Lecture 10

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ENGR 390 Lecture 10 Bonds Winter 2007 S.V. Atre 1 Chapter 6 Principles of Investing Investing in Financial Assets Investing in Stocks Investing in Bond Investment Strategies Investment Basics Liquidity – How accessible is your money? Risk – What is the safety involved? Return – How much profit will you be able to expect from your investment?

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Engineering Economics 390. Courtesy of Atre, Sundar V Associate Professor, Oregon State University.

Transcript of Lecture 10

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ENGR 390 Lecture 10 Bonds Winter 2007

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Chapter 6Principles of Investing

Investing in Financial AssetsInvesting in StocksInvesting in BondInvestment Strategies

Investment Basics

Liquidity – How accessible is your money?Risk – What is the safety involved?Return – How much profit will you be able to expect from your investment?

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Investing in Bond

Bonds: Loans that investors make to corporations and governments.Face (par) value: Principal amountCoupon rate: yearly interest paymentMaturity: the length of the loan

Types of Bonds and How They Are Issued in the Financial Market

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AT&T 7s05Closing price: 108 1/ 4$1,082.50

Coupon rate Maturity date2005

No meaning,Spacing

Market price

Bond Price Notation Used in Financial Markets

29/32=$9.062530/32=$9.375031/32=$9.687532/32=$10

13/32=$4.062514/32=$4.37515/32=$4.687516/32=$5.00

1=$101/2=$5.00

25/32=$7.812526/32=$8.125027/32=$8.437528/32=$8.75

9/32=$2.812510/32=$3.125011/32=$3.437512/32=$3.75

7/8=$8.753/8=$3.75

21/32=$6.562522/32=$6.875023/32=$7.187524/32=$7.50

6/32=$1.56257/32=$1.87507/32=$2.18758/32=$2.50

3/4=$7.501/4=$2.50

17/32=$5.312518/32=$5.625019/32=$5.937520/32=$6.25

1/32=$0.31252/32=$0.6250 3/32=$0.93754/32=$1.25

5/8=$6.251/8=$1.25

Treasury BondsCorporate Bonds

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How Do Prices and Yields Work?

Yield to Maturity: The actual interest (%) earned from a bond over the holding period

Current Yield: The annual interest (%) earned as a percentage of the current market price

Bond Quotes

AT&T 7s05 6.5% 5 million 108 1/4

Coupon rate of 7%

Maturity (2005)

Current yield

Trading volume

ClosingMarket price

$1,082.50$70/108.25= 6.47%

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BOND TERMINOLOGYBOND TERMINOLOGY1. Face Value, Par Value, Maturity Value

– How much the borrower will pay the holder when it matures.

2. Coupon Rate, Nominal Annual Interest Rate– Paid yearly on face value.

3. Frequency of Interest Payments4. Maturity Date

– Date at which you receive the face value5. Current Price, Market Value

– What someone is willing to pay for the future cash flows.

6. Yield to Maturity– Actual interest earned over holding period

Problem 1Problem 1You desire to make an investment in You desire to make an investment in bonds provided you can earn 12% per bonds provided you can earn 12% per year, compounded monthly on your year, compounded monthly on your investment. investment.

How much can you afford to pay for a How much can you afford to pay for a bond with a face value of $10,000 that bond with a face value of $10,000 that pays a coupon rate of 10% in quarterly pays a coupon rate of 10% in quarterly payments, and will mature in 20 years?payments, and will mature in 20 years?

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Problem 1Problem 1

P ?80 QUARTERS

DIAGRAM: $10,000

1 2 3 4 0

AB

GIVEN:FACE VALUE = $10,000COUPON RATE = 10% (APR) PAID QUARTERLYMATURITY = 20 YEARSDESIRED YIELD RATE = 12%/YR, CPD MONTHLY

FIND MAXIMUM MARKET PRICE TO BUY BOND:

Problem 1Problem 1

1. How much is quarterly interest rate, iB currently ?

P ?80 QUARTERS

DIAGRAM: $10,000

1 2 3 4 0

AB

QUARTERPER

CKri

rKCC

%5.2

14)1(

10.01

11

1.0 ;4 ;1

1

=

−⎟⎟⎠

⎞⎜⎜⎝

⎛+=

−⎟⎠⎞

⎜⎝⎛ +=

===

2. How much is quarterly interest amount, AB currently ?

AB = $10,000 (0.025)= $250 / QUARTER

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Problem 1Problem 1

3. How much is ieff for your expectation?P ?

80 QUARTERS

DIAGRAM: $10,000

1 2 3 4 0

$250

QUARTERPER

CKri

rKCC

%0301.3

14)3(

12.01

11

12.0 ;4 ;3

3

=

−⎟⎟⎠

⎞⎜⎜⎝

⎛+=

−⎟⎠⎞

⎜⎝⎛ +=

===

Problem 1Problem 1

4. How much are you willing to offer ?P

P ?80 QUARTERS

DIAGRAM: $10,000

1 2 3 4 0

$250

P = $250(P|A, 3.0301%, 80) + $10,000(P|F, 3.0301%, 80)

= $250(29.9635) + $10,000(0.0918)

= $7,491 + $918

= $8,409

NOTE: IF ieff ROUNDED OFF TO 3%/QUARTER, PRICE IS $8,490 !!!

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Problem 2Problem 2A $1000 face value bond will mature A $1000 face value bond will mature in 10 years. The annual rate of in 10 years. The annual rate of interest is 6% payable semiinterest is 6% payable semi--annually. annually.

If compounding is semiIf compounding is semi--annual and annual and the bond can be purchased for $870, the bond can be purchased for $870, what is the yield to maturity in terms what is the yield to maturity in terms of the effective annual rate earned?of the effective annual rate earned?

Problem 2Problem 2GIVEN:

FACE VALUE = $1,000COUPON RATE = 6% (APR) PAID SEMI-ANNUALLYMATURITY = 10 YEARSMARKET PRICE = $870

FIND YIELD TO MATURITY (ANNUAL EFFECTIVE RATE):

$87020 PERIODS

DIAGRAM: $1,000

1 2 3 4 0

AB

ia = ?

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Problem 2Problem 2

$87020 PERIODS

DIAGRAM: $1,000

1 2 3 4 0

AB

ia = ?

1. How much is semi-annual interest rate, iB currently ?

ANNUALLYSEMI

CKri

rKCC

−=

−⎟⎟⎠

⎞⎜⎜⎝

⎛+=

−⎟⎠⎞

⎜⎝⎛ +=

===

%3

12)1(

06.01

11

06.0 ;2 ;1

1

2. How much is semi-annual interest amount, AB currently ?

AB = $1,000 (0.03)= $30 SEMI-ANNUALLY

Problem 2Problem 2

3. How much is effective semi-annual interest rate, iEFF ?

$87020 PERIODS

DIAGRAM: $1,000

1 2 3 4 0

$30

ia= ?

$870 = $30(P|A, i, 20) + $1,000(P|F, i, 20)

TRY 3% = $30(14.8775) + $1000(0.5537)

= $1000TRY 4% = $30(13.5903) + $1,000(0.4564)

= $864

INTERPOLATE (OR APPROXIMATE) iEFF = 3.96%

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Problem 2Problem 2

2. How much is effective annual interest rate, ia ?

$87020 PERIODS

DIAGRAM: $1,000

1 2 3 4 0

$30

ia = ?

YEAR / %08.81]0396.01[ 2

=−+=Ai

(a) Yield to maturity:

per semiannual period

(b) Current yield:

per semiannual period

$996. $48. ( / , ,20) $1, ( / , ,20).

( . ) .

$48.$996.

.

25 13 0004 84%

1 0 0484 1 9 91%

1325

4 83%

2

= +=

= + − =

=

P A i P F ii

ia

YieldYield

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Investment Strategies

Trade-Off between Risk and RewardCash: the least risky with the lowest returnsDebt: moderately risky with moderate returnsEquities: the most risky but offering the greatest payoff

Broader diversification reduces riskBroader diversification increase expected return

Broader Diversification Increases Return

15%Mutual fund (stocks)$2,000

10%Corporate bond$2,000

5%Term deposit (CD)$2,000

0%Under the mattress$2,000

-100% (?)Buying lottery tickets$2,000

Expected ReturnInvestmentAmount

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$65,83815%Mutual fund (stocks)

$2,000

$96,280

$21.66910%Corporate bond$2,000

$6,7735%Term deposit (CD)$2,0002

$2,0000%Mattress$2,000

$0-100%Lottery tickets$2,000

$54,2747%Bond$10,0001

Value in 25 years

Expected Return

InvestmentAmountOption

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SummaryThe three basic investment objects are: growth, income, and liquidity.The two greatest risks investors face are inflation and market volatility.Diversification by combining assets with different patterns of return, it is possible to achieve a higher rate of return without increasing significant risk.Investing in stocks and bonds is one of the most common investment activities among the American investors.