Section 9: Bonds (Details)Concepts you’ll learn

1. Absolute Priority2. Treasuries3. Municipal Bond4. Corporate Bond5. Coupon6. Zero Coupon Bond7. Par Value (aka Face Value)8. Discount Bond9. Premium Bond10. Maturity Date11. Current Yield12. Yield to Maturity13. Required Yield14. Bond Rating15. Bond Ladder16. Callable Bond

Problems you’ll solve– Understand how bonds are issued and paid back– Understand how to evaluate bonds as potential investments– Understand the relationship between interest rates and bond

market prices– Calculate appropriate bond pricing given market interest rates

©2014 D. M. Kaufman. All rights reserved

Bonds – Definitions• Absolute Priority: A rule that stipulates the order of payment -

creditors before shareholders - in the event of liquidation. The absolute priority rule is used in bankruptcies to decide what portion of payment will be received by which participants. Debts to creditors will be paid first and shareholders (partial owners) divide what remains.

• Treasuries: A marketable U.S. debt security.• Municipal Bond: A debt security issued by a state, municipality or county

to finance its capital expenditures. Municipal bonds are exempt from federal taxes and from most state and local taxes, especially if you live in the state in which the bond is issued.

• Corporate Bond: A debt security issued by a corporation.• Coupon: The interest rate stated on a bond when it's issued. The coupon is

typically paid semiannually. (Ha! You know what this means, don’t you? When you set up your financial calculator for bond valuation problems, you need to set it for 2 P/YR.)

• Zero Coupon Bond: A debt security that doesn't pay interest (a coupon) but is traded at a deep discount, rendering profit at maturity when the bond is redeemed for its full face value.

• Par Value: The face value of a bond. • Discount Bond: A bond that is issued for less than its par (or face) value,

or a bond currently trading for less than its par value in the secondary market (typically because prevailing interest rates are higher then the bond coupon).

• Premium Bond: A bond that is priced higher than its par value – typically because prevailing interest rates are lower than the bond coupon.

• Maturity Date: The date on which the principal amount of a debt instrument becomes due and is repaid to the investor and interest payments stop.

Bonds – Definitions (cont.)• Current Yield: The annual coupon payout divided by the bond’s current market

price. • Yield to Maturity: The rate of return anticipated on a bond if it is held until the

maturity date. YTM is considered a long-term bond yield expressed as an annual rate. The calculation of YTM takes into account the current market price, par value, coupon interest rate and time to maturity. It is also assumed that all coupons are reinvested at the same rate. Sometimes this is simply referred to as "yield" for short, but its calculation involves a lot of assumption and trial-and-error.

• Required Yield: The return a bond must offer in order to be a worthwhile investment. Required yield is set by the market and sets the precedent for how current bond issues will be priced.

• Bond Rating: A grade given to bonds that indicates their credit quality. Private independent rating services such as Standard & Poor's, Moody's and Fitch provide these evaluations of a bond issuer's financial strength, or its the ability to pay a bond's principal and interest in a timely fashion.

• Bond Ladder: A strategy for managing fixed-income investments by which the investor builds a ladder by dividing his or her investment dollars evenly among bonds that mature at regular intervals simultaneously (for example, every six months, once a year or every two years). The advantages to this strategy are 1) increased liquidity, 2) improved risk management, and 3) sometimes, having a mix of short and long term interest rates in a bond portfolio.

• Callable Bond: A bond that can be redeemed by the issuer prior to its maturity. Usually a premium is paid to the bond owner when the bond is called. Typically a bond is called if interest rates fall too far below the bond’s coupon rate – the issuer simply buys the bond back early and issues a new one with the lower prevailing interest rate, much like a consumer might refinance a mortgage or other personal debt.

In a Nutshell – How Bonds Work

• Most bonds are initially purchased at par value, and pay regular interest every 6 months until the bond matures, at which time the par value amount is returned.

• Callable bonds are similar, but they allow the issuer to repay the bond before maturity. Callable bonds will sometimes pay a higher interest rate than a non-callable bond

• Zero-coupon bonds offer a deep discount and pay accumulated interest at maturity – no regular interest payments are made.

Most Bonds

Callable Bonds

Zero Coupon Bonds

Notice: this is very different from those amortized loans that you and I have to borrow. Under this scheme, the payments are smaller or non-existent. The bulk of the money is paid at the end of the loan with

cheaper (inflation adjusted) dollars.

Who Issues Bonds?Government entities and corporations issue bonds to raise money for their endeavors. There are five major types of bonds in the U.S. market, representing the five major issuers:

Bond Type Description

Government (Treasury) The U.S. Treasury issues bonds to pay for government activities and pay off the national debt.Yield is lowest among bonds, but considered low in risk if held until maturity. Bonds are exempt from

state and local taxes.

Agency (GSE) U.S. Government agencies (also called Government Sponsored Enterprises) issue bonds to support their

mandates, typically to ensure that various constituencies, like farmers, students, and homeowners, have

access to sufficient credit at affordable rates. Examples include Fannie Mae, Freddie Mac, and TVA.

The yield is slightly higher than government bonds and still very low risk. Some agency bonds like Fannie

Mae and Freddie Mac are taxable. Others are exempt from state and local taxes.

Municipal States, cities, counties, and towns issue bonds to pay for public projects (roads, etc.) and finance other

activities.

The majority of munis are exempt from federal, state, and local taxes. This can raise the effective yield of

munis above other types of bonds, depending on your tax bracket. Of course, to offset this benefit, the

coupon rate of most municipals is less than that of similarly rated taxable bonds.

Corporate Corporations issue bonds to expand, modernize, cover expenses, and finance other activities.

The yield and risk are generally higher than government and municipals. Rating agencies help you assess

the credit risk. Corporate bonds are fully taxable. Rating agencies help investors assess the credit risk.

Mortgage-backed Banks and other lending institutions pool mortgages and offer them as a security to investors. This raises money so the institutions can offer more mortgages. Examples include Ginnie Mae, Fannie Mae, and Freddie Mac.

Mortgage-backed bonds have a yield that typically exceeds high-grade corporate bonds with comparable

maturity, and have a low credit risk. The major risk of these bonds is if lenders repay their mortgages early

(for example, if interest rates drop), which can result in lower interest payments to the investor. Mortgage-

backed bonds are fully taxable.

Once bonds are purchased from these primary issuers, they can be re-sold on the secondary market

Bond Ratings

Bond Rating Grade Risk

Moody's S&P/ Fitch

Aaa AAA InvestmentHighest Quality

Aa AA Investment High Quality

A A Investment Strong

Baa BBB InvestmentMedium Grade

Ba, B BB, B Junk Speculative

Caa/Ca/C CCC/CC/C JunkHighly Speculative

C D Junk In Default

Again, investors are rewarded for risk. The lower the bond rating, the less creditworthy the bond issuer is thought to be, and the higher the interest

rate (coupon) on the bonds issued.

Bond Basics – Current Yield Calculation

• The formula for current yield is:

• So, say you’re offered a bond, with a $10,000 par value and a 6% coupon, at a price of $9,500. What’s the current yield?– First, find the annual cash inflows (i.e. the annual income from holding the

bond).• 10,000*.06 = $600

– Next, divide through by the market price.• 600 / 9,500 = .063 or 6.3%

– Note: because the yield is higher than the coupon rate, and because the market price of the bond is less than par value, we can assume that prevailing interest rates have increased since the bond was issued.

– Why? Because as prevailing interest rates go up, the required yield associated with existing bonds goes up as well. If you can acquire a newly issued bond at a higher interest rate than an existing bond’s coupon rate, you’ll demand a discount on the market price before buying the existing bond. And, since the coupon rate stays fixed, lowering the price you pay for the bond increases your yield, or the return on your investment.

The most basic truism of bond pricing is: the market prices for existing bonds will move in the opposite direction vs. prevailing interest rates.

Not As Basic – Calculating Bond Prices

• So, now let’s say there’s a bond with a $10,000 par value, a ten year maturity, and a 6% coupon. Interest rates have fallen to 5%. Coupon payments are made semi-annually and the next coupon payment is expected in six months.

• What should you be willing to pay for the bond?• As an experiment, do the following calculation:

– Set your calculator up for 2 P/YR.– FV = 10,000, since this is what you’ll collect at maturity– PMT = 300, since 10,000*.06 = 600, and dividing into 2 payments per year = 300.– I/YR = 6– Life = 10 shift N– Solve for PV. You should get -10,000. Perfect! You’ve confirmed that as long as prevailing interest

rates = the coupon rate, the FV and the PV remain mirror images of each other.• Don’t hit clear!• Now, you need to solve for what the PV should be when prevailing interest

rates diverge from the coupon rate. The prevailing interest rate is your required yield (in this case, 5%)

– So, change I/YR to 5%– Solve for PV again. Aha. The PV went up to $10,779.46. That’s the price you should be willing to

pay, assuming, of course, that you expect prevailing interest rates to remain a point below the coupon rate for the next ten years.

• Want to see the “by hand” formula for this? No? Well, here it is anyway:

• Be thankful for your calculators.

C = coupon payment n = number of payments i = interest rate, or required yield M = value at maturity, or par value

Pricing Zero Coupon Bonds

• Now, suppose you’re looking at a zero coupon bond with a $10,000 par value, a ten year maturity, and no coupon. Your required yield is 5%. What should you be willing to pay for the bond?– Most of this problem is the same as the previous one. The key

difference is that no interest payments are being made – the bond’s par value will be paid to you in ten years, and that’s it. So:• FV = 10,000• PMT = 0• I/YR = 5%• Life = 10 shift N• Solve for PV. You should get $6,102.71.

– Notice how steep the discount is now that you can no longer count on those semi-annual payments.

Section 9: Practice Problems

1. True or False?– If a corporation goes bankrupt, its bond holders will be reimbursed

before its stockholders.– Junk bonds are a good way to reduce risk in your asset portfolio.– Bond prices tend to move in the same direction as interest rates.

2. What is the current yield of a bond with a par value of $1,000 and a coupon rate of 8% if the market price is $900?

3. Calculate the price of a bond with a par value of $1,000 to be paid in ten years, a coupon rate of 10%, and a required yield of 12%. Coupon payments are made semi-annually and the next coupon payment is expected in six months.

4. Calculate the price of a zero coupon bond that is maturing in five years, has a par value of $1,000 and a required yield of 6%.