Strategic Capital Group Workshop #4: Bond Valuation

AgendaThe Bond Market

Types of Bonds

Present Value and the Time-Value of Money

Valuing a Bond and its Cash Flows

Zero-Coupon Bonds

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)

Remembering bonds…Each bond has a face-value, coupon rate, and maturity date.

Face value is the amount of money the issuer (typically a company or government) will pay the person holding 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 maturityMatures in 1 year on Jan 1Pays out 2.5% of par value

semiannually

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

Being a Bond TraderWhat are some ways traders/investors can make 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…

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 are considering buying, NOT THE COUPON RATE!

• The coupon rate is only used in computing interest payments, NOT DISCOUNTING!

Getting a desired Yield from a bond sale

Consider an investor that demands an 8% return on his investments. This investor wants to purchase a $10, 000 bond issue from a company, but the coupon rate on the bonds are only 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.

Price, Yield, and Interest RatesWhen market interest rates go up, it means investors can now

buy bonds with higher interest rates.

MFST Bond5% interest rate

MFST Bond6% 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%.

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.

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.

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)

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

An Introduction to Present Value

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

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

How about now?

Today

$100

5-Years from Now

$105

FV=PV*(1+i)^nFV=100*(1+.0067)^(5)FV=$103.39

Going back to the futureWe 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”

The previous example:

Today

$100

5-Years from Now

$105

FV

(1 + i) ^ nPV =

105

(1 + .0067) ^ 5PV =

PV = $101.55

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.

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.

Applying this to bonds

• You’re thinking about buying a bond at face-value for $10,000. Its coupon rate is 5%, maturity is in 3 years and pays out interest every year. How much should you be willing to pay for this bond given that the effective interest rate is 6%?

• We must use present value to find what interest payments and the principal being returned in the future is worth today

• PV of bond = PV(interest payments) + PV(face-value)

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

Solving the problem

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

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.

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

Buying a Zero-Coupon BondFace-Value: $10,000Coupon Rate: 0%Maturity: 3 yearsCredit Rating: AA

AAA: Average 5% Interest RateAA: Average 7% interest RateA: Average 9% Interest RateBBB: Average 12% Interest Rate

What is the most you would be willing to pay for this investment?

Solving the problem

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

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

Solving the problem

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

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.

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?

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.