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Chapter 2-1 Asset Classes and Financial Instruments Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin

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Chapter 2-1

Asset Classes and Financial Instruments

Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

2-2

2.1 Money Market Instruments

• Treasury Bills: Fed• Certificates of Deposit: Banks• Commercial Paper: Corp & banks• Bankers’ Acceptances : Bank• Eurodollars: bank & Corp• Repos and Reverses• Federal Funds: Deposit in Fed• LIBOR (London Interbank Offer Rate):Banks

2-3

Treasury Bills

• Treasury bills– Issued by– Denomination– Maturity– Liquidity– Default risk– Interest type– Taxation

Federal Government

$100, commonly $10,000

4, 13, 26, or 52 weeks

Highly liquid

None, why?

Discount-(later on this)

Federal taxes owed, exempt from state and local taxes

2-4

Certificates of Deposit (CD)

– Issued by– Denomination

– Maturity– Liquidity– Default risk– Interest type– Taxation

Depository Institutions

Any, $100,000 or more are marketable

Varies, typically 14 day minimum3 months or less are liquid ( marketable)

First $100,000 ($250,000) is insured

Add on ( you get the deposit + interset)

Interest income is fully taxable

2-5

Commercial Paper• Commercial Paper

– Issued by

– Maturity– Denomination– Liquidity– Default risk– Interest type– Taxation

Large creditworthy corporations and

financial institutions

Maximum 270 days, usually 1 to 2 months

Minimum $100,000

3 months or less are liquid if marketable

Unsecured, Rated, Mostly high quality

Discount

Interest income is fully taxable

2-6

Bankers Acceptances & Eurodollars

• Bankers Acceptances– Originates when a purchaser of goods authorizes its

bank to pay the seller for the goods at a date in the future (time draft).

– When the purchaser’s bank ‘accepts’ the draft it becomes a contingent liability of the bank and becomes a marketable security.

• Eurodollars– Dollar denominated (time) deposits held outside the

U.S.– Pay a higher interest rate than U.S. deposits.

2-7

Federal Funds and LIBOR• Federal Funds

– Depository institutions must maintain deposits with the Federal Reserve Bank.

– Federal funds represents trading in reserves held on deposit at the Federal Reserve.

– Key interest rate for the economy

• LIBOR (London Interbank Offer Rate)– Rate at which large banks in London (and

elsewhere) lend to each other. – Base rate for many loans and derivatives.

2-8

Repurchase Agreements and Reverses

• Repurchase Agreements (RPs or repos) and Reverse RPs– Short term sales of securities arranged with an

agreement to repurchase the securities a set higher price.

– A RP is a collateralized loan, many are overnight, although “Term” RPs may have a one month maturity.

– A Reverse Repo is lending money and obtaining security title as collateral.

– “Haircuts” may be required depending on collateral quality

2-9

2-10

Haircut

• The buyer assumes the collateral as repayment should the seller default. If the collateral has a volatile price history the buyer is at risk.

• To reduce this risk, a haircut is imposed. The haircut is some percentage of the market value the buyer holds back from the cash payment to account for the price volatility as well as counterparty risk.

• Ex. If the haircut is 10% on 10mm market value bonds, the buyer receives 10mm in bonds and the seller receives 9mm in cash. At the end of the repo term, the seller pays the 9mm cash back plus interest and receives the same 10mm bonds back

2-11

Money Market Instruments

• Call Money Rate (later ch 3)– Investors who buy stock on margin borrow money from

their brokers to purchase stock. The borrowing rate is the call money rate.

– The loan may be ‘called in’ by the broker.

2-12

Figure 2.2 Treasury Bills (T-bills)

• Given the above, can you figure out the ask yield? can you calculate bid ask price of the bill?

2-13

Price = $10,000 x [ 1 – T-bill rate x (N/360)]

BID:

$10,000 X [1 - .0120 X (161/360)] = $9,946.33

ASK:

$10,000 X (1 - .01190x(161/360) = $9,946.80.

nx

P

BDR

36010000

10000

]360/(1[000,10)( nbidxbidP

2-14

BEY: Bond-Equivalent Yield• An investor who buys the bill for the asked price

and holds it until maturity will see her investment grow over 161 days by a multiple of

• $10,000/$9,946.80 = 1.00535, or .535%. But this is the return for 161 days only.

• Annualizing this return using a 365-day year results in a yield of .535% X 365/161 = 1.213%.

• In short:

nx

PP

BEYR

3651000 161365

8.99468.99461000x

BEYR

2-15

Notice

• Bank discount

• BEY

nx

P

BDR

36010000

10000

nx

PP

BEYR

36510000

2-16

• Exercise

• Do the same for

• Jan 29

• March 26

BID ASK bond-equivalent yield9979 9979.525 0.594%

BID ASK bond-equivalent yield9927.453 9927.706 1.46%

2-17

SummarizingBEY-Ask Yield

• If given the ask price, get the ASK yield on March 26

nx

PP

BEYR

36510000

46.1%182365

706.9927706.992710000 x

BEYR

2-18

Exercise

• the price for T-Bill is $ 9979 and there is 126 days left.

• compute the Bank discount rate.

• = .006

rrBDBD == $10,000$10,000 -- $9,979$9,979

$10,000$10,000 x x

360360126126 == .6%.6%

2-19

Example: Bank Discount Rate Given T-Bill price

• rrBDBD = bank discount rate= bank discount rate

• PP = market price of the T-bill= market price of the T-bill

• nn = number of days to maturity= number of days to maturity90-day T-bill, P = $9,87590-day T-bill, P = $9,875

rrBDBD == $10,000$10,000 -- $9,875$9,875

$10,000$10,000 x x

360360

9090== 5%5%

2-20

Bond Equivalent Yield

P = price of the T-billP = price of the T-bill

n = number of days to maturityn = number of days to maturity

rr BEYBEY == 10,00010,000 -- PP

PP xx 365365

nn

rrBEYBEY == 10,00010,000 -- 9,8759,875

9,8759,875 x x 365365

9090

rrBEYBEY = .0127 x 4.0556 = .0513 = 5.13% = .0127 x 4.0556 = .0513 = 5.13%

Example Using Sample T-BillExample Using Sample T-Bill

rBD=5%

2-21

Example*

• An investor buys a T-bill at a bank discount quote of 4.80 with 150 days to maturity. What is the investor's actual annual rate of return on this investment was ?

2-22

Money Market Instrument Yields

• Yields on money market instruments are not always directly comparable

Factors influencing “quoted” yields

• Par value vs. investment value

• 360 vs. 365 days assumed in a year (366 leap year)

• Simple vs. Compound Interest

2-23

Effective Annual Yield

P = price of the T-billP = price of the T-bill

n = number of days to maturityn = number of days to maturity

rEAY = 5.23%

Example Using Sample T-BillExample Using Sample T-Bill

rBD=5%

rBEY=5.13%

rEAY=5.23%

1000,10$

1

365

n

EAY P

Pr

1875,9$

875,9$000,10$1

90

365

EAYr

2-24

Effective Annual Yield

P = price of the T-billP = price of the T-bill

n = number of days to maturityn = number of days to maturity

rrEAYEAY = 5.23% = 5.23%

Example Using Sample T-BillExample Using Sample T-Bill

rr EAYEAY == (1+ (1+ PPPP

))365/n365/n10000 -

rr EAYEAY == (1+ (1+ 98759875

98759875 ))365/90365/9010000 -

rBD=5%

rBEY=5.13%

rEAY=5.23%

2-25

Money Market Instruments• Treasury bills

• Certificates of deposit

• Commercial Paper

• Bankers Acceptances

• Eurodollars

• Federal Funds

• Repurchase Agreements (RPs) and Reverse RPs

Discount

BEY*

Discount

Discount

BEY*

BEY*

Discount

2-26

2.2 The Bond Market

2-27

Capital Market - Fixed Income Instruments

Government Issues

• US Treasury Bonds and Notes– Bonds (10-30 years) versus Notes ( up to

10 years)

– Denomination ($100, mostly $1000)

– Interest type ( semi-annual)

– Risk? Taxation?

Variation: Treasury Inflation Protected Securities (TIPS)•Tips have principal adjusted for increases in the Consumer Price Index

2-28

Capital Market - Fixed Income Instruments

Buy the bond at = 105.6875x 1000 = 1056.875

Coupon = .04 x 1000 = 40

CY = PMT/Price = 40/1056.875 = 3.784%

2-29

Capital Market - Fixed Income Instruments

Government Issues

• Agency Issues (Fed Gov)– Most are home mortgage related

• Issuers: FNMA, FHLMC, GNMA, Federal Home Loan Banks

– Risk of these securities?• Implied backing by the government• In September 2008, Federal government took

over FNMA and FHLMC.(sup-prime)

2-30

Capital Market - Fixed Income Instruments

Government Issues

• Municipal Bonds– Issuer? municipalities– Differ from Treasuries and Agencies?

• Risk?o G.O. vs Revenueo Industrial development

• Taxation?

Rate)Tax (1rrTaxableExemptTax

r = interest rate

2-31

Table 2.3 Equivalent Taxable Yields

Rate)Tax (1rrTaxableExemptTax

2-32

Example

• A municipal bond carries a coupon rate of 6% and is trading at par. What would be the equivalent taxable yield of this bond to a taxpayer in a 35% tax bracket?

• Taxable equivalent yield = .06 / (1-.35) = .0923

2-33

Example

An investor is in a 30% combined federal plus state tax bracket. If corporate bonds offer 9% yields, what must municipals offer for the investor to prefer them to corporate bonds?

[0.09 x (1 – 0.30)] = 0.0630 = 6.30%. Therefore, the municipals must offer at least 6.30% yields.

2-34

Example

• Suppose that short-term municipal bonds (M) currently offer yields of 4%, while comparable taxable bonds (B) pay 5%. Which gives you the higher after-tax yield if your tax bracket is:

• a. Zero B• b. 10% B• c. 20% equal• d. 30% M

Rate)Tax (1rrTaxableExemptTax

2-35

Continue from previous

Find the equivalent taxable yield of the municipal bond in the pervious slide for tax brackets of zero, 10%, 20%, and 30%.

– 4.00%– 4.44%– 5.00%– 5.71%

)1(

rr ExemptTax

Taxable Tax

2-36

Example

• From Feb 2012:

• How much would you have to pay to purchase one of these bonds? 107:27 = 107.8438% of par = $1,078.438

• What is its coupon rate? $48.75 annually or, $24.375 if

semiannually.• What is the current yield (i.e., coupon income as a fraction of

bond price) of the bond? 48.75/1078.438 = 4.52%

2-37

Capital Market - Fixed Income Instruments

Private Issues

• Corporate Bonds– Investment grade vs speculative grade

– Risker than Gov bond– Coupon : semi– Callable

2-38

Capital Market - Fixed Income Instruments

• Mortgage-Backed Securities (read book 34-36)

– Pass-through

• A security backed by a pool of mortgages. The

pool backer ‘passes through’ monthly mortgage

payments made by homeowners and covers

payments from any homeowners that default.

• Collateral:

– Traditionally all mortgages were conforming mortgages

but since 2006, Alt-A and subprime mortgages were

included in pools

2-39

Capital Market - Fixed Income Instruments

• Mortgage-Backed Securities• Political encouragement to spur affordable

housing led to increase in subprime lending

• Private banks began to purchase and sell pools of subprime mortgages

• Pool issuers assumed housing prices would continue to rise, but they began to fall as far back as 2006 with disastrous results for the markets.

2-40

The U.S. Bond Market

2-41

2.3 Equity Securities

2-42

Capital Market - Equity• Common stock (p 36-37)

– Residual claim• Cash flows to common stock?• In the event of bankruptcy, what will

stockholders receive?

– Limited liability• What is the maximum loss on a stock

purchase?

2-43

Capital Market - Equity• Preferred stock

– Fixed dividends: limited gains, non-voting

– Priority over common

– Tax treatment• Preferred & common dividends are not tax

deductible to the issuing firm• Corporate tax exclusion on 70% dividends

earned

2-44

Capital Market - Equity• Depository Receipts

– American Depository Receipts (ADRs) also called American Depository Shares (ADSs) are certificates traded in the U.S. that represent ownership in a foreign security.

2-45

Capital Market - Equity• Capital Gains and Dividend Yields

– You buy a share of stock for $50, hold it for one year, collect a $1.00 dividend and sell the stock for $54. What were your dividend yield, capital gain yield and total return? (Ignore taxes)

– Dividend yield: = Dividend / Pbuy

$1.00 / $50 = 2%

– Capital gain yield: = (Psell – Pbuy)/ Pbuy

($54 - $50) / $50 = 8%

– Total return: = Dividend yield + Capital gain yield

2% + 8% = 10%

gPD

K

PPP

g 1

2-46

Uses• Track average returns• Comparing performance of managers• Base of derivatives

Factors in constructing or using an index• Representative?• Broad or narrow?• How is it constructed?

2.4 Stock and Bond Indexes

2-47

Construction of Indexes• How are stocks weighted?

– Price weighted (DJIA)

– Market-value weighted (S&P500, NASDAQ)

– Equally weighted (Value Line Index)

How much money How much money do you put in each do you put in each stock in the index?stock in the index?

2-48

Constructing market indices

• Indexes can be distinguished in four ways:– The market covered,– The types of stocks included,– How many stocks are included, and– How the index is calculated (price-weighted,

e.g. DJIA, versus value-weighted, e.g. S&P 500).

2-49

Constructing market indices• Price weighted average assumes buy 1 share each stock

and invest cash and stock dividends proportionately. • For a price-weighted index (i.e., the DJIA), higher priced

stocks receive higher weights.• Value weighted: considers not only price but also # shares :

– $ invested in each stock are proportional to market value of each stock

– For a value-weighted index (i.e., the S&P 500), companies with larger market values have higher weights.

• Equal weighted: considers not only price but also # shares:– invest same amount of $ in each stock regardless of

market value of stock

2-50

Example Price weighted

• Three stocks have share prices of $12, $75, and $30 with total market values of $400 million, $350 million and $150 million respectively. If you were to construct a price-weighted index of the three stocks what would be the index value? 

• Index = (12 + 75 + 30)/3 = 39

2-51

Price weightedDay 1

Stock Price (KD)NBK 1.2Zain 2.1

Kipico 0.8

Index 1.37

37.13/)8.1.22.1( Index

2-52

Day 2Stock Price (KD)NBK 1.3Zain 2.2

Kipico 1Index 1.50

50.13/)12.23.1( Index

2-53

Change in index

• 150-137 / 1.37 = 9.76%

2-54

Split- divisor??

Days 2 Going to Day 3

Stock Price (KD) Stock Price (KD)NBK 1.3 NBK 1.3Zain 2.2 Zain 1.1

Kipico 1 Kipico 1

Index 1.50 Index 1.13??

50.1/)11.13.1( x

267.2xdvisor

2-55

Going to day 3 ( divisor = 2.267)Stock Price (KD)

NBK 1.4Zain 1.1

Kipico 1.1

Sum 3.6

588.1267.2/)1.11.14.1( Index

2-56

Summary

Day 1 Day2 Day3index 1.37 1.50 1.588change 9.76% 5.88%

2-57

a) Price weighted series

Time 0 index value is

Time 1 index value = 190/3 = 63.33 Problem? split

Refigure denominator (10+25+140) / Denom = 66.67

Denominator ( divisor) = 2.624869

Time 1 index value = (15+25+150) / 2.624869 = 72.38

Other problems

– similar % change movements in higher price stocks cause proportionately larger changes in the index

(10+50+140)/3 = 200/3 = 66.67

2-58

Example• The Hydro Index is a price weighted stock index

based on the 5 largest boat manufacturers in the nation. The stock prices for the five stocks are $10, $20, $80, $50 and $40. The price of the last stock was just split 2 for 1 and the stock price was halved from $40 to $20. What is the new divisor for a price weighted index? 

2-59

2-3 handout Price-Weighted Portfolio

Example I: $1,000,000 to Invest,

Note: Shares = $1,000,000 / 131.130 = 7,626

PricePrice

WeightCompanyBoeing 67.50 0.5148Nordstrom 41.93 0.3198Lowe's 21.70 0.1655

131.130 1.000

2-60

Example II: Changing the Divisor

Day 1 of Index: Company Price

Boeing 67.50Nordstrom 41.93Lowe's 21.70Sum: 131.13

Index:131.13/3= 43.71 (Divisor = 3)

Before Day 2 starts, you want to replace Lowe's with Home Depot, selling at $32.90.

To keep the value of the Index the same, i.e., 43.71:

Boeing 67.50Nordstrom 41.93Home Depot 32.90Sum: 142.33

142.33 / Divisor = 43.71, if Divisor is: 3.256234

What would have happened to the divisor if Home Depot shares were selling at $65.72 per share instead of $32.90?

2-61

To keep the value of the Index the same, i.e., 43.71:

Boeing 67.50Nordstrom 41.93Home Depot 65.72Sum: 175.15

175.15 / Divisor = 43.71, if Divisor is: 4.00709

What would have happened to the divisor if Home Depot shares were selling at $65.72 per share instead of $32.90?

2-62

Examples :Price weighted• An index consists of the following securities and has an

index divisor of 3.0. What is the price- weighted index return?    

Price-weighted index = {[($19 + $11 + $33)/3] - [($17 + $14 + $26)/3]} / [($17+ $14 + $26)/3]

= 10.53 %

2-63

Examples :Price weighted• An index consists of the following securities and has an

index divisor of 2.0. What is the price- weighted index return?    

• Price-weighted index = • {[($51 + $36)/2] - [($54 + $33)/2]}/[($54 + $33)/2] = 0

percent

2-64

Example

• A price-weighted index consists of stocks A, B, and C which are priced at $38, $21, and $26 a share, respectively. The current index divisor is 2.7. What will the new index divisor be if stock B undergoes a 3-for-1 stock split? (38 + 21 + 26)/2.7 = 31.48

• [38 + (21/3) + 26]/x = 31.48

• x = 2.2553

2-65

Example

• A price-weighted index consists of stocks A, B, and C which are priced at $27, $11, and $18 a share, respectively. The current index divisor is 2.24. If stock B undergoes a 1-for-3 reverse stock split, the new index divisor will be: 

•   = [(27 + 11 + 18)/2.24] = 25• [27 + (11 3) + 18]/x = 25• x = 3.12

2-66

P-weight

• You have the following information:   

You want the beginning price-weighted index of these two stocks to be 100. Given this, what is the ending index value? 

• Beginning price-weighted index = [(35 + 22)/(35 + 22)] 100 = 100Ending price-weighted index = [(38 + 23)/(35 + 22)] 100 = 107.02

2-67

Value weighted

Computed by calculating a weighted average of the returns of each security in the index, with weights proportional to outstanding market value.

2-68

V-Weight

• An index consists of the following securities. What is the value-weighted index return?    

• Beginning value = (5,000 21) + (2,000 39) = 183,000Ending value = (5,000 27) + (2,000 42) = 219,000Return = (219,000 - 183,000)/183,000 = 19.67 percent

2-69

Index=100

Value weighted series

Equal weighted series: invest $300 in each

Small cap increase will have more effect on EW than VW

106.1410050)(14080)(5040)(10

50)(150160)(2540)(15indexV

119.05100)143.2(1406)(5030)(10

)143.2(150)21(2530)(15indexE

2-70

# shares:$1,000,000 to Invest,

Value-Weighted Portfolio

Total Market Market- Market-

Shares Capitalization Value SharesCompany Price (millions) (millions) Weight to Buy

Boeing 67.50 732.74 49,460.0 0.5550 8,223

Nordstrom 41.93 219.65 9,210.0 0.1034 2,465

Lowe's 21.70 1,402.76 30,440.0 0.3416 15,742

Total: 131.130 Total: 89,110.0 1.0000 26,430

Note: Shares to Buy = $1,000,000*Weight / Price

2-71

Example IV: How Does the Value-Weighted Index Change?

Total Shares Market Capitalization

Day 1: Company Price (millions) (millions)

Boeing 67.50 732.74 49,460Nordstrom41.93 219.65 9,210Lowe's 21.70 1402.76 30,440

Total MV(1): 89,110

Divisor (Set by Vendor): 89.11

Day 1 Index Level: 1,000.00

Total Shares Market CapitalizationDay 2: Company Price (millions) (millions)

Boeing 69.00 732.74 50,559Nordstrom 41.93 219.65 9,210Lowe's 21.70 1402.76 30,440

Total MV(2): 90,209

Day 2 Index Level: 1,012.33

Using the Portfolio from Example III:

2-72

The Day 3 Index Can be Calculated in

Two Ways:

Total Shares Market Capitalization

Day 3: Company Price (millions) (millions)Boeing 71.10 732.740 52,098Nordstrom 41.93 219.650 9,210Lowe's 21.70 1,402.760 30,440

Total MV(3): 91,748

Total MV(2): 90,209

Day 2 Index Level: 1,012.33

Day 3 Index Level: 1,029.60

Total MV(1): 89,110

1Day LevelIndex 1Day ValueMarket 3Day ValueMarket

Index 3Day

or

2Day LevelIndex 2Day ValueMarket 3Day ValueMarket

Index 3Day

2-73

Why do the two differ?

Case 1: 20% change in price of small cap firm.

invest $100 in each stock

100.43100200)(5080)(10040)(10

0)20(500)8(10040)(12indexV

106.671002)(50)1(10010)(10

2)(501)(10010)(12indexE

2-74

Why do the two differ?

Case 2: 20% change in price of large cap firm.

Assume that we invest $100 in each stock

110.86100200)(5080)(10040)(10

0)20(600)8(10040)(10indexV

106.671002)(50)1(10010)(10

2)(601)(10010)(10indexE

Case 1 VW = 100.43

Case 1 EW = 106.67

Large cap increase will have more effect on vW than eW

2-75

2.5 Derivative MarketsRead the book (P 45)

• Listed Call Option: – Holder the right to buy 100 shares of the

underlying stock at a predetermined price on or before some specified expiration date.

• Listed Put Option: – Holder the right to sell 100 shares of the

underlying stock at a predetermined price on or before some specified expiration date.

2-76

Figure 2.10 Stock Options on Apple

What does the term ‘strike’ or exercise price refer to?

What is an option premium?

2-77

Using the Stock Options on Apple

The right to buy 100 shares of stock at a stock price of $110 using the October contract would cost ________.

(Ignoring commissions)

Is this contract “in the money?”

When should you buy this contract? •Stock price was equal to $110.35 & you will make money if the stock price increases above $110.35 + $7.45 = $117.80 by contract expiration.

When should you write it ( sell it) ?

$745

2-78

Using the Stock Options on Apple

The right to sell 100 shares of stock at a stock price of $110 using the October contract would cost ________.

(Ignoring commissions)

Is this contract “in the money?”

Why do the two option prices differ?

$810

2-79

Using the Stock Options on AppleLook at Figure 2.10 to answer the following questions:

1.How does the exercise or strike price affect the value of a call option? A put option? Why?The higher Strike price for a Call (Put), the lower ( Higher) the option value for the call (PUT)

2.How does a greater time to contract expiration affect the value of a call option? A put option? Why?The longer expiration date for the option, the higher option value.

3.How is ‘volume’ different from ‘open interest?’Volume is what is traded on a day.

Open interest: The total number of buy options that are not closed on a particular day

2-80

2-81

Example

• Suppose you buy an April expiration call option with exercise price 105.

• a. If the stock price in April is $111, will you exercise your call? What are the profit and rate of return on your position?

As long as the stock price at expiration exceeds the exercise price, it makes sense to exercise the call.

Gross profit is: $111 - $ 105 = $6

Net profit = $6 – $ 22.40 = $16.40 loss

Rate of return = -16.40 / 22.40 = - .7321 or 73.21% loss

• c. What if you had bought an April put with exercise price 105?

2-82

Continue

• c. What if you had bought an April put with exercise price 105?

– A put with exercise price $105 would expire worthless for any stock price equal to or greater than $105. An investor in such a put would have a rate of return over the holding period of –100%.

2-83

Continue

• b. What if you had bought the April call with exercise price 100?

– Yes, exercise. • Gross profit is: $111 - $ 100 = $11• Net profit = $11 – $ 25.10 = $14.10 loss• Rate of return = -14.10 / 25.10 = 0.5618 or 56.18 % loss

2-84

17. Stock XYZ has a call and a put with strike or exercise price equal to $50 and six month maturities. What will be the profit to an investor who buys the call for $4 if in six months the price of XYZ stock is a) $40, b) $50, c) $60? What about for an investor who buys a put for $6?

XYZ 6moValue of

call at expiration

Initial Cost Profit

a. $40 0 4 -4

b. $50 0 4 -4

c. $60 10 4 6

XYZ 6moValue of

put at expiration

Initial Cost Profit

a. $40 10 6 4

b. $50 0 6 -6

c. $60 0 6 -6

5.

2-85

Selected Problems

1. Find the after tax rate of return to a corporation that buys preferred stock at $40, holds it one year and sells it at $40 after collecting a $4 dividend. The firm’s tax rate is 30%.

• (Pretax rate or return = ____________ )• The total before-tax income is $4. After the 70% exclusion, taxable

income is:• 0.30 $4 = $1.20 taxable income• Therefore Taxes owed are Tax rate taxable income• Taxes = 0.30 $1.20 = $0.36• After-tax income = $4 – $0.36 = $3.64• After-tax rate of return = $3.64 / $40 = 9.10%

$4 / $40 = 10%

2-86

2. a) Using the quote find GD’s closing price the day before the quote appeared

The closing price is $94.80, which is $1.14 higher than yesterday’s price. Therefore, yesterday’s closing price was: $94.80 – $1.14 = $93.66

b) How many shares could you buy for $5000?

You could buy: $5,000/$94.80 = 52.74 shares

c) Total annual dividend income from the __ shares?

$1.44 * 52 = $74.88

d) What are EPS? (Approximate)

P / (P/E) = EPS = $94.80 / 18 = $5.27

NEW YORK STOCK EXCHANGE COMPOSITE TRANSACTIONS 52 -WEEK YLD VOL NET HI LO STOCK (SYM) DIV % PE 100s CLOSE CHG 97 64.32 GenDynam GD 1.44 1.5 18 5583 94.80 1.14

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