulative financing requirement”
-
Lập bảng Sources of cash, Uses of cash, Cash budgeting
-
Áp dụng công thức:
Changes in cash = Sources of cash – Uses of cash
Ending (Cash) = Beginning (Cash) + Changes in cash
Cash requirement = Ending (Cash) – Minimum Cash
-
Nếu Cash requirement > 0: surplus; Nếu Cash requirement < 0: shortage.
1. Complete the uses of cash and cumulative financing requirement on February and March.
February
1. Purchases of materials
GV: TS. Ngô Nguyễn Quỳnh Như
March
Purchases:
+ Jan (credit)
20
+ For cash
40
40
+ For credit
10
20
Minimum Cash
50
10
10
Cash at start Feb.
60
3. Taxes, interest, …
5
5
4. Capital investment
20
0
2. Other expenses
Sources of cash
- Sale
February
+ Credit
1 month
March
90
100
54
60
+ Sale in last period
28
36
+ Total collection
82
96
- Collection
+ Sale in current
period
2. Complete the Cash Budgeting on February and March.
Sources of cash
- Sale
February
March
90
100
+ Sale in current period
54
60
+ Sale in last period
28
36
+ Total collection
82
96
- Collection
Uses of cash
February
March
- Purchases of materials
+ For cash
40
40
+ For credit
20
10
- Other expenses
10
10
- Taxes, interest,
5
5
- Capital investment
20
0
Total uses
95
65
GV: TS. Ngô Nguyễn Quỳnh Như
Minimum Cash:
50
Cash at start Feb:
60
3. Complete the sources and the uses of cash on February and March.
Sales
Purchases
+ For cash
60%
+ Jan (credit)
+ For credit
40%
+ Credit
+ Jan
70
February
1. Total sales
March
90
100
+ For cash
40
40
+ For credit
10
20
3. Other expenses
10
10
4. Taxes, interest,
5
5
20
0
20
1 month
Minimum Cash
50
Cash at start Feb.
60
2. Purchases of materials
5. Capital investment
4. Most of Tesla’s cash flow inflow comes from the sale of soup. We therefore start with a sales
forecast by quarter for 2014:
First
Second
Third
Fourth
Quarter
Quarter
Quarter
Quarter
Receivables at start of period ($
millions)
187
Sales ($ millions)
650
748
585
234
We assume that sales in the last quarter of the previous year were $ 250 million.
Cash at start of period
First
Second
Third
Fourth
Quarter
Quarter
Quarter
Quarter
50
Sales become accounts receivable before they become cash. Cash flow comes from collections on
account receivable. Suppose that 65% of sales are cashed in in the immediate quarter and 35% are
cashed in the following quarter.
Uses of cash:
GV: TS. Ngô Nguyễn Quỳnh Như
Uses of cash
First
Second
Third
Fourth
Quarter
Quarter
Quarter
Quarter
Payments on account payable
220
210
367
252
Increase in inventory
150
150
170
180
Labor and Other expenses
136
136
136
136
Capital expenditures
70
10
8
14.5
Taxes, interest and dividends
46
46
46
46
Total uses
622
552
727
628.5
a. Calculate receivables at the end of period in 2014.
b. Construct table showing Tesla’s cumulative financing requirement in 2014. We assume that
Tesla’s minimum operating cash balance is $30 million.
5. Most of Vingroup’s cash flow inflow comes from the sale of mattresses. We therefore start
with a sales forecast by quarter for 2015:
First
Second
Third
Fourth
Quarter
Quarter
Quarter
Quarter
502
742
836
Receivables at start of
period ($ millions)
150
Sales ($ millions)
560
We assume that sales in the last quarter of the previous year were $ 240 million.
Cash at start of period
25
Sales become accounts receivable before they become cash. Cash flow comes from
collections on account receivable. Suppose that 65% of sales are cashed in in the
immediate quarter and 35% are cashed in the following quarter.
GV: TS. Ngô Nguyễn Quỳnh Như
Uses of cash:
Uses of cash
Payments on account payable
250
250
267
261
Increase in inventory
150
150
170
180
Labor and Other expenses
136
136
136
136
Capital expenditures
70
10
8
14.5
Taxes, interest and dividends
46
46
46
46
Total uses
652
592
627
637.5
a. Calculate receivables at the end of period in 2015.
b. Construct table showing Vingroup’s cumulative financing requirement in 2015. We assume that
Vingroup’s minimum operating cash balance is $28 million.
GV: TS. Ngô Nguyễn Quỳnh Như
CHAPTER 11
PAYOUT POLICY
Key terms cần nhớ:
1. Firms can pay out cash to their shareholders in the following ways: Dividends and Share
repurchases.
2. Dividends are decided by the board of directors.
3. Payment date occurs last in time (when arranged in the chronological order).
4. Lists events in the chronological order from earliest to latest:
Declaration date => ex-dividend date => record date
5. Stock dividend is never in the form of cash.
6. The par value of the outstanding shares is defined as legal capital.
7. According to financial executives' views about dividend policy, we try to avoid reducing the
dividend.
8. Generally, investors interpret the announcement of an increase in dividends as good news and
the stock price increases.
9. Generally, investors view the announcement of open-market repurchase of stocks as good news
and the stock price increases.
10. One key assumption of the Miller and Modigliani (MM) dividend irrelevance argument is that
new shares are sold at a fair price.
11. The indifference proposition regarding dividend policy assumes that investors are indifferent
about the timing of dividend payments.
12. One key assumption of the Miller and Modigliani (MM) dividend irrelevance is that capital
markets are efficient.
13. The dividend-irrelevance proposition of Miller and Modigliani: “The investment policy is set
before the dividend decision and not changed by dividend policy” depends on the following
relationship between investment policy and dividend policy.
14. One possible reason that shareholders often insist on higher dividends is they do not trust
managers to spend retained earnings wisely.
15. The rightist position is that the market will reward firms that have high dividend yield.
16. According to behavioral finance investors prefer dividends because investors prefer the
discipline that comes from spending only the dividends.
GV: TS. Ngô Nguyễn Quỳnh Như
17. If investors do not like dividends because of the additional taxes that they have to pay, you
expect stock prices to behave on the ex-dividend date will fall by more than the amount of the
dividend.
18. If both dividends and capital gains are taxed at the same ordinary income tax rate, the effect of
tax is different because dividends are taxed when distributed while capital gains are deferred
until the stock is sold.
19. If dividends are taxed more heavily than capital gains, the investors should be willing to pay
more for stocks with low dividend yields.
20. If investors have a marginal tax rate of 20% and a firm has announced a dividend of $5, the
price of stock should decrease by $4 on the ex-dividend date.
11.1
Dạng Stock price
1. Company X has 100 shares outstanding. It earns $1,000 per year and expects to pay all of it as
dividends. If the firm expects to maintain this dividend forever, Calculate the stock price today.
(The required rate of return is 10%)
 $100
2. Company X has 100 shares outstanding. It earns $1,000 per year and expects to pay all of it as
dividends. If the firm expects to maintain this dividend forever, Calculate the stock price after
the dividend payment. (The required rate of return is 10%)
 $90
3. Company X has 100 shares outstanding. It earns $1,000 per year and expects repurchase its
shares in the open market instead of paying dividends. Calculate the number of shares
outstanding at the end of year-1, if the required rate of return is 10%.
 90
11.2
Dạng Value of dividend
1. Two corporations A and B have exactly the same risk and both have a current stock price of
$100. Corporation A pays no dividend and will have a price of $120 one year from now.
Corporation B pays dividends and will have price of $113 one year from now after paying the
dividend. The corporations pay no taxes and investors pay no taxes on capital gains but pay a
tax of 30% income tax on dividends. What is the value of the dividend that investors expect
corporation B to pay one year from today?
 $10
GV: TS. Ngô Nguyễn Quỳnh Như
2. A firm in Australia earns a pretax profit of $A10 per share. It pays a corporate tax of $3 per
share (30% tax rate) in taxes. The firm pays the remaining $A7 in dividends to a shareholder
in 30% tax bracket. What is the amount of tax paid by the shareholder under the imputation
tax system?
 Zero
11.3
Dạng Stock outstanding / Split stocks
1. FPT has excess cash of $2,187.5 and other assets of $35,500. Equity is worth $25,000. The
firm has 2,000 shares of stock outstanding and net income of $3,750. The firm has decided to
spend all of its excess cash on a share repurchase program. How many shares of stock will be
outstanding after the stock repurchase is completed? Knowing that A firm has a market value
equal to its book value.
2. DHG has 20,000 shares of stock outstanding with a par value of $1 per share and a market
price of $17.50 a share. The balance sheet shows $20,000 in the common stock account,
$425,000 in the capital in excess of par value account, and $98,000 in the retained earnings
account. The firm just announced a 5-for-3 stock split. What will the market price per share be
after the split?
GV: TS. Ngô Nguyễn Quỳnh Như