Fin323 Interest Rate And Bond Valuation

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interest rate

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compensation paid by borrower of funds to the lender; from the borrower's point of view, the cost of borrowing funds.

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required return

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cost of funds obtained by selling an ownership interest; it reflects the funds supplier's level of expected return. the money a person gets from selling bonds.

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Federal Reserve System

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The Board of Governors of the Federal Reserve System regularly asses economic conditions and,
when necessary, initiate actions to change interest rates to control inflation and economic
growth.

they set interest rates to alter the economy

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real interest rate

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the rate that creates an equilibrium between the supply of savings and
the demand for investment funds in a perfect world.
• In this context, a perfect world is one in which there is no inflation, where suppliers and
demanders have no liquidity preference, and where all outcomes are certain.

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supply-demand for funds

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cheaper interest...more deman.

the lower the interest rate, the greater the funds flow and vice versa

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risk-free rate of interest

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RF, which is typically measured by a 3-month U.S. Treasury bill (Tbill)
compensates investors only for the real rate of return and for the expected rate of
inflation.

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nominal rate of interest

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is the actual rate of interest charged by the supplier of funds and
paid by the demander.

nominal rate differs from the real rate of interest, k* as a result of two factors:
• Inflationary expectations reflected in an inflation premium (IP), and
• Issuer and issue characteristics such as default risks and contractual provisions as
reflected in a risk premium (RP).

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term structure of interest rates

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the relationship btw the interest rate or rate of return and the time to maturity

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yield to maturity

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annual rate of return earned on a debt security purchased on a given day and held to maturity.

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yield curve

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shows the yeild to maturity for debts of equal quality and different maturities; it is a graphical depiction of the term structure of interest rates.

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inverted yield curves

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a downward-sloping yield curve that indicates generally cheaper long-term borrowing costs than short-term borrowing costs.

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normal yield curve

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an upward-sloping yield curve that indicates generally cheaper short-term borrowing costs than long-term borrowing costs

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flat yield curves

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a yield curve that reflects relatively similar borrowing costs for both short- and longer-term loans

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Theories of Term Structure: Expectations Theory

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• This theory suggest that the shape of the yield curve reflects investors expectations about the
future direction of inflation and interest rates.
• Therefore, an upward-sloping yield curve reflects expectations of higher future inflation and
interest rates.
• In general, the very strong relationship between inflation and interest rates supports this
theory.

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Theories of Term Structure: Liquidity Preference Theory

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This theory contends that long term interest rates tend to be higher than short term rates for
two reasons:
– long-term securities are perceived to be riskier than short-term securities
– borrowers are generally willing to pay more for long-term funds because they can lock
in at a rate for a longer period of time and avoid the need to roll over the debt.

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Theories of Term Structure: Market Segmentation Theory

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equilibrium btw suppliers and demanders of short-term funds, such as seasonal business loans, would determine prevailing short-term interest rates.

market for loans is segmented on the basis of maturity and that the supply of and demand for loans within each segment determine its prevailing interest rate

low rates in short-term segment and high rates in long-term segment cause the yield curve to be upward-sloping.

it depends...if it's a short term (seasonal) or long term (real estate)

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three theories of term structure

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1. inflationary expectataion
2. liquidity preferences
3. comparative equilibrium of supply and demand in short and long term market segment.

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risk premium

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amount by which the interest rate or required return on a security exceeds the risk-free rate of interest Rf; it varies with specific issuer and issue characteristics

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default risk

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possiblity that issuerer of debt will not pay contractual interest or principal as schedualed.

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maturity risk

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the longer the maturity, the more value of a security will change in response to a given change in interest rates.

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contractual provision risk

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conditions that are often includes in a debt agreement or a stock issue

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corporate bond

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a long-term debt instrument indicating that a corporation has borrowed a certain amount of money and promises to repay it in the future under clearly defined terms.

par value = face value of the bond. usually $1000

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coupon interest rate

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percentage of a bond's par value that will be paid annually, typically in two equal semicannual payments, as interest.

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bond indenture

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a legal doc. that specifies both the rights of the bondholders and the duties of the issuing corporation.

included in indenture are: amount, timing of all interest, principal payments, standard and restrictive provisions, frequently, sinking-fund requirements and security interest provisions

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standard debt provisions

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specify certain record-keeping and general business practices that the bond issuer must follow...is in the bond indenture

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Restrictive debt provisions

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are contractual clauses in a bond indenture that place operating and
financial constraints on the borrower.
• Common restrictive covenants include provisions that specify:
• Minimum equity levels
• Prohibition against factoring receivables
• Fixed asset restrictions
• Constraints on subsequent borrowing
• Limitations on cash dividends.
• In general, violations of restrictive covenants give bondholders the right to demand immediate
repayment.

without them, borrower could increase the firm's risk but not have to pay increased interest to compenstate for the increased risk

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sinking-fund requirement

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a restrictive provision often included in a bond indenture, providing for the systematic retirement of bonds prior to their maturity

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trustee

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a thrid party to a bond indenture...they are the watchdog on behalf of the bondholders

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Corporate Bonds: Cost of Bonds to the Issuer

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In general, the longer the bond’s maturity, the higher the interest rate (or cost) to the firm.
• In addition, the larger the size of the offering, the lower will be the cost (in % terms) of the
bond.
• Also, the greater the risk of the issuing firm, the higher the cost of the issue.
• Finally, the cost of money in the capital market is the basis form determining a bond’s coupon
interest rate.

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conversion feature of convertible bonds

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allows bondholders to exchange their bonds for a
specified number of shares of common stock.

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call feature

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in nearly all bonds, gives issuer the opportunity to repurchase bonds prior to maturity.

issuers will exercise the call feature when interest rates fall and the issuer can
refund the issue at a lower cost.

Issuers typically must pay a higher rate to investors for the call feature compared to issues
without the feature.

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call price

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stated price at which a bond may be repurchased, by use of a call feature, prior to maturity

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call premium

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amount by which a bond's call price exceeds it's par value

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stock purchase warrants

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Warrants give the bondholder the right to purchase a certain number of shares of the same
firm’s common stock at a specified price during a specified period of time.
• Including warrants typically allows the firm to raise debt capital at a lower cost than would be
possible in their absence.

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Bond Yields

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A bond’s yield or rate of return is frequently used to assess its performance over a given period,
typically 1 year

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bond rating

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high-quality (high-rated) bonds provide lower returns than lower-quality (low-rated) bonds. this reflects lender's risk-return trade-off

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bond type:

debentures

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unsecured bond that only creditworthy firms can issue. convertible bonds are normally debentures

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bond type:

subordinated debentures

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unsecured bond. claims are not satisfied until those of the creditors holding certain (senior) debts have been fully satisfied.

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bond type:

income bonds

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payment of interest is required only when earnings are available. commonly issued in reorganization of a failing firm. unsecured bond

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bond type:

mortgage bonds

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secrued by real estate or buildings

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bond type:

collateral trust bonds

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secured by stock and (or) bonds that are owned by the issuer. collateral value is generally 25% to 35% greater than bond value

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bond type:

equipment trust certificates

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used to finance "rolling stock" - airplanes, trucks, boats, railroad cars. a type of leasing

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bond type:

zero or low coupon bond

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a significant portion of the investor's return comes from gain in value (ie par value minus purchase price)

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junk bond

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debt rated as Ba or lower. they are high risk bonds with high yields

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extendible notes

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short maturities, 1-5 years, can be renewed for a similar period at the option of holder.

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bond type:

floating-rate bonds

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interest rate is adjusted periodically within stated limits in repsonse to changes in specified money market or captial market rates

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bond type:

putable bonds

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bonds that can be redeemed at par at the optio of their holder either at specific dates after the date of issue and every 1 -5 years thereafter or when the firm takes specified actions.

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valuation

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process that links risk and return to determine the worth of an asset

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three inputs to valuation process

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1. cash flow
2. timing
3. measure of risk

The (market) value of any investment asset is simply the present value of expected cash flows.
• The interest rate that these cash flows are discounted at is called the asset’s required return.
• The required return is a function of the expected rate of inflation and the perceived risk of the
asset.
• Higher perceived risk results in a higher required return and lower asset market values.

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express the value of any asset at time zero

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vo = (CF1/(1+k)^1) + (CF2/(1+k)^2) + (CF3/(1+k)^3) +.....+ (CFn/(1+k)^n)

Vo= value of asset at time zero
CFt= cash flow expected at end of year t
k = appropriate required return
n = relevant time period

can also be writen as Vo= [CF1 x (PVIFk,1)] +......+ [CFn x (PVIFk,n)]

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bond valuation

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Bo= I x (PVIFA kd,n) + M x (PVIF kd, n)

Bo = value of the bond at time zero
I = annual interest paid in dollars
n = number of years to maturity
M = par value in dollars
kd = required return on a bond

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required return is likely to differ from coupon interest rate because....

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1. economic conditions have changes, causing a shift in the basic cost of long-term funds
2. the firm's risk have changed.

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relationship of required returns and bond values:

Discount

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when teh required return is greater than the coupon interest rate, the bond value, Bo, will be less than its par value, M.

M-Bo

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relationship of required returns and bond values:

premium

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when the required return falls below the coupon interest rate, the bond value will be greater than par.

Bo - M

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interest rate risk

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the chance that interset rates will change and thereby change the required return and bond value. rising rates, which result in decreaing bond values, are the greatest concern.

bondholders are typically more concerned with rising interest rates because a rise in interest rates, and therefore in the required return, causes a decrease in bond value..... short maturities have less interest rate risk than long maturities when all other features are the same.

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yield to maturity (YTM)

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the rate of return that investors earn if they buy a bond at a specific price and hold it until maturity.

the required return is the bond's yield to maturity. as a stockholder, higher required return is bad....it means that the value of the bond has gone down.

The yield to maturity measures the compound annual return to an investor and considers all
bond cash flows. It is essentially the bond’s IRR based on the current price.
• Note that the yield to maturity will only be equal if the bond is selling for its face value ($1,000).
• And that rate will be the same as the bond’s coupon rate.
• For premium bonds, the current yield > YTM.
• For discount bonds, the current yield < YTM.

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what do you in a semiannual interest and bond value

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divide or multiply n,i,pv,pmt by 2.

bond value is lower when semiannual interst is paid. this will always occur when the bond sells at a discount. for bonds selling at a premium, the opposite will occur.

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Current Yield

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The current yield measures the annual return to an investor based on the current price
Current Yield = Annual Coupon Interest / Current Market Price
Example, for a 10% coupon bond with price = 1,150:
CY = 100 / 1,150 = 8.7%

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Eurobonds

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are bonds issued by an international borrower and sold to investors in countries with
currencies other than that in which the bond is denominated. For example, a dollar-denominated
Eurobond issued by an American corporation can be sold to French, German, Swiss, or Japanese
investors. A foreign bond, on the other hand, is issued by a foreign borrower in a host country’s
capital market and denominated in the host currency. An example is a French-franc denominated
bond issued in France by an English company.