Unit 5 - Bond and Stock Valuation and Capital Budgeting
Value of a Bond
The value of a bond is obtained by discounting the bond's expected cash flows to the present using an appropriate discount rate.
Time to Maturity
"Time to maturity" refers to the length of time before the par value of a bond must be returned to the bondholder.
Yield to maturity (YTM) = [
(Face value/Present value)1/Time period] - 1.
Letting r denote the real interest rate
, i denote the nominal interest rate, and let π denote the inflation rate, the Fisher equation is: i = r + π. In the Fisher equation, π is the inflation premium.
Callable
A callable bond (also called "redeemable bond") is a type of bond (debt security) that allows the issuer of the bond to retain the privilege of redeeming the bond at some point before the bond reaches its date of maturity.
A callable bond
A callable bond allows the issuer to redeem the bond before the maturity date; this is likely to happen when interest rates go down.
Debentures:
A debenture is a document that either creates a debt or acknowledges it, and it is a debt without collateral.
Puttable
A puttable bond (put bond, putable, or retractable bond) is a bond with an embedded put option. The holder of the puttable bond has the right, but not the obligation, to demand early repayment of the principal.
inking Funds
A sinking fund is a fund into which money can be deposited, so that over time preferred stock, debentures or stocks can be retired.
Straight bond
A straight bond is a bond with no embedded options (call or put options).
Inflation Premium
An inflation premium is the part of prevailing interest rates that results from lenders compensating for expected inflation.
Pull to par is the effect in which the price of a bond converges to par value as time passes.
At maturity, the price of a debt instrument in good standing should equal its par (or face value).
For the creditors, the fund reduces the risk the organization will default when the principal is due: it reduces credit risk.
However, if the bonds are callable, this comes at a cost to creditors, because the organization has an option on the bonds.
Internal rate of return:
IRR is the rate of return on an investment which causes the net present value of all future cash flows to be zero
Yield to maturity:
the internal rate of return on a bond held to maturity, assuming scheduled payment of principal and interest.
If the YTM is less than the bond's coupon rate, then the market value of the bond is greater than par value (premium bond).
If a bond's coupon rate is less than its YTM, then the bond is selling at a discount. If a bond's coupon rate is equal to its YTM, then the bond is selling at par.
If a bond's coupon rate is less than its YTM, then the bond is selling at a discount.
If a bond's coupon rate is more than its YTM, then the bond is selling at a premium. If a bond's coupon rate is equal to its YTM, then the bond is selling at par.
Systematic risks:
In finance and economics, systematic risk (sometimes called aggregate risk, market risk, or undiversifiable risk), is vulnerability to events which affect aggregate outcomes such as broad market returns, total economy-wide resource holdings, or aggregate income.
Inflation-linked bonds:
Inflation-indexed bonds (also known as inflation-linked bonds or colloquially as linkers) are bonds where the principal is indexed to inflation. They are thus designed to cut out the inflation risk of an investment.
As long as all due payments have been made,
the issuer has no further obligations to the bond holders after the maturity date.
Maturity Date
Maturity date refers to the final payment date of a loan or other financial instrument.
Nominal Rate
Nominal rate refers to the rate before adjustment for inflation; the real rate is the nominal rate minus inflation: r = R - i or, 1 + r = (1 + r)(1 + E(r)).
Other Features
Other important features of bonds include the yield, market price and putability of a bond.
Par Value Maturity
Par value is stated value or face value, with a typical bond making a repayment of par value at maturity.
Par Value
Par value is the amount of money a holder will get back once a bond matures; a bond can be sold at par, at premium, or discount.
Payment Frequency
Payment frequency can be annual, semi-annual, quarterly, or monthly; the more frequently a bond makes coupon payments, the higher the bond price.
Price of callable bond = Price of straight bond - Price of call option.
Price of a callable bond is always lower than the price of a straight bond because the call option adds value to an issuer.
Price Risk vs Reinvestment Risk
Price risk is positively correlated to changes in interest rates, while reinvestment risk is inversely correlated.
Price Risk
Price risk is the risk that the market price of a bond will fall, usually due to a rise in the market interest rate.
Refunding Bonds
Refunding occurs when an entity that has issued callable bonds calls those debt securities to issue new debt at a lower coupon rate.
Reinvestment Risk
Reinvestment risk is the risk resulting from the fact that interest or dividends earned from an investment may not be able to be reinvested in such a way that they earn the same rate of return as the invested funds that generated them.
Coupon Interest Rate
The coupon rate is the amount of interest that the bondholder will receive per payment, expressed as a percentage of the par value.
Issue date:
The date a bond is issued and from which a bondholder is entitled to receive interest irrespective of the date the bond was purchased or delivered.
Bond price is the sum of the present value of face value paid back at maturity and the present value of an annuity of coupon payments.
The present value of face value received at maturity is the same. However, the present values of annuities of coupon payments vary among payment frequencies.
esale market
The resale market, also called "secondary market" or "aftermarket," is the financial market in which previously issued financial instruments, such as stock, bonds, options, and futures, are bought and sold.
Par value
The stated value or amount of a bill or a note.
Yield to Maturity-
The yield to maturity is the discount rate that returns the bond's market price: YTM = [(Face value/Bond price)1/Time period] - 1.
Mutual funds: a type of professionally-managed collective investment vehicle that pools money from many investors to purchase securities.
While there is no legal definition, the term is most commonly applied only to those collective investment vehicles that are regulated, available to the general public and open-ended in nature.
Most callable bonds allow the issuer to repay the bond at par.
With some bonds, the issuer has to pay a premium, known as the call premium.
Formula for yield to maturity:
Yield to maturity (YTM) = [(Face value/Bond price)1/Time period ] - 1.
Yield to Maturity
Yield to maturity is the discount rate at which the sum of all future cash flows from the bond are equal to the price of the bond.
Not all bonds have coupons.
Zero-coupon bonds are those that pay no coupons and thus have a coupon rate of 0%
A bond that takes longer to mature necessarily has
a greater duration. The bond price in this type of a situation, therefore, is more sensitive to changes in interest rates.
The maturity can be any length of time, but debt securities with
a term of less than one year are generally not designated as bonds. Instead, they are considered money market instruments.
Payment frequency can be
annual, semi-annual, quarterly, monthly, weekly, daily, or continuous.
Fisher equation states that the real interest rate is
approximately the nominal interest rate minus the inflation rate: 1 + i = (1 + r) (1 + E(r)).
The decision of whether to refund a p
articular debt issue is usually based on a capital budgeting (present value) analy
Some bonds give the holder the right to force the issuer to repay the
bond before the maturity date on the put dates. These are referred to as retractable or puttable bonds.
A callable bond is a type of bond that allows the issuer of the
bond to retain the privilege of redeeming the bond at some point before the bond reaches its date of maturity.
The yield to maturity is the internal rate of return earned by an investor who
bought the bond today at the market price, assuming that the bond will be held until maturity, and that all coupon and principal payments will be made on schedule.
Actual interest rates (without factoring in inflation) are viewed
by economists and investors as being the nominal (stated) interest rate minus the inflation premium.
Investors seek this premium to
compensate for the erosion in the value of their capital due to inflation.
Sinking fund provision of the
corporate bond indenture requires a certain portion of the issue to be retired periodically.
The market price of a tradable bond will be influenced by the amounts,
currency and timing of the interest payments and capital repayment due, the quality of the bond, and the available redemption yield of other comparable bonds which can be traded in the markets.
Two factors that have a bearing on the
degree of reinvestment risk are maturity of the bond and the coupon interest rate.
The present value of an annuity is the value of a stream of payments,
discounted by the interest rate to account for the payments being made at various moments in the future.
Yield to maturity: The yield to maturity (YTM) or redemption yield of a bond or other fixed-interest security, such as gilts, is the internal rate of return (IRR, overall interest rate)
earned by an investor who buys the bond today at the market price, assuming that the bond will be held until maturity, and that all coupon and principal payments will be made on schedule.
Par:
equal value; equality of nominal and actual value; the value expressed on the face or in the words of a certificate of value, as a bond or other commercial paper.
Based on different coupon rates, there are fixed rate bonds,
floating rate bonds, and inflation linked bonds.
Nominal rate refers to the rate before adjustment
for inflation; the real rate is the nominal rate minus inflation.
Discount rate: the interest rate used to discount
future cash flows of a financial instrument; the annual interest rate used to decrease the amounts of future cash flow to yield their present value.
Annuity: a specified income payable at stated intervals for a fixed or a contingent period, often for the recipient's life,
in consideration of a stipulated premium paid either in prior installment payments or in a single payment. For example, a retirement annuity paid to a public officer following his or her retirement.
Purchasing power: Purchasing power (sometimes retroactively called adjusted for inflation)
is the amount of goods or services that can be purchased with a unit of currency.
When a bond trades at a price above the face value,
it is said to be selling at a premium. When a bond sells below face value, it is said to be selling at a discount.
The issue of new,
lower-interest debt allows the company to prematurely refund the older, higher-interest debt.
Price changes in a bond will immediately affect
mutual funds that hold these bonds. If the value of the bonds in their trading portfolio falls, the value of the portfolio also falls.
Simple equation between
nominal rates and real rates: i = R - r.
The length of time until the maturity date is
often referred to as the term or tenor or maturity of a bond.
Unless you plan to buy or sell them in the
open market, changing interest rates do not affect the interest payments to the bondhold
A typical bond makes coupon payments at fixed intervals during the life of it and a final repayment of
par value at maturity. Together with coupon payments, the par value at maturity is discounted back to the time of purchase to calculate the bond price.
The present value of coupon payments is the
present value of an annuity of coupon payments.
A sinking fund reduces credit risk but
presents reinvestment risk to bondholders.
Sinking fund: A sinking fund is a fund established by a government agency or business for the
purpose of reducing debt by repaying or purchasing outstanding loans and securities held against the entity. It helps keep the borrower liquid so it can repay the bondholde
The yield is the rate of return
received from investing in the bond. It usually refers either to the current yield, or to the yield to maturity or redemption yield.
A bond's price fluctuates throughout its life in
response to a number of variables, including interest rates and time to maturity.
Preferred Stock:
stock with a dividend, usually fixed, that is paid out of profits before any dividend can be paid on common stock. It also has priority to common stock in liquidation.
Money market: a market for trading short-term debt instruments,
such as treasury bills, commercial paper, bankers' acceptances, and certificates of deposit.
Discount rate:
t he interest rate used to discount future cash flows of a financial instrument; the annual interest rate used to decrease the amounts of future cash flow to yield their present value.
Call premium:
the additional cost paid by the issuer for the right to buy back the bond at a predetermined price at a certain time in the future.
To achieve a return equal to YTM (i.e., where it is the required return on the bond),
the bond owner must buy the bond at price P0, hold the bond until maturity, and redeem the bond at par.
London Interbank Offer Rate (LIBOR):
the equivalent to the federal funds rate, or the interest rate one bank charges another for a loan
The more frequent a bond makes coupon payments,
the higher the bond price, given equal coupon, par, and face.
If interest rates in the market have gone down by the time of the call date,
the issuer will be able to refinance its debt at a cheaper level and so will be incentivized to call the bonds it originally issued.
The bond price can be summarized as the sum of the present value of
the par value repaid at maturity and the present value of coupon payments.
Clean price:
the price of a bond excluding any interest that has accrued since issue or the most recent coupon payment.
Federal Funds Rate (FFR):
the rate at which depository institutions (banks) lend reserve balances to other banks on an overnight basis.
Call provision:
the right for the issuer to buy back the bond at a predetermined price at a certain time in future.
Bond refunding occurs when a) interest rates in the market are sufficiently less than the coupon rate on the old bond, b) the price of the old bond is less than par, and c)
the sinking fund has accumulated enough money to retire the bond issue.
Time value of money:
the value of money, figuring in a given amount of interest, earned over a given amount of time.
In the market for United States Treasury securities
there are three categories of bond maturities: short term, medium term, and long term.
In the market for United States Treasury securities,
there are three categories of bond maturities: short-term, medium-term and long-term bonds.
Quote:
to name the current price, notably of a financial security.
Price risk and reinvestment risk are both the
uncertainty associated with the effects of changes in market interest rates.
Coupon interest rate is
usually fixed throughout the life of the bond. It can also vary with a money market index.
The market price of bonds will decrease in
value when the generally prevailing interest rates rise and vice versa.
Reinvestment risk is more likely
when interest rates are declining.
Reinvestment risk affects the yield-to-maturity of a bond,
which is calculated on the premise that all future coupon payments will be reinvested at the interest rate in effect when the bond was first purchased.
Par value of a bond usually does not change, except for inflation-linked bonds
whose par value is adjusted by inflation rates every predetermined period of time.
A bond selling at par has a coupon rate such that the bond is
worth an amount equivalent to its original issue value or its value upon redemption at maturity.
There are some variants of YTM:
yield to call, yield to put, yield to worst.
