Interest Rates and Bond Valuation

•Which bonds will have the higher coupon, all else equal?

-Secured debt versus a debenture debenture -Subordinated debenture versus senior debt subordinated debenture -A bond with a sinking fund versus one without one without -A callable bond versus a non-callable bond callable bond

Zero Coupon Bonds

Make no periodic interest payments (coupon rate = 0%) The entire yield-to-maturity comes from the difference between the purchase price and the par value cannot sell for more than par value Treasury Bills and principal-only Treasury strips are good examples of zeroes

Debt vs Equity Equity

Ownership interest Common stockholders vote for the board of directors and other issues Dividends are not considered a cost of doing business and are not tax deductible Dividends are not a liability of the firm, and stockholders have no legal recourse if dividends are not paid An all equity firm can not go bankrupt merely due to debt since it has no debt

A sinking fund

a fund containing money set aside or saved to pay off a debt or bond a sinking fund helps to soften the hardship of a large outlay of revenue a sinking fund is established so the company can contribute to the fund in the years leading up to the bond's maturity

call provision

a stipulation on the contract for a bond-- or other fixed-income instruments--that allows the issuer (borrowers) to repurchase and retire the debt security

Current yield

annual coupon/price

Real rate of interest

change in purchasing power

Yield to Maturity

current yield + capital gains yield EX: •Example: 10% coupon bond, with semiannual coupons, face value of 1,000, 20 years to maturity, $1,197.93 price -Current yield = 100 / 1,197.93 = .0835 = 8.35% -Price in one year, assuming no change in YTM = 1,193.68 -Capital gain yield = (1,193.68 - 1,197.93) / 1,197.93 = -.0035 = -.35% -YTM = 8.35 - .35 = 8%, which is the same YTM computed earlier

factors that affect bond yields

default risk premium - remember bond ratings Taxability premium - remember municipal vs taxable liquidity premium - bonds that have more frequent trading will generally have lower required returns Anything else that affects the risk of the cash flows to the bondholders will affect the required returns

Price Risk

Change in price due to changes in interest rates Long-term bonds have more price risk than short-term bonds Low coupon rate bonds have more price risk than high coupon rate bonds

Bond indenture

Contract between the company and the bondholders that includes: - The basic terms of the bonds - The total amount of bonds issued - A description of property used as security, if applicable - Sinking fund provisions - Call provisions - Details of protective covenants

Debt vs equity Debt

Not an ownership interest Creditors do not have voting rights Interest is tax deductible Creditors have legal recourse if interest or principal payments are missed Excess debt can lead to financial distress and bankruptcy

debentures

unsecured bonds backed only by the credit worthiness of the bond issuer

notes

unsecured debt with original maturity less than 10 years

Collateral

secured by financial securities

Mortgage

secured by real property, normally land or buildings

Normal yield curve

upward-sloping; long-term yields are higher than short-term yields

Maturity Date

the date on which the principal amount of a note, draft, acceptance bond or other debt instrument becomes due

Coupon rate

the rate of interest paid by bond issuers on the bond's face value. It is the periodic rate of interest paid by bond issuers to its purchasers.

Yield

the return to an investor from the bond's coupon and maturity cash flows.

Bond

A bond is a fixed income instrument that represents a loan made by an investor to a borrower (typically corporate or governmental). A bond could be thought of as an I.O.U. between the lender and borrower that includes the details of the loan and its payments.

protective covenant

A part of an indenture or loan agreement that limits certain actions a company may take during the term of the loan to protect the lender's interests.

Present Value of Cash Flows as Rates Change

As interest rates increase, present values decrease so, as interest rates increase, bond prices decrease and vice versa

Bond Pricing Theorems

Bonds of similar risk (and maturity) will be priced to yield about the same return, regardless of the coupon rate If you know the price of one bond, you can estimate its YTM and use that to find the price of the second bond This is a useful concept that can be transferred to valuing assets other than bonds

Floating-Rate Bonds

Coupon rate floats depending on some index value Examples: - adjustable rate mortgages and inflation-linked Treasuries There is less price risk with floating rate bonds - The coupon floats, so it is less likely to differ substantially from the yield-to-maturity Coupons may have a "collar" - the rate cannot go above a specified "ceiling" or below a specified "floor"

Government bonds: Municipal Securities

Debt of state and local governments Varying degrees of default risk, rated similar to corporate debt Interest received is tax-exempt at the federal level

Government bonds: Treasury Securities

Federal government debt T-bills- pure discount bonds with original maturity of one year or less T-notes - coupon debt with original maturity between one and ten years T-bonds - coupon debt with original maturity greater than ten years

Bond Prices: Relationship Between Coupon and Yield

If YTM = coupon rate, then par value = bond price if YTM > coupon rate, then par value > bond price - The discount provides yield above coupon rate - Price below par value, called discount bond if YTM < coupon rate, then par value < bond price - Higher coupon rate causes value above par - Price above par value, called a premium bond

Term Structure of Interest Rates

Term structure is the relationship between time to maturity and yields, all else equal

Par value (face value)

The par value of a bond also called the face amount or face value is the value written on the front of the bond. This is the amount of money that bond issuers promise to be repaid bondholders at a future date. For instance, a company might issue $500, 15-year bonds to the public. The par value of these bonds is $500. In other words, the company promises to pay the public back $500 15 years from the bond issuance.

Seniority

The person with the most seniority gets paid off first Seniority is defined contractually in the nome on the bond, nothing to do with time

Reinvestment Rate Risk

Uncertainty concerning rates at which cash flows can be reinvested Short-term bonds have more reinvestment rate risk than long-term bonds High coupon rate bonds have more reinvestment rate risk than lower coupon rate bonds Reinvestment risk refers to the possibility that an investor will be unable to reinvest cash flows (e.g., coupon payments) at a rate comparable to their current rate of return.

Computing Yield to Maturity

Yield to Maturity is the rate implied by the current bond price

Registered bonds

a debt instrument whose bondholder's information is kept on record with the issuing party By archiving the owner's name, address, and other details, issuers ensure they're making the bond's coupon payments to the correct person

Bearer forms

a fixed-income security that is owned by the holder, or bearer, rather than by a registered owner. The coupons for the interest payments are physically attached to the security The bondholder is required to submit the coupons to the bank for payment and then redeem the physical certificate when the bond reaches the maturity date

Inverted yield curve

downward-sloping; long-term yields are lower than short-term yields

Yield curve

graphical representation of the term structure

ex ante nominal rate of interest

includes our desired real rate of return plus an adjustment for expected inflation

Nominal rate of interest

quoted rate of interest, change in the actual number of dollars