Chapter 23
Derivatives and Risk Management
ANSWERS TO BEGINNING-OF-CHAPTER QUESTIONS
23-1
“Managing Risks” means taking steps to mitigate the effects of adverse
events.
Buying fire insurance is an attempt to mitigate the adverse
consequences of a fire.
Risk managers attempt to identify all the
risks a firm faces, and then consider what steps might be taken to
mitigate them. Buying insurance is one form of mitigation for certain
risks.
The most prevalent risk most firms face is that customers will not
want to buy enough of their products at a price that will permit the
firm to earn a profit.
Only good general management, not by risk
management as we define it, can generally mitigate that particular
risk. However, risk managers can often use hedging techniques to guard
against adverse price, interest rate, and exchange rate changes.
In general, stockholders dislike risk, so if a firm can stabilize
its earnings by using hedging techniques and the like without unduly
high costs, this will benefit its stock price. Of course, stockholders
can themselves diversify.
For example, an increase in the price of
copper might hurt a firm that uses copper, but copper producers will
benefit, so the effect on a diversified investor’s portfolio should be
small.
Even so, investors prefer predictability in earnings, so even
if they can diversify themselves, they probably prefer to have firms
diversify, provided the cost is not too high.
Another reason for managing risk has to do with capital investment
programs. If a firm’s earnings are unstable, it might not be able to
obtain financing to meet its capital expenditure program requirements.
This can be disruptive and costly, for a start-stop long-term
construction program is less efficient than one that proceeds smoothly.
23-2
Swaps are transactions where two parties swap payment streams.
For
example, one firm might have to make floating rate payments and another
firm have to make fixed rate payments. The firms can use a swap under
which each agrees to make the other’s payments. Similarly, firms with
debt denominated in different currencies can arrange swaps.
For
example, a U.S. firm may have borrowed in the U.S. to finance its
Italian operations, which will provide Euros, which would then have to
be converted to dollars to make payments on the debt.
If the dollar
rises against the Euro, the Euros the firm earns may not buy enough
dollars to make the required payments. So, the U.S. firm might want to
swap its dollar payment obligation for Euro payments. An Italian firm
(or any other Euro bloc firm) that has to make Euro payments derived
from U.S. operations would be a logical counter-party to the swap.
More likely, though, an international bank would serve as counter-party
to both firms, and if it had both ends of the ultimate transaction, it
would be hedged itself.
Companies whose earnings rise with interest rate (like many banks)
might prefer floating rate to fixed rate debt, while other companies
would want to lock in fixed payment obligations.
If two such firms
Answers and Solutions: 23 - 1
both had the “wrong” kind of debt, they could arrange a swap. Again, a
bank would probably be the counter-party, and again, it would be
internally hedged.
23-3
See the Excel model for an answer to Question 3.
Here we show that
both companies get the payment pattern they prefer, and at a lower cost
than if they borrowed directly with the desired pattern.
23-4
Futures contracts are deals where one party agrees to buy, and the
other agrees to sell, something a specified future date. For example,
a T-bond futures contract is a contract to buy (or to sell) $100,000 of
a hypothetical 20 year, 6%, Treasury bond at some specified future
date.
As market interest rates in the economy change, so will the
value of the T-bond contract. Interest rate futures are used to hedge
against changes adverse changes in interest rates.
For example, if a
firm plans to issue new bonds to refund a currently outstanding highrate issue, and if it is that afraid interest rates will rise before it
can bring out the new issue, then it can hedge by shorting Treasury
bond futures. Then, if market rates do rise, it will earn a profit on
its short positions and thus offset the higher interest rate it will
have to pay on its refunding bonds.
23-5
See the BOC Excel model for the answer to Question 5. Here we show the
number of T-bond futures contracts that would be used in the hedge (500
contract, with a nominal value of $50 million), the cost of setting up
the hedge, and the results under different assumptions interest rate
changes over the next 6 months.
Answers and Solutions: 23 - 2
ANSWERS TO END-OF-CHAPTER QUESTIONS
23-1
a. A derivative is an indirect claim security which derives its value,
in whole or in part, by the market price (or interest rate) of some
other security (or market).
Derivatives include options, interest
rate futures, exchange rate futures, commodity futures, and swaps.
b. Corporate risk management relates to the management of unpredictable
events that have adverse consequences for the firm.
This effort
involves reducing the consequences of risk to the point where there
would be no significant adverse impact on the firm’s financial
position.
c. Financial futures provide for the purchase or sale of a financial
asset at some time in the future, but at a price established today.
Financial futures exist for Treasury bills, Treasury notes and
bonds, CDs, Eurodollar deposits, foreign currencies, and stock
indexes. While physical delivery of the underlying asset is
virtually never taken, under forward contracts goods are actually
delivered.
e. A hedge is a transaction which lowers a firm’s risk of damage due to
fluctuating stock prices, interest rates, and exchange rates.
A
natural hedge is a transaction between two counterparties where both
parties’ risks are reduced. The two basic types of hedges are long
hedges, in which futures contracts are bought in anticipation of (or
to guard against) price increases, and short hedges, in which
futures contracts are sold to guard against price declines.
A
perfect hedge occurs when the gain or loss on the hedged transaction
exactly offsets the loss or gain on the unhedged position.
f. A swap is an exchange of cash payment obligations, which usually
occurs because the parties involved prefer someone else’s payment
pattern or type.
A structured note is a debt obligation derived
from another debt obligation, and permits a partitioning of risks to
give investors what they want.
g. Commodity futures are futures contracts which involve the sale or
purchase
of
various
commodities,
including
grains,
oilseeds,
livestock, meats, fiber, metals, and wood.
Answers and Solutions: 23 - 3
23-2
If the elimination of volatile cash flows through risk management
techniques does not significantly change a firm’s expected future cash
flows and WACC, investors will be indifferent to holding a company with
volatile cash flows versus a company with stable cash flows. Note that
investors can reduce volatility themselves:
(1) through portfolio
diver-sification, or (2) through their own use of derivatives.
23-3
Six reasons why risk management might increase the value of a firm is
that it allows corporations to (1) increase their use of debt; (2)
maintain their capital budget over time; (3) avoid costs associated
with financial distress; (4) utilize their comparative advantages in
hedging relative to the hedging ability of individual investors; (5)
reduce both the risks and costs of borrowing by using swaps; and (6)
reduce the higher taxes that result from fluctuating earnings.
23-4
There are several ways to reduce a firm's risk exposure. First, a firm
can transfer its risk to an insurance company, which requires periodic
premium payments established by the insurance company based on its
perception of the firm's risk exposure. Second, the firm can transfer
risk-producing functions to a third party.
For example, contracting
with a trucking company can in effect, pass the firm's risks from
transportation to the trucking company.
Third, the firm can purchase
derivatives contracts to reduce input and financial risks. Fourth, the
firm can take specific actions to reduce the probability of occurrence
of adverse events.
This includes replacing old electrical wiring or
using fire resistant materials in areas with the greatest fire
potential. Fifth, the firm can take actions to reduce the magnitude of
the loss associated with adverse events, such as installing an
automatic sprinkler system to suppress potential fires.
Finally, the
firm can totally avoid the activity that gives rise to the risk.
23-5
The futures market can be used to guard against interest rate and input
price risk through the use of hedging. If the firm were concerned that
interest rates will rise, it would use a short hedge, or sell financial
futures contracts. If interest rates do rise, losses on the issue due
to the higher interest rates would be offset by gains realized from
repurchase of the futures at maturity--because of the increase in
interest rates, the value of the futures would be less than at the time
of issue. If the firm were concerned that the price of an input will
rise, it would use a long hedge, or buy commodity futures.
At the
future's maturity date, the firm will be able to purchase the input at
the original contract price, even if market prices have risen in the
interim.
Answers and Solutions: 23 - 4
23-6
Swaps allow firms to reduce their financial risk by exchanging their
debt for another party's debt, usually because the parties prefer the
other's debt contract terms.
There are several ways in which swaps
reduce risk. Currency swaps, where firms exchange debt obligations
denominated in different currencies, can eliminate the exchange rate
risk created when currency must first be converted to another currency
before making scheduled debt payments.
Interest rate swaps, where
counterparties trade fixed-rate debt for floating rate debt, can reduce
risk for both parties based on their individual views concerning future
interest rates.
Answers and Solutions: 23 - 5
SOLUTIONS TO END-OF-CHAPTER PROBLEMS
23-1
Futures contract settled at 100 16/32% of $100,000 contract value, so
PV = 1.005  $1,000 = $1,005  100 bonds = $100,500. Using a financial
calculator, we can solve for rd as follows:
N = 40; PV = -1005; PMT = 30; FV = 1000; solve for I = rd = 2.9784%  2
= 5.9569%  5.96%.
If interest rates increase to 6.9569%, then we would solve for PV as
follows: N = 40; I = 6.9569/2 = 3.47845; PMT = 30; FV = 1000; solve for
PV = $897.4842  100 = $89,748.42.
Thus, the contact’s value has
decreased from $100,500 to $89,748.42.
23-2
a. In this situation, the firm would be hurt if interest rates were to
rise by June, so it would use a short hedge, or sell futures
contracts. Since futures contracts are for $100,000 in Treasury
bonds, the firm must sell 100 contracts to cover the planned
$10,000,000 June bond issue.
Since futures maturing in June are
selling for 95 17/32 of par, the value of Zinn's futures is about
$9,553,125.
Should interest rates rise by June, Zinn Company will
be able to repurchase the futures contracts at a lower cost, which
will help offset their loss from financing at the higher interest
rate. Thus, the firm has hedged against rising interest rates.
b. The firm would now pay 13 percent on the bonds. With an 11 percent
coupon rate, the bond issue would bring in only $8,898,149, so the
firm would lose $10,000,000 - $8,898,149 = $1,101,851:
N = 20; I = 13/2 = 6.5; PMT = 0.11/2  10,000,000 = 550000; FV =
10000000; and solve for PV = $8,898,149.
However, the
$9,553,125:
value
of
the
short
futures
position
began
at
95 17/32 of $10,000,000 = 0.9553125($10,000,000) = $9,553,125, or
roughly N = 40; PMT = 300000; FV = 10000000; PV = -9553125; solve
for I = 3.200% per six months.
The nominal annual yield is
2(6.400%) = 6.40%.
(Note that the future contracts are on
hypothetical 20-year, 6 percent semiannual coupon bonds which are
yielding 6.40 percent.)
Now, if interest rates increased by 200 basis points, to 8.40
percent, the value of the futures contract will drop to $7,693,948:
N = 40; I = 6.40/2 = 4.20; PMT = 300000; FV = 10000000; and solve
for PV = $7,693,948.
Answers and Solutions: 23 - 6
Since Zinn Company sold the futures contracts for $9,553,125, and
will, in effect, buy them back at $7,693,948, the firm would make a
$9,553,125 - $7,693,948 = $1,859,177 profit on the transaction
ignoring transaction costs.
Thus, the firm gained $1,859,177 on its futures position, but
lost $1,101,851 on its underlying bond issue.
On net, it gained
$1,859,177 - $1,101,851 = $757,326.
c. In a perfect hedge, the gains on futures contracts exactly offset
losses due to rising interest rates. For a perfect hedge to exist,
the underlying asset must be identical to the futures asset. Using
the Zinn Company example, a futures contract must have existed on
Zinn's own debt (it existed on Treasury bonds) for the company to
have an opportunity to create a perfect hedge.
In reality, it is
virtually impossible to create a perfect hedge, since in most cases
the underlying asset is not identical to the futures asset.
23-3
If Carter issues floating rate debt and then swaps, its net cash flows
will be: -(LIBOR + 2%) – 7.95% + LIBOR = -9.95%. This is less than the
10% rate at which it could directly issue fixed rate debt, so the swap
is good for Carter.
If Brence issues fixed rate debt and then swaps, its net cash flows
will be: -11% + 7.95% - LIBOR = -(LIBOR + 3.05%).
This is less than
the rate at which it could directly issue floating rate debt (LIBOR +
3%), so the swap is good for Brence.
Answers and Solutions: 23 - 7
SOLUTION TO SPREADSHEET PROBLEM
23-4
The detailed solution for the problem is available both on the
instructor’s resource CD-ROM (in the file Solution to Ch 23-4 Build a
Model.xls)
and
on
the
instructor’s
side
of
the
web
site,
http://brigham.swcollege.com.
Solution to Spreadsheet Problem: 23 - 8
MINI CASE
ASSUME THAT YOU HAVE JUST BEEN HIRED AS A FINANCIAL ANALYST BY TENNESSEE
SUNSHINE INC., A MID-SIZED TENNESSEE COMPANY THAT SPECIALIZES IN CREATING
EXOTIC SAUCES FROM IMPORTED FRUITS AND VEGETABLES.
THE FIRM'S CEO, BILL
STOOKSBURY, RECENTLY RETURNED FROM AN INDUSTRY CORPORATE EXECUTIVE CONFERENCE
IN SAN FRANCISCO, AND ONE OF THE SESSIONS HE ATTENDED WAS ON THE PRESSING
NEED FOR SMALLER COMPANIES TO INSTITUTE CORPORATE RISK MANAGEMENT PROGRAMS.
SINCE NO ONE AT TENNESSEE SUNSHINE IS FAMILIAR WITH THE BASICS OF DERIVATIVES
AND CORPORATE RISK MANAGEMENT, STOOKSBURY HAS ASKED YOU TO PREPARE A BRIEF
REPORT
THAT
THE
FIRM'S
EXECUTIVES
COULD
USE
TO
GAIN
AT
LEAST
A
CURSORY
UNDERSTANDING OF THE TOPICS.
TO BEGIN, YOU GATHERED SOME OUTSIDE MATERIALS ON DERIVATIVES AND CORPORATE
RISK
MANAGEMENT
AND
USED
THESE
MATERIALS
QUESTIONS THAT NEED TO BE ANSWERED.
TO
DRAFT
A
LIST
OF
PERTINENT
IN FACT, ONE POSSIBLE APPROACH TO THE
PAPER IS TO USE A QUESTION-AND-ANSWER FORMAT.
NOW THAT THE QUESTIONS HAVE
BEEN DRAFTED, YOU HAVE TO DEVELOP THE ANSWERS.
A.
WHY MIGHT STOCKHOLDERS BE INDIFFERENT WHETHER OR NOT A FIRM REDUCES
THE VOLATILITY OF ITS CASH FLOWS?
ANSWER:
IF VOLATILITY IN CASH FLOWS IS NOT CAUSED BY SYSTEMATIC RISK, THEN
STOCKHOLDERS
CAN
ELIMINATE
THE
DIVERSIFYING THEIR PORTFOLIOS.
RISK
OF
VOLATILE
CASH
FLOWS
BY
ALSO, IF A COMPANY DECIDED TO HEDGE
AWAY THE RISK ASSOCIATED WITH THE VOLATILITY OF ITS CASH FLOWS, THE
COMPANY WOULD HAVE TO PASS ON THE COSTS OF HEDGING TO THE INVESTORS.
SOPHISTICATED INVESTORS CAN HEDGE RISKS THEMSELVES AND THUS THEY ARE
INDIFFERENT AS TO WHO ACTUALLY DOES THE HEDGING.
Mini Case: 23 - 9
B.
WHAT ARE SIX REASONS RISK MANAGEMENT MIGHT INCREASE THE VALUE OF A
CORPORATION?
ANSWER:
THERE ARE NO STUDIES PROVING THAT RISK MANAGEMENT EITHER DOES OR
DOES
NOT
ADD
VALUE.
HOWEVER,
THERE
ARE
SIX
REASONS
MANAGEMENT MIGHT INCREASE THE VALUE OF A FIRM.
WHY
RISK
RISK MANAGEMENT
ALLOWS CORPORATIONS TO (1) INCREASE THEIR USE OF DEBT; (2) MAINTAIN
THEIR
CAPITAL
FINANCIAL
BUDGET
DISTRESS;
OVER
(4)
TIME;
UTILIZE
(3)
AVOID
THEIR
COSTS
ASSOCIATED
COMPARATIVE
WITH
ADVANTAGES
IN
HEDGING RELATIVE TO THE HEDGING ABILITY OF INDIVIDUAL INVESTORS; (5)
REDUCE BOTH THE RISKS AND COSTS OF BORROWING BY USING SWAPS; AND (6)
REDUCE THE HIGHER TAXES THAT RESULT FROM FLUCTUATING EARNINGS.
C.
WHAT IS CORPORATE RISK MANAGEMENT?
WHY IS IT IMPORTANT TO ALL
FIRMS?
ANSWER:
CORPORATE RISK MANAGEMENT IS THE MANAGEMENT OF UNPREDICTABLE EVENTS
THAT HAVE ADVERSE CONSEQUENCES FOR THE FIRM.
THIS FUNCTION IS VERY
IMPORTANT TO A FIRM SINCE IT INVOLVES REDUCING THE CONSEQUENCES OF
RISK
TO
THE
POINT
WHERE
THERE
SHOULD
BE
NO
SIGNIFICANT
ADVERSE
EFFECTS ON THE FIRM’S FINANCIAL POSITION.
D.
RISKS THAT FIRMS FACE CAN BE CATEGORIZED IN MANY WAYS.
DEFINE THE
FOLLOWING TYPES OF RISK: (1) SPECULATIVE RISKS; (2) PURE RISKS; (3)
DEMAND RISKS; (4) INPUT RISKS; (5) FINANCIAL RISKS; (6) PROPERTY
RISKS; (7) PERSONNEL RISKS; (8) ENVIRONMENTAL RISKS; (9) LIABILITY
RISKS; AND (10) INSURABLE RISKS.
ANSWER:
1. SPECULATIVE RISKS ARE THOSE THAT OFFER THE CHANCE OF A GAIN AS
WELL AS A LOSS, SUCH AS BUYING AN OWNERSHIP SHARE IN A COMPANY.
2. PURE RISKS ARE THOSE THAT ONLY OFFER THE PROSPECT OF LOSSES,
SUCH AS A PRODUCT LIABILITY OR MALPRACTICE LAWSUIT (FROM THE
DEFENDANT'S STANDPOINT).
Mini Case: 23 - 10
3. DEMAND RISKS ARE THOSE ASSOCIATED WITH THE DEMAND FOR A FIRM'S
PRODUCTS
OR
SERVICES,
SUCH
AS
NEW
PRODUCTS
DEVELOPED
BY
COMPETITORS.
4. INPUT RISKS ARE THOSE ASSOCIATED WITH A FIRM'S INPUT COSTS,
INCLUDING MATERIALS AND LABOR.
5. FINANCIAL
RISKS
ARE
THOSE
THAT
RESULT
FROM
FINANCIAL
TRANSACTIONS, SUCH AS INTEREST RATE AND CURRENCY EXCHANGE RATE
RISKS.
6. PROPERTY
RISKS
ARE
ASSOCIATED
WITH
DESTRUCTION
OF
A
FIRM'S
PRODUCTIVE ASSETS, INCLUDING THE THREAT OF FIRE, FLOODS, AND
RIOTS.
7. PERSONNEL RISKS ARE RISKS THAT RESULT FROM HUMAN ACTIONS, SUCH
AS THEFT AND FRAUD.
8. ENVIRONMENTAL
RISKS
INCLUDE
THOSE
RISKS
ASSOCIATED
WITH
POLLUTING THE ENVIRONMENT.
9. LIABILITY RISKS ARE CONNECTED WITH PRODUCT, SERVICE, OR EMPLOYEE
LIABILITY,
ACTIONS
BY
SUCH
AS
COSTS
EMPLOYEES
OR
INCURRED
DAMAGES
AS
A
RESULT
RESULTING
OF
FROM
IMPROPER
DEFECTIVE
PRODUCTS.
10. INSURABLE RISKS ARE THOSE WHICH TYPICALLY CAN BE COVERED BY
INSURANCE.
E.
WHAT ARE THE THREE STEPS OF CORPORATE RISK MANAGEMENT?
ANSWER:
THE THREE STEPS ARE:
IDENTIFY THE RISKS FACED BY THE FIRM;
MEASURE THE POTENTIAL IMPACT OF THE RISKS IDENTIFIED; AND
DECIDE HOW EACH RELEVANT RISK SHOULD BE HANDLED.
Mini Case: 23 - 11
F.
WHAT ARE SOME ACTIONS THAT COMPANIES CAN TAKE TO MINIMIZE OR REDUCE
RISK EXPOSURES?
ANSWER:
THERE ARE SEVERAL ACTIONS THAT COMPANIES CAN TAKE TO MINIMIZE OR
REDUCE THEIR RISK EXPOSURE.
FIRST, COMPANIES CAN TRANSFER RISK TO
AN INSURANCE COMPANY BY PAYING PERIODIC PREMIUMS.
SECOND, COMPANIES
CAN TRANSFER FUNCTIONS WHICH PRODUCE RISK TO THIRD PARTIES, SUCH AS
ELIMINATING RISKS ASSOCIATED WITH TRANSPORTATION BY CONTRACTING WITH
A TRUCKING COMPANY.
THIRD, PURCHASE DERIVATIVES CONTRACTS TO REDUCE
INPUT AND FINANCIAL RISK.
FOURTH, COMPANIES CAN TAKE ACTIONS TO
REDUCE THE PROBABILITY OF OCCURRENCE OF AN ADVERSE EVENT, SUCH AS
REPLACING OLD WIRING TO REDUCE THE POSSIBILITY OF FIRE.
FIFTH,
ACTIONS CAN BE TAKEN TO REDUCE THE MAGNITUDE OF THE LOSS ASSOCIATED
WITH ADVERSE EVENTS, SUCH AS INSTALLING AUTOMATIC SPRINKLER SYSTEMS.
FINALLY, COMPANIES CAN SIMPLY AVOID THE ACTIVITIES THAT GIVE RISE TO
RISK.
G.
WHAT IS FINANCIAL RISK EXPOSURE?
DESCRIBE THE FOLLOWING CONCEPTS
AND TECHNIQUES THAT CAN BE USED TO REDUCE FINANCIAL RISKS:
(1)
DERIVATIVES; (2) FUTURES MARKETS; (3) HEDGING; AND (4) SWAPS.
ANSWER:
FINANCIAL RISK EXPOSURE REFERS TO THE RISK INHERENT IN THE FINANCIAL
MARKETS DUE TO PRICE FLUCTUATIONS.
1. A DERIVATIVE IS A SECURITY WHOSE VALUE STEMS, OR IS DERIVED, FROM
THE VALUES OF OTHER ASSETS.
OPTIONS AND FUTURES CONTRACTS ARE
TWO TYPES OF DERIVATIVES THAT ARE USED TO MANAGE SECURITY PRICE
EXPOSURE.
2. FUTURES MARKETS INVOLVE CONTRACTS WHICH CALL FOR THE PURCHASE OR
SALE OF A FINANCIAL (OR REAL) ASSET AT SOME FUTURE DATE, BUT AT A
PRICE WHICH IS FIXED TODAY.
THUS, THESE MARKETS PROVIDE THE
OPPORTUNITY TO REDUCE FINANCIAL RISK EXPOSURE.
3. HEDGING
IS
GENERALLY
CONDUCTED
WHERE
NEGATIVELY AFFECT A FIRM'S PROFITS.
PURCHASE
Mini Case: 23 - 12
OF
FUTURE
CONTRACTS
IN
A
PRICE
CHANGE
COULD
A LONG HEDGE INVOLVES THE
ANTICIPATION
OF,
OR
TO
GUARD
AGAINST, PRICE INCREASES.
A SHORT HEDGE, OR SALE OF FUTURES, IS
MADE
CONCERNED
WHEN
THE
FIRM
IS
ABOUT
PRICE
DECLINES
IN
COMMODITIES OR FINANCIAL SECURITIES.
4. SWAPS INVOLVE THE EXCHANGE OF CASH PAYMENT OBLIGATIONS ON DEBT
BETWEEN TWO PARTIES, USUALLY BECAUSE EACH PARTY PREFERS THE TERMS
OF
THE
OTHER'S
FINANCIAL RISK.
DEBT
CONTRACT.
SWAPS
CAN
REDUCE
EACH
FIRM'S
FOR EXAMPLE, CURRENCY EXCHANGE RATE RISK CAN BE
ELIMINATED IF A U.S. FIRM WITH A POUND-DENOMINATED DEBT COULD
SWAP
THEIR
DEBT
WITH
A
BRITISH
FIRM
THAT
HAS
AN
EQUIVALENT
DOLLAR-DENOMINATED DEBT.
H.
DESCRIBE HOW COMMODITY FUTURES MARKETS CAN BE USED TO REDUCE INPUT
PRICE RISK.
ANSWER:
ESSENTIALLY, PURCHASE OF A COMMODITY FUTURES CONTRACT WILL ALLOW A
FIRM TO MAKE A FUTURE PURCHASE OF THE INPUT MATERIAL AT TODAY'S
PRICE, EVEN IF THE MARKET PRICE ON THE GOOD HAS RISEN SUBSTANTIALLY
IN THE INTERIM.
Mini Case: 23 - 13