Lecture 10

ENGR 390 Lecture 10 Bonds

Winter 2007

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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ENGR 390 Lecture 10 Bonds

Winter 2007

Investing in Bond † Bonds: Loans that

investors make to corporations and governments. † Face (par) value: Principal amount † Coupon rate: yearly interest payment † Maturity: the length of the loan

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

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ENGR 390 Lecture 10 Bonds

Winter 2007

No meaning, Spacing

Coupon rate

Maturity date 2005

AT&T 7s05 Closing price: 108 1/ 4 $1,082.50 Market price

Bond Price Notation Used in Financial Markets Corporate Bonds

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Treasury Bonds

1/8=$1.25

5/8=$6.25

1/32=$0.3125 2/32=$0.6250 3/32=$0.9375 4/32=$1.25

17/32=$5.3125 18/32=$5.6250 19/32=$5.9375 20/32=$6.25

1/4=$2.50

3/4=$7.50

6/32=$1.5625 7/32=$1.8750 7/32=$2.1875 8/32=$2.50

21/32=$6.5625 22/32=$6.8750 23/32=$7.1875 24/32=$7.50

3/8=$3.75

7/8=$8.75

9/32=$2.8125 10/32=$3.1250 11/32=$3.4375 12/32=$3.75

25/32=$7.8125 26/32=$8.1250 27/32=$8.4375 28/32=$8.75

1/2=$5.00

1=$10

13/32=$4.0625 14/32=$4.375 15/32=$4.6875 16/32=$5.00

29/32=$9.0625 30/32=$9.3750 31/32=$9.6875 32/32=$10

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ENGR 390 Lecture 10 Bonds

Winter 2007

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 Maturity (2005)

AT&T 7s05

Trading volume

6.5% 5 million 108 1/4

Coupon rate of 7% Current yield $70/108.25 = 6.47%

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Closing Market price $1,082.50

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ENGR 390 Lecture 10 Bonds

Winter 2007

BOND TERMINOLOGY 1. 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 Payments 4. Maturity Date – Date at which you receive the face value 5. 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 1 You desire to make an investment in bonds provided you can earn 12% per year, compounded monthly on your investment. How much can you afford to pay for a bond with a face value of $10,000 that pays a coupon rate of 10% in quarterly payments, and will mature in 20 years?

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ENGR 390 Lecture 10 Bonds

Winter 2007

Problem 1 GIVEN: FACE VALUE = $10,000 COUPON RATE = 10% (APR) PAID QUARTERLY MATURITY = 20 YEARS DESIRED YIELD RATE = 12%/YR, CPD MONTHLY FIND MAXIMUM MARKET PRICE TO BUY BOND:

DIAGRAM:

$10,000 AB 0

1 2 3 4 P?

80 QUARTERS

Problem 1 DIAGRAM:

$10,000 AB 0

1 2 3 4 P?

80 QUARTERS

1. How much is quarterly interest rate, iB currently ? C = 1; K = 4; r = 0.1 C

r ⎞ ⎛ i = ⎜1 + ⎟ −1 ⎝ CK ⎠ 1

⎛ 0.10 ⎞ ⎟ −1 = ⎜⎜1 + (1)4 ⎟⎠ ⎝ = 2.5% PER QUARTER

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

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

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ENGR 390 Lecture 10 Bonds

Winter 2007

Problem 1 DIAGRAM:

$10,000 $250 0

1 2 3 4 P?

80 QUARTERS

3. How much is ieff for your expectation? C = 3; K = 4; r = 0.12 C

r ⎞ ⎛ i = ⎜1 + ⎟ −1 ⎝ CK ⎠ 3

⎛ 0.12 ⎞ ⎟⎟ − 1 = ⎜⎜1 + ⎝ (3)4 ⎠ = 3.0301% PER QUARTER

Problem 1 DIAGRAM:

$10,000 $250 0

1 2 3 4 P?

80 QUARTERS

4. How much are you willing to offer ? P 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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ENGR 390 Lecture 10 Bonds

Winter 2007

Problem 2 A $1000 face value bond will mature in 10 years. The annual rate of interest is 6% payable semi-annually. If compounding is semi-annual and the bond can be purchased for $870, what is the yield to maturity in terms of the effective annual rate earned?

Problem 2 GIVEN: FACE VALUE = $1,000 COUPON RATE = 6% (APR) PAID SEMI-ANNUALLY MATURITY = 10 YEARS MARKET PRICE = $870 FIND YIELD TO MATURITY (ANNUAL EFFECTIVE RATE):

DIAGRAM:

$1,000 AB 0

1 2 3 4 $870

20 PERIODS ia = ?

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ENGR 390 Lecture 10 Bonds

Winter 2007

Problem 2

DIAGRAM:

$1,000 AB

0

1 2 3 4 $870

20 PERIODS ia = ?

1. How much is semi-annual interest rate, iB currently ? C = 1; K = 2; r = 0.06 C

r ⎞ ⎛ i = ⎜1 + ⎟ −1 ⎝ CK ⎠

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

1

⎛ 0.06 ⎞ ⎟ −1 = ⎜⎜1 + (1)2 ⎟⎠ ⎝ = 3% SEMI − ANNUALLY

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

Problem 2

DIAGRAM:

$1,000 $30

0

1 2 3 4 $870

20 PERIODS ia= ?

3. How much is effective semi-annual interest rate, iEFF ? $870 = $30(P|A, i, 20) + $1,000(P|F, i, 20) TRY 3% = $30(14.8775) + $1000(0.5537) = $1000 TRY 4% = $30(13.5903) + $1,000(0.4564) = $864 INTERPOLATE (OR APPROXIMATE) iEFF = 3.96%

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ENGR 390 Lecture 10 Bonds

Winter 2007

Problem 2 DIAGRAM:

$1,000 $30 0

1 2 3 4 $870

20 PERIODS ia = ?

2. How much is effective annual interest rate, ia ? iA = [1 + 0 .0396 ]2 − 1 = 8 .08 % / YEAR

Yield

(a) Yield to maturity: $996.25 = $48.13( P / A, i,20) + $1,000 ( P / F , i,20) i = 4.84% per semiannual period ia = (1 + 0.0484 ) 2 − 1 = 9.91% (b) Current yield: $48.13 = 4.83% per semiannual period $996.25

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ENGR 390 Lecture 10 Bonds

Winter 2007

Investment Strategies † Trade-Off between Risk and Reward „ Cash: the least risky with the lowest returns „ Debt: moderately risky with moderate returns „ Equities: the most risky but offering the greatest payoff † Broader diversification reduces risk † Broader diversification increase expected

return

Broader Diversification Increases Return

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Amount

Investment

Expected Return

$2,000

Buying lottery tickets

$2,000

Under the mattress

0%

$2,000

Term deposit (CD)

5%

$2,000

Corporate bond

10%

$2,000

Mutual fund (stocks)

15%

-100% (?)

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ENGR 390 Lecture 10 Bonds

Winter 2007

Option

Amount

1 1

$10,000

Bond

$2,000

Lottery tickets

$2,000

Mattress

0%

$2,000

$2,000

Term deposit (CD)

5%

$6,773

$2,000

Corporate bond

10%

$21.669

$2,000

Mutual fund (stocks)

15%

$65,838

2

Investment

Expected Return 7% -100%

Value in 25 years $54,274 $0

$96,280

Summary † The 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.

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