CHAPTER 1 :

INTRODUCTION TO CORPORATE
Concept Questions
1. AGENCY PROBLEMS:
● Who owns a corporation?
- The shareholders
● Describe the process whereby the owners control the firm's management.
- The have the right to elect directors, vote on major actions and share in the profits of the
corporation
● The main reason that an agency relationship exists in the corporale fre form of organization?
- This separation of ownership from control in the corporate form of organization is what
causes agency problems to exists. Management may act in its own of someone else's best
interests, rather than those of the shareholders. If such events occur, they may contradict
of the goal of maximizing the share price of the equity of the firm
- The separation of ownership from control

● In this text, what kinds of problems can arise?

- The problem between manager is shareholders
- The conflict - high cost leading to lower net income
- Agency problem Shareholders and Creditors

2. Not-for-Profit Firm Goals. Suppose you were the financial manager of

a not-for-profit business (a not-for-profit hospital, perhaps). What kinds
of goals do you think would be appropriate?
Such organizations frequently pursue social or political missions, so many different goals are
conceivable. One goal that is often cited is revenue minimization; i.e., provide whatever goods and
services are offered at the lowest possible cost to society. A better approach might be to observe that even
a not-for-profit business has equity. Thus, one answer is that the appropriate goal is to maximize the value
of the equity.

3. Goal of the Firm. Evaluate the following statement: Managers should

not focus on the current stock value because doing so will lead to an
overemphasis on short-term profits at the expense of long-term profits.
- Managers should not focus on the current stock value because doing so will lead to an overemphasis on
short term profits and the expense of long term profits. True.
Managers should focus on how to maximize their business valuation, which means adding more value to
the organization. The current stock value will be moving along with the investor's expectation and other
market factors. Focusing on long-term value would strengthen the stock's intrinsic value, rather than
concentrating on current value. The current stock value would be judged by periodic earnings or potential
profits. Therefore, focusing on short-term value would force the manager to polish short-term earnings,
which ignores the company's direction on the long term. Expenses would not be allocated properly in the
long term due to the overemphasis on the short-term expenses. This is a myopic view.

4. Ethics and Firm Goals. Can the goal of maximizing the value of the
stock conflict with other goals, such as avoiding unethical or illegal
behavior? In particular, do you think subjects like customer and
employee safety, the environment, and the general good of society fit in
this framework, or are they essentially ignored? Think of some specific
scenarios to illustrate your answer.
The goal of maximizing the value of a company's stock can conflict with other goals, such as avoiding unethical or
illegal behavior. While maximizing stock value is a primary objective for many businesses, it is important to
consider the broader impact of the company's actions on various stakeholders, including customers, employees, the
environment, and society as a whole.
• Customer Safety: A company may be tempted to cut corners on product safety measures to reduce costs and
increase profits. However, prioritizing stock value over customer safety can lead to legal liabilities, reputational
damage, and loss of customer trust.

• Employee Safety: Similarly, a company that disregards employee safety to maximize stock value may face legal
consequences, damage to its reputation, and a decline in employee morale and productivity.

• Environmental Impact: Companies that prioritize short-term financial gains over environmental sustainability
may engage in practices that harm the environment, such as excessive pollution or deforestation. These actions can
lead to legal penalties, public backlash, and long-term damage to the company's reputation.

• Social Responsibility: Ignoring the broader impact of business activities on society can result in negative
consequences. For example, a company that exploits vulnerable communities or engages in discriminatory practices
may face legal action, boycotts, and damage to its brand image.
• the goal of maximizing stock value is crucial for businesses, it should not be pursued at the expense of ethical and
legal behavior. Companies should strive to balance the interests of all stakeholders and consider the broader impact
of their actions on customer safety, employee well-being, the environment, and society as a whole.

5. International Firm Goal Would the goal of maximizing the value of the
stock differ for financial management in a foreign country? Why or why
not?
The goal will be the same, but the best course of action toward that goal may be different because of
differing social, political, and economic institutions.

6. Agency problems. Suppose you own stock in a company. The current

price per share is $25. Another company has just announced that it
wants to buy your company and will pay $35 per share to acquire all the
outstanding stock. Your company ’ s management immediately begins
fighting off this hostile bid. Is management acting in the shareholders ’
best interests? Why or why not?
The goal of management should be to maximize the share price for the current shareholders. If
management believes that it can improve the profitability of the firm so that the share price will exceed
$35, then they should fight the offer from the outside company. If management believes that this bidder or
other unidentified bidders will actually pay more than $35 per share acquire the company, then they
should still fight the offer. However, if the current management cannot increase the value of the firm
beyond the bid price, and no other higher bids come in, then management is not acting in the interests of
the shareholders by fighting the offer. Since current managers often lose their jobs when the corporation is
acquired, poorly monitored managers have an incentive to fight corporate takeovers in situations such as
this.

7. Agency problems and corporate ownership. Corporate ownership

varies around the world. Historically, individuals have owned the
majority of shares in public corporations in the United States. In
Germany and Japan, however, banks, other
large financial institutions, and other companies own most of the stock in
public corporations. Do you think agency problems are likely to be more
or less severe in Germany and Japan than in the United States?

We would expect agency problems to be less severe in other countries, primarily due to the relatively
small percentage of individual ownership. Fewer individual owners should reduce the number of diverse
opinions concerning corporate goals. The high percentage of institutional ownership might lead to a
higher degree of agreement between owners and managers on decisions concerning risky projects. In
addition, institutions may be better able to implement effective monitoring mechanisms on l managers
than can individual owners, based on the institutions deeper resources and experiences with their own
management.

8. Agency Problems and Corporate Ownership. In recent years, large

financial institutions such as mutual funds and pension funds have
become the dominant owners of stock in the United States, and these
institutions are becoming more active in corporate affairs. What are the
implications of this trend for agency problems and corporate control?

In recent years, large financial institutions such as mutual funds and pension funds have become the
dominant owners of stock in the United States, and these institutions are becoming more active in
corporate affairs. What are the implications of this trend for agency problems and corporate control?

The increase in institutional ownership of stock in the United States and the growing activism of
these large shareholder groups may lead to a reduction in agency problems for U.S. corporations and
a more efficient market for corporate control. However, this may not always be the case. If the
managers of the mutual fund or pension plan are not concerned with the interests of the investors, the
agency problem could potentially remain the same, or even increase since there is the possibility of
agency problems between the fund and its investors.

9. Executive Compensation. Critics have charged that compensation to

top managers in the United States is simply too high and should be cut
back. For example, focusing on large corporations, Larry Ellison of
Oracle has been one of the bestcompensated CEOs in the United States,
earning about $130 million in 2010 alone and over $1 billion during the
2006 – 2010 period. Are such amounts excessive? In answering, it might
be helpful to recognize that superstar athletes such as Tiger Woods, top
earners in the entertainment field such as James Cameron and Oprah
Winfrey, and many others at the top of their respective fields earn at
least as much, if not a great deal more.
I think paying high salaries and bonuses motivates them to work more productively. And the higher their
position, the greater their responsibility. They are the ones who will take on all risks and solve problems
that the company has. The fact that they are paid too high a salary compared to employees because the
benefits or profits they bring to the company are huge. That's a reward they deserve
 CHAPTER 2:
FINANCIAL STATEMENT ANALYSIS
****What is the difference between book value and market value? Which should we use
for decision-making purposes? ****

Book value:
- Book value is the value of an asset or a company as reported on the balance sheet. It is the
original cost of the asset minus any accumulated depreciation or amortization.
- Book value is based on historical costs and does not necessarily reflect the current market value
of the asset.
- Book value is typically used for accounting purposes to calculate metrics like return on assets
or to determine the net worth of a company based on its financial statements.
Market Value:
- Market value is the current price at which an asset or a company could be bought or sold in the
open market.
- Market value is determined by supply and demand dynamics, investor sentiment, future growth
prospects, and other market factors.
- Market value is a more dynamic and reflective measure of the perceived value of an asset or a
company by investors and the market at a given point in time.

****Which should we use to decision making purpose?****

Market value is primary for investment and acquisition decisions, book value can still be useful
as a secondary measure to provide a baseline and to identify potential undervaluation or
overvaluation when compared with market value. Because of:
-Market value provides a real-time measure of what investors are willing to pay, making it more
relevant for timely decisions.
-Market value often includes expectations about future performance, making it more
forward-looking than book value.
-Market value reflects the current valuation by the market, incorporating all available
information, investor sentiment, and future growth prospects.

*****The difference between accounting income and cash flow****

Accounting Income
 ● Definition: is the amount of revenue left after subtracting all expenses, including
operating expenses, taxes, depreciation, and amortization, as reported on the income
statement.
● Basis: It is based on accrual accounting
● Components: Includes revenues, cost of goods sold, operating expenses, interest, taxes,
and non-cash items like depreciation and amortization.
● Purpose: Used to assess the profitability of a company over a specific period. It helps in
evaluating performance and making long-term strategic decisions.

Cash Flow

● Definition: is the net amount of cash and cash equivalents moving into and out of a
business over a specific period, as shown in the cash flow statement.
● Basis: It is based on actual cash transactions. It includes cash received and spent from
operating activities, investing activities, and financing activities.
● Components: Operating cash flow, investing cash flow, and financing cash flow.
● Purpose: Used to assess the liquidity and financial health of a company. It helps in
understanding the company's ability to generate cash to meet short-term obligations and
fund operations.

Decision-Making: Which to Use?

Example 1: Evaluating Profitability

● Scenario: A company wants to assess its overall performance for the year.
● Metric to Use: Accounting Income
● Reason: Accounting income provides a comprehensive view of profitability, considering
all revenues and expenses, including non-cash items like depreciation.

Example 2: Managing Daily Operations

● Scenario: A company needs to ensure it has enough cash to cover payroll and other
immediate expenses.
● Metric to Use: Cash Flow
● Reason: Cash flow reflects actual cash available, which is crucial for meeting short-term
financial obligations and managing liquidity.

Example 3: Deciding on an Investment

● Scenario: A company is considering purchasing new equipment.

● Metric to Use: Cash Flow
● Reason: The company needs to ensure it has sufficient cash flow from operating activities
to fund the investment without jeopardizing its liquidity.
Example 4: Performance Reporting

● Scenario: Reporting quarterly financial results to shareholders.

● Metric to Use: Accounting Income
● Reason: Accounting income provides a standardized measure of performance that
shareholders and analysts use for comparison with other companies.

Summary

● Accounting Income: Use when assessing profitability and making long-term strategic
decisions.
● Cash Flow: Use when managing liquidity, ensuring short-term financial stability, and
making decisions that depend on actual cash availability.

CONCEPT QUESTION:
2. Accounting and Cash Flows: Why might the revenue and cost figures
shown on a standard income statement not represent the actual cash
inflows and outflows that occurred during a period?
- Revenue and cost figures are based on accrual accounting, income and expenses are
recorded based on when the transactions occurred, NOT cash transactions
- When the revenue is completed, not when cash is paid ( Cô sửa)

6. Cash Flow from Assets. Why is it not necessarily bad for the cash flow
from assets to be negative for a particular period?
- When money is spent wisely ( Cô sửa )
7. Operating Cash Flow. Why is it not necessarily bad for the operating
cash flow to be negative for a particular period?
A negative operating cash flow means a company is spending more cash on its operations than
it's generating. While this might sound alarming, it's not necessarily a red flag. Here's why:
a. Growth Investments:
Increased inventory: Companies might invest heavily in inventory to meet anticipated demand,
leading to a temporary cash outflow.
Capital expenditures: Investing in new equipment, technology, or facilities can boost future
earnings but negatively impact short-term cash flow.
Research and development: Innovation often requires upfront costs, which can result in negative
operating cash flow.
b. Timing Differences:
Accounts receivable: If customers take longer to pay, cash inflow is delayed, leading to a
temporary negative cash flow.
Accrued expenses: Expenses might be recorded before cash is paid out, causing a short-term
cash surplus.
c. Non-cash Expenses:
Depreciation and amortization: These are non-cash expenses that reduce net income but don't
impact cash flow directly.
 d. Seasonal Business Cycles:
Some businesses experience seasonal fluctuations in cash flow. For example, retailers might
have negative operating cash flow during peak inventory stocking periods.
e. One-time Expenses:
Significant legal settlements, natural disasters, or restructuring costs can cause temporary
negative operating cash flow.

QUESTIONS AND PROBLEMS:

Question 1: Building a Balance Sheet
Bishop, Inc., has current assets of $5,700, net fixed assets of $27,000,
current liabilities of $4,400, and long-term debt of $12,900. What is the
value of the shareholders’ equity account for this firm? How much is net
working capital?

. the total assets = Current Assets + Net Fixed Assets

= $5,700 + $27,000 = $32,700

. the total liabilities = Current Liabilities + Long-term Debt

= $4,400 + $12,900 = $17,300

using the balance sheet equation:

Shareholders' Equity = Total Assets - Total Liabilities
= $32,700 - $17,300 = $15,400

Net Working Capital = Current Assets - Current Liabilities

= $5,700 - $4,400 = $1,300

Question 2. Building an Income Statement

Travis, Inc., has sales of $387,000, costs of $175,000, depreciation expense
of $40,000, interest expense of $21,000, and a tax rate of 35 percent.
What is the net income for the firm? Suppose the company paid out
$30,000 in cash dividends. What is the addition to retained earnings?
a. Earnings Before Tax (EBT):
EBT=Sales−Costs−Depreciation Expense−Interest Expense
 = $387,000 − $175,000 −$40,000−$21,000
=$151,000
b. Calculate Taxes:
Taxes = EBT × Tax Rate
=$151,000 × 0.35
=$52,850
c. Calculate Net Income

= EBT − Taxes
=$151,000−$52,850
=$98,150

d. Determine Addition to Retained Earnings

= Net Income − Cash Dividends

=$98,150−$30,000
=$68,150

Question 3. Market Values and Book Values Klingon Cruisers, Inc.,

purchased new cloaking machinery three years ago for $9.5 million. The
machinery can be sold to the Romulans today for $6.5 million. Klingon’s
current balance sheet shows net fixed assets of $5.2 million, current
liabilities of $2.4 million, and net working capital of $800,000. If all the
current assets were liquidated today, the company would receive $2.6
million cash. What is the book value of Klingon’s assets today? What is
the market value?

- Net working capital = current assets - current liabilities

⇒ current assets = $800,000 + $2,4milion = $3,200,000

- Book value CA: $3,200,000

- Book value NFA : $5,200,000
- Book value assets: $8,400,000
 - Market value CA : $2,600,000
- Book value NFA : $6,500,000
- Book value assets: $9,100,000

Question 4: Calculating Taxes:

The Locker Co. had $273,000 in taxable income. Using the rates from
Table 2.3 in the chapter, calculate the company’s income taxes. What is
the average tax rate? What is the marginal tax rate?

● Compute income tax:

Slab ($) Tax Rate Income ($) Tax ($)

0-50.000 15% 50.000 7.500

50.001-75.000 25% 25.000 6.250

75.001-100.000 34% 25.000 8.500

100.001-335.000 39% 173.000 67.470

335.001-10.000.000 34%

10.000.001-15.000.00 35%
0

15.000.001-18.333.33 38%
3

18.333.334 trở lên 35%

Tổng cộng 273.000 89.720

The total income tax to be paid by the company is $89,720.

● Compute average tax:

Average Tax Rate = ( Tax paid: Total income) x 100

= ( $89,720 : $273,000) x 100

= 32,86%
● The marginal tax rate is the rate that would be applicable for the one more dollar earned
by the company. That is, in the present case the company has earned $273,000. So the
marginal tax rate is the tax rate applicable on 1$ earned over $273,000. The marginal tax
rate for the company is 39%
 Chapter 4:
Discounted Cash Flow Valuation
QUESTION: (page 123)
1.Compounding and Period
As you increase the length of time involved, what happens to future
values? What happens to present values
- Assuming positive cash flows
- The present value decreases as the length of time increases. The future value increases as
the length of time increases.
2. Interest Rates What happens to the future value of an annuity if you
increase the rate r ? What happens to the present value?
- Obviously, an increase in annual interest rate (r) will raise the corresponding
compounding factor for each year. Hence, the future value will increase.
- The annual interest rate has an inverse relationship with the present value of an annuity.
Thus, an increase in the annual interest will lower the present value of an annuity.
3. Present Value Suppose two athletes sign 10-year contracts for $80
million. In one case, we’re told that the $80 million will be paid in 10
equal installments. In the other case, we’re told that the $80 million will
be paid in 10 installments, but the installments will increase by 5 percent
per year. Who got the better deal?

4. APR and EAR Should lending laws be changed to require lenders to

report EARs instead of APRs? Why or why not?

Yes, the lending laws should be changed to require the lenders to report EARs instead of APRs
as:

-EAR are the actual rate that is to be borne by the borrowers.

-EAR allows easy comparability among the loans offered by different lenders.

-Lenders usually quote APR and naive borrowers get fooled as the effective rate is very high

-Some countries already have the rules in place that require lenders to quote EAR. US also required some
type of lenders to quote EAR

5. Time Value On subsidized Stafford loans, a common source of

financial aid for college students, interest does not begin to accrue until
repayment begins. Who receives a bigger subsidy, a freshman or a
senior? Explain.
Toyota Motor Credit Corporation (TMCC), a subsidiary of Toyota Motor Corporation,
offered some securities for sale to the public on March 28, 2008. Under the terms of the
deal, TMCC promised to repay the owner of one of these securities $100,000 on March
28, 2038, but investors would receive nothing until then. Investors paid TMCC $24,099 for
each of these securities; so they gave up $24,099 on March 28, 2008, for the promise of a
$100,000 payment 30 years later.
​The key to understanding this lies in the term "subsidized." The government pays the interest on
the loan while the student is in school and during grace periods. This means the student doesn't
accrue any interest during these periods.

● Freshmen have a longer period of time before entering the workforce and starting
repayment. This means they benefit from the government paying the interest for a longer
duration.
● Seniors are closer to graduation and thus have a shorter period of time before repayment
begins. Consequently,they receive a smaller subsidy compared to freshmen.

Therefore, the longer a borrower can delay the start of interest accrual, the greater the subsidy
they receive. In the case of subsidized Stafford loans, freshmen generally benefit more than
seniors due to their longer time in school.

6. Time Value of Money Why would TMCC be willing to accept such a

small amount today ($24,099) in exchange for a promise to repay about
four times that amount ($100,000) in the future?
- TMCC may agree to accept a smaller amount ($24,099) today because it may receive
larger payments in the future ($100,000). This may be related to actual benefits or
attractive opportunities that they believe will bring them greater profits in the future.
QUESTION & PROBLEM
7. Calculating Present Values ( Page.124)
Imprudential, Inc., has an unfunded pension liability of $630 million that must be paid in
20 years. To assess the value of the firm’s stock, financial analysts want to discount this
liability back to the present. If the relevant discount rate is 7.1 percent, what is the present
value of this liability?

(r) = 7.1% ÷ 100 = 0.071

⇒ PV = 630/(1+0.071)^20 = 159.791

8. Calculating Rates of Return

Although appealing to more refined tastes, art as a collectible has not
always performed so profitably. During 2010, Deutscher-Menzies sold
Arkies under the Shower, a painting by renowned Australian painter
Brett Whiteley, at auction for a price of $1,100,000. Unfortunately for the
previous owner, he had purchased it three years earlier at a price of
$1,680,000. What was his annual rate of return on this painting?
- 1.100.000 = 1.680.000 * (1+r)^3
⇒ r = -0.13165 = -13.17%
⇒ the price has fallen by 13.17% every year for over a period of 3 years

10. Continuous Compounding Compute the future value of $1,900

continuousl compounded for
a. 7 years at a stated annual interest rate of 12 percent = 1900*e^401
b. 5 years at a stated annual interest rate of 10 percent.
c. 12 years at a stated annual interest rate of 5 percent.
d. 10 years at a stated annual interest rate of 7 percent.
 CHAPTER 5 :
Net Present Value &
Other Investment Rules
Questions and Problems : (PAGE.162)
1. Calculating Payback Period and NPV : Fuji Software, Inc., has the
following mutually exclusive projects.

a. Suppose Fuji’s payback period cutoff is two years. Which of these two
projects should be chosen?
b. Suppose Fuji uses the NPV rule to rank these two projects. Which
project should be chosen if the appropriate discount rate is 15 percent?
 2. Calculating Payback: An investment project provides cash inflows
of $840 per yearfor eight years. What is the project payback period
if the initial cost is $3,200? What if the initial cost is $4,800? What
if it is $7,300?
1. An investment project provides cash inflows of $745 per year for eight
years. What is the project payback period if the initial cost is $1,700?
What if the initial cost is $3,300? What if it is $6,100?
Dựa theo tính lại nha
Payback = 2 + ($210/$745)
Payback = 2.28 years
the payback period is:
Payback = $3,300/$745
Payback = 4.43 years
Total cash inflows = 8($745)
Total cash inflows = $5,960
Payback = $6,100/$745
Payback = 8.19 years

3. Calculating Discounted Payback An investment project has annual

cash inflows of $5,000, $5,500, $6,000, and $7,000, and a discount
rate of 14 percent. What is the discounted payback period for these
 cash flows if the initial cost is $8,000? What if the initial cost is
$12,000? What if it is $16,000?

4 Calculating Discounted Payback : An investment project costs

$15,000 and has annual cash flows of $3,800 for six years. What is the
discounted payback periodif the discount rate is 0 percent? What if the
discount rate is 10 percent? If it is 15 percent?

PV=Cash Flow​/(1+r)^t
Discount Rate: 0%
Payback Period= 15000/3800= 3.95

Discount Rate: 10%

PV¹= 3800/(1+0.1)^1 =3.454
Pv2= 3800/(1+0.1)^2=3.140
Pv3= 3800/(1+0.1)^3 =2.855
PV4= 3800/(1+0.1)^4= 2.595
PV5= 3800/(1+0.1)^5= 2.359
PV6= 3800/(1+0.1)^6= 2.145

Cumulative discounted cash flow by year 5: 14.403

Cumulative discounted cash flow by year 6: 16.548
Payback Period= 5+(15000-14,407.5)/ 2.145= 5.28
Discount Rate: 15%
PV1= 3800/(1+0.15)^1 = 3.304
….
Cumulative discounted cash flow by year 6:
14.390
=>The project does not pay back within 6 years at a 15% discount rate.

5. Calculating IRR Stone Sour, Inc., has a project with the following cash
flows:

The company evaluates all projects by applying the IRR rule. If the
appropriate interest rate is 9 percent, should the company accept the
project?
NPV = 0 = -C0 + C1/(1+IRR) + C2/(1+IRR)^2 + ... + Cn/(1+IRR)^n
0 = -20000 + 8500/(1+IRR) + 10200/(1+IRR)^2 + 6200/(1+IRR)^3
IRR ≈ 12.41%.
=> 12.41% > 9%, the company should accept the project.

7. Calculating Profitability Index Bill plans to open a self-serve

grooming center in a storefront. The grooming equipment will cost
$385,000, to be paid immediately. Bill expects aftertax cash inflows of
$84,000 annually for seven years, after which he plans to scrap the
equipment and retire to the beaches of Nevis. The first cash inflow
occurs at the end of the first year. Assume the required return is 13
percent. What is the project’s PI? Should it be accepted?
8. Calculating Profitability
Index Suppose the following two independent investment opportunities are
available to Greenplain, Inc. The appropriate discount rate is 10 percent .

a. Compute the profitability index for each of the two projects.

Present Value of Cash Inflows:
Project A

● Year 1: 1,200 / (1 + 0.10)^1 = 1,090.91

● Year 2: 1,100 / (1 + 0.10)^2 = 826.45
● Year 3: 900 / (1 + 0.10)^3 = 620.92
Project B

● Year 1: 800 / (1 + 0.10)^1 = 727.27

● Year 2: 2,300 / (1 + 0.10)^2 = 1,760.33
● Year 3: 2,900 / (1 + 0.10)^3 = 2,057.85
⇒ Profitability Index = Present Value of Cash Inflows / Initial Investment
Project A:
● Profitability Index = (1,090.91 + 826.45 + 620.92) / 2,300
● Profitability Index = 2,538.28 / 2,300
● Profitability Index = 1.10
Project B:
● Profitability Index = (727.27 + 1,760.33 + 2,057.85) / 3,900
● Profitability Index = 4,545.45 / 3,900
● Profitability Index = 1.17
b. Which project(s) should Greenplain accept based on the profitability index rule?
Greenplain Inc. should accept Project B as it has a higher profitability index
(1.17) compared to Project A (1.10).

11. NPV versus IRR Consider the following cash flows on two mutually
exclusive projects for the Bahamas Recreation Corporation (BRC). Both
projects require an annual return of 14 percent.

As a financial analyst for BRC, you are asked the following questions:
a. If your decision rule is to accept the project with the greater IRR,
which project should you choose?
b. Because you are fully aware of the IRR rule’s scale problem, you
calculate the incremental IRR for the cash flows. Based on your
computation, which project should you choose?

c. To be prudent, you compute the NPV for both projects. Which project
should you choose? Is it consistent with the incremental IRR rule?

12. Problems with Profitability Index The Robb Computer Corporation

is trying to choose between the following two mutually exclusive design
projects:
a. If the required return is 10 percent and Robb Computer applies the
profitability index decision rule, which project should the firm accept?
b. If the company applies the NPV decision rule, which project should it
take?
c. Explain why your answers in (a) and (b) are different.

a. Project I:

Present Value = annual cash inflow * [(1 - (1 + required return)^- number of year)
Present Value of Future Cash Flows = $18,000 * (1 + 0.10)^-1 + $18,000 * (1 + 0.10)^-2
+ $18,000 * (1 + 0.10)^-3 ≈ $46,255.37

PI = $46,255.37 / $30,000 ≈ 1.54

Project II:

● Present Value of Future Cash Flows = $7,500 * (1 + 0.10)^-1 + $7,500 * (1 +

0.10)^-2 + $7,500 * (1 + 0.10)^-3 ≈ $19,685.04
● PI = $19,685.04 / $12,000 ≈ 1.64

=> Project II should be accepted as it has a higher PI (1.64) than Project I (1.54).

b. NPV Decision Rule

Net Present Value (NPV) = Present Value of Future Cash Flows - Initial Investment
Project I:

● NPV = $46,255.37 - $30,000 = $16,255.37

Project II:

● NPV = $19,685.04 - $12,000 = $7,685.04

=> Project I should be accepted as it has a higher NPV ($16,255.37) than Project II
($7,685.04).

c. Explanation of Different Results

The discrepancy between the PI and NPV decisions arises due to the scale difference
between the two projects. Project I has a higher initial investment and higher cash flows,
leading to a higher NPV. However, when considering the return per dollar invested (as
measured by PI), Project II is more efficient.

In summary:

● NPV focuses on the absolute dollar value created by the project.

● PI focuses on the return per dollar invested.

In this case, while Project I creates more total value (NPV), Project II provides a higher
return on the initial investment (PI). The choice between the two depends on the
company's specific goals and constraints.

14. Comparing Investment Criteria

Mario Brothers, a game manufacturer, has a new idea for an adventure
game. It can market the game either as a traditional board game or as an
interactive DVD, but not both. Consider the following cash flows of the
two mutually exclusive projects for Mario Brothers. Assume the discount
rate for Mario Brothers is 10 percent.
a. Based on the payback period rule, which project should be chosen? Q anh
Board game:
Payback period = 1 + ($750 – 600) / $450
Payback period = 1.33 years
DVD:
Payback period = 1 + ($1,800 – 1,300) / $850
Payback period = 1.59 years
Since the board game has a shorter payback period than the DVD project, the company
should choose the board game

b. Based on the NPV, which project should be chosen? Ly

Board game
NPV = –$750 + $600 / 1.10 + $450 / 1.10^2 + $120 / 1.10^3
NPV = $257.51

DVD:
NPV = –$1,850 + $1,300 / 1.10 + $850 / 1.102 + $350 / 1.103
NPV = $347.26

Since the NPV of the DVD is greater than the NPV of the board game, choose the DVD.

c. Based on the IRR, which project should be chosen? Thái thư

Board game:
0 = –$750 + $600 / (1 + IRR) + $450 / (1 + IRR)2 + $120 / (1 + IRR)3
⇒ IRR = 33.79%

DVD:
0 = –$1,850 + $1,300 / (1 + IRR) + $850 / (1 + IRR)2 + $350 / (1 + IRR)3
⇒ IRR = 23.31%
Choose Board game as it has the higher IRR

d. Based on the incremental IRR, which project should be chosen? Giao

Incremental Cash Flow=Cash Flow of DVD−Cash Flow of Board Game
 Year Board Game DVD Incremental Cash Flow (
DVD-Board Game)

0 -$750 -$1,800 -1800 - (-750)= -150

1 $600 $1,300 1300 - 600 = 700

2 $450 $850 850 - 450 = 400

3 $150 $350 350 - 120 = 230

0 = C0 + C1 / (1 + IRR) + C2 / (1 + IRR)2 + C3 / (1 + IRR)3

0 = –$1,050 + $700 / (1 + IRR) + $400 / (1 + IRR)2 + $230 / (1 + IRR)3

⇒ Incremental IRR = 15.86 %

For investing-type projects, accept the larger project when the incremental IRR is greater
than the discount rate. Since the incremental IRR, 15.86%, is greater than the required
rate of return of 10 percent, choose the DVD project.

C0: Dòng tiền hiện tại

 CHAPTER 8:
Interest Rates and Bond Valuation

Question and problems: (PAGE.267)

1. Valuing Bonds What is the price of a 15-year, zero coupon bond
paying $1,000 at maturity if the YTM is:
a. 5 percent?
b. 10 percent?
c. 15 percent?

a. YTM = 5%
P = $1,000 / (1 + 0.05) ^15 = $481.02
b. YTM = 10%
P = $1,000 / (1 + 0.10) ^15 = $239.39
c. YTM = 15%
P = $1,000 / (1 + 0.15) ^15 = $122.89

2. Valuing Bonds Microhard has issued a bond with the following

characteristics:
Par: $1,000
Time to maturity: 15 years
Coupon rate: 7 percent
Semiannual payments
Calculate the price of this bond if the YTM is:
a. 7 percent
b. 9 percent
c. 5 percent

a. C= (0.7 * $1000)/2 = $35

r=0,07/2 = 0,035
n= 15 * 2= 30
P= $35({1- [1/(1+.035)]^30}/0.035) + $1,000/(1+.035)^30
P= $1,000.00

b. C= 35
r= 0,09/2= 0,045
n= 30
P= $35({1- [1/(1+.045)]^30}/0.045) + $1,000/(1+0.045)^30
P= $837.11

c. C= 35
r= 0,05/2= 0,025
n= 30
P= $35({1-[1/(1+.025)]^30}/0.025)+ $1,000/(1+0.025)^30
P = $1,209.30

3. Bond Yields Watters Umbrella Corp. issued 15-year bonds 2 years ago
at a coupon rate of 6.4 percent. The bonds make semiannual payments.
If these bonds currently sell for 105 percent of par value, what is the
YTM?
4. Coupon Rates Rhiannon Corporation has bonds on the market with
11.5 years to maturity, a YTM of 7.6 percent, and a current price of
$1,060. The bonds make semiannual payments. What must the coupon
rate be on these bonds?

= $41.96
5. Valuing Bonds Even though most corporate bonds in the United States
make coupon payments semiannually, bonds issued elsewhere often have
annual coupon payments. Suppose a German company issues a bond
with a par value of €1,000, 19 years to maturity, and a coupon rate of 4.5
percent paid annually. If the yield to maturity is 3.9 percent, what is the
current price of the bond?

Coupon payment = Par value * Coupon rate = €1,000 * 4.5% = €45

PV = C * [(1 - (1 + r)^-n) / r]
= €45 * [(1 - (1 + 0.039)^-19)
PV = FV / (1 + r)^n
= €1,000 / (1 + 0.039)^19 ≈ €482.78
Bond price = Present value of annuity + Present value of par value
Bond price = €591.37 + €482.78 = €1,074.15

10. Nominal versus Real Returns Say you own an asset that had a total
return last year of 12.5 percent. If the inflation rate last year was 5.3
percent, what was your real return?
11. Using Treasury Quotes Locate the Treasury bond in Figure 8.4
maturing in February 2037. What is its coupon rate? What is its bid
price? What was the previous day’s asked price?

* Nominal return: The raw rate of return on an investment before factoring in inflation.
* Real return: The adjusted rate of return that reflects the effects of inflation.
→ Real Return = Nominal Return - Inflation Rate
= 12.5% - 5.3% = 7.2%
Therefore, your real return on the asset was 7.2%.
This means that while your investment grew by 12.5% in nominal terms, its purchasing
power increased by only 7.2% after accounting for inflation.

12. Using Treasury Quotes Locate the Treasury bond in Figure 8.4
maturing in November 2039. Is this a premium or a discount bond?
What is its current yield? What is its yield to maturity? What is the
bid-ask spread?
 ● The bond has a coupon rate of 4.375% and a current yield of 4.2306%. As the
coupon rate is higher than the current yield, the bond is selling at a premium.
● Current Yield:
● The current yield is 4.2306%.
● Yield to Maturity (YTM):
● Unfortunately, the YTM is not directly provided in the table. Calculating the YTM
requires more detailed information, including the bond's exact price (bid or ask),
the time to maturity, and the frequency of coupon payments.
● Bid-Ask Spread:
● The bid-ask spread is the difference between the bid price and the ask price. For
the November 2039 bond, it's 102:11 - 102:12 = 1/32 or 0.03125%

Analysis:

● Premium or Discount Bond: Since the bond's price is above 100 (102:09), it is a
premium bond.
● Current Yield: The current yield is approximately 4.2240%.
● Yield to Maturity (YTM): The YTM for this bond is 4.2240%.
● Bid-Ask Spread: The bid-ask spread is the difference between the bid and ask
prices:
○ Bid: 102:11 (102.34375)
○ Ask: 102:09 (102.28125)
○ Bid-Ask Spread: 102.34375 - 102.28125 = 0.0625% or 0:02 (2/32nds).

This bond is currently trading at a premium, with a yield to maturity of 4.2240%, and a
bid-ask spread of approximately 0.0625%.

13. Zero Coupon Bonds You buy a zero coupon bond at the beginning of
the year that has a face value of $1,000, a YTM of 7 percent, and 25
years to maturity. If you hold the bond for the entire year, how much in
interest income will you have to declare on your tax return?
Interest = Bond face value x YTM = $1,000 x 7% = $70. Therefore, the amount of
interest you must declare on your tax return is $70.
14. Bond Price Movements Miller Corporation has a premium bond
making semiannual payments. The bond pays a coupon of 8 percent, has
a YTM of 6 percent, and has 13 years to maturity. The Modigliani
Company has a discount bond making semiannual payments. This bond
pays a coupon of 6 percent, has a YTM of 8 percent, and also has 13
years to maturity. If interest rates remain unchanged, what do you
expect the price of these bonds to be 1 year from now? In 3 years? In 8
years? In 12 years? In 13 years? What’s going on here? Illustrate your
answers by graphing bond prices versus time to maturity.

15. Interest Rate Risk Laurel, Inc., and Hardy Corp. both have 7 percent
coupon bonds outstanding, with semiannual interest payments, and both
are priced at par value. The Laurel, Inc., bond has 2 years to maturity,
whereas the Hardy Corp. bond has 15 years to maturity. If interest rates
suddenly rise by 2 percent, what is the percentage change in the price of
these bonds? If interest rates were to suddenly fall by 2 percent instead,
what would the percentage change in the price of these bonds be then?
Illustrate your answers by graphing bond prices versus YTM. What does
this problem tell you about the interest rate risk of longer-term bonds?
 CHAPTER 10,11
Questions and Problems: (page.329)

1. Calculating Returns.
Suppose a stock had an initial price of $75 per share, paid a dividend of
$1.20 per share during the year, and had an ending share price of $86.
Compute the percentage total return.
- Initial share price: $75
- Dividend paid: $1.20 per share
- Ending share price: $86.
Capital gain = ending price - initial price = 86-75 = 11
Total return = Capital gain + dividend = 11 +1.20 = 12.20
Percentage total return = ($12.2 / 75) * 100% = 16.27%
⇒ đã sửa

5. Nominal versus Real Returns.

What was the arithmetic average annual return on large-company stocks
from 1926 through 2011?
a. In nominal terms?
- The arithmetic average annual return on large-company stocks from 1926 through
2011 in nominal terms is approximately 11.8%.

b. In real terms?
Assuming an average inflation rate of around 3% over this period, we can use the
formula:

- Real Return=[(1+Inflation Rate)/(1+Nominal Return)]​−1

=[(1+0.03)/(1+0.118)]​−1≈0.085 or 8.5%
6. Bond Returns.
What is the historical real return on long-term government bonds? On
long-term corporate bonds?
1. Long-Term Government Bonds
- Historically, the real return on long-term government bonds has been around 2-3% per
year. This takes into account inflation over the long term.
2. Long-Term Corporate Bonds
Long-term corporate bonds typically offer a higher historical real return than government
bonds, but they also carry higher risk
- The real return on long-term corporate bonds has been in the range of 3-4% per year

8. Risk Premiums.
Refer to Table 10.1 in the text and look at the period from 1973 through 1978.

a. Calculate the arithmetic average returns for large-company stocks and T-bills
over this period.
The average return of large company stock is 3.24% and the average return of t-bill is
6.55%.

b. Calculate the standard deviation of the returns for large-company stocks and
T-bills over this period.

The variance for large company stock is 0.058136 and the variance for t-bills is 0.000153.
The standard deviation for large company stock is 24.11% and the standard deviation for
t-bills is 1.24%.

c. Calculate the observed risk premium in each year for the large-company
stocks versus the T-bills. What was the arithmetic average risk premium over
this period? What was the standard deviation of the risk premium over this Period
Compute the average observed risk premium:

The average observed risk premium is -3.32%, variance is 0.062078, and the standard
deviation is 24.92%.

9. Calculating Returns and Variability

You’ve observed the following returns on Mary Ann Data Corporation’s
stock over the past five years: 27 percent, 13 percent, 18 percent, 214
percent, and 9 percent.
a. What was the arithmetic average return on Mary Ann’s stock over this
five-year period?
b. What was the variance of Mary Ann’s returns over this period? The
standard Deviation?
10. Calculating Real Returns and Risk Premiums
In Problem 9, suppose the average inflation rate over this period was 4.2
percent, and the average T-bill rate over the period was 5.1 percent.
a. What was the average real return on Mary Ann’s stock?
b. What was the average nominal risk premium on Mary Ann’s stock?
 18. Return Distributions.
Refer back to Table 10.2 . What range of returns would you expect to see 68
percent of the time for large-company stocks? What about 95 percent of the
time?
68% Range

The range within one standard deviation (±1σ) of the mean:

Lower bound=μ−σ=11.8%−20.3%=−8.5%

Upper bound=μ+σ=11.8%+20.3%=32.1%

So, the expected range for 68% of the time is: −8.5% to 32.1%

95% Range

The range within two standard deviations (±2σ) of the mean:

Lower bound=μ−2σ=11.8%−2×20.3%=−28.8%

Upper bound=μ+2σ=11.8%+2×20.3%=51.4%

So, the expected range for 95% of the time is: −28.8% to 51.4%

19. Calculating Returns and Variability.

You find a certain stock that had returns of 12 percent, -21 percent, 9
percent, and 32 percent for four of the last five years. If the average return
of the stock over this period was 11 percent, what was the stock’s return for
the missing year? What is the standard deviation of the stock’s returns?

Rate of return Squared of deviation

1 12% 0,01%

2 -21% 10,24%

3 9% 0,04%

4 32% 4,41%

5 x 1,44%
Expected return 23%

variance 0,03228

Standard deviation 17,97%

Expected return = (12% + (-21%) + 9% + 32% + x)/5 = 11%

=> the stock’s return for the missing year = x = 23%