5-1 k* = 3%; I
1
= 2%; I
2
= 4%; I
3
= 4%; MRP = 0; k
T-2
= ?; k
T-3
= ? k = k* + IP + DRP + LP + MRP.
Since these are Treasury securities, DRP = LP = 0. k
T-3
= k* + IP
3
.
IP
3
= (2% + 4% + 4%)/3 = 3.33%. k
T-3
= 3% + 3.33% = 6.33%.
5-2 k
T-10
= 6%; k
C-10
= 8%; LP = 0.5%; DRP = ? k = k* + IP + DRP + LP + MRP. k
T-10
= 6% = k* + IP + MRP; DRP = LP = 0. k
T-2
= k* + IP
2
.
IP
2
= (2% + 4%)/2 = 3%. k
T-2
= 3% + 3% = 6%. k
C-10
= 8% = k* + IP + DRP + 0.5% + MRP.
Because both bonds are 10-year bonds the inflation premium and maturity risk premium on both bonds are equal. The only difference between them is the liquidity and default risk premiums. k
C-10
= 8% = k* + IP + MRP + 0.5% + DRP. But we know from above that k* +
IP + MRP = 6%; therefore, k
C-10
= 8% = 6% + 0.5% + DRP
1.5% = DRP.
5-3 k
T-1, 1
= 5%; k
T-1, 2
= 6%; k
T-2
= ? k
T-2
=
5% + 6%
= 5.5%.
2
5-4 k* = 3%; IP = 3%; k
T-2
= 6.2%; MRP
2
= ? k
T-2
= k* + IP + MRP = 6.2% k
T-2
= 3% + 3% + MRP = 6.2%
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Answers and Solutions: 5 - 1
MRP = 0.2%.
Answers and Solutions: 5 - 2 Harcourt, Inc. items and derived items copyright © 2000 by Harcourt, Inc.
5-5 Let x equal the yield on 1-year securities 1 year from now:
(5.6% + x)/2 = 6%
5.6% + x = 12%
x = 6.4%.
5-6 Let x equal the yield on 2-year securities 4 years from now:
7.5% = [(4)(7%) + 2x]/6
0.45 = 0.28 + 2x
x = 0.085 or 8.5%.
5-7 k = k* + IP + MRP + DRP + LP. k* = 0.03.
IP = [0.03 + 0.04 + (5)(0.035)]/7 = 0.035.
MRP = 0.0005(6) = 0.003.
DRP = 0.
LP = 0. k = 0.03 + 0.035 + 0.003 = 0.068 = 6.8%.
5-8 a. k
1
= 3%, and k
2
=
3% + k
1 in Year 2
2
= 4.5%,
Solving for k
1
in Year 2, we obtain k
1
in Year 2 = (4.5% × 2) - 3% = 6%. b. For riskless bonds under the expectations theory, the interest rate for a bond of any maturity is k n
= k* + average inflation over n years. If k* = 1%, we can solve for IP n
:
Year 1: k
1
= 1% + I
1
= 3%;
I
1
= expected inflation = 3% - 1% = 2%.
Year 2: k
1
= 1% + I
2
= 6%;
I
2
= expected inflation = 6% - 1% = 5%.
Note also that the average inflation rate is (2% + 5%)/2 = 3.5%, which, when added to k* = 1%, produces the yield on a 2-year bond, 4.5 percent. Therefore, all of our results are consistent.
Alternative solution: Solve for the inflation rates in Year 1 and Year
2 first: k
RF
= k* + IP
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Answers and Solutions: 5 - 3
Year 1: 3% = 1% + IP
1
; IP
1
= 2%, thus I
1
= 2%.
Year 2: 4.5% = 1% + IP
2
; IP
2
= 3.5%.
IP
2
= (I
1
+ I
2
)/2
3.5% = (2% + I
2
)/2
I
2
= 5%.
Then solve for the yield on the one-year bond in the second year:
5-9 k* = 2%; MRP = 0%. k
1
= 5%; k
2
= 7%.
Year 2: k
1
= 1% + 5% = 6%. k
2
= k
1
+ k
1 in
2
Year 2
,
7% =
5% + k
1 in Year 2
2
,
9% = k
1
in Year 2. k
1
in Year 2 = k* + I
2
,
9% = 2% + I
2
7% = I
2
.
5-10 First, note that we will use the equation k t
= 3% + IP t
+ MRP t
. We have the data needed to find the IPs:
IP
5
=
8% + 5% + 4% + 4% + 4%
5
=
25%
5
= 5%.
The average interest rate during the 2-year period differs from the 1-year interest rate expected for Year 2 because of the inflation rate reflected in the two interest rates. The inflation rate reflected in the interest rate on any security is the average rate of inflation expected over the security’s life.
IP
2
=
8% + 5%
2
= 6.5%.
Now we can substitute into the equation: k
2
= 3% + 6.5% + MRP
2
= 10%. k
5
= 3% + 5% + MRP
5
= 10%.
Answers and Solutions: 5 - 4 Harcourt, Inc. items and derived items copyright © 2000 by Harcourt, Inc.
Now we can solve for the MRPs, and find the difference:
Difference = (2% - 0.5%) = 1.5%.
5-11 Basic relevant equations: k t
= k* + IP t
+ DRP t
+ MRP t
+ LP t
.
But here IP is the only premium, so k t
= k* + IP t
.
IP t
= Avg. inflation = (I
1
+ I
2
+ ...)/N.
MRP
5
= 10% - 8% = 2%. MRP
2
= 10% - 9.5% = 0.5%.
We know that I
1
= IP
1
= 3% and k* = 2%. Therefore, k
1
= 2% + 3% = 5%. k
3
= k
1
+ 2% = 5% + 2% = 7%. But, k
3
= k* + IP
3
= 2% + IP
3
= 7%, so
IP
3
= 7% - 2% = 5%.
We also know that I t
= Constant after t = 1.
We can set up this table:
k* I Avg. I = IP t
k = k* + IP t
1 2 3 3%/1 = 3% 5%
2 2 I (3% + I)/2 = IP
2
3 2 I (3% + I + I)/3 = IP
3
k
3
= 7%, so IP
3
= 7%-2% = 5%.
Avg. I = IP
3
= (3% + 2I)/3 = 5%
2I = 12%
I = 6%.
5-12 a. Real
Years to Risk-Free
Maturity Rate (k*) IP** MRP k
T
= k* + IP + MRP
1 2% 7.00% 0.2% 9.20%
2 2 6.00 0.4 8.40
3 2 5.00 0.6 7.60
4 2 4.50 0.8 7.30
5 2 4.20 1.0 7.20
10 2 3.60 1.0 6.60
20 2 3.30 1.0 6.30
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Answers and Solutions: 5 - 5
**The computation of the inflation premium is as follows:
Expected Average
Year Inflation Expected Inflation
1 7% 7.00%
2 5 6.00
3 3 5.00
4 3 4.50
5 3 4.20
10 3 3.60
20 3 3.30
For example, the calculation for 3 years is as follows:
7% + 5% + 3%
= 5.00%.
3
Thus, the yield curve would be as follows:
8.5
8.0
7.5
7.0
6.5
Interest Rate
(%)
11.0
10.5
10.0
9.5
9.0
LILCO
Exxon
T-bonds
0 2 4 6 8 10 12 14 16 18 20
Years to Maturity b. The interest rate on the Exxon bonds has the same components as the
Treasury securities, except that the Exxon bonds have default risk, so a default risk premium must be included. Therefore, k
Exxon
= k* + IP + MRP + DRP.
For a strong company such as Exxon, the default risk premium is virtually zero for short-term bonds. However, as time to maturity increases, the probability of default, although still small, is sufficient to warrant a default premium. Thus, the yield risk curve for the
Exxon bonds will rise above the yield curve for the Treasury
Answers and Solutions: 5 - 6 Harcourt, Inc. items and derived items copyright © 2000 by Harcourt, Inc.
securities. In the graph, the default risk premium was assumed to be
1.0 percentage point on the 20-year Exxon bonds. The return should equal 6.3% + 1% = 7.3%. c. LILCO bonds would have significantly more default risk than either
Treasury securities or Exxon bonds, and the risk of default would increase over time due to possible financial deterioration. In this example, the default risk premium was assumed to be 1.0 percentage point on the 1-year LILCO bonds and 2.0 percentage points on the
20-year bonds. The 20-year return should equal 6.3% + 2% = 8.3%.
5-13 Term Rate
6 months 5.1%
1 year 5.5
2 years 5.6
Interest Rate
10
(%)
8
3 years 5.7
4 years 5.8
5 years 6.0
10 years 6.1
6
4
20 years 6.5
30 years 6.3
2
0
0 5 10 15 20 25
Years to Maturity
30
5-14 a. The average rate of inflation for the 5-year period is calculated as:
Average inflation = (0.13 + 0.09 + 0.07 + 0.06 + 0.06)/5 = 8.20%. rate b. k = k* + IP
Avg.
= 2% + 8.2% = 10.20%. c. Here is the general situation:
Arithmetic
1-Year Average Maturity Estimated
Expected Expected Risk Interest
Year Inflation Inflation k* Premium Rates
1 13% 13.0% 2% 0.1% 15.1%
2 9 11.0 2 0.2 13.2
3 7 9.7 2 0.3 12.0
5 6 8.2 2 0.5 10.7
. . . . . .
. . . . . .
. . . . . .
10 6 7.1 2 1.0 10.1
20 6 6.6 2 2.0 10.6
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Answers and Solutions: 5 - 7
Interest Rate
(%)
15.0
12.5
10.0
7.5
5.0
2.5
0 2 4 6 8 10 12 14 16 18 20
Years to Maturity d. The “normal” yield curve is upward sloping because, in “normal” times, inflation is not expected to trend either up or down, so IP is the same for debt of all maturities, but the MRP increases with years, so the yield curve slopes up. During a recession, the yield curve typically slopes up especially steeply, because inflation and consequently shortterm interest rates are currently low, yet people expect inflation and interest rates to rise as the economy comes out of the recession. e. If inflation rates are expected to be constant, then the expectations theory holds that the yield curve should be horizontal. However, in this event it is likely that maturity risk premiums would be applied to long-term bonds because of the greater risks of holding long-term rather than short-term bonds:
Percent
(%)
Actual yield curve
A
Maturity risk premium
Pure expectations yield curve
Years to Maturity
If maturity risk premiums were added to the yield curve in Part e above, then the yield curve would be more nearly normal; that is, the long-term end of the curve would be raised. (The yield curve shown in this answer is upward sloping; the yield curve shown in Part c is downward sloping.)
Answers and Solutions: 5 - 8 Harcourt, Inc. items and derived items copyright © 2000 by Harcourt, Inc.
5-15 The detailed solution for the spreadsheet problem is available both on the instructor’s resource CD-ROM and on the instructor’s side of the Harcourt
College Publishers’ web site, http://www.harcourtcollege.com/finance/ brigham.
5-16 The detailed solution for the cyberproblem is available on the instructor’s side of the Harcourt College Publishers’ web site, http://www. harcourtcollege.com/finance/brigham.
Harcourt , Inc. items and derived items copyright © 2000 by Harcourt, Inc.
Computer/Internet Applications: 5 - 9
5-17 ASSUME THAT YOU RECENTLY GRADUATED WITH A DEGREE IN FINANCE AND HAVE
JUST REPORTED TO WORK AS AN INVESTMENT ADVISOR AT THE BROKERAGE FIRM OF
SMYTH BARRY & CO. YOUR FIRST ASSIGNMENT IS TO EXPLAIN THE NATURE OF
THE U. S. FINANCIAL MARKETS TO MICHELLE VARGA, A PROFESSIONAL TENNIS
PLAYER WHO HAS JUST COME TO THE UNITED STATES FROM MEXICO. VARGA IS A
HIGHLY RANKED TENNIS PLAYER WHO EXPECTS TO INVEST SUBSTANTIAL AMOUNTS
OF MONEY THROUGH SMYTH BARRY. SHE IS ALSO VERY BRIGHT, AND, THEREFORE,
SHE WOULD LIKE TO UNDERSTAND IN GENERAL TERMS WHAT WILL HAPPEN TO HER
MONEY. YOUR BOSS HAS DEVELOPED THE FOLLOWING SET OF QUESTIONS THAT YOU
MUST ASK AND ANSWER TO EXPLAIN THE U. S. FINANCIAL SYSTEM TO VARGA.
A. WHAT IS A MARKET? HOW ARE PHYSICAL ASSET MARKETS DIFFERENTIATED FROM
FINANCIAL MARKETS?
ANSWER: [SHOW S5-1 AND S5-2 HERE.] A MARKET IS ONE IN WHICH ASSETS ARE BOUGHT
AND SOLD. THERE ARE MANY DIFFERENT TYPES OF FINANCIAL MARKETS, EACH
ONE DEALING WITH A DIFFERENT TYPE OF FINANCIAL ASSET, SERVING A
DIFFERENT SET OF CUSTOMERS, OR OPERATING IN A DIFFERENT PART OF THE
COUNTRY. FINANCIAL MARKETS DIFFER FROM PHYSICAL ASSET MARKETS IN THAT
REAL, OR TANGIBLE, ASSETS SUCH AS MACHINERY, REAL ESTATE, AND
AGRICULTURAL PRODUCTS ARE TRADED IN THE PHYSICAL ASSET MARKETS, BUT
FINANCIAL SECURITIES REPRESENTING CLAIMS ON ASSETS ARE TRADED IN THE
FINANCIAL MARKETS.
B. DIFFERENTIATE BETWEEN MONEY MARKETS AND CAPITAL MARKETS.
ANSWER: MONEY MARKETS ARE THE MARKETS IN WHICH DEBT SECURITIES WITH MATURITIES
OF LESS THAN ONE YEAR ARE TRADED. NEW YORK, LONDON, AND TOKYO ARE
MAJOR MONEY MARKET CENTERS. LONGER-TERM SECURITIES, INCLUDING STOCKS
AND BONDS, ARE TRADED IN THE CAPITAL MARKETS. THE NEW YORK STOCK
Integrated Case: 5 - 10 Harcourt, Inc. items and derived items copyright © 2000 by Harcourt, Inc.
EXCHANGE IS AN EXAMPLE OF A CAPITAL MARKET, WHILE THE NEW YORK
COMMERCIAL PAPER AND TREASURY BILL MARKETS ARE MONEY MARKETS.
C. DIFFERENTIATE BETWEEN A PRIMARY MARKET AND A SECONDARY MARKET. IF
APPLE COMPUTER DECIDED TO ISSUE ADDITIONAL COMMON STOCK, AND VARGA
PURCHASED 100 SHARES OF THIS STOCK FROM MERRILL LYNCH, THE UNDERWRITER,
WOULD THIS TRANSACTION BE A PRIMARY MARKET TRANSACTION OR A SECONDARY
MARKET TRANSACTION? WOULD IT MAKE A DIFFERENCE IF VARGA PURCHASED
PREVIOUSLY OUTSTANDING APPLE STOCK IN THE DEALER MARKET?
ANSWER: A PRIMARY MARKET IS ONE IN WHICH COMPANIES RAISE CAPITAL BY SELLING
NEWLY ISSUED SECURITIES, WHEREAS PREVIOUSLY OUTSTANDING SECURITIES ARE
TRADED AMONG INVESTORS IN THE SECONDARY MARKETS. IF VARGA PURCHASED
NEWLY ISSUED APPLE STOCK, THIS WOULD CONSTITUTE A PRIMARY MARKET
TRANSACTION, WITH MERRILL LYNCH ACTING AS AN INVESTMENT BANKER IN THE
TRANSACTION. IF VARGA PURCHASED “USED” STOCK, THEN THE TRANSACTION
WOULD BE IN THE SECONDARY MARKET.
D. DESCRIBE THE THREE PRIMARY WAYS IN WHICH CAPITAL IS TRANSFERRED BETWEEN
SAVERS AND BORROWERS.
ANSWER: [SHOW S5-3 AND S5-4 HERE.] TRANSFERS OF CAPITAL CAN BE MADE (1) BY
DIRECT TRANSFER OF MONEY AND SECURITIES, (2) THROUGH AN INVESTMENT
BANKING HOUSE, OR (3) THROUGH A FINANCIAL INTERMEDIARY. IN A DIRECT
TRANSFER, A BUSINESS SELLS ITS STOCKS OR BONDS DIRECTLY TO INVESTORS
(SAVERS), WITHOUT GOING THROUGH ANY TYPE OF INSTITUTION. THE BUSINESS
BORROWER RECEIVES DOLLARS FROM THE SAVERS, AND THE SAVERS RECEIVE
SECURITIES (BONDS OR STOCK) IN RETURN.
IF THE TRANSFER IS MADE THROUGH AN INVESTMENT BANKING HOUSE, THE
INVESTMENT BANK SERVES AS A MIDDLEMAN. THE BUSINESS SELLS ITS
SECURITIES TO THE INVESTMENT BANK, WHICH IN TURN SELLS THEM TO THE
SAVERS. ALTHOUGH THE SECURITIES ARE SOLD TWICE, THE TWO SALES
CONSTITUTE ONE COMPLETE TRANSACTION IN THE PRIMARY MARKET.
IF THE TRANSFER IS MADE THROUGH A FINANCIAL INTERMEDIARY, SAVERS
INVEST FUNDS WITH THE INTERMEDIARY, WHICH THEN ISSUES ITS OWN
SECURITIES IN EXCHANGE. BANKS ARE ONE TYPE OF INTERMEDIARY, RECEIVING
DOLLARS FROM MANY SMALL SAVERS AND THEN LENDING THESE DOLLARS TO
Harcourt, Inc. items and derived items copyright © 2000 by Harcourt, Inc. Integrated Case: 5 - 11
BORROWERS TO PURCHASE HOMES, AUTOMOBILES, VACATIONS, AND SO ON, AND
ALSO TO BUSINESSES AND GOVERNMENT UNITS. THE SAVERS RECEIVE A
CERTIFICATE OF DEPOSIT OR SOME OTHER INSTRUMENT IN EXCHANGE FOR THE
FUNDS DEPOSITED WITH THE BANK. MUTUAL FUNDS, INSURANCE COMPANIES, AND
PENSION FUNDS ARE OTHER TYPES OF INTERMEDIARIES.
E. WHAT ARE THE TWO LEADING STOCK MARKETS? DESCRIBE THE TWO BASIC TYPES
OF STOCK MARKETS.
ANSWER: [SHOW S5-5 HERE.] THE TWO LEADING STOCK MARKETS TODAY ARE THE NEW YORK
STOCK EXCHANGE AND THE NASDAQ STOCK MARKET. THERE ARE JUST TWO BASIC
TYPES OF STOCK MARKETS: (1) PHYSICAL LOCATION EXCHANGES, WHICH INCLUDE
THE NEW YORK STOCK EXCHANGE (NYSE), THE AMERICAN STOCK EXCHANGE (AMEX),
AND SEVERAL REGIONAL STOCK EXCHANGES, AND (2) ELECTRONIC DEALER-BASED
MARKETS THAT INCLUDE THE NASDAQ STOCK MARKET, THE LESS FORMAL OVER-THE-
COUNTER MARKET, AND THE RECENTLY DEVELOPED ELECTRONIC COMMUNICATIONS
NETWORKS (ECNs).
THE PHYSICAL LOCATION EXCHANGES ARE FORMAL ORGANIZATIONS HAVING
TANGIBLE, PHYSICAL LOCATIONS AND TRADING IN DESIGNATED SECURITIES.
THERE ARE EXCHANGES FOR STOCKS, BONDS, COMMODITIES, FUTURES, AND
OPTIONS. THE PHYSICAL LOCATION EXCHANGES ARE CONDUCTED AS AUCTION
MARKETS WITH SECURITIES GOING TO THE HIGHEST BIDDER. BUYERS AND
SELLERS PLACE ORDERS WITH THEIR BROKERS WHO THEN EXECUTE THOSE ORDERS
BY MATCHING BUYERS AND SELLERS, ALTHOUGH SPECIALISTS ASSIST IN
PROVIDING CONTINUITY TO THE MARKETS.
THE ELECTRONIC DEALER-BASED MARKET IS MADE UP OF HUNDREDS OF BROKERS
AND DEALERS AROUND THE COUNTRY WHO ARE CONNECTED ELECTRONICALLY BY
TELEPHONES AND COMPUTERS. THE DEALER-BASED MARKET FACILITATES TRADING
OF SECURITIES THAT ARE NOT LISTED ON A PHYSICAL LOCATION EXCHANGE. A
DEALER MARKET IS DEFINED TO INCLUDE ALL FACILITIES THAT ARE NEEDED TO
CONDUCT SECURITY TRANSACTIONS NOT MADE ON THE PHYSICAL LOCATION
EXCHANGES. THESE FACILITIES INCLUDE (1) THE RELATIVELY FEW DEALERS WHO
HOLD INVENTORIES OF THESE SECURITIES AND WHO ARE SAID TO MAKE A MARKET
IN THESE SECURITIES; (2) THE THOUSANDS OF BROKERS WHO ACT AS AGENTS IN
BRINGING THE DEALERS TOGETHER WITH INVESTORS; AND (3) THE COMPUTERS,
TERMINALS, AND ELECTRONIC NETWORKS THAT PROVIDE A COMMUNICATION LINK
BETWEEN DEALERS AND BROKERS. DEALERS CONTINUOUSLY POST A PRICE AT
Integrated Case: 5 - 12 Harcourt, Inc. items and derived items copyright © 2000 by Harcourt, Inc.
WHICH THEY ARE WILLING TO BUY THE STOCK (THE BID PRICE) AND A PRICE AT
WHICH THEY ARE WILLING TO SELL THE STOCK (THE ASK PRICE). THE ASK
PRICE IS ALWAYS HIGHER THAN THE BID PRICE, AND THE DIFFERENCE (OR “BID-
ASK SPREAD”) REPRESENTS THE DEALER’S MARKUP, OR PROFIT.
F. WHAT DO WE CALL THE PRICE THAT A BORROWER MUST PAY FOR DEBT CAPITAL?
WHAT IS THE PRICE OF EQUITY CAPITAL? WHAT ARE THE FOUR MOST
FUNDAMENTAL FACTORS THAT AFFECT THE COST OF MONEY, OR THE GENERAL LEVEL
OF INTEREST RATES, IN THE ECONOMY?
ANSWER: [SHOW S5-6 AND S5-7 HERE.] THE INTEREST RATE IS THE PRICE PAID FOR
BORROWED CAPITAL, WHILE THE RETURN ON EQUITY CAPITAL COMES IN THE FORM
OF DIVIDENDS PLUS CAPITAL GAINS. THE RETURN THAT INVESTORS REQUIRE ON
CAPITAL DEPENDS ON (1) PRODUCTION OPPORTUNITIES, (2) TIME PREFERENCES
FOR CONSUMPTION, (3) RISK, AND (4) INFLATION.
PRODUCTION OPPORTUNITIES REFER TO THE RETURNS THAT ARE AVAILABLE
FROM INVESTMENT IN PRODUCTIVE ASSETS: THE MORE PRODUCTIVE A PRODUCER
FIRM BELIEVES ITS ASSETS WILL BE, THE MORE IT WILL BE WILLING TO PAY
FOR THE CAPITAL NECESSARY TO ACQUIRE THOSE ASSETS.
TIME PREFERENCE FOR CONSUMPTION REFERS TO CONSUMERS’ PREFERENCES FOR
CURRENT CONSUMPTION VERSUS SAVINGS FOR FUTURE CONSUMPTION: CONSUMERS
WITH LOW PREFERENCES FOR CURRENT CONSUMPTION WILL BE WILLING TO LEND AT
A LOWER RATE THAN CONSUMERS WITH A HIGH PREFERENCE FOR CURRENT
CONSUMPTION.
INFLATION REFERS TO THE TENDENCY OF PRICES TO RISE, AND THE HIGHER
THE EXPECTED RATE OF INFLATION, THE LARGER THE REQUIRED RATE OF RETURN.
RISK, IN A MONEY AND CAPITAL MARKET CONTEXT, REFERS TO THE CHANCE
THAT A LOAN WILL NOT BE REPAID AS PROMISED--THE HIGHER THE PERCEIVED
DEFAULT RISK, THE HIGHER THE REQUIRED RATE OF RETURN.
RISK IS ALSO LINKED TO THE MATURITY AND LIQUIDITY OF A SECURITY. THE
LONGER THE MATURITY AND THE LESS LIQUID (MARKETABLE) THE SECURITY, THE
HIGHER THE REQUIRED RATE OF RETURN, OTHER THINGS CONSTANT.
THE PRECEDING DISCUSSION RELATED TO THE GENERAL LEVEL OF MONEY
COSTS, BUT THE LEVEL OF INTEREST RATES WILL ALSO BE INFLUENCED BY SUCH
THINGS AS FED POLICY, FISCAL AND FOREIGN TRADE DEFICITS, AND THE LEVEL
OF ECONOMIC ACTIVITY. ALSO, INDIVIDUAL SECURITIES WILL HAVE HIGHER
Harcourt, Inc. items and derived items copyright © 2000 by Harcourt, Inc. Integrated Case: 5 - 13
YIELDS THAN THE RISK-FREE RATE BECAUSE OF THE ADDITION OF VARIOUS
PREMIUMS AS DISCUSSED BELOW.
G. WHAT IS THE REAL RISK-FREE RATE OF INTEREST (k*) AND THE NOMINAL RISK-
FREE RATE (k
RF
)? HOW ARE THESE TWO RATES MEASURED?
ANSWER: [SHOW S5-8 AND S5-9 HERE.] KEEP THESE EQUATIONS IN MIND AS WE DISCUSS
INTEREST RATES. WE WILL DEFINE THE TERMS AS WE GO ALONG: k = k* + IP + DRP + LP + MRP. k
RF
= k* + IP.
THE REAL RISK-FREE RATE, k*, IS THE RATE THAT WOULD EXIST ON DEFAULT-
FREE SECURITIES IN THE ABSENCE OF INFLATION.
THE NOMINAL RISK-FREE RATE, k
RF
, IS EQUAL TO THE REAL RISK-FREE RATE
PLUS AN INFLATION PREMIUM, WHICH IS EQUAL TO THE AVERAGE RATE OF
INFLATION EXPECTED OVER THE LIFE OF THE SECURITY.
THERE IS NO TRULY RISKLESS SECURITY, BUT THE CLOSEST THING IS A
SHORT-TERM U. S. TREASURY BILL (T-BILL), WHICH IS FREE OF MOST RISKS.
THE REAL RISK-FREE RATE, k*, IS ESTIMATED BY SUBTRACTING THE EXPECTED
RATE OF INFLATION FROM THE RATE ON SHORT-TERM TREASURY SECURITIES. IT
IS GENERALLY ASSUMED THAT k* IS IN THE RANGE OF 1 TO 4 PERCENTAGE
POINTS. THE T-BOND RATE IS USED AS A PROXY FOR THE LONG-TERM RISK-FREE
RATE. HOWEVER, WE KNOW THAT ALL LONG-TERM BONDS CONTAIN INTEREST RATE
RISK, SO THE T-BOND RATE IS NOT REALLY RISKLESS. IT IS, HOWEVER, FREE
OF DEFAULT RISK.
H. DEFINE THE TERMS INFLATION PREMIUM (IP), DEFAULT RISK PREMIUM (DRP),
LIQUIDITY PREMIUM (LP), AND MATURITY RISK PREMIUM (MRP). WHICH OF
THESE PREMIUMS IS INCLUDED WHEN DETERMINING THE INTEREST RATE ON
(1) SHORT-TERM U. S. TREASURY SECURITIES, (2) LONG-TERM U. S. TREASURY
SECURITIES, (3) SHORT-TERM CORPORATE SECURITIES, AND (4) LONG-TERM
CORPORATE SECURITIES? EXPLAIN HOW THE PREMIUMS WOULD VARY OVER TIME
AND AMONG THE DIFFERENT SECURITIES LISTED ABOVE.
Integrated Case: 5 - 14 Harcourt, Inc. items and derived items copyright © 2000 by Harcourt, Inc.
ANSWER: [SHOW S5-10 HERE.] THE INFLATION PREMIUM (IP) IS A PREMIUM ADDED TO
THE REAL RISK-FREE RATE OF INTEREST TO COMPENSATE FOR EXPECTED
INFLATION.
THE DEFAULT RISK PREMIUM (DRP) IS A PREMIUM BASED ON THE PROBABILITY
THAT THE ISSUER WILL DEFAULT ON THE LOAN, AND IT IS MEASURED BY THE
DIFFERENCE BETWEEN THE INTEREST RATE ON A U. S. TREASURY BOND AND A
CORPORATE BOND OF EQUAL MATURITY AND MARKETABILITY.
A LIQUID ASSET IS ONE THAT CAN BE SOLD AT A PREDICTABLE PRICE ON
SHORT NOTICE; A LIQUIDITY PREMIUM IS ADDED TO THE RATE OF INTEREST ON
SECURITIES THAT ARE NOT LIQUID.
THE MATURITY RISK PREMIUM (MRP) IS A PREMIUM THAT REFLECTS INTEREST
RATE RISK; LONGER-TERM SECURITIES HAVE MORE INTEREST RATE RISK (THE
RISK OF CAPITAL LOSS DUE TO RISING INTEREST RATES) THAN DO SHORTER-TERM
SECURITIES, AND THE MRP IS ADDED TO REFLECT THIS RISK.
1. SHORT-TERM TREASURY SECURITIES INCLUDE ONLY AN INFLATION PREMIUM.
2. LONG-TERM TREASURY SECURITIES CONTAIN AN INFLATION PREMIUM PLUS A
MATURITY RISK PREMIUM. NOTE THAT THE INFLATION PREMIUM ADDED TO
LONG-TERM SECURITIES WILL DIFFER FROM THAT FOR SHORT-TERM SECURITIES
UNLESS THE RATE OF INFLATION IS EXPECTED TO REMAIN CONSTANT.
3. THE RATE ON SHORT-TERM CORPORATE SECURITIES IS EQUAL TO THE REAL
RISK-FREE RATE PLUS PREMIUMS FOR INFLATION, DEFAULT RISK, AND
LIQUIDITY. THE SIZE OF THE DEFAULT AND LIQUIDITY PREMIUMS WILL VARY
DEPENDING ON THE FINANCIAL STRENGTH OF THE ISSUING CORPORATION AND
ITS DEGREE OF LIQUIDITY, WITH LARGER CORPORATIONS GENERALLY HAVING
GREATER LIQUIDITY BECAUSE OF MORE ACTIVE TRADING.
4. THE RATE FOR LONG-TERM CORPORATE SECURITIES ALSO INCLUDES A PREMIUM
FOR MATURITY RISK. THUS, LONG-TERM CORPORATE SECURITIES GENERALLY
CARRY THE HIGHEST YIELDS OF THESE FOUR TYPES OF SECURITIES.
I. WHAT IS THE TERM STRUCTURE OF INTEREST RATES? WHAT IS A YIELD CURVE?
ANSWER: [SHOW S5-11 HERE.] THE TERM STRUCTURE OF INTEREST RATES IS THE
RELATIONSHIP BETWEEN INTEREST RATES, OR YIELDS, AND MATURITIES OF
Harcourt, Inc. items and derived items copyright © 2000 by Harcourt, Inc. Integrated Case: 5 - 15
SECURITIES. WHEN THIS RELATIONSHIP IS GRAPHED, THE RESULTING CURVE IS
CALLED A YIELD CURVE.
(SKETCH OUT A YIELD CURVE ON THE BOARD.)
J. SUPPOSE MOST INVESTORS EXPECT THE INFLATION RATE TO BE 5 PERCENT NEXT
YEAR, 6 PERCENT THE FOLLOWING YEAR, AND 8 PERCENT THEREAFTER. THE REAL
RISK-FREE RATE IS 3 PERCENT. THE MATURITY RISK PREMIUM IS ZERO FOR
BONDS THAT MATURE IN 1 YEAR OR LESS, 0.1 PERCENT FOR 2-YEAR BONDS, AND
THEN THE MRP INCREASES BY 0.1 PERCENT PER YEAR THEREAFTER FOR 20 YEARS,
AFTER WHICH IT IS STABLE. WHAT IS THE INTEREST RATE ON 1-YEAR,
10-YEAR, AND 20-YEAR TREASURY BONDS? DRAW A YIELD CURVE WITH THESE
DATA. WHAT FACTORS CAN EXPLAIN WHY THIS CONSTRUCTED YIELD CURVE IS
UPWARD SLOPING?
ANSWER: [SHOW S5-12 THROUGH S5-18 HERE.] S5-12 SHOWS A RECENT (AUGUST 1999)
TREASURY YIELD CURVE.
STEP 1: FIND THE AVERAGE EXPECTED INFLATION RATE OVER YEARS 1 TO 20:
YR 1: IP = 5.0%.
YR 10: IP = (5 + 6 + 8 + 8 + 8 + ... + 8)/10 = 7.5%.
YR 20: IP = (5 + 6 + 8 + 8 + ... + 8)/20 = 7.75%.
STEP 2: FIND THE MATURITY PREMIUM IN EACH YEAR:
YR 1: MRP = 0.0%.
YR 10: MRP = 0.1
×
9 = 0.9%.
YR 20: MRP = 0.1
×
19 = 1.9%.
STEP 3: SUM THE IPs AND MRPs, AND ADD k* = 3%:
YR 1: k
RF
= 3% + 5.0% + 0.0% = 8.0%.
YR 10: k
RF
= 3% + 7.5% + 0.9% = 11.4%.
YR 20: k
RF
= 3% + 7.75% + 1.9% = 12.65%.
THE SHAPE OF THE YIELD CURVE DEPENDS PRIMARILY ON TWO FACTORS:
(1) EXPECTATIONS ABOUT FUTURE INFLATION AND (2) THE RELATIVE RISKINESS
OF SECURITIES WITH DIFFERENT MATURITIES.
Integrated Case: 5 - 16 Harcourt, Inc. items and derived items copyright © 2000 by Harcourt, Inc.
Interest rate (%)
13
12
11
10
9
8
0 1 5 10 15 20
Years to maturity
THE CONSTRUCTED YIELD CURVE IS UPWARD SLOPING. THIS IS DUE TO
INCREASING EXPECTED INFLATION AND AN INCREASING MATURITY RISK PREMIUM.
K. AT ANY GIVEN TIME, HOW WOULD THE YIELD CURVE FACING AN AAA-RATED
COMPANY COMPARE WITH THE YIELD CURVE FOR U. S. TREASURY SECURITIES? AT
ANY GIVEN TIME, HOW WOULD THE YIELD CURVE FACING A BB-RATED COMPANY
COMPARE WITH THE YIELD CURVE FOR U. S. TREASURY SECURITIES?
DRAW A
GRAPH TO ILLUSTRATE YOUR ANSWER.
ANSWER: [SHOW S5-19 THROUGH S5-21 HERE.] (CURVES FOR AAA-RATED AND BB-RATED
SECURITIES HAVE BEEN ADDED TO DEMONSTRATE THAT RISKIER SECURITIES
REQUIRE HIGHER RETURNS.) THE YIELD CURVE NORMALLY SLOPES UPWARD,
INDICATING THAT SHORT-TERM INTEREST RATES ARE LOWER THAN LONG-TERM
INTEREST RATES. YIELD CURVES CAN BE DRAWN FOR GOVERNMENT SECURITIES OR
FOR THE SECURITIES OF ANY CORPORATION, BUT CORPORATE YIELD CURVES WILL
ALWAYS LIE ABOVE GOVERNMENT YIELD CURVES, AND THE RISKIER THE
CORPORATION, THE HIGHER ITS YIELD CURVE. THE SPREAD BETWEEN A
CORPORATE YIELD CURVE AND THE TREASURY CURVE WIDENS AS THE CORPORATE
BOND RATING DECREASES.
Harcourt, Inc. items and derived items copyright © 2000 by Harcourt, Inc. Integrated Case: 5 - 17
Interest
Rate (%)
15
10
5
5.4%
5.7%
15
6.0%
BB-Rated
AAA-Rated
Treasury yield curve
Years to
20 maturity
0
0 1 5 10
L. WHAT IS THE PURE EXPECTATIONS THEORY? WHAT DOES THE PURE EXPECTATIONS
THEORY IMPLY ABOUT THE TERM STRUCTURE OF INTEREST RATES?
ANSWER: [SHOW S5-22 AND S5-23 HERE.] THE PURE EXPECTATIONS THEORY ASSUMES THAT
INVESTORS ESTABLISH BOND PRICES AND INTEREST RATES STRICTLY ON THE
BASIS OF EXPECTATIONS FOR INTEREST RATES. THIS MEANS THAT THEY ARE
INDIFFERENT WITH RESPECT TO MATURITY IN THE SENSE THAT THEY DO NOT VIEW
LONG-TERM BONDS AS BEING RISKIER THAN SHORT-TERM BONDS. IF THIS WERE
TRUE, THEN THE MATURITY RISK PREMIUM WOULD BE ZERO, AND LONG-TERM
INTEREST RATES WOULD SIMPLY BE A WEIGHTED AVERAGE OF CURRENT AND
EXPECTED FUTURE SHORT-TERM INTEREST RATES. IF THE PURE EXPECTATIONS
THEORY IS CORRECT, YOU CAN USE THE YIELD CURVE TO “BACK OUT” EXPECTED
FUTURE INTEREST RATES.
M. SUPPOSE THAT YOU OBSERVE THE FOLLOWING TERM STRUCTURE FOR TREASURY
SECURITIES:
MATURITY
1 YEAR
2 YEARS
3 YEARS
4 YEARS
5 YEARS
YIELD
6.0%
6.2
6.4
6.5
6.5
ASSUME THAT THE PURE EXPECTATIONS THEORY OF THE TERM STRUCTURE IS
CORRECT. (THIS IMPLIES THAT YOU CAN USE THE YIELD CURVE GIVEN ABOVE TO
Integrated Case: 5 - 18 Harcourt, Inc. items and derived items copyright © 2000 by Harcourt, Inc.
“BACK OUT” THE MARKET’S EXPECTATIONS ABOUT FUTURE INTEREST RATES.)
WHAT DOES THE MARKET EXPECT WILL BE THE INTEREST RATE ON 1-YEAR
SECURITIES, ONE YEAR FROM NOW? WHAT DOES THE MARKET EXPECT WILL BE THE
INTEREST RATE ON 3-YEAR SECURITIES, TWO YEARS FROM NOW?
ANSWER: [SHOW S5-24 THROUGH S5-27 HERE.] CALCULATION FOR k ON 1-YEAR
SECURITIES, ONE YEAR FROM NOW:
6.2% =
6 .
0 %
2
+
X
12.4% = 6.0% + X
6.4% = X.
1-YEAR SECURITIES, ONE YEAR FROM NOW WILL YIELD 6.4%.
CALCULATION FOR k ON 3-YEAR SECURITIES, TWO YEARS FROM NOW:
6.5% =
6 .
2 %)
+
3 X
5
32.5% = 12.4% + 3X
20.1% = 3X
6.7% = X.
3-YEAR SECURITIES, TWO YEARS FROM NOW WILL YIELD 6.7%.
N. FINALLY, VARGA IS ALSO INTERESTED IN INVESTING IN COUNTRIES OTHER THAN
THE UNITED STATES. DESCRIBE THE VARIOUS TYPES OF RISKS THAT ARISE WHEN
INVESTING OVERSEAS.
ANSWER: [SHOW S5-28 AND S5-29 HERE.] FIRST, VARGA SHOULD CONSIDER COUNTRY
RISK, WHICH REFERS TO THE RISK THAT ARISES FROM INVESTING OR DOING
BUSINESS IN A PARTICULAR COUNTRY. THIS RISK DEPENDS ON THE COUNTRY’S
ECONOMIC, POLITICAL, AND SOCIAL ENVIRONMENT. COUNTRY RISK ALSO
INCLUDES THE RISK THAT PROPERTY WILL BE EXPROPRIATED WITHOUT ADEQUATE
COMPENSATION, AS WELL AS NEW HOST COUNTRY STIPULATIONS ABOUT LOCAL
PRODUCTION, SOURCING OR HIRING PRACTICES, AND DAMAGE OR DESTRUCTION OF
FACILITIES DUE TO INTERNAL STRIFE.
SECOND, VARGA SHOULD CONSIDER EXCHANGE RATE RISK. VARGA NEEDS TO
KEEP IN MIND WHEN INVESTING OVERSEAS THAT MORE OFTEN THAN NOT THE
SECURITY WILL BE DENOMINATED IN A CURRENCY OTHER THAN THE DOLLAR, WHICH
Harcourt, Inc. items and derived items copyright © 2000 by Harcourt, Inc. Integrated Case: 5 - 19
MEANS THAT THE VALUE OF THE INVESTMENT WILL DEPEND ON WHAT HAPPENS TO
EXCHANGE RATES. TWO FACTORS CAN LEAD TO EXCHANGE RATE FLUCTUATIONS.
CHANGES IN RELATIVE INFLATION WILL LEAD TO CHANGES IN EXCHANGE RATES.
ALSO, AN INCREASE IN COUNTRY RISK WILL ALSO CAUSE THE COUNTRY’S
CURRENCY TO FALL. CONSEQUENTLY, INFLATION RISK, COUNTRY RISK, AND
EXCHANGE RATE RISK ARE ALL INTERRELATED.
Integrated Case: 5 - 20 Harcourt, Inc. items and derived items copyright © 2000 by Harcourt, Inc.