WS4-10.11.2012

7/29/2019 WS4-10.11.2012

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Strategic Capital Group

Workshop #4: BondValuation

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Agenda

The Bond Market

Types of Bonds

Present Value and the Time-Value of Money

Valuing a Bond and its Cash Flows

Zero-Coupon Bonds

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Bonds

• Remember back to when we had the option of

issuing debt or equity to finance our T-shirt

company?

• Equity was sold to investors as stocks

• Debt was either issued in the form of bonds or

loans (the difference is bonds are publicly-

traded)

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Remembering bonds…

Each bond has a face-value, couponrate, and maturity date.

Face value is the amount of money

the issuer (typically a company or

government) will pay the personholding the bond at the specified

maturity date.

Coupon rate is essentially the interest

rate specified by the bond to be paid

out at regular intervals. Zero-coupon

means there are no interest payments

BOND

$1000 to be paid at maturity

Matures in 1 year on Jan 1

Pays out 2.5% of par value

semiannually

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Quick Check for Understanding

If I buy a $1000 face-value bond at par-value (for

$1000) that matures in exactly one year and I

can expect to receive two $25 over the course of

the bond’s life, what is the coupon rate?

a.) 5%

b.) 2.5%

c.) 62.78%

(2*25)/1000 = .05

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Being a Bond Trader

What are some ways traders/investors canmake money off bonds?

Buy bonds in large sets (typically in

increments of $10,000) and hold them to

maturity, picking up interest along the way.

There is another way… but first we need to

understand a bit more about buying bonds…

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The Effective Interest Rate

• Effective interest rate is essentially the going-

market rate for bonds of similar credit-

worthiness. We use the effective interest rate

as a discount rate for a bond we areconsidering buying, NOT THE COUPON RATE!

• The coupon rate is only used in computing

interest payments, NOT DISCOUNTING!

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Getting a desired Yield from a bond

saleConsider an investor that demands an 8% return on hisinvestments. This investor wants to purchase a $10, 000 bondissue from a company, but the coupon rate on the bonds areonly 7%.

In order to make 8% on the investment, the investor can pay less

for the bond than its face-value, effectively increasing the return

the investor will make.

10,000 Bond @ 7% for 1 year = $10,700 payout

If we were only to pay $9,900 for the bond issue, we would still

receive a total of $10,700 in payout, but we would “effectively” yield

800 dollars beyond what we paid for the investment, or 8%. This is

also referred to as “pricing to yield” an effective interest rate.

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Price, Yield, and Interest Rates

When market interest rates go up, it means investors can nowbuy bonds with higher interest rates.

MFST Bond

5% interest rate

MFST Bond

6% interest rate

Market interest

rates increase

First Bond

issue

Second

Bond issue

Since investors can now get

MFST bonds that yield 6%,

5% bonds need to reduce

their price to effectively

yield 6%.

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Price, Yield, and Interest Rates

So as interest rates increase, yields of new bond

issues increase.

As yields increase, bond price must decrease in

order to effectively yield the new interest rates.

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Bond Trading

Traders can buy bonds during times of high

interest rates when bonds are yielding a lot,

then sell them for more than they paid when

interest rates decrease and drive down yields.

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Types of BondsLess Risk

More Risk

Government-AKA “Treasuries”

-Least risky because governments are typically the most stable

institutions in the world

-Debt of developing countries is significantly more risky

Municipal

-AKA “Muni’s”

-City governments aren’t likely to go bankrupt often, but it can happen

-Free from government taxation

Corporate-Much more risk than government or municipal bonds, depending on

the company and its financial situation.

-Higher risk, but also higher returns (in the form of higher yields)

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Credit Ratings

Bonds and their issuing institutions are rated by

major credit agencies like S&P, Moody’s, and

Fitch to designate how likely the institution is to

pay the interest and principal back.

Investment Grade

Speculative

AAA and AA are

considered “risk-free”

investments

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An Introduction to Present Value

Would you rather have $100 today or $110dollars a year from now?

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We have a choice…

Today

$100

1-Year from Now

$110

What if there was a way to figure out how

much money in the future is worth in

today’s terms…

5% Interest

Rate

Future Value = Present Value(1+Interest Rate)^(Number of Years)

FV= PV*(1+i)^nFV= 100*(1+.05)^(1)

FV= $105

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How about now?

Today

$100

5-Years from Now

$105

FV=PV*(1+i)^nFV=100*(1+.0067)^(5)

FV=$103.39

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Going back to the future

We can also do the opposite of calculating future value. We can

discount a future value back to the

present value to make direct

comparisons:

FV = PV * (1 + i) ^ n

(1 + i) ^ n(1 + i) ^ n

FV

(1 + i) ^ n = PV

We also refer to this as the

“discount rate”

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The previous example:

Today

$100

5-Years from Now

$105

FV

(1 + i) ^ nPV =

105

(1 + .0067) ^ 5

PV =

PV = $101.55

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So…

A dollar today is worth more than a dollar in the

future because we can invest the dollar today

and get interest by the time the future comes

around. We refer to this as the time-value of

money .

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But Parker…

When will a stranger ever offer me the choice of having

$100 now or $105 later? What use do I have for this

stuff?

We use present value to find the value of

a bond, calculate terminal value and cash

flow value of a company in order to form

a DCF, and can use it to calculate internal

rate of return.

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Applying this to bonds

• You’re thinking about buying a bond at face-valuefor $10,000. Its coupon rate is 5%, maturity is in 3years and pays out interest every year. How muchshould you be willing to pay for this bond given

that the effective interest rate is 6%?

• We must use present value to find what interestpayments and the principal being returned in the

future is worth today• PV of bond = PV(interest payments) + PV(face-

value)

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Solving the problem

Value of the Bond = PV(Face-value) + PV(Interest)

500

(1 + .06) ^ 1PV(1st Interest) =

500

(1 + .06) ^ 3PV(3rd Payment) =

Why don’t we use 5%?

Because we care about

the market rate to

discount.

500

(1 + .06) ^ 2PV(2nd Payment) =

= 471.70

= 445.00

= 419.90

Note that the first interest

payment occurs at year =1, so we

discount by 1 year

$1336.60

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Solving the problem


10,000

(1 + .06) ^ 3PV(Face-value) = = $8396.19

Why is this 3?

Because we wont have the

principal of the bond returned to

us until the end of the 3rd year.$ 9732.79

PV(Interest Payments) = $1336.60

You should pay no more than

$9732.79 for this bond.

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Zero-Coupon Bonds

• Sometimes bonds do not pay interest, why

would investors be interested in this kind of

investment?

• Remember, bonds can be sold for less than

their face-value when first auctioned off. If the

PV of the face-value is greater than what you

paid for the bond, you will make money

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Buying a Zero-Coupon Bond

Face-Value: $10,000

Coupon Rate: 0%

Maturity: 3 years

Credit Rating: AA

AAA: Average 5% Interest Rate

AA: Average 7% interest Rate

A: Average 9% Interest Rate

BBB: Average 12% Interest Rate

What is the most you would be willing to

pay for this investment?

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Solving the problem


What is the PV of the interest payments?

What is the interest payment?

There is no interest on a zero-coupon bond!

We just want to calculate the PV of the face-

value

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Solving the problem


10,000

(1 + .07) ^ 3PV(Face-value) = = $8162.98

$ 8162.98

PV(Interest Payments) = $0

You should pay no more than

$8162.98 for this bond.

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Say we are approached by a bank…

Bank of America approaches you to be a potential debt-holder.

They offer you ten $10,000 zero-coupon bond to be repaid in 5

years for $85,000. After doing your research you determine that

you would only be willing to take this investment risk if it

yielded 8%. Should you take the deal?

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Solving the problem by calculating

future value…

= 85,000 * (1 + .08) ^ 5Future Value of

your investment = $124,892.89

We can invest 85,000 at 8% and make

turn it into $125,000 in 5 years, so we

should not take the bonds.

WS4-10.11.2012

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