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Bonds

- Type of debt or long-term promissory note, issued by a borrower, promising to its holder a predetermined and fixed amount of interest per year.

Types of Bonds

- Debentures
- Subordinated Debentures
- Mortgage Bonds
- Eurobonds
- Zero and Very Low Coupon Bonds
- Junk Bonds (High-Yield Bonds)

Debentures

- Any unsecured long-term debt
- Viewed as more risky than secured bonds and provide a higher yield than secured bonds

Subordinated Debenture

- Hierarchy of payout in case of insolvency
- The claims of subordinated debentures are honored only after the claims of secured debt and unsubordinated debentures have been satisfied.

Mortgage Bond

- A bond secured by a lien on real property
- Typically, the value of the real property is greater than that of the bonds issued.

Eurobonds

- Securities (bonds) issued in a country different from the one in whose currency the bond is denominated

Zero and Very Low Coupon Bonds

- Issued at a substantial discount from the $1,000 face value with a zero or very low coupon rate.
- Return comes from appreciation of the bond

Junk Bonds (High-Yield Bonds)

- High risk debt with ratings of BB or below by Moody’s and Standard & Poor’s
- High yield — typically pay 3%-5% more than AAA grade long-term bonds

Other types (features) of bonds

- Convertible bond – may be exchanged for common stock of the firm, at the holder’s option.
- Warrant – long-term option to buy a stated number of shares of common stock at a specified price.
- Putable bond – allows holder to sell the bond back to the company prior to maturity.
- Income bond – pays interest only when interest is earned by the firm.
- Indexed bond – interest rate paid is based upon the rate of inflation.

Terminology

- Claims on assets and income
- Par value
- Current yield
- Coupon interest rate
- Maturity
- Convertibility
- Call provision
- Indenture
- Bond ratings
- Sinking fund

Claims on Assets and Income

- In the case of insolvency, claims of debt, including bonds are honored before those of common or preferred stock.

Par Value

- Face value of the bond, returned to the bondholder at maturity
- In general, corporate bonds are issued at denominations of $1,000.
- Prices are represented as a % of face value.

Coupon Interest Rate

- The percentage of the par value of the bond that will be paid out annually in the form of interest.

Maturity

- The length of time until the bond issuer returns the par value to the bondholder and terminates or redeems the bond.

Convertibility

- May allow the investor to exchange the bond for a predetermined number of the firm’s shares of common stock

Call Provision

- A provision such that if the prevailing interest rate declines, the firm may want to pay off the bonds early and reissue at a more favorable interest rate.
- Issuer must pay the bondholders a premium
- There is also a call protection period where the firm cannot call the bond for a specified period of time.

Indenture

- The legal agreement between the firm issuing the bond and the trustee who represents the bondholders
- Provides for specific terms of the loan agreement

Bond Ratings

- Bonds are rated by the future risk potential of the bond-default risk
- The poorer the bond rating, the higher the rate of return demanded by the capital markets.

Favorable Factors affecting Bonds Rating

- A greater reliance on equity as opposed to debt in financing the firm
- Profitable operations
- Low variability in past earnings
- Large firm size
- Minimal use of subordinated debt

Bond Ratings

- AAA is the highest rating assigned by Standard & Poor’s
- AAA indicates a strong capacity to pay principal and interest

What is a sinking fund?

- Provision to pay off a loan over its life rather than all at maturity.
- Similar to amortization on a term loan.
- Reduces risk to investor, shortens average maturity.
- But not good for investors if rates decline after issuance.

Value

- Book value: value of an asset as shown on a firm’s balance sheet
- Liquidation value: the dollar sum that could be realized if an asset were sold individually and not as part of a going concern.
- Market value: the observed value for the asset in the marketplace
- Intrinsic or economic value: also called fair value—the present value of the asset’s expected future cash flows

Efficient Market

- The values of all securities at any instant fully reflect all available public information, which results in the market and the intrinsic value being the same.

Valuation: The Basic Process

- Assigning a value to an asset by calculating the present value of its expected future cash flows using the investor’s required rate of return as the discount rate.

Determinants of Value

- Amount and timing of the asset’s expected cash flows to be received by the
- Riskiness of the cash flows
- Investor’s required rate of return for undertaking the investment

Bond Valuation

- The value of a bond is a combination of:
- The amount and timing of the cash flows to be received by investors
- The time to maturity of the loan
- The investor’s required rate of return

VB

1,372

1,211

1,000

837

775

kd = 7%.

kd = 10%.

kd = 13%.

Years

to Maturity

30 25 20 15 10 5 0

The price path of a bond- What would happen to the value of this bond if its required rate of return remained at 10%, or at 13%, or at 7% until maturity?

Bond values over time

- At maturity, the value of any bond must equal its par value.
- If kd remains constant:
- The value of a premium bond would decrease over time, until it reached $1,000.
- The value of a discount bond would increase over time, until it reached $1,000.
- A value of a par bond stays at $1,000.

Yield to Maturity

- To measure the bondholder’s expected rate of return, we would find the discount rate that equates the present value of the future cash flows with the current market price of the bond.
- YTM and expected rate of return are used interchangeably when referring to bonds.

What is the YTM on a 10-year, 9% annual coupon, $1,000 par value bond, selling for $887?

- Must find the kd that solves this model.

Using a financial calculator to find YTM

- Solving for I/YR, the YTM of this bond is 10.91%. This bond sells at a discount, because YTM > coupon rate.

10

- 887

90

1000

INPUTS

N

I/YR

PV

PMT

FV

OUTPUT

10.91

Find YTM, if the bond price was $1,134.20.

- Solving for I/YR, the YTM of this bond is 7.08%. This bond sells at a premium, because YTM < coupon rate.

10

-1134.2

90

1000

INPUTS

N

I/YR

PV

PMT

FV

OUTPUT

7.08

Discount

- The market value of a bond will be below the par or face when the investor’s required rate is greater than the coupon interest rate. The bond will sell at a discount or below face value.

Premium

- The market value of a bond will be above the par or face value when the investor’s required rate is lower than the coupon interest rate. The bond will sell at a premium or above face value.

Bond Valuation: Three Important Relationships

- The value of a bond is inversely related to changes in the investor’s present required rate of return (the current interest rate).
- As interest rates increase(decrease), the value of the bond decreases(increases).

Bond Valuation : Three Important Relationships

- The market value of a bond will be less than the par value if the investor’s required rate of return is above the coupon interest rate, but it will be valued above par value if the investor’s required rate of return is below the coupon interest rate.

Bond Valuation : Three Important Relationships

- Long-term bonds have greater interest rate risk than do short-term bonds.

An example: Current and capital gains yield

- Find the current yield and the capital gains yield for a 10-year, 9% annual coupon bond that sells for $887, and has a face value of $1,000.

Current yield = $90 / $887

= 0.1015 = 10.15%

Calculating capital gains yield

YTM = Current yield + Capital gains yield

CGY = YTM – CY

= 10.91% - 10.15%

= 0.76%

Could also find the expected price one year from now and divide the change in price by the beginning price, which gives the same answer.

What is interest rate (or price) risk?

- Interest rate risk is the concern that rising kd will cause the value of a bond to fall.

% change 1 yr kd 10yr % change

+4.8% $1,0485%$1,386 +38.6%

$1,000 10% $1,000

-4.4% $95615%$749 -25.1%

The 10-year bond is more sensitive to interest rate changes, and hence has more interest rate risk.

What is reinvestment rate risk?

- Reinvestment rate risk is the concern that kd will fall, and future CFs will have to be reinvested at lower rates, hence reducing income.

EXAMPLE: Suppose you just won

$500,000 playing the lottery. You

intend to invest the money and

live off the interest.

Reinvestment rate risk example

- You may invest in either a 10-year bond or a series of ten 1-year bonds. Both 10-year and 1-year bonds currently yield 10%.
- If you choose the 1-year bond strategy:
- After Year 1, you receive $50,000 in income and have $500,000 to reinvest. But, if 1-year rates fall to 3%, your annual income would fall to $15,000.
- If you choose the 10-year bond strategy:
- You can lock in a 10% interest rate, and $50,000 annual income.

Conclusions about interest rate and reinvestment rate risk

- CONCLUSION: Nothing is riskless!

Semiannual bonds

- Multiply years by 2 : number of periods = 2n.
- Divide nominal rate by 2 : periodic rate (I/YR) = kd / 2.
- Divide annual coupon by 2 : PMT = ann cpn / 2.

2n

kd / 2

OK

cpn / 2

OK

INPUTS

N

I/YR

PV

PMT

FV

OUTPUT

What is the value of a 10-year, 10% semiannual coupon bond, if kd = 13%?

- Multiply years by 2 : N = 2 * 10 = 20.
- Divide nominal rate by 2 : I/YR = 13 / 2 = 6.5.
- Divide annual coupon by 2 : PMT = 100 / 2 = 50.

20

6.5

50

1000

INPUTS

N

I/YR

PV

PMT

FV

OUTPUT

- 834.72

Would you prefer to buy a 10-year, 10% annual coupon bond or a 10-year, 10% semiannual coupon bond, all else equal?

The semiannual bond’s effective rate is:

10.25% > 10% (the annual bond’s effective rate), so you would prefer the semiannual bond.

A 10-year, 10% semiannual coupon bond selling for $1,135.90 can be called in 4 years for $1,050, what is its yield to call (YTC)?

- The bond’s yield to maturity can be determined to be 8%. Solving for the YTC is identical to solving for YTM, except the time to call is used for N and the call premium is FV.

8

- 1135.90

50

1050

INPUTS

N

I/YR

PV

PMT

FV

OUTPUT

3.568

If you bought these callable bonds, would you be more likely to earn the YTM or YTC?

- The coupon rate = 10% compared to YTC = 7.137%. The firm could raise money by selling new bonds which pay 7.137%.
- Could replace bonds paying $100 per year with bonds paying only $71.37 per year.
- Investors should expect a call, and to earn the YTC of 7.137%, rather than the YTM of 8%.

When is a call more likely to occur?

- In general, if a bond sells at a premium, then (1) coupon > kd, so (2) a call is more likely.
- So, expect to earn:
- YTC on premium bonds.
- YTM on par & discount bonds.

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