3. ii
Solutions Manual
to accompany
Financial Management: Principles and Practice
4rd Edition
by Timothy J. Gallagher and Joseph D. Andrew, Jr.
This solutions manual provides the answers to all the review questions and end-of-chapter problems
in Financial Management: Principles and Practice, by Gallagher and Andrew. The answers and the steps
taken to obtain the answers are shown.
We remind our readers that in finance there is often more than one answer to a question or to a
problem, depending on one’s viewpoint and assumptions. We provide one answer to each question and show
one approach to solving each problem. Other answers and approaches may be equally valid, or judged even
better according to each individual’s preference.
6. 5
Chapter 1 Solutions
Answers to Review Questions
1. How is finance related to the disciplines of accounting and economics?
Financial management is essentially a combination of accounting and economics. First, financial
managers use accounting information—balance sheets, income statements, and so on—to analyze,
plan, and allocate financial resources for business firms. Second, financial managers use economic
principles to guide them in making financial decisions that are in the best interest of the firm. In other
words, finance is an applied area of economics that relies on accounting for input.
2. List and describe the three career opportunities in the field of finance.
Finance has three main career paths: financial management, financial markets and institutions, and
investments.
Financial management involves managing the finances of a business. Financial managers—people
who manage a business firm's finances—perform a number of tasks. They analyze and forecast a
firm's finances; assess risk, evaluate investment opportunities, decide when and where to find money
sources and how much money to raise, and decide how much money to return to the firm's investors.
Bankers, stockbrokers, and others who work in financial markets and institutions focus on the flow of
money through financial institutions and the markets in which financial assets are exchanged. They
track the impact of interest rates on the flow of that money.
People who work in the field of investments locate, select, and manage income-producing assets. For
instance, security analysts and mutual fund managers both operate in the investment field.
3. Describe the duties of the financial manager in a business firm.
Financial managers measure the firm's performance, determine what the financial consequences will
be if the firm maintains its present course or changes it, and recommend how the firm should use its
assets. Financial managers also locate external financing sources and recommend the most beneficial
mix of financing sources, and they determine the financial expectations of the firm's owners.
All financial managers must be able to communicate, analyze, and make decisions based on
information from many sources. To do this, they need to be able to analyze financial statements,
forecast and plan, and determine the effect of size, risk, and timing of cash flows.
4. What is the basic goal of a business?
The primary financial goal of the business firm is to maximize the wealth of the firm's owners.
Wealth, in turn, refers to value. If a group of people owns a business firm, the contribution that firm
makes to that group's wealth is determined by the market value of that firm.
7. 6
5. List and explain the three financial factors that influence the value of a business.
The three factors that affect the value of a firm's stock price are cash flow, timing, and risk.
The Importance of Cash Flow: In business, cash is what pays the bills. It is also what the firm
receives in exchange for its products and services. Cash is therefore of ultimate importance, and the
expectation that the firm will generate cash in the future is one of the factors that gives the firm its
value.
The Effect of Timing on Cash Flows: Owners and potential investors look at when firms can expect
to receive cash and when they can expect to pay out cash. All other factors being equal, the sooner
companies expect to receive cash and the later they expect to pay out cash, the more valuable the
firm and the higher its stock price will be.
The Influence of Risk: Risk affects value because the less certain owners and investors are about a
firm's expected future cash flows, the lower they will value the company. The more certain owners
and investors are about a firm's expected future cash flows, the higher they will value the company.
In short, companies whose expected future cash flows are doubtful will have lower values than
companies whose expected future cash flows are virtually certain.
6. Explain why accounting profits and cash flows are not the same thing.
Stock value depends on future cash flows, their timing, and their riskiness. Profit calculations do not
consider these three factors. Profit, as defined in accounting, is simply the difference between sales
revenue and expenses. It is true that more profits are generally better than less profits, but when the
pursuit of short-term profits adversely affects the size of future cash flows, their timing, or their
riskiness, then these profit maximization efforts are detrimental to the firm.
7. What is an agent? What are the responsibilities of an agent?
An agent is a person who has the implied or actual authority to act on behalf of another. The owners
whom the agents represent are the principals. Agents have a legal and ethical responsibility to make
decisions that further the interests of the principals.
8. Describe how society's interests can influence financial managers.
Sometimes the interests of a business firm's owners are not the same as the interests of society. For
instance, the cost of properly disposing of toxic waste can be so high that companies may be tempted
to simply dump their waste in nearby rivers. In so doing, the companies can keep costs low and
profits high, and drive their stock prices higher (if they are not caught). However, many people
suffer from the polluted environment. This is why we have environmental and other similar laws:
So that society's best interests take precedence over the interests of individual company owners.
When businesses take a long-term view, the interests of the owners and society often (but not always)
coincide. When companies encourage recycling, sponsor programs for disadvantaged young people,
8. 7
run media campaigns promoting the responsible use of alcohol, and contribute money to worthwhile
civic causes, the goodwill generated as a result of these activities causes long-term increases in the
firm's sales and cash flows, which translate into additional wealth for the firm's owners.
9. Briefly define the terms proprietorship, partnership, and corporation.
A proprietorship is a business owned by one person.
Two or more people who join together to form a business make up a partnership. This can be done on
an informal basis without a written partnership agreement, or a contract can spell out the rights and
responsibilities of each partner.
A limited liability company is a hybrid between a partnership and a corporation. Profits and losses
pass through to the members. Members generally enjoy limited liability.
Corporations are legal entities separate from their owners. To form a corporation, the owners specify
the governing rules for the running of the business in a contract known as the articles of
incorporation. They submit the articles to the government of the state in which the corporation is
formed, and the state issues a charter that creates the separate legal entity.
10. Compare and contrast the potential liability of owners of proprietorships, partnerships (general
partners), and corporations.
The sole proprietor has unlimited liability for matters relating to the business. This means that the
sole proprietor is responsible for all the obligations of the business, even if those obligations exceed
the amount the proprietor has invested in the business.
Each partner in a partnership is usually liable for the activities of the partnership as a whole. Even if
there are a hundred partners, each one is technically responsible for all the debts of the partnership.
If ninety-nine partners declare personal bankruptcy, the hundredth partner still is responsible for all
the partnership's debts.
A corporation is a legal entity that is liable for its own activities. Stockholders, the corporation's
owners, have limited liability for the corporation's activities. They cannot lose more than the amount
they paid to buy the corporation’s stock.
Answers to End-of-Chapter Problems
1. An accountant prepares financial statements while a financial analyst interprets them.
2. A financial manager’s role in a publicly traded company is to make financial decisions so as to
best serve the principal stockholders.
9. 8
3. a. The value of the firm would go down due to the increase in the amount of time it takes to
receive the cash inflows.
b. The value of the firm would go up due to the increase in expected cash inflows.
c. If expected future cash flows do not change the value of the firm would go down due to the
increased riskiness of the firm.
4. This practice obviously takes advantage of people who are in a difficult financial situation. This
transaction is voluntary, however, and high risk loans have high interest rates.
5. LLCs have a small number of members like partnerships and each of these members is likely to
have an active voice in the company like a partnership. The LLC is taxed like a partnership.
Unlike a partnership, and more like a corporation, the owners generally enjoy limited liability.
10. 9
Chapter 2 Solutions
Answers to Review Questions
1. What are financial markets? Why do they exist?
Financial markets are where financial securities are bought and sold. They exist primarily to bring
deficit economic units (those needing money) and surplus economic units (those having extra money)
together.
2. What is a security?
Securities are claims on financial assets. They can be described as “claim checks” that give their
owners the right to receive funds in the future. Securities are traded in both the money and capital
markets. Money market securities include Treasury bills, negotiable certificates of deposit,
commercial paper, and banker’s acceptances. Capital market securities include bonds and stock.
3. What are the characteristics of an efficient market?
The term market efficiency refers to the ease, speed, and cost of trading securities. In an efficient
market, securities can be traded easily, quickly, and at low cost. Markets lacking these qualities are
considered to be inefficient.
4. How are financial trades made on an organized exchange?
Each exchange-listed security is traded at a specified location on the trading floor called the post. The
trading is supervised by specialists who act either as brokers (bringing together buyers and sellers) or
as dealers (buying or selling the stock themselves). Prominent international securities exchanges
include the New York Stock Exchange (NYSE) and major exchanges in Tokyo, London,
Amsterdam, Frankfurt, Paris, Hong Kong, and Mexico.
5. How are financial trades made in an over-the-counter market? Discuss the role of a dealer in the OTC
market.
In contrast to the organized exchanges, which have physical locations, the over-the-counter market
has no fixed location,or more correctly, it is everywhere. The over-the-counter market, or OTC, is a
network of dealers around the world who maintain inventories of securities for sale. If you wanted to
buy a security that is traded OTC, you would call your broker, who would then shop among
competing dealers who have the security in their inventory. After locating the dealer with the best
price, your broker would buy the security on your behalf.
11. 10
The role of dealers: Dealers make their living buying securities and reselling them to others. They
operate just like car dealers who buy cars from manufacturers for resale to others. Dealers make
money by buying securities for one price (called the bid price) and selling them for a higher price,
(called the ask price). The difference, or spread, between the bid price and the ask price represents
the dealer’s fee.
6. What is the role of a broker in security transactions? How are brokers compensated?
Brokers handle orders to buy or sell securities. Brokers are agents who work on behalf of an investor.
When investors call with an order, brokers work on their behalf to find someone to take the other side
of the proposed trade. If investors want to buy, brokers find sellers. If investors want to sell, brokers
find buyers. Brokers are compensated for their services when the person whom they represent, the
investor, pays them a commission on the sale or purchase of securities.
7. What is a Treasury bill? How risky is it?
Treasury bills are short-term debt instruments issued by the U.S. Treasury that are sold at a discount
and pay face value at maturity. They are very nearly risk-free as they are backed by the U.S.
Government which could, if need by, print money to pay their holders at maturity.
8. Would there be positive interest rates on bonds in a world with absolutely no risk (no default risk,
maturity risk, and so on)? Why would a lender demand, and a borrower be willing to pay, a positive
interest rate in such a no-risk world?
Yes, there would be a positive rate of interest in a risk-free world. This is because regardless of risk,
lenders of money must postpone spending during the time the money is loaned. Lenders, then, lose
the opportunity to invest their money for that period of time. To compensate for the cost of losing
investment opportunities while they postpone their spending, lenders demand, and borrowers pay, a
basic rate of return, the real rate of interest.
Answers to End of Chapter Problems
2-1. a. Surplus economic units have income that exceeds their expenditures. Wealthy families in the
household sector and most states (which have balanced budget requirements) are surplus economic
units.
b. Deficit economic units have expenditures that exceed their incomes. Home buyers and college
students are likely to be deficit economic units.
2.2. a. false
b. false
c. false
d. false
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2-3. a. 2 3 4 1
b. The money market is dominated by large institutional traders and there is much competition. The
New York Stock Exchange tends to have larger more actively traded stocks. The over-the-counter
market tends to have smaller less actively traded securities. The real estate market has very high
transaction costs and trades take months.
2.4. a. A money market security is short term and actively traded.
b. Treasury bills and commercial paper are both traded in the money market.
2-5. $66.25/$1,000 = 6 5/8 % coupon rate
2-6. The yield on a Bonds-R-Us bond:
Real rate of interest...................... 2%
Inflation premium........................ 3%
Default risk premium................... 1%
Liquidity risk premium................ 1%
Maturity risk premium................. 1%
Total yield on Bonds-R-Us Bond: 8%
(reference figure 2-2)
2-7. Treasury Yield Curve:
Given:
Treasury Security Yields:
Maturity in Years (for Chart)
Three-month T-bills 4.50% 0.25
Six-month T-bills 4.75% 0.5
One-year T-notes 5.00% 1
Two-year T-notes 5.25% 2
Three-year T-bonds 5.50% 3
Five-year T-bonds 5.75% 5
Ten-year T-bonds 6.00% 10
Thirty-year T-bonds 6.50% 30
Chart: (see next page)
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Implications:
a. For borrowers: Borrowers tend to look for the low point of the curve, which indicates the least
expensive loan maturity. In this case the low point is 3 months, leading the borrower to seek a short-
term loan. However, if a firm borrows long-term and obtains the higher interest rate, that rate is
locked in for the life of the loan (30 years in this case). If interest rates rise the borrower may be glad
he/she locked in the long-term rate.
b. Lenders face the opposite situation. Granting short-term-term loans at relatively low interest rates
may look unattractive now; but if short-term rates rise, the lenders will be able to roll over
investments at higher and higher rates.
14. 13
Chapter 3 Solutions
Answers to Review Questions
1. Define intermediation.
The financial system makes it possible for surplus and deficit economic units to come together,
exchanging funds for securities, to their mutual benefit. When funds flow from surplus economic
units to a financial institution to a deficit economic unit, the process is known as intermediation. The
financial institution acts as an intermediary between the two economic units.
2. What can a financial institution often do for a surplus economic unit that it would have difficulty
doing for itself if the surplus economic unit (SEU) were to deal directly with a deficit economic unit
(DEU)?
Surplus economic units do not usually have the expertise to determine whether deficit economic units
can and will make good on their obligations, so it is difficult for them to predict when a would-be
deficit economic unit will fail to pay what it owes. Such a failure is likely to be devastating to a
surplus economic unit that has lent a proportionately large amount of money. In contrast, a financial
institution is in a better position to predict who will pay and who won't. It is also in a better position,
having greater financial resources, to occasionally absorb a loss when someone fails to pay. (This is
just one example of the beneficial things financial institutions do for SEUs)
3. What can a financial institution often do for a deficit economic unit (DEU)that it would have
difficulty doing for itself if the DEU were to deal directly with an SEU?
SEUs typically want to supply a small amount of funds, while DEUs typically want to obtain a large
amount of funds. Thus it is often difficult for surplus and deficit economic units to come together on
their own to arrange a mutually beneficial exchange of funds for securities. A financial institution
can step in and save the day. A bank, savings and loan, or insurance company can take in small
amounts of funds from many individuals, form a large pool of funds, and then use that large pool to
purchase securities from individual businesses and governments. (This is just one example of the
beneficial things financial institutions do for DEUs)
4. What are a bank's primary reserves? When the Fed sets reserve requirements, what is its primary
goal?
Vault cash and deposits in the bank's account at the Fed are used to satisfy these reserve
requirements; they are called primary reserves. These primary reserves are non-interest-earning
assets held by financial institutions.
The Federal Reserve requires all commercial banks to keep a minimum amount of reserves on hand
to meet the withdrawal demands of its depositors and to pay other obligations as they come due.
15. 14
Many would argue, however, that the reserve requirement is set more with monetary policy in mind
than to ensure that banks meet their depositors' withdrawal requests.
5. Compare and contrast mutual and stockholder-owned savings and loan associations.
Some savings and loan associations are owned by stockholders, just as commercial banks and other
corporations are owned by their stockholders. Other S&Ls, called mutuals, are owned by their
depositors. When a person deposits money in an account at a mutual S&L, that person becomes a
part owner of the firm. The mutual S&L's profits (if any) are put into a special reserve account from
which dividends are paid from time to time to the owner/depositors.
6. Who owns a credit union? Explain.
Credit unions are owned by their members. When credit union members put money in their credit
union, they are not technically "depositing" the money. Instead, they are purchasing shares of the
credit union. In general, credit unions exist to pay interest on shares bought by, and collect interest
on loans made to, the members.
7. Which type of insurance company generally takes on the greater risks: a life insurance company or a
property and casualty insurance company?
The risks protected against by property and casualty companies are much less predictable than are the
risks insured by life insurance companies. Hurricanes, fires, floods, and trial judgments are all much
more difficult to predict than the number of sixty-year-old females who will die this year among a
large number in this risk class. This means that property and casualty insurance companies must
keep more liquid assets than do life insurance companies.
8. Compare and contrast a defined benefit and a defined contribution pension plan.
In a defined benefit plan, retirement benefits are determined by a formula that usually considers the
worker's age, salary, and years of service. The employee and/or the firm contribute the amounts
necessary to reach the goal. In a defined contribution plan, the contributions to be made by the
employee and/or employer are spelled out, but retirement benefits depend on the total accumulation
in the individual's account at the retirement date.
9. Special security software is used such that customers who enter their identification and password
information can keep sensitive information out of the hands of hackers.
16. 15
Answers to End-of-Chapter Problems
3-1. a) If there were no financial institutions the SEUs and the DEUs would find that the amount of
money needed by a given DEU did not match the amount of money available by a given SEU. The
money available would not be put to work and the economic activity that would have otherwise taken
place would not.
b) If financial institutions were available in this society they could position themselves between the
SEUs and DEUs. The financial institution could pool the $1,000 available (100 SEUs times $10
each) and pass that money along in $100 increments to the DEUs. This could be done via either a
debt or equity claim that the financial institution would accept from the DEU in return for the money.
3-2. a) .10 rate on loans made - .05 rate paid to depositors = .05 = 5% interest rate spread
b) (.5 x .10) + (.5 x .12) = .11 = 11% weighted average loan rate
(.5 x .05) + (.5 x .07) = .06 = 6% weighted average deposit rate
11% - 6% = 5% interest rate spread
3-3. ($48,300,000 - $7,800,000) x .03) + (($60,000,000 - $48,300,000) x .10) + ($20,000,000 x 0) +
($10,000,000 x 0) = $6,732,000
3-4. a) The FOMC should buy government securities in the open market. This would increase the
reserves of the banking system and would put downward pressure on the federal funds rate.
b) The Fed’s trader at the New York Federal Reserve Bank would contact various government
securities dealers and would buy the Treasury securities from them. Payment would be made by
crediting the accounts at the Fed of these dealers. This would make more funds available and would
tend to put downward pressure on the cost of these funds, the federal funds rate.
3-5. a) ($1,000,000 x .08) – ($1,000,000 x .07) = $10,000 a profit of $10,000
b) ($1,000,000 x .08) – ($1,000,000 x .09) = -$10,000 a loss of $10,000
17. 16
Chapter 4 Solutions
Answers to Review Questions
1. Why do total assets equal the sum of total liabilities and equity? Explain.
Assets = Liabilities + Equity
Assets are the items of value a business owns. Liabilities are claims on the business by non-owners,
and equity is the owners' claim on the business. The sum of the liabilities and equity is the total
capital contributed to the business, which, by definition, equals the total value of the assets.
2. What are the time dimensions of the income statement, the balance sheet, and the statement of cash
flows? Hint: Are they videos or still pictures? Explain.
The income statement is like a video: It measures a firm's profitability over a period of time (which
can be a week, a month, a year, or any other time period).
The balance sheet is like a still photograph. The balance sheet shows the firm's assets, liabilities, and
equity at a given point in time.
This cash flow statement like the income statement, can be compared to a video: It shows how cash
flows into and out of a company over a given period of time.
3. Define depreciation expense as it appears on the income statement. How does depreciation affect
cash flow?
Accounting depreciation is the allocation of an asset's initial cost over time. Depreciation expense on
an income statement is the amount of the asset=s initial cost allocated to the period covered by the
income statement.
Depreciation expense is not a cash flow. Depreciation as an expense category affects cash flow,
however, because it is tax-deductible. Depreciation expense lowers a company’s taxable income
and, therefore its income tax liability. In this way depreciation reduces cash outflows..
4. What are retained earnings? Why are they important?
Retained earnings represents the sum of all the earnings available to common stockholders of a
business during its entire history, minus the sum of all the common stock dividends which it has ever
paid. Those earnings that were not paid out were, by definition, retained.
Retained earnings are important because they represent amounts reinvested in a company on behalf
of the company’s owners instead of being paid out in the form of dividends.
18. 17
5. Explain how earnings available to common stockholders and common stock dividends paid from the
current income statement affect the balance sheet item retained earnings.
The change in the retained earnings account from one balance sheet to the next equals net income
less preferred stock dividends (which is the amount of earnings available to common stockholders)
less common stock dividends.
6. What is accumulated depreciation?
Depreciation is the allocation of an asset's initial cost over time. Accumulated depreciation is the
total of all the depreciation expense that has been recognized to date.
7. What are the three major sections of the statement of cash flows?
Cash flows from Operations
Cash flows from investing activities
Cash flows from financing activities
Net change in cash balance
Cash balance at beginning of period
Cash balance at end of period
8. How do financial managers calculate the average tax rate?
Average tax rates are calculated by dividing tax dollars paid by earnings before taxes (EBT).
9. Why do financial managers calculate the marginal tax rate?
Financial managers use marginal tax rates to estimate the future after-tax cash flows from
investments. Since they are interested in how much of the next dollar earned from new investments
will have to be paid in taxes, they use the marginal tax rate (rather than the average tax rate) to
calculate the tax liability.
10. Identify whether the following items belong on the income statement or the balance sheet.
a. Interest Expense IS l. Cash BS
b. Preferred Stock Dividends Paid IS m. Capital in Excess of Par BS
c. Plant and Equipment BS n. Operating Income IS
d. Sales IS o. Depreciation Expense IS
e. Notes Payable BS p. Marketable Securities BS
f. Common Stock BS q. Accounts Payable BS
g. Accounts Receivable BS r. Prepaid Expenses BS
h. Accrued Expenses BS s. Inventory BS
i. Cost of Goods Sold IS t. Net Income IS
j. Preferred Stock BS u. Retained Earnings BS
k. Long-Term Debt BS
19. 18
11. Indicate in which section the following balance items belong (current assets, fixed assets, current
liabilities, long-term liabilities, or equity).
a. Cash CA h. Capital in Excess of Par EQ
b. Notes Payable CL i. Marketable Securities CA
c. Common Stock EQ j. Accounts Payable CL
d. Accounts Receivable CA k. Prepaid Expenses CA
e. Accrued Expenses CL l. Inventory CA
f. Preferred Stock EQ m. Retained Earnings EQ
g. Plant and Equipment FA
Answers to End-of-Chapter Problems
4-1.
CASE A CASE B
Revenues 200,000 110,000
Expenses 160,000 70,000
Net Income 40,000 40,000
Retained Earnings, Jan 1 300,000 100,000
Dividends Declared 70,000 30,000
Retained Earnings, Dec 31 270,000 110,000
Current Assets, Dec 31 80,000 230,000
Non-current Assets, Dec 31 850,000 180,000
Total Assets, Dec 31 930,000 410,000
Current Liabilities, Dec 31 40,000 60,000
Non-current Liabilities, Dec 31 100,000 140,000
Total Liabilities, Dec 31 140,000 200,000
CS & Cap. in Excess of Par, Dec 31 520,000 100,000
Total Stockholders’ Equity, Dec 31 790,000 210,000
4-2.
CASE A CASE B
Sales 500,000 250,000
COGS 200,000 100,000
Gross Profit 300,000 150,000
Operating Expenses 60,000 60,000
Operating Income (EBIT) 240,000 90,000
Interest Expense 10,000 10,000
Earnings Before Taxes (EBT) 230,000 80,000
Tax Expense (40%) 92,000 32,000
Net Income 138,000 48,000
4-3. a) 15%; $48,000 X 0.15 = $7,200
b) $7,200/$48,000 = 0.15 or 15%
20. 19
4-4. a) Tax = $50,000 X 0.15 + $25,000 X 0.25 + $25,000 X 0.34 + $50,000 X 0.39
= $41,750
b) Effective tax rate = $41,750/$150,000 = 0.2783 or 27.83%
4-5. The marginal tax rate is the tax rate applied to the next dollar of income. Therefore, the marginal tax
rate is 34%.
The average tax rate is 34%
50,000 * .15 = 7,500
25,000 * .25 = 6,250
25,000 * .34 = 8,500
235,000 * .39 = 91,650
2,865,000 * .34 = 974,100
$1,088,000
$1,088,000/$3,200,000 = 34%
4-6. $1 + $400,000/200,000 = $3.00 per share
4-7. Sales $10,000,000
- Operating Costs 5,200,000
- Interest Expense 200,000
= EBT $4,600,000
- Taxes (40%) 1,840,000
Net after-tax income $2,760,000
Simon’s net after-tax income was $2,760,000 for the year.
4-8. Depreciation expense in 2006 = $70,000 - $60,000 = $10,000.
4-9
a) Cash + Marketable Securities + Inventory + Accounts Receivable + Prepaid expenses.
(11,000,000 + 9,000,000 + 11,000,000 + 3,000,000 + 1,000,000) = 35,000,000
Current Assets = $35,000,000
b) Fixed assets – depreciation
30,000,000 – 8,000,000 = 22,000,000
Net Fixed Assets = $22,000,000
c) Notes Payable + Accrued Expenses
4,000,000 + 2,000,000 = 6,000,000
Current Liabilities = $6,000,000
21. 20
d) Current Assets – Current Liabilities
(11,000,000 + 9,000,000 + 11,000,000 + 3,000,000 + 1,000,000) – (4,000,000 + 2,000,000)
35,000,000 – 6,000,000 = 29,000,000
Net Working Capital = $29,000,000
4-10. a ) Gross Profit $440,000 - $200,000 = $240,000
b ) Operating Income (EBIT) $240,000 - $40,000 - 85,000 = $115,000
c ) Earning Before Taxes (EBT) $ 115,000 - $40,000 = $75,000
d ) Income Taxes $ 75,000 X 0.4 = $30,000
e ) Net Income $75,000 - $30,000 = $45,000
4-11 $1,500,000 – $200,000 = $1,300,000
Simon and Pieman had a net worth of $1,300,000 at the end of the year.
4-12 a ) 2006 Depreciation Expense for this process line
($131,000 + $12,000) X (0.245) = $35,035
b ) Amount of tax savings due to this investment.
$35,035 X 0.4 = $14,014
4-13. Operating Income (EBIT) = $768,000
+ Depreciation = $42,000
+ Amortization = $15,000
$825,000
Target Telecom’s EBITDA = $825,000.
4-14 a ) The company's 2006 taxable income = ($400,000 - $130,000 X 0.2)
= $374,000
b ) Income tax = $374,000 X 0.34 = $127,160
4-15. a) Earnings = [($600,000 - 50,000) X (1 - .34) - $63,000] = $300,000
Earnings per share = $300,000 / 100,000 = $3 per share
b) Addition to Retained Earnings = $300,000 - 100,000 = $200,000
22. 21
4-16. a ) Current Assets: 2005: $5,534 + 14,745 + 10,733 + 952 + 3,234 = $35,198
2006: $9,037 + 15,943 + 11,574 + 1,801 + 2,357=$40,712
b ) Total Assets: 2005: $35,198+(57,340 - 29,080)+1,010+2,503 = $66,971
2006: $40,712+(60,374 - 32,478)+1,007+4,743 = $74,358
c ) Current Liabilities: 2005: $3,253 + 6,821 = $10,074
2006: $2,450 + 7,330 = $9,780
d ) Total Liabilities: 2005: $10,074 + 2,389 = $12,463
2006: $9,780 + 2,112 = $11,892
e ) Total Stockholders' Equity: 2005: $8,549 + 45,959 = $54,508
2006: $10,879 + 51,587 = $62,466
4-17. 2005: $12,463 TL + $54,508 EQ = $66,971 TA
2006: $11,892 TL + $62,466 EQ = $74,358 TA
4-18. (Dollars)
a ) Accumulated Depreciation 3,398 Inflow
b ) Accounts Receivable (net) 1,198 Outflow
c ) Inventories 841 Outflow
d ) Prepaid Expenses 877 Inflow
e ) Accounts Payable 803 Outflow
f ) Accrued Expenses 509 Inflow
g ) Plant and Equipment (gross) 3,034 Outflow
h ) Marketable Securities 849 Outflow
i ) Land 3 Inflow
j ) Long Term Investments 2,240 Outflow
k ) Common Stock 2,330 Inflow
l ) Bonds Payable 277 Outflow
4-19. Pinewood Company and Subsidiaries
Statement of Cash Flows
For the year 2006
Operations: Net Income 10,628
Add: Depreciation Exp. 3,398
Decrease in Prepaid Expenses 877
Increase in Accrued Expenses 509
Less: Increase in A/C Receivable (1,198)
Increase in Marketable Securities ( 849)
Increase in Inventories ( 841)
Decrease in A/C Payable ( 803)
Total Cash Flow from Operations $11,721
Investments:
Add: Decrease in Land 3
Less: Increase in Plant and Equipment (3,034)
Increase in Long Term Investment (2,240)
Total Cash Flow from Investments ($5,271)
23. 22
Financing:
Add: Increase in Common Stock 2,330
Less: Common Stock Dividends (5,000)
Decrease in Bonds Payable ( 277)
Cash Flow from Financing ($2,947)
Net Cash Flow $3,503
4-20. $3,503 = $9,037 end of ‘02 cash - $5,534 end of ‘01 cash Yes, the net cash flow figure from
problem #16 gives the same answer as calculating the change in the cash figures from the end of 2005 to the
end of 2006 balance sheets.
4-21. Sales 900,000
COGS 300,000
Gross Profit 600,000
Operating Expenses 200,000
Operating Income (EBIT) 400,000
Interest Expense 100,000
Income before taxes (EBT) 300,000
Tax Expense (30%) 90,000
Net Income $210,000
4-22. Retained Earnings end of 2006 $8,700,000
Retained Earnings end of 2005 8,000,000
Addition to retained earnings 2006 700,000
Earnings Available to Common Stockholders $1,500,000
-Addition to Retained Earnings -700,000
Dividends paid to Common Stockholders 2006 = $ 800,000
4-23. Year Deprec. % * Depreciable Base = Depreciation
1 10% $385,000 $38,500
2 18% $385,000 $69,300
3 14.4% $385,000 $55,440
4 11.5% $385,000 $44,275
5 9.2% $385,000 $35,420
6 7.4% $385,000 $28,490
7 6.6% $385,000 $25,410
8 6.6% $385,000 $25,410
9 6.5% $385,000 $25,025
10 6.5% $385,000 $25,025
11 3.3% $385,000 $12,705
4-24. Basis = $1,000,000 + $100,000 + $50,000 = $1,150,000
Year 3 depreciation = $1,150,000 * .148 = $170,200
24. 23
4-25. Year 1 $7,000,000 * .1 = $700,000
Year 2 $7,000,000 * .18 = $1,260,000
Year 3 $7,000,000 * .144 = $1,008,000
Year 4 $7,000,000 * .115 = $805,000
Year 5 $7,000,000 * .092 = $644,000
Year 6 $7,000,000 *.074 = $518,000
Year 7 $7,000,000 * .066 = $462,000
Year 8 $7,000,000 * .066 = $462,000
Year 9 $7,000,000 * .065 = $455,000
Year 10 $7,000,000 * .065 = $455,000
Year 11 $7,000,000 * .033 = $231,000
25. 24
Chapter 5 Solutions
Answers to Review Questions
1. What is a financial ratio?
A financial ratio is a number that expresses the value of one financial variable relative to another.
Put more simply, a financial ratio is the result you get when you divide one financial number by
another. Calculating an individual ratio is simple, but each ratio must be analyzed carefully to
effectively measure a firm's performance.
2. Why do analysts calculate financial ratios?
Ratios are comparative measures. Because the ratios show relative value, they allow financial
analysts to compare information that could not be compared in its raw form. For example, ratios may
be used to compare one ratio to a related ratio, a firm's performance to management's goals, a firm's
past and present performance, or a firm's performance to similar firms
3. Which ratios would a banker be most interested in when considering whether to approve an
application for a short-term business loan? Explain.
Bankers and other lenders use liquidity ratios to see whether to extend short-term credit to a firm.
Liquidity ratios measure the ability of a firm to meet its short-term obligations. These ratios are
important because failure to pay such obligations can lead to bankruptcy. Generally, the higher the
liquidity ratio, the more able a firm is to pay its short-term obligations.
4. Which ratios would a potential long-term bond investor be most interested in? Explain.
Current and potential lenders of long-term funds, such as banks and bondholders, are interested in
debt ratios. When a business's debt ratios increase significantly, bondholder and lender risk increases
because more creditors compete for that firm's resources if the company runs into financial trouble.
5. Under what circumstances would market to book value ratios be misleading? Explain.
The Market to Book ratio is useful, but it is only a rough approximation of how liquidation and going
concern values compare. This is because the Market to Book ratio uses accounting-based book
values. The actual liquidation value of a firm is likely to be different than the book value. For
instance, the assets of a firm may be worth more or less than the value at which they are currently
carried on the company's balance sheet. In addition, the current market price of the company's bonds
and preferred stock may also differ from the accounting value of these claims.
26. 25
6. Why would an analyst use the Modified Du Pont system to calculate ROE when ROE may be
calculated more simply? Explain.
Actually, an analyst would not use the Modified Du Pont equation to calculate ROE for precisely the
reason stated above. What an analyst would use the Modified Du Pont equation for is to help analyze
the factors that contribute to a firm's ROE. In other words, analysts use the Modified Du Pont system
to “take apart” ROE to see what factors are influencing it.
7. Why are trend analysis and industry comparison important to financial ratio analysis?
Trend analysis helps financial managers and analysts see whether a company's current financial
situation is improving or deteriorating.
Cross-sectional analysis, or industry comparison, allows analysts to put the value of a firm's ratios in
the context of its industry.
Answers to End-of-Chapter Problems
5-1. a) Gross Profit Margin = Gross Profit/Sales
20,000,000/35,000,000 = .5714
Gross Profit margin = 57.14%
b) Operating Profit Margin = EBIT/Sales
16,000,000/35,000,000 = .4571
Operating Profit Margin = 45.71%
c) Net Profit Margin = Net Income/Sales
8,100,000/35,000,000 = .2314
Net Profit Margin = 23.14%
5-2. Current Ratio = Total Current Assets/Total Current Liabilities
(5,000) / (500 +850 + 600) = 2.56
Current Ratio = 2.56
Quick Ratio = (Total Current Assets - Inventory)/Total Current Liabilities
(5,000 – 900)/(500 + 850 + 600) = 2.10
Quick Ratio = 2.10
5-3. Average Daily Credit Sales = Annual credit sales/365
5,000,000/365 = $13,698.63
Average Collection Period = Accounts Receivable/Average Daily Credit Sales
$500,000/13,698.63 = 36.5
Average Collection Period = 36.5 days
27. 26
5-4. Inventory Turnover = Sales/Inventory
35,000,000/2,400,000 = 14.58
Inventory Turnover = 14.58 X
Total Asset Turnover = Sales/Total Assets
35,000,000/(15,000,000 + 20,000,000) = 1
Total Asset Turnover = 1 X
5-5. a) Book value per share
Book price per share = Common Stock Equity/Number of shares Outstanding
$4,500,000/650,000 =$6.92
BPS = $6.92
b) Market to book value ratio
Market to book value ratio = Market price per share/Book value per share
$25.00/$6.92 = 3.61
Market to book value ratio = 3.61
5-6. a) Gross profit margin: $47,378/$94,001 = 50.40%
b) Operating profit margin $12,941/$94,001 = 13.77%
c) Net profit margin $8,620/$94,001 = 9.17%
d) Return on assets $8,620/$66,971 = 12.87%
e) Return on equity $8,620/$54,508 = 15.81%
While the Net profit margin is higher than the industry average, the Return on assets is lower. Pinewood
may consider increasing its debt to leverage profits.
5-7. a) Current assets = $5,534 + $14,745 + $10,733 + $952 + $3,234 = $35,198
Current ratio = $35,198/$10,074 = 3.494
b) Quick ratio = ($35,198 - $10,733)/$10,074 = 2.429
Pinewood seems highly capable of paying off short-term debts.
5-8. a) Total debt = $3,253 + $6,821 + $2,389 = $12,463
Debt to total assets = $12,463/$66,971 = 18.61%
b) Times interest earned = $12,941/$48 = 270 times
Yes. The Pinewood has very low debt and its earnings are extremely high compared to its interest
expense.
5-9. a. Average collection period $14,745/($94,001 / 365) = 57.25 days
b. Inventory turnover $94,001/$10,733 = 8.76
c. Total asset turnover $94,001/$66,971 = 1.404
We would need to know the industry averages for these figures, and also know about Pinewood’s
credit and inventory management practices to comment meaningfully on the above figures.
28. 27
5-10. Modified Du Pont: ROE = Net Profit Margin X Total Asset Turnover X Assets over Equity
= 0.0917 X 1.404 X $66,971/$54,508 = 15.82%
5-11. a) EVA = EBIT (1- tax rate) – (invested capital * investor’s required rate of return)
EVA = $12,941,000 * (1 - 0.35) – ($77,389,000 * 0.10) = $672,750
b) Pinewood has a true economic profit of $672,750. This is the amount by which its
earnings exceed the returned expected by the firm’s investors.
c) MVA = Total market value – invested capital
MVA = ($75,000,000 + $2,389,000) – ($54,508,000 + $2,389,000) = $20,492,000
d) Pinewood has a total market value that is $20,492,000 greater that the amount of capital
invested in the firm.
5-12. a) EVA = EBIT (1 – Tax Rate) – (invested capital * investors required rate of return)
EVA = $8,000 (.65) – ($33,000 * .12)
= $5,200 – $3,960
EVA = $1,240
b) The economic value is positive; therefore, Eversharp earned a sufficient amount during the
year to provide more than the expected rate of return from the investors and lenders who
contributed to the capital of the company.
c) MVA = Total market value – invested capital
MVA = $33,000 - $21,000 = $12,000
d) Eversharp’s total market value exceeds its invested capital by $12,000.
5-13.
EVA & MVA Calculation:
Income tax rate 35%
Cost of Capital 12% Ka
Stock Price (ref) $9
Number of shares outstanding (ref) 3,000
Market Value of Common Equity (ref) $27,000
Book Value of Common Equity $15,210
Debt Capital (ref) $6,630 (Notes payable + Long-Term Debt )
Total Invested Capital (ref) $33,630 (Debt + Common)
EVA
MVA
a. EVA $189 EBIT(1-Tr) - (Invested Capital * Ka)
b. Comment on EVA: This year T & J earned enough to exceed the return expected by the
contributors of the firm's capital by $189.
29. 28
5-14. a. Du Pont: ROA = Net Profit Margin X Total Asset Turnover
= (80/1,000) X (1,000/500) = 16%
Modified Du Pont: ROE = Net Profit Margin X Total Asset Turnover X Assets over
Equity
= ($80/$1,000) X ($1,000/$500) X (1/(1-0.5) = 32%
b. ROE = ($80/$1,000) X ($1,000/$500) X (1/(1-0.7) = 53.3%
c. ROE = ($80/$1,000) X ($1,000/$500) X (1/(1-0.9) = 160%
d. ROE = ($80/$1,000) X ($1,000/$500) X (1/(1-0.1) = 17.78%
5-15.
Assets Liabilities + Equity
Cash $6,000 Accounts Payable $6,000
Accounts Receivable 15,068 Notes Payable 2,739
Inventory 6,667 Accrued Expenses 600
Prepaid Expenses 282 Total Current Liabilities 9,339
Total Current Assets 28,017 Bonds Payable 15,661
Fixed Assets 34,483 Common Stock 16,000
Retained Earnings 21,500
Total Assets $62,500 Total Liabilities + Equity $62,500
Total Assets = Sales / Total Asset Turnover = $100,000/1.6 = $62,500
Fixed Assets = Sales / Fixed Asset Turnover = $100,000/2.9 = $34,483
Total Current Assets = $62,500 - $34,483 = $28,017
Accounts Receivable = Sales/day X Ave. Collection Period = ($100,000/365) X 55 = $15,068
Inventory = Sales / Inventory Turnover = $100,000/15 = $6,667
Prepaid Expenses = $28,017 - ($15,068 + $6,667 + $6,000) = $282
Total Debt = Total Assets X Debt to Asset Ratio = $62,500 X 0.4 = $25,000
Total Current Liabilities = Total Current Assets / Current Ratio = $28,017/3 = $9,339
Bonds Payable = Total Debt - Total Current Liabilities = $25,000 - $9,339 = $15,661
Retained Earnings = $62,500 - ($16,000 + $25,000) = $21,500
Notes Payable = $9,339 - ($600 + $6,000) = $2,739
5-16. NI/$5,000 = 0.10
NI = $500
TE = TA - TL = $10,000 - $6,000 = $4,000
ROE = $500/$4,000 = .125 = 12.5%
5-17. Current Liability = $20,000 - $18,000 = $2,000
Current Ratio = $5,000/$2,000 = 2.5 times
5-18. Return on Assets = Net Profit Margin X Total Asset Turnover
0.12 = 0.04 X Total Asset Turnover
Total Asset Turnover = 0.12/0.04 = 3
30. 29
5-19. Gross Profit = 0.50 X $5,000,000 = $2,500,000
5-20. EBIT = $2,500,000 - $200,000 - $50,000 = $2,250,000
Operating Profit Margin = $2,250,000/$5,000,000 = .45 = 45%
5-21. Net Income = 0.20 X $5,000,000 = $1,000,000
5-22. Net Income = 0.20 X $5,000,000 = $1,000,000
ROA = $1,000,000/$20,000,000 = .05 = 5%
5-23. Net Income = 0.10 X $15,000,000 = $1,500,000
5-24. Current Ratio = (20,000,000 - 2,000,000)/4,000,000 = 4.5
5-25. Quick Ratio = ($20,000,000 - $2,000,000 - $3,000,000)/$4,000,000 = 3.75 times
5-26. Total Debt = 0.30 X $20,000,000 = $6,000,000
Debt to Equity ratio = $6,000,000/$14,000,000 = 0.43
5-27. Inventory Turnover = 5,000,000/3,000,000 = 1.67
5-28. Return on Assets = 0.20 X 0.25 = 0.05 = 5%
5-29. a) Du Pont: ROA = Net Profit Margin X Total Asset Turnover
= ($200/$2,000) X ($2,000/$1,000) = .20 = 20%
Modified Du Pont: ROE = Net Profit Margin X Total Asset Turnover X Assets over Equity
= ($200/$2,000) X ($2,000/$1,000) X (1/(1-0.6)) = .50 = 50%
b) ROE = ($200/$2,000) X ($2,000/$1,000) X (1/(1-0.8)) = 100%
c) ROE = ($200/$2,000) X ($2,000/$1,000) X (1/(1-0.2)) = 25%
5-30. Notoriously Niagara Niagara’s Notions
a) NPM = $100,000/$500,000 = 0.20 NPM = $10,000/$500,000 = 0.02
b) TATO = $500,000/$500,0000 = 0.10 TATO = $500,000/$500,000 = 1.0
c) ROA = 0.20 X 0.10 = 0.02 ROA = 0.02 X 1.0 = 0.02
31. 30
d) Notoriously Niagara must have a higher net profit margin because their asset turnover is low
compared to that of Niagara’s Notions even though they have the same ROA. Niagra’s Notions has a high
asset turnover but a low net profit margin.
5-31. a ) $2,250,000/1,750,000=$1.29
b ) $40/$1.29 = 31
c ) $15,000,000/1,750,000 = $8.57
d ) $40/$8.57 = 4.67
e ) Yes, the market seems to believe that the company has going-concern value as evidenced by
the market to book ratio greater than 1.
5-32. Net Profit Margin Current Ratio Total Asset Turnover
Year NI/Sales CA/CL Sales/TA
2004 10.00% .94 1.05
2005 9.44% 1.02 1.15
2006 9.36% 1.08 1.18
Golden Products
Industry averages: 9.42% 1.13 2.00
The NPM is about average, although it is deteriorating. The liquidity, as measured by the current
ratio, is below average but improving. Asset utilization, as measured by the total asset turnover is way below
average.
5-33. The Industry averages are:
Fixed Asset Turnover Return on Assets Debt to Assets Ratio Return on equity
1.33 11.00% 0.60 26%
YEAR PM CR TATO FATO ROA D/A ROE
2004 10.00% 0.94 1.05 1.21 10.53% 0.68 33.33%
2005 9.44% 1.02 1.15 1.33 10.90% 0.64 30.36%
2006 9.36% 1.08 1.18 1.36 11.00% 0.60 27.50%
Golden Products has an improving ROA that now equals that of the industry norm. The ROE has
slipped a little, but is still above the industry norm in spite of the fact that Golden has a little less debt
in its capital structure in 2006. Overall, Johnny should be pleased.
5-34. ( Figures in $ '000) Mining Smelting Rolling Extrusion Whole Company
NPM 3.3% 8.7% 11.7% 10.0% 9.7%
ROA 4.2% 10.4% 17.9% 13.9% 13.4%
32. 31
5-35.
National Glass Company
Income Statement (in $ 000's) Ratios:
2006
ACP 48.7 days
Sales $45,000 Inventory Turnover 9 X
Cost of Goods Sold 23,000 Debt to Assets 40%
Gross Profit 22,000 Current Ratio 1.6250
Selling and Admin Expenses 13,000 Total Asset turnover 1.50
Depreciation 3,000 Fixed Asset Turnover 2.6471
Operating Income 6,000 Return on Equity 19.33%
Interest Expense 200 Return on Assets 11.6%
Earnings Before Tax 5,800 Operating Profit Margin 13.33%
Income Taxes 2,320 Gross Profit Margin 48.89%
Net Income $3,480
Preferred Dividends $0
Earnings Available to Common $3,480
Balance Sheet (in $ 000's)
As of Dec 31
2006
Assets
Current Assets:
Cash $2,000
Accounts Receivable 6,000
Inventory 5,000
Total Current Assets 13,000
Plant & Equipment, Net 16,000
Land 1,000
Total Assets $30,000
Liabilities & Equity
Current Liabilities:
Accounts Payable $2,000
Notes Payable 3,000
Accrued Expenses 3,000
Total Current Liabilities 8,000
Bonds Payable 4,000
Total Liabilities 12,000
Common Stock 4,000
Retained Earnings 14,000
Total Stockholders' Equity 18,000
Total Liabilities & Equity $30,000
5-36.
a.) (Industry) Kingston, 2006 Kingston, 2007
i. Gross Profit Margin (50%) 48.9% 48.9%
ii. Operating Profit Margin (15%) 15.1% 13.3%
iii. Net Profit Margin (8%) 8.5% 7.5%
iv. Return on Assets (10%) 11.56% 9.97%
v. Return on Equity (20%) 19.3% 16.3%
vi. Current Ratio (1.5) 1.63 1.62
vii. Quick Ratio (1.0) 1.00 1.04
viii. Debt to Total Asset (0.5) .4 .39
ix. Times Interest Earned (25) 15.5X 14.6X
33. 32
x. Average Collection Period (45 days) 53.5days 61.6days
xi. Inventory Turnover (8) 8.18X 8.62X
xii. Total Asset Turnover (1.6) 1.4X 1.3X
b.) Kingston has about the same net profit margin and return on equity as the industry norm. The return on
assets ratio for Kingston is about the same as than the industry norm.
c.) Determine the sources and uses of funds and prepare a statement of cash flows for 2007.
(1) Sources and Uses of Funds:
Change,
2006 to 2007
Balance SheetSources Uses
Net Income $3,353
Dividends paid $733
Depreciation $3,000
Cash ($200) $200
Accounts Receivable, Net $1,600 $1,600
Inventory $220 $220
Property, Plant & Equipment, Gross $5,000 $5,000
Land $0
Accounts Payable $600 $600
Notes Payable $300 $300
Accrued expenses $100 $100
Bonds Payable $0
Common Stock $0
Totals $7,553$7,553
(2) Statement of Cash Flows:
Kingston Tool Company
Statement of Cash Flows for the year 2007
( in $ 000s)
Cash Flows from Operations:
Net Income $3,353
Depreciation 3,000
Decrease(Increase) in Accounts Receivable (1,600)
Decrease(Increase) in Inventory (220)
Increase(Decrease) in Accounts Payable 600
Increase(Decrease) in Notes Payable 300
Increase(Decrease) in Accrued Expenses 100
Total Cash Flows from Operations $5,533
Cash Flows from Investments:
New Property, Plant, & Equipment($5,000)
Total Cash Flows from Investments ($5,000)
Cash Flows from Financing:
Dividends Paid ($733)
Total Cash Flows from Financing (733)
-
Net Cash Flow ($200)
Beginning Cash Balance $2,000
Ending Cash Balance $1,800
34. 33
d.) Profit margins are eroding and generally a little below the industry norm. Liquidity is about average.
Debt is low, but interest coverage is below the industry norm in spite of the low debt load. Inventory
turnover is way below average. The negative cash flow of $200,000 came mainly from the buildup of
accounts receivable and plant & equipment.
e.) The current ratio, quick ratio, and times interest earned would get the most scrutiny from loan officers.
5-36b. EVA = EBIT * (1 – tax rate) – (invested capital * investor’s required rate of return)
EVA = ($4,000 * 0.60) – ($60,000 * 0.10) = -$3,600
EVA = -$3,600
MVA = Total market value – invested capital
MVA = $50,000 - $60,000 = -$10,000
MVA = -$10,000
5.37. a) Accounts Receivable/Average Daily Credit Sales
$564,000.00 / ($3,814,000 / 365)= 53.71 = 54 days
b) Super Dot Com was more profitable in 2006 than it was in 2004.
2004 2006_________
$519,000/$2,100,000 $1,115,000/$3,814,000
Net Profit Margin 24.71% 29.23%
$519,000/$2,859,000 $1,115,000/$5,316,000
Return on Assets 18.15% 20.97%
Both the NPM and ROA ratios were better in 2006.
c) Super Dot Com was less liquid at the end of 2006 than it was at the end of 2004.
2004 2006_________
$981,000/$245,000 $1,720,000/$623,000
Current Ratio 4.00 2.76
($981,000 - $307,000)/$245,000 ($1,720,000 - $960,000)/$623,000
Quick Ratio 2.75 1.22
35. 34
Chapter 6 Solutions
Answers to Review Questions
1. Why do businesses spend time, effort, and money to produce forecasts? Explain.
Businesses succeed or fail depending on how well prepared they are to deal with the situations they
confront in the future. Therefore they expend considerable sums making estimates (forecasts) of
what the future situation is likely to be. Businesses develop new products, set production quotas, and
select financing sources based on forecasts about the future economic environment and the firm's
condition. If economists predict interest rates will be relatively high, for example, firms may plan to
limit borrowing and defer expansion plans.
2. What is the primary assumption behind the experience approach to forecasting?
The experience approach to forecasting is based on the assumption that things will happen a certain
way in the future because they happened that way in the past. For instance, if it has always taken you
fifteen minutes to drive to the grocery store, then you will probably assume that it will take you about
fifteen minutes the next time you drive to the store. Similarly, financial managers often assume sales,
expenses, or earnings will grow at certain rates in the future because they grew at that rate in the past.
3. Describe the sales forecasting process.
Sales forecasting is a group effort. Sales and marketing personnel usually provide assessments of
demand and the competition. Production personnel usually provide estimates of manufacturing
capacity and other production constraints. Top management will make strategic decisions affecting
the firm as a whole. Financial managers coordinate, collect, and analyze the sales forecasting
information. Figure 6-1 in the text shows a diagram of the process.
4. Explain how the cash budget and the capital budget relate to pro forma financial statements.
The cash budget shows the projected flow of cash in and out of the firm for specified time periods.
The capital budget shows planned expenditures for major asset acquisitions. Forecasters incorporate
data from these budgets into pro forma financial statements under the assumption that the budget
figures will, in fact, occur.
5. Explain how management goals are incorporated into pro forma financial statements.
Management sets a target goal, and forecasters produce pro forma financial statements under the
assumption that the goal will be reached. For example, if management’s goal is to pay off all short-
term notes during the coming year, forecasters would incorporate this into the pro forma balance
sheet by setting Notes Payable to zero.
36. 35
6. Explain the significance of the term additional funds needed.
When the pro forma balance sheet is completed, total assets and total liabilities and equity will rarely
match. The discrepancy between forecasted assets and forecasted liabilities and equity results when
either too little or too much financing is projected for the amount of asset growth expected. The
discrepancy is called additional funds needed (AFN) when forecast assets exceed forecast liabilities
and equity, and excess financing when forecast liabilities and equity exceed forecast assets.
7. What do financial managers look for when they analyze pro forma financial statements?
After the pro forma financial statements are complete, financial managers analyze the forecast to
determine (1) what current trends suggest what will happen to the firm in the future, (2) what effect
management's current plans and budgets will have on the firm, and (3) what actions to take to avoid
problems revealed in the pro forma statements
8. What action(s) should be taken if analysis of pro forma financial statements reveals positive trends?
Negative trends?
When analyzing the pro forma statements, managers often see signs of emerging positive or negative
conditions. If forecasters discover positive indicators, they will recommend that current plans be
continued. If forecasters see negative indicators, they will recommend corrective action.
Answers to End-of-Chapter Problems
6-1.
Sales Record for The Miniver Corporation
Sales in 2007 is expected to be approximately $215,000 following the trend of the last six years as shown
above.
$0
$50,000
$100,000
$150,000
$200,000
$250,000
1997 1998 1999 2000 2001 2002 2003
37. 36
6-2.
This year Next Year Forecasting Assumption
Sales 100 120 Sales will grow 20%(100 X 1.2)
- Variable Costs 50 60 Constant % of sales(120 X 0.5)
- Fixed Costs 40 40 Remains same
= Net Income 10 20 (120 - 60 - 40)
Dividends 5 10 Keep 50% Payout Ratio(20 X 0.5)
Current Assets 60 72 Constant % of sales(120 X 0.6)
Fixed Assets 100 100 Remains same
Total Assets 160 172 (100 + 72)
Current Liabs. 20 24 Constant % of sales (120 X 0.2)
Long-term Debt 20 20 Remains same
Common Stock 20 20 Remains same
Retained Earns. 100 110 (100+20-10)
Tot Liabs & Eq 160 174
AFN = 172-174= -2 (Negative AFN means there are excess funds.)
6-3. Jolly Joe's Pizza, Inc.
Financial Status and Forecast
2006 Est. for 2007
Sales $10,000 20,000
COGS 4,000 8,000
Gross Profit 6,000 12,000
Fixed Expenses 3,000 3,000
Before-Tax Profit 3,000 9,000
Tax @ 33.33% 1,000 3,000
Net Profit $2,000 6,000
Dividends $0 0
Current Assets $25,000 50,000
Net Fixed Assets 15,000 15,000
Total Assets $40,000 65,000
Current Liabilities $17,000 34,000
Long-term debt 3,000 3,000
Common Stock 7,000 7,000
Retained Earnings 13,000 19,000
Total Liabs & Eq $40,000 63,000
Joe will need $2,000 in additional funds in 2007 ($65,000 - $63,000).
38. 37
6-4. Sugar Cane Alley
Financial Status and Forecast
2006 Est. for 2007
Sales $90,000 110,000
COGS 48,000 58,667
Gross Profit 42,000 51,333
Selling and
marketing expenses 13,000 15,889
General and admini-
strative expenses 5,000 5,000
Depreciation Expense 2,000 2,000
Operating Income 22,000 28,444
Interest Expense 800
EBT 27,644
Tax @ 30% 8,293
Net Profit 19,351
Dividends 10,000
Addition to RE 9,351
6-5. a ) Cash .111111 X $110,000 = $12,222
Accounts Receivable .024667 X $110,000 = $2,713
Inventory .088889 X $110,000 = $9,778
b ) Property and Equipment, gross $25,000
Accumulated Depreciation $6,000
Property and Equipment, net $19,000
Total Assets $19,000 + $12,222 + $2,713 + $9,778 = $43,713
c ) Accounts Payable .015333 X $110,000 = $1,687
d ) Total Liabilities = $8,000 + $1,687 = $9,687
e ) Total Liabilities and Equity = $9,687 + $9,351 + $5,000 + $26,840
= $50,878
f ) Total Assets = $12,222 + $2,713 + $9,778 + $19,000 = $43,713
AFN = $43,713 - $50,878 = -$7,165
There are excess funds of $7,165.
g ) 2006: Net Profit Margin = $14,840/$90,000 = 16.49%
2007: Net Profit Margin = $19,351/$110,000 = 17.6%
39. 38
6-6.
Assets 2006 2007 Liabilities 2006 2007
Cash $10,000 $12,500 Accounts Payable $10,500 $13,125
Acct Rec. 25,000 31,250 Notes Payable 10,000 12,500
Inventory 20,000 25,000 Accrued Expenses 11,000 13,750
Prepaid Exp 2,000 2,500 Long Term Debt 15,000 15,000
Total Current Common Equity 38,500 38,500
Assets 57,000 71,250 Total Liabilities
Fixed Assets 32,000 32,000 Equity 85,000 $92,875
Depreciation 4,000 4,000
Total Assets 85,000 $99,250
*Net Sales for 2007 = $150 million * 1.25 = $187.5 million
Additional funds needed = $99,250 - $92,875 = $6,375
6-7.
2006 2007
Sales 1,000 1,250
Variable Costs 500 562.50
Fixed Costs 160 160
Net Income 340 527.50
Dividends 136 290.13
6-8. Pro Forma Balance Sheets
End of Year
Assets 2006 2007 Liabilities + Equity 2006 2007
Cash $4,000 4,400 Accounts Payable $4,400 4,840
Accounts Rec 10,000 11,000 Notes Payable 4,000 4,400
Inventory 13,000 14,300 Accrued Expenses 5,000 5,500
Prepaid Exp 400 440 Tot.Current Liabilities13,400 14,740
Current Assets27,400 30,140 Bonds Payable 6,000 6,000
Fixed Assets 11,000 11,000 Common Equity 19,000 21,468
Total Assets $38,400 $41,140 Tot.Liab. + Equity $38,400 $42,208
In 2007 there would be $1,068 ($42,208-$41,140) in excess funds. This assumes, as the problem states, that
notes payable would increase by 10% along with other current liabilities. Notes payable usually does not
increase with sales.
Year Total Sales PBT NI Addition to RE
2007 $85,000 X 1.1 $93,500 X .11 $10,285 X .6 $6,171 X .40
= $93,500 = $10,285 = $6,171 = $2,468
40. 39
6-9.
Compute the following ratios for 2006 and 2007:
2006 2007
Current Ratio 3 3
Debt to Assets Ratio 25% 25.3%
Sales to Assets Ratio 62.5% 66.27%
Net Profit Margin 10% 13.64%
Return on Assets 6.25% 9.04%
Return on Equity 8.33% 12.10%
Liquidity seems strong and stable. Debt is modest and stable. Asset utilization is improving slightly while
all the profit margins calculated show marked improvement.
6-10.
BRIGHT FUTURE CORPORATION
Historical and Projected Income Statements
Historical Projected
2006 2007
Sales $10,000,000 $12,000,000
Cost of goods Sold $4,000,000 $4,800,000
Gross Profit $6,000,000 $7,200,000
Selling & Admin. Expenses $800,000 $960,000
Depreciation Expense $2,000,000 $2,000,000
Operating Income (EBIT) $3,200,000 $4,240,000
Interest Expenses $1,350,000 $1,350,000
Earnings Before Tax (EBT) $1,850,000 $2,890,000
Income Tax (40%) $740,000 $1,156,000
Net Income (NI) $1,110,000 $1,734,000
Common Stock Dividends paid $400,000 $400,000
Addition to Retained earnings $710,000 $1,334,000
Earnings per Share (1,000,000 shares) $1.11 $1.73
BRIGHT FUTURE CORPORATION
Historical and Projected Balance Sheets
Projection with AFN
Historical Projected Excess Financing
Dec 31, 2006 Dec 31, 2007 Incorporated
ASSETS
Current Assets:
Cash $9,000,000 $10,800,000 $10,800,000
Marketable Securities $8,000,000 $9,600,000 $9,600,000
Accounts Receivable (gross) $1,200,000 $1,440,000 $1,440,000
Less: Allowance for bad Debts $200,000 $240,000 $240,000
Accounts Receivable (Net) $1,000,000 $1,200,000 $1,200,000
Inventory $20,000,000 $24,000,000 $24,000,000
Prepaid Expenses $1,000,000 $1,200,000 $1,200,000
Total Current Assets $39,000,000 $46,800,000 $46,800,000
Plant and Equipment (gross) $20,000,000 $20,000,000 $20,000,000
Less: Accumulated Depreciation $9,000,000 $11,000,000 $11,000,000
Plant and equipment (net) $11,000,000 $9,000,000 $9,000,000
TOTAL ASSETS $50,000,000 $55,800,000 $55,800,000
LIABILITIES AND EQUITY
Current Liabilities:
Accounts payable $12,000,000 $14,400,000 $14,400,000
Notes Payable $5,000,000 $5,000,000 $5,000,000
41. 40
Accrued Expenses $3,000,000 $3,600,000 $3,600,000
Total Current Liabilities $20,000,000 $23,000,000 $23,000,000
L-T Debt (Bonds Payable, 5%, due 2015) $20,000,000 $20,000,000 $21,466,000
Total Liabilities $40,000,000 $43,000,000 $44,576,000
Common Stock (1,000,000 shares, $1 par) $1,000,000 $1,000,000 $1,000,000
Capital in Excess of Par $4,000,000 $4,000,000 $4,000,000
Retained Earnings $5,000,000 $6,334,000 $6,334,000
Total Equity $10,000,000 $11,224,000 $11,224,000
TOTAL LIABILITIES AND EQUITY $50,000,000 $54,224,000 $55,800,000
Question 2a. Excess Financing (Additional Funds Needed) $1,466,000
AFN is incorporated in L-T debt. If $1,466,000 of new L-T debt is issued the financing need will be met.
Other financing sources could be used but we chose new L-T debt in this illustration.
Question 2, Ratios:
2006 2007
b. Current Ratio 1.95 2.03
c. Total Asset Turnover 0.20 0.22
Inventory Turnover 0.50 0.50
d. Total Debt to Assets 0.80 0.77
e. Net Profit Margin 11.10% 14.45%
Return on Assets 2.22% 3.11%
Return on Equity 11.10% 15.30%
Question 3, Comments on liquidity, asset productivity, debt management, and profitability:
Liquidity is improving. Debt is high but stable. Inventory and overall asset utilization are stable. The net
profit margin appears healthy. The return on assets ratio is much lower than the net profit margin because of
the low asset turnover. The return on equity ratio is much higher than the return on assets because of the
high debt load.
Question 4, Recommendations:
A 20% projected increase in sales is quite impressive. Management should prepare now, however, to raise
the $1,466,000 that will be needed in 2007 to support the necessary new investments if the projected sales
increase is to be achieved.
42. 41
Chapter 7 Solutions
Answers to Review Questions
1. What is risk aversion? If common stockholders are risk averse, how do you explain the fact that they
often invest in very risky companies?
Risk aversion is the tendency to avoid additional risk. Risk-averse people will avoid risk if they can,
unless they receive additional compensation for assuming that risk. In finance, the added
compensation is a higher expected rate of return.
People are not all are equally risk averse. For example, some people are willing to buy risky stocks,
while others are not. The ones that do, however, almost always demand an appropriately high
expected rate of return for taking on the additional risk.
2. Explain the risk–return relationship.
The relationship between risk and required rate of return is known as the risk–return relationship. It
is a positive relationship because the more risk assumed, the higher the required rate of return most
people will demand.
Risk aversion explains the positive risk–return relationship. It explains why risky junk bonds carry a
higher market interest rate than essentially risk-free U.S. Treasury bonds.
3. Why is the coefficient of variation often a better risk measure when comparing different projects than
the standard deviation?
Whenever we want to compare the risk of investments that have different means, we use the
coefficient of variation (CV). The CV represents the standard deviation's percentage of the mean.
Because the CV is a ratio, it adjusts for differences in means, while the standard deviation does not.
therefore the CV provides a standardized measure of the degree of risk that can be used to compare
alternatives.
4. What is the difference between business risk and financial risk?
Business risk refers to the uncertainty a company has with regard to its operating income (also
known as earnings before interest and taxes or EBIT). Business risk is brought on by sales volatility
and intensified by the presence of fixed operating costs.
Financial risk is the additional volatility of net income caused by the presence of interest expense.
Firms that have only equity financing have no financial risk because they have no debt on which to
make fixed interest payments. Conversely, firms that operate primarily on borrowed money are
exposed to a high degree of financial risk.
43. 42
5. Why does the riskiness of portfolios have to be looked at differently than the riskiness of individual
assets?
The riskiness of portfolios has to be looked at differently than the riskiness of individual assets
because the weighted average of the standard deviations of returns of individual assets does not result
in the standard deviation of a portfolio containing the assets. There is a reduction in the fluctuations
of the returns of portfolios which is called the diversification effect.
6. What happens to the riskiness of a portfolio if assets with very low correlations (even negative
correlations) are combined?
How successfully diversification reduces risk depends on the degree of correlation between the two
variables in question. When assets with very low or negative correlations are combined in portfolios,
the riskiness of the portfolios (as measured by the coefficient of variation) is greatly reduced.
7. What does it mean when we say that the correlation coefficient for two variables is -1? What does it
mean if this value were zero? What does it mean if it were +1?
Correlation is measured by the correlation coefficient, represented by the letter r. The correlation
coefficient can take on values between +1.0 (perfect positive correlation) to -1.0 (perfect negative
correlation). The closer r is to +1.0, the more the two variables will tend to move with each other at
the same time. The closer r is to -1.0, the more the two variables will tend to move opposite each
other at the same time. An r value of zero indicates that the variables’ values aren't related at all.
This is known as statistical independence.
8. What is nondiversifiable risk? How is it measured?
Unless the returns of one-half the assets in a portfolio are perfectly negatively correlated with the
other half—which is extremely unlikely—some risk will remain after assets are combined into a
portfolio. The degree of risk that remains is nondiversifiable risk, the part of a portfolio's total risk
that can't be eliminated by diversifying.
Nondiversifiable risk is measured by a term called beta (). The ultimate group of diversified assets,
the market, has a beta of 1.0. The betas of portfolios, and individual assets, relate their returns to
those of the overall stock market. Portfolios with betas higher than 1.0 are relatively more risky than
the market. Portfolios with betas less than 1.0 are relatively less risky than the market. (Risk-free
portfolios have a beta of zero.)
9. Compare diversifiable and nondiversifiable risk. Which do you think is more important to financial
managers in business firms?
Diversifiable risk can be dealt with by, of course, diversifying. Nondiversifiable risk is generally
compensated for by raising one’s required rate of return. Both types of risk are important to financial
managers.
44. 43
10. How do risk-averse investors compensate for risk when they take on investment projects?
Because of risk aversion, people demand higher rates of return for taking on higher-risk projects.
11. Given that risk-averse investors demand more return for taking on more risk when they invest, how
much more return is appropriate for, say, a share of common stock, than is appropriate for a Treasury
bill?
Although we know that the risk–return relationship is positive, the question of much return is
appropriate for a given degree of risk is especially difficult. Unfortunately, no one knows the answer
for sure. One well-known model used to calculate the required rate of return of an investment, given
its degree of risk, is the Capital Asset Pricing Model (CAPM).
12. Discuss risk from the perspective of the Capital Asset Pricing Model (CAPM).
The Capital Asset Pricing Model, or CAPM, can be used to calculate the appropriate required rate of
return for an investment project given its degree of risk as measured by beta (). A project's beta
represents its degree of risk relative to the overall stock market. In the CAPM, when the beta term is
multiplied by the market risk premium term, the result is the additional return over the risk-free rate
that investors demand from that individual project. High-risk (high-beta) projects have high required
rates of return, and low-risk (low-beta) projects have low required rates of return.
Answers to End-of-Chapter Problems
7-1.
Cash Flow Probability
Estimate of Occurrence
CF P CF x P CF - mean (CF - mean)2
P x (CF - mean)2
$10,000 5.00% $500 ($9,000) $81,000,000 $4,050,000
$13,000 10.00% $1,300 ($6,000) $36,000,000 $3,600,000
$16,000 20.00% $3,200 ($3,000) $9,000,000 $1,800,000
$19,000 30.00% $5,700 $0 $0 $0
$22,000 20.00% $4,400 $3,000 $9,000,000 $1,800,000
$25,000 10.00% $2,500 $6,000 $36,000,000 $3,600,000
$28,000 5.00% $1,400 $9,000 $81,000,000 $4,050,000
Sum of (R x P) = mean: $19,000
Sum of P x (CF- mean)2
= variance: $18,900,000
Square root of variance = standard deviation of the variance: $4,347
Coefficient of Variation = std.dev./mean = 22.88%
45. 44
7-2.
EXPECTED VALUE, STANDARD DEVIATION AND COEFFICIENT OF VARIATION OF OPERATING INCOME
Operating
Sales Variable Fixed Income Prob.
Estimate Expenses Expenses Estimate of Occurrence
CF P CF x P CF - mean (CF - mean)2
Px(CF - mean2
$500 $250 $250 $0 2.00% $0 ($350) $122,500 $2,450
$700 $350 $250 $100 8.00% $8 ($250) $62,500 $5,000
$1,200 $600 $250 $350 80.00% $280 $0 $0 $0
$1,700 $850 $250 $600 8.00% $48 $250 $62,500 $5,000
$1,900 $950 $250 $700 2.00% $14 $350 $122,500 $2,450
a. Sum of (R x P) = mean: $350
Sum of (CF- mean)2
x P= variance $14,900
b. Square root of variance = standard deviation: $122
c. Coeff. of Variation = std.dev/mean: 34.88%
d. New expected value, standard deviation, and coefficient of variation based on revised sales forecast:
Operating
Sales Variable Fixed Income Probability
Estimate Expenses Expenses Estimate of Occurrence
CF P CF x P CF - mean (CF - mean)2
Px(CF - mean)2
$500 $250 $250 $0 10.00% $0 ($350) $122,500 $12,250
$700 $350 $250 $100 15.00% $15 ($250) $62,500 $9,375
$1,200 $600 $250 $350 50.00% $175 $0 $0 $0
$1,700 $850 $250 $600 15.00% $90 $250 $62,500 $9,375
$1,900 $950 $250 $700 10.00% $70 $350 $122,500 $12,250
a. Sum of (R x P) = mean: $350
Sum of P x (CF - mean)2
= variance: $43,250
b. Square root of variance = standard deviation: $208
c. Coeff. of Variation = std. dev./mean: 59.43%
e. Comments: Note how the increased possibilities that sales will be other than $1,200 caused the standard deviation
and coefficient of variation of operating income to nearly double.
7-3. Mean:
.10(1,000) + .2(5,000) + .45(10,000) + .15(15,000) + .10(20,000) =
100 + 1,000 + 4,500 + 2,250 + 2,000
Mean = $9,850
Standard Deviation:
ơ 2
= .1(1,000 – 9,850)2
+ .2(5,000 – 9,850)2
+ .45(10,000 – 9,850)2
+ .15(15,000 – 9,850)2
+
.1(20,000 – 9,850)2
ơ 2
= 7,832,250 + 4,704,500 + 10,125 + 3,978,375 + 10,302,250
ơ 2
= 26,827,500
ơ = √ 26,827,500
ơ = 5,179.53
Standard deviation = 5,179.53
46. 45
7-4.
I. EQUITY EDDIE'S COMPANY:
Operating
Income Interest Before-Tax Net Probability
Estimate Expense Income Taxes Income of Occurrence
CF P CF x P CF - mean (CF - mean)2 Px(CF -
mean)2
$100 $0 $100 $28 $72 5.00% $4 ($216) $46,656 $2,333
$200 $0 $200 $56 $144 10.00% $14 ($144) $20,736 $2,074
$400 $0 $400 $112 $288 70.00% $202 $0 $0 $0
$600 $0 $600 $168 $432 10.00% $43 $144 $20,736 $2,074
$700 $0 $700 $196 $504 5.00% $25 $216 $46,656 $2,333
a. Sum of (R x P) = mean: $288
Sum of P x (CF - mean)2
= variance: $8,813
b. Square root of variance = standard deviation: $94
c. Coeff. of Variation = std. dev./mean: 32.60%
II. BARRY BORROWER'S COMPANY:
Operating
Income Interest Before-Tax Net Probability
Estimate Expense Income Taxes Income of Occurrence
CF P CF x P CF - mean (CF - mean)2 Px(CF -
mean)2
$110 $40 $70 $19.6 $50.4 5.00% $2.52 ($237.60) $56,453.76 $2,822.69
$220 $40 $180 $50.4 $129.6 10.00% $12.96 ($158.40) $25,090.56 $2,509.06
$440 $40 $400 $112.0 $288.0 70.00% $201.60 $0.00 $0.00 $0.00
$660 $40 $620 $173.6 $446.4 10.00% $44.64 $158.40 $25,090.56 $2,509.06
$770 $40 $730 $204.4 $525.6 5.00% $26.28 $237.60 $56,453.76 $2,822.69
a. Sum of (R x P) = mean: $288.00
Sum of P x (CF - mean)2
= variance: $10,663.49
b. Square root of variance = standard deviation= $103.26
c. Coeff. of Variation = std. dev./ mean: 35.86%
e. Comments: Note how Barry Borrower's use of debt financing causes his company to have a higher
standard deviation and coefficient of variation of net income than Equity Eddie's.
7-5.
STANDARD DEVIATION AND COEFFICIENT OF VARIATION OF CASH FLOWS FOR THE GO-RILLA PROJECT
Cash Flow Probability
Estimate of Occurrence
CF P CF x P CF - mean (CF - mean)2
P x (CF - mean)2
$20,000 1.00% $200 ($6,000) $36,000,000 $360,000
$22,000 12.00% $2,640 ($4,000) $16,000,000 $1,920,000
$24,000 23.00% $5,520 ($2,000) $4,000,000 $920,000
$26,000 28.00% $7,280 $0 $0 $0
$28,000 23.00% $6,440 $2,000 $4,000,000 $920,000
47. 46
$30,000 12.00% $3,600 $4,000 $16,000,000 $1,920,000
$32,000 1.00% $320 $6,000 $36,000,000 $360,000
Sum of (R x P) = mean: $26,000
Sum of P x (CF - mean)2
= variance: $6,400,000
a. Square root of variance = standard deviation: $2,530
b. Coefficient of Variation = std. dev./mean: 9.73%
c. Comment: Given that the average coefficient of variation of George's other product lines is 12%, we would
say that the Go-Rilla project is LESS risky than average
7-6.
Effect of Adding Asset B to Existing Portfolio A
Correlation coefficient r between existing portfolio A and new asset B: 0
Amount invested in Portfolio A: $700,000
Amount invested in Asset B: $200,000
Total value of combined portfolio: $900,000
Weight of existing assets in combined portfolio: 77.8%
Weight of new asset B in combined portfolio: 22.2%
Expected Return of existing portfolio A: 9.00%
Standard deviation of existing portfolio A: 3.00%
Coefficient of variation of existing portfolio A: 33.33%
Expected Return of new asset B: 12.00%
Standard deviation of new asset B: 4.00%
Coefficient of variation of new asset B: 33.33%
Expected Return of combined portfolio per equation 7-1: 9.67%
Standard deviation of combined portfolio per equation 7-5: 2.50%
Coefficient of Variation of combined portfolio: 25.83%
a. Comparison of standard deviations of existing portfolio A and the new combined portfolio:
Standard deviation of existing portfolio A: 3.00%
Standard deviation of combined portfolio: 2.50%
a. Comparison of coefficients of variation of existing portfolio A and the new combined portfolio:
Coefficient of variation of existing portfolio A: 33.33%
Coefficient of variation of combined portfolio: 25.83%
48. 47
7-7. Coefficient of variation (CV) = Standard Deviation/Mean
288/1,200 = .24
CVzazzle = 24%
7-8. Total Portfolio = $10,000
Weights: Stock A: 4,000/10,000 = .4
Stock B: 6,000/10,000 = .6
.4(13) + .6(9) = 10.6%
Expected Rate of Return = 10.6%
7-9. ơp = √ (0.3)2
* (0.05)2
+ (0.7)2
* (0.02)2
+ ( 2 * 0.3 * 0.7 * 0.6 * 0.05 * 0.02)
ơp = √0.000673
ơp = 0.0259
ơp = 2.59%
7-10.
Effect of Adding PROJ1 to Existing Portfolio
Expected Return of existing portfolio: 11.00%
Standard deviation of existing portfolio: 4.00%
a. Coefficient of variation of existing portfolio: 36.36%
Expected Return of new PROJ1: 13.00%
Standard deviation of new PROJ1: 5.00%
b. Coefficient of variation of new PROJ1: 38.46%
Amount invested in existing portfolio: $820,000
Amount invested in PROJ1: $194,000
Total value of combined portfolio: $1,014,000
c. Weight of existing assets in combined portfolio: 80.9%
d. Weight of new PROJ1 in combined portfolio: 19.1%
Correlation coefficient r between existing portfolio and new PROJ1: 0
e. Standard deviation of combined portfolio: 3.37%
(lower than existing portfolio)
: Expected Return of combined portfolio per equation 7-1 11.38%
f.: Coefficient of Variation of combined portfolio 29.63%
(lower than existing portfolio)
g. Firm's risk decreases with the addition of PROJ1 to the portfolio
49. 48
7-11.
Required Rate of Return per the CAPM
Risk free rate (kRF) 5.0%
Expected rate of return on the market (km) 15.0%
Beta 1.2
Required rate of return on stock per the CAPM: 17.0%
(equation 7-6)
7-12. kl = 4.5 + .5(12.5) = 10.75%
ka = 4.5 + 1.0(12.5) = 17%
kh = 4.5 + 1.6(12.5) = 24.5%
7-13.
Effect on CAPM Required Rate of Return of Adding a New Project
Risk free rate (kRF) 5.0%
Expected rate of return on the market (km) 15.0%
Existing firm's Beta 1.5
New Project's Beta 0.8
a. Required rate of return on company per the CAPM: 20.0%
b. Required rate of return on new project per the CAPM: 13.0%
Weight of new project in firm's portfolio: 20.0%
Weight of firm's other assets: 80.0%
c. Beta of firm with new project 1.36
7-14.
STANDARD DEVIATION AND COEFFICIENT OF VARIATION OF PSC SALES REVENUE
Sales Probability
Estimate of Occurrence
CF P CF x P CF - mean (CF - mean)2
P x (CF - mean)2
$800 2.00% $16 ($1,200) $1,440,000 $28,800
$1,000 8.00% $80 ($1,000) $1,000,000 $80,000
$1,400 20.00% $280 ($600) $360,000 $72,000
$2,000 40.00% $800 $0 $0 $0
$2,600 20.00% $520 $600 $360,000 $72,000
$3,000 8.00% $240 $1,000 $1,000,000 $80,000
$3,200 2.00% $64 $1,200 $1,440,000 $28,800
Sum of (R x P) = exp val: $2,000
50. 49
Sum of P x (CF - mean)2
= variance: $361,600
Square root of variance = standard deviation: $601
Coefficient of Variation = std. dev./mean: 30.07%
7-15.
COEFFICIENT OF VARIATION OF PSC'S OPERATING INCOME
Operating
Sales Variable Fixed Income Probability
Estimate Expenses Expenses Estimate of Occurrence
CF P CF x P CF - mean (CF - mean)2
Px(CF - mean)2
$800 $480 $0 $320 2.00% $6 ($480) $230,400 $4,608
$1,000 $600 $0 $400 8.00% $32 ($400) $160,000 $12,800
$1,400 $840 $0 $560 20.00% $112 ($240) $57,600 $11,520
$2,000 $1,200 $0 $800 40.00% $320 $0 $0 $0
$2,600 $1,560 $0 $1,040 20.00% $208 $240 $57,600 $11,520
$3,000 $1,800 $0 $1,200 8.00% $96 $400 $160,000 $12,800
$3,200 $1,920 $0 $1,280 2.00% $26 $480 $230,400 $4,608
Sum of (R x P) = mean: $800
Sum of P x (CF - mean)2
= variance: $57,856
Square root of variance = standard deviation: $241
Coefficient of Variation = std. dev./mean: 30.07%
7-16.
COEFFICIENT OF VARIATION OF PSC'S OPERATING INCOME
Operating
Sales Variable Fixed Income Probability
Estimate Expenses Expenses Estimate of Occurrence
CF P CF x P CF - mean (CF - mean)2
Px(CF - mean)2
$800 $480 $400 ($80) 2.00% ($2) ($480) $230,400 $4,608
$1,000 $600 $400 $0 8.00% $0 ($400) $160,000 $12,800
$1,400 $840 $400 $160 20.00% $32 ($240) $57,600 $11,520
$2,000 $1,200 $400 $400 40.00% $160 $0 $0 $0
$2,600 $1,560 $400 $640 20.00% $128 $240 $57,600 $11,520
$3,000 $1,800 $400 $800 8.00% $64 $400 $160,000 $12,800
$3,200 $1,920 $400 $880 2.00% $18 $480 $230,400 $4,608
Sum of (R x P) = mean: $400
51. 50
Sum of P x (CF - mean)2
= variance: $57,856
Square root of variance = standard deviation: $241
Coefficient of Variation = std. dev./mean: 60.13%
Comment:
Note how the addition of fixed costs caused the coefficient of variation of PSC's operating income to
double from what it was in problem 7-10
7-17.
MEASURING PSC'S FINANCIAL RISK
I. Expected value, standard deviation, and coefficient of variation of PSC's net income when no interest expense is
present
Sales Variable Fixed Operating Interest Before-
Tax
Probability of
Estimate Expenses Expenses Income Expense Income Taxes Net
Income
Occurrence
NI P NI X P NI - mean (NI -
mean)2
P X (NI -
mean)2
$800 $480 $400 -$80 $0 -$80 -$56 -$24 2% $0 -$144 $20,736 $415
$1,000 $600 $400 $0 $0 $0 $0 $0 8% $0 -$120 $14,400 $1,152
$1,400 $840 $400 $160 $0 $160 $112 $48 20% $10 -$72 $5,184 $1,037
$2,000 $1,200 $400 $400 $0 $400 $280 $120 40% $48 $0 $0 $0
$2,600 $1,560 $400 $640 $0 $640 $448 $192 20% $38 $72 $5,184 $1,037
$3,000 $1,800 $400 $800 $0 $800 $560 $240 8% $19 $120 $14,400 $1,152
$3,200 $1,920 $400 $880 $0 $880 $616 $264 2% $5 $144 $20,736 $415
Sum of (NI X P) = mean $ 120
Sum of P X (CF - mean)2
= variance: $5,207
Square root of variance = standard deviation: $72
Coefficient of Variation = std. dev./mean: 60.1%
II. Expected value, standard deviation, and coefficient of variation of PSC's net income when interest expense is
present
Sales Variable Fixed Operating Interest Before-
Tax
Probability of
Estimate Expenses Expenses Income Expense Income Taxes Net
Income
Occurrence
NI P NI X P NI - mean (NI -
mean)2
P X (NI -
mean)2
$800 $480 $400 ($80) $60 ($140) ($42) ($98) 2% ($2) ($336) $112,896 $2,258
$1,000 $600 $400 $0 $60 ($60) ($18) ($42) 8% ($3) ($280) $78,400 $6,272
$1,400 $840 $400 $160 $60 $100 $30 $70 20% $14 ($168) $28,224 $5,645
$2,000 $1,200 $400 $400 $60 $340 $102 $238 40% $95 $0 $0 $0
$2,600 $1,560 $400 $640 $60 $580 $174 $406 20% $81 $168 $28,224 $5,645
$3,000 $1,800 $400 $800 $60 $740 $222 $518 8% $41 $280 $78,400 $6,272
$3,200 $1,920 $400 $880 $60 $820 $246 $574 2% $11 $336 $112,896 $2,258
Sum of (R X P) = mean = $ 238
Sum of P X (CF - mean)2
= variance = $28,349
Square root of variance = standard deviation = $168
Coefficient of variation equals std. dev./mean = 70.7%
52. 51
7-18.
I. New coefficient of variation of PSC's operating income:
Operating
Sales Variable Fixed Income Probability of
Estimate Expenses Expenses Estimate Occurrence
EBIT P EBIT X
P
EBIT -
mean
(EBIT -
mean)2
P X (EBIT - mean)2
$800 $480 $250 $70 1% $0.70 ($480) $230,400 $2,304
$1,000 $600 $250 $150 6% $9.00 ($400) $160,000 $9,600
$1,400 $840 $250 $310 13% $40.30 ($240) $57,600 $7,488
$2,000 $1,200 $250 $550 60% $330.00 $0 $0 $0
$2,600 $1,560 $250 $790 13% $102.70 $240 $57,600 $7,488
$3,000 $1,800 $250 $950 6% $57.00 $400 $160,000 $9,600
$3,200 $1,920 $250 $1,030 1% $10.30 $480 $230,400 $2,304
Sum of (EBIT X P) = mean = $550.00
Sum of P X (CF - mean)2
= variance = $38,784
Square root of variance = standard deviation = $197
Coefficient of Variation = std. dev./mean = 35.8%
II. New coefficient of variation of PSC's net income when no interest expense is present
Sales Variable Fixed Operating Interest Before-
Tax
Net Probability of
Estimate Expenses Expenses Income Expense Income Taxes Income Occurrence
NI P NI X
P
(NI -
mean)2
P X (NI
-
mean)2
$800 $480 $250 $70 $0 $70 $21 $49 1% $0 $112,896 $1,129
$1,000 $600 $250 $150 $0 $150 $45 $105 6% $6 $78,400 $4,704
$1,400 $840 $250 $310 $0 $310 $93 $217 13% $28 $28,224 $3,669
$2,000 $1,200 $250 $550 $0 $550 $165 $385 60% $231 $0 $0
$2,600 $1,560 $250 $790 $0 $790 $237 $553 13% $72 $28,224 $3,669
$3,000 $1,800 $250 $950 $0 $950 $285 $665 6% $40 $78,400 $4,704
$3,200 $1,920 $250 $1,030 $0 $1,030 $309 $721 1% $7 $112,896 $1,129
Sum of (NI X P) = mean = $385
Sum of P X (CF - mean)2
= variance = $19,004
Square root of variance = standard deviation = $138
Coefficient of Variation = std. dev./mean = 35.8%
III. New coefficient of variation of PSC's net income when interest expense is present
Sales Variable Fixed Operating Interest B-T Net Probability of
Estimate Expenses Expenses Income Expense Income Taxes Income Occurrence
NI P NI X
P
(NI -
mean)2
P X (NI
-
mean)2
$800 $480 $250 $70 $40 $30 $9 $21 1% $0 $112,896 $1,129
$1,000 $600 $250 $150 $40 $110 $33 $77 6% $5 $78,400 $4,704
$1,400 $840 $250 $310 $40 $270 $81 $189 13% $25 $28,224 $3,669
$2,000 $1,200 $250 $550 $40 $510 $153 $357 60% $214 $0 $0
$2,600 $1,560 $250 $790 $40 $750 $225 $525 13% $68 $28,224 $3,669
$3,000 $1,800 $250 $950 $40 $910 $273 $637 6% $38 $78,400 $4,704
$3,200 $1,920 $250 $1,030 $40 $990 $297 $693 1% $7 $112,896 $1,129
Sum of (NI X P) = mean = $357
53. 52
Sum of P X (CF - mean)2
= variance = $19,004
Square root of variance = standard deviation = $138
Coefficient of Variation = std. dev./mean = 38.62%
Summary:
Old Coefficient of variation of operating income (business risk) 60.13%
New coefficient of variation of operating income (business risk) 35.81%
Old difference between the coefficient of variation of net income with and without interest expense
(financial risk)
-10.6%
New difference between the coefficient of variation of net income with and without interest expense
(financial risk)
-2.8%
Comments: The effect of PSC's risk reduction measures was to lower business risk substantially, but
financial risk increased slightly. Managers must evaluate this trade-off and proceed accordingly.
54. 53
Chapter 8 Solutions
Answers to Review Questions
1. What is the time value of money?
The time value of money means that money you hold in your hand today is worth more than money
you expect to receive in the future. Similarly, money you must pay out today is a greater burden than
the same amount paid in the future.
2. Why does money have time value?
Positive interest rates indicate that money has time value. When one person lets another borrow
money, the first person requires compensation in exchange for reducing current consumption. The
person who borrows the money is willing to pay to increase current consumption. The required rate
of return on an investment reflects the pure time value of money, an adjustment for expected
inflation, and any risk premiums present.
3. What is compound interest? Compare compound interest to discounting.
Compound interest occurs when interest is earned on interest and on the original principal of an
investment. Discounting is the inverse of compounding. Compound interest causes the value of a
beginning amount to increase at an increasing rate. Discounting causes the present value of a future
amount to decrease at an increasing rate.
4. How is present value affected by a change in the discount rate?
Present value is inversely related to the discount rate. In other words, present value moves in the
opposite direction of the discount rate. If the discount rate increases, present value decreases. If the
discount rate decreases, present value increases.
5. What is an annuity?
An annuity is a series of equal cash flows, spaced evenly over time.
6. Suppose you are planning to make regular contributions in equal payments to an investment fund for
your retirement. Which formula would you use to figure out how much your investments will be
worth at retirement time, given an assumed rate of return on your investments?
To figure out how much your investments will be worth at retirement time, given an assumed rate of
return on your investments, you would use the future value of an annuity formula:
55. 54
Future Value of an Annuity Formula
k
k
PMTFVA
n
1)1(
where: FVA = Future Value of an Annuity
PMT = Amount of each annuity payment
k = Interest rate per time period
n = Number of annuity payments
7. How does continuous compounding benefit an investor?
The effect of increasing the number of compounding periods per year is to increase the future value
of the investment. The more frequently interest is compounded, the greater the future value. The
smallest compounding period is used when we do continuous compounding--compounding that
occurs every tiny unit of time (the smallest unit of time imaginable).
8. If you are doing PVA and FVA problems, what difference does it make if the annuities are "ordinary
annuities" or "annuities due"?
In FVA or a PVA of annuity due problems, annuity payments earning interest one period sooner than
in ordinary annuity problems. So, higher FVA and PVA values result with an annuity due. The first
payment occurs sooner in the case of a future value of an annuity due. In present value of annuity due
problems, each annuity payment occurs one period sooner, so the payments are discounted less
severely.
9. Which formula would you use to solve for the payment required for a car loan if you know the
interest rate, length of the loan, and the borrowed amount? Explain.
To solve for k when the known values are PVA, n, and PMT, start with the present value of an
annuity formula, Equation 8-3b, as follows:
Present Value of an Annuity Formula, Table Method
PVA = PMT(PVIFA k, n)
Next, rearrange terms and solve for (PVIFA k, n) as follows
PVA / PMT = (PVIFA k, n)
Now refer to the PVIFA values in the text, Table IV. You know n, so find the n row corresponding
to the number of periods in your problem on the left hand side of the table. You have also determined
the PVIFA, so move across the n row until you find (or come close to) the value of PVIFA that you
have solved for. The percent column in which the value is located is the interest rate.
56. 55
Answers to End-of-Chapter Problems
8-1. $1,000 X (1 + 0.07)5
= $1,402.55
8-2. a) 0% $50,000 X (1 + 0.00)10
= $50,000.00
b) 5% $50,000 X (1 + 0.05)10
= $81,444.73
c) 10% $50,000 X (1 + 0.10)10
= $129,687.12
d) 20% $50,000 X (1 + 0.20)10
= $309,586.82
8-3. $5,000 * (1 + 0.08)10
= $10,794.62
8-4. a) 3% $100,000 * (1 + 0.03)15
= $155,796.74
b) 6% $100,000 * (1 + 0.06)15
= $239,655.82
c) 9% $100,000 * (1 + 0.09)15
= $364,248.25
d) 12% $100,000 * (1 + 0.12)15
= $547,356.58
8-5 a) 50,000 $50,000 * (1 + 0.10)25
= $541,735.30
b) 75,000 $75,000 * (1 + 0.10)25
= $812,602.95
c) 100,000 $100,000 * (1 + 0.10)25
= $1,083,470.59
d) 125,000 $125,000 * (1 + 0.10)25
= $1,354,338.24
8-6 a) 5 years $60,000 * (1 + 0.12)5
= $105,740.50
b) 10 years $60,000 * (1 + 0.12)10
= $186,350.89
c) 15 years $60,000 * (1 + 0.12)15
= $328,413.95
d) 20 years $60,000 * (1 + 0.12)20
= $578,777.59
8-7. PV = $20,000 X [1/(1 + .12)10
] = $6,439.46
8-8. a) 0% $60,000 X [1/(1+0.00)20
] = $60,000.00
b) 5% $60,000 X [1/(1+0.05)20
] = $22,613.37
c) 10% $60,000 X [1/(1+0.10)20
] = $8,918.62
d) 20% $60,000 X [1/(1+0.20)20
] = $1,565.04
8-9 $9,000 * [1/(1+0.08)4
] = $6,615.27
8-10 a) 3% $25,000 * [1/(1 + 0.03)10
] = $18,602.35
b) 6% $25,000 * [1/(1 + 0.06)10
] = $13,959.87
c) 9% $25,000 * [1/(1 + 0.09)10
] = $10,560.27
d) 12% $25,000 * [1/(1 + 0.12)10
] = $8,049.33
57. 56
8-11. a)$50,000 $50,000 * [1/(1 + 0.06)15
= $20,863.25
b)$75,000 $75,000 * [1/(1 + 0.06)15
= $31,294.88
c)$100,000 $100,000 * [1/(1 + 0.06)15
= $41,726.51
d)$125,000 $125,000 * [1/(1 + 0.06)15
= $52,158.13
8-12. a) 5 years $80,000 * [1/(1 + 0.09)5
] = $51,994.51
b) 10 years $80,000 * [1/(1 + 0.09)10
] = $33,792.86
c) 15 years $80,000 * [1/(1 + 0.09)15
] = $21,963.04
d) 20 years $80,000 * [1/(1 + 0.09)20
] = $14,274.47
8-13. PVA = $500 X [(1-1/1.0610
)/0.06] = $3,680.04
8-14. a) 0% $10,000 X 30 = $300,000
b) 10% $10,000 X [(1-1/1.1030
)/0.10] = $94,269.14
c) 20% $10,000 X [(1-1/1.2030
)/0.20] = $49,789.36
d) 50% $10,000 X [(1-1/1.5030
)/0.50] = $19,999.90
8-15. $20,000 * [(1-1/1.0710
)/0.07] = $140,471.63
8-16. a) 9 % $10,000 * [(1-1/1.095
)/0.09] = $38,896.51
b) 13% $10,000 * [(1-1/1.135
)/0.13] = $35,173.31
c) 15%$10,000 * [(1-1/1.155
)/0.15] = $33,521.55
d) 21% $10,000 * [(1-1/1.215
)/0.21] = $29,259.84
8-17. FVA = $500 X [(1.095
-1)/.09] = $2,992.36
8-18. a) 0% $6,000 X 12 = $72,000.00
b) 2% $6,000 X [(1.0212
-1)/0.02] = $80,472.54
c) 10% $6,000 X [(1.1012
-1)/0.10] = $128,305.70
d) 20% $6,000 X [(1.2012
-1)/0.20] = $237,483.01
8-19. $5,000 * [(1.0610
– 1)/0.06] = $65,903.97
8-20. $5,000 * [(1.118
– 1)/0.11] = $59,297.17
8-21. a) $1,000 $1,000 * [(1.105
– 1)/0.10] = $6,105.10
b) $10,000 $10,000 * [(1.105
– 1)/0.10] = $61,051.00
c) $75,000 $75,000 * [(1.105
– 1)/0.10] = $457,882.50
d) $125,000 $125,000 * [(1.105
– 1)/0.10] = $763,137.50
59. 58
5.6502 = PVIFA k,10
k = 12%
8-36 PVA = PMT X PVIFA k,n
$200,000 = $1,330.61 X PVIFA k,360
150.3070 = PVIFA k,360
k = .5833% per month X 12 = 7% annual rate
8-37. a ) 5 years? 10,000/(1+.07)5
= 7130
b ) 10 years? 10,000/(1+.07)10
= 5083
c ) 20 years? 10,000/(1+.07)20
= 2584
8-38. PV = $16,850.58 X [1/(1+.11)5
]
PV = $10,000
8-39. a ) FV = $20,000 X (1 + .05)7
= $28,142.01
b ) FV = $20,000 X (1 + .07)10
= $39,343.03
8-40. $55.00 = $67.73 X [PVIFk%, 12 years ]
.8120 = PVIFk%, 12 years; k = 1.75%
8-41. 1,000 = 2653.3 X [PVIF5%, ?];
.3769 = PVIF5%,?; ? = 20 semi-annual periods, so it will take 10 years.
8-42. PV = 20,000 X [(1-1/1.0615
)/0.06] = $194,244.98
8-43. $4,000 * [(1.0920
–1)/0.09] * 1.09 = $223,058.12
8-44. $100 * [(1.0220
–1)/0.02] = $2,429.74
8-45. $2,000 X [((1+.08)10
- 1)/.08] = $2,000 X 14.4866 = $28,973
8-46. a ) $300 X [((1+.02)120
- 1)/.02] = $146,477
b ) $146,477 = $6,000 X [PVIFA2%, n quarters ]
PVIFA2%, n quarters = 24.4128; n = 34 quarters or 8.5 years
60. 59
8-47. $30,000 = PMT X [(1-1/(1+0.1)7
)/0.1];
$30,000 = PMT X 4.86841882; PMT = $6,162.16
8-48. $10,000/.12 = $83,333.33
8-49. FV = $500 X e.05 x 23
= $1,579.10
8-50. FVIF k=8%, n=? = 2
n = 9 years
8-51. PVA = PMT X PVIFA k,n
$4,000 = $200 X PVIFA k=.195/12, n=?
20 = PVIFA k=.01625, n=?
n = 24.39 months
8-52. $14,568.50 = $5,000 X [PVIFAk%,4 years], assuming payments start one year from the date of
borrowing
[PVIFAk%,4 years] = 2.9137; k = 14%
8-53. a) FVA = $1,000 X [[(1+.02)60
- 1]/.02] = $114,051.54
b) $114,051.54 = $6,000 X PVIFA.02, n quarters
PVIFA.02, n quarters = 19.00859; n = 24 quarters = 6 years
8-54. Option 1) PV = $5,650
Option 2) PV = $6,750 X [1/1.028
] = $5,761.06
Option 3) PV = $800 X [(1-(1/(1+.02)8
)/.02] = $5,860.39
Option 4) PV = $1,000 + $5,250 X (1/(1+.02)8
) = $5,480.82
Option 4) is the one with lowest cost to Jack.
8-55. n = 30 X 12 = 360
k = .09/12 =0 .0075 or 0.75%
$120,000 = PMT X [(1-1/1.0075360
)/0.0075]
PMT = $120,000/124.28186568 = $965.55
8-56. PVA = PMT [(1-1/1.005 180
)/.005]
$250,000 = PMT X 118.5035147
PMT = $2,109.64
8-57. a) n = 4 X 12 = 48
k = .06/12 =0 .005 or 0.5%
61. 60
$18,000 = PMT X [(1-1/1.00548
)/0.005]
PMT = $18,000/42.58031778 = $422.73
b) n = 6 X 12 = 72
k = .06/12 =0 .005 or 0.5%
$18,000 = PMT X [(1-1/1.00572
)/0.005]
PMT = $18,000/60.33951394 = $298.31
8-58, Missing Cash Flow Problem
I. Given Information:
Discount Rate 10%
Known Cash Flows
Time 0
Time 1 $100
Time 2 $150
Time 3
Time 4 $100
Total Present Value of all Cash Flows, including the missing cash flow $320.74
II. Solution: The value of the missing cash flow at Time 3:
Known Cash Flows Present Value of Known Cash Flows
Time 0
Time 1 $100 $90.9091
Time 2 $150 $123.9669
Time 3
Time 4 $100 $68.3013
Total Present Value of all Cash Flows, including the missing cash flow $320.74 (given)
Total present value of known cash flows only $283.1774
Difference (Present Value of missing cash flow) $37.5657
Future Value of Missing Cash Flow at Time 3 $50
8-59. a) n = 5*12 = 60
k = .08/12 = .0066666
$22,000 = PMT * [1-1/1.00666666760
)/0.006666667]
PMT = $22,000/118.5035147 = $446.0806 = $446.08
