Principles of Finance C708 V4 - UG: Unit 5 Module 10

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.

Yield to maturity

the internal rate of return on a bond held to maturity, assuming scheduled payment of principal and interest.

Clean price

the price of a bond excluding any interest that has accrued since issue or the most recent coupon payment.

Call provision

the right for the issuer to buy back the bond at a predetermined price at a certain time in future.

Time value of money

the value of money, figuring in a given amount of interest, earned over a given amount of time.

Par value

The stated value or amount of a bill or a note.

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. Key Points *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. *In the market for United States Treasury securities, there are three categories of bond maturities: short-term, medium-term and long-term bonds. *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. *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. *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. *Formula for yield to maturity: Yield to maturity (YTM) = [(Face value/Bond price)1/Time period ] - 1. Equation: Yield to maturity (YTM) = (Face value/Bond price)^1/Time period−1

A sinking fund may operate in one or more of the following ways:

*The firm may repurchase a fraction of the outstanding bonds in the open market each year. *The firm may repurchase a fraction of outstanding bonds at a special call price associated with the sinking fund provision (they are callable bonds). *The firm has the option to repurchase the bonds at either the market price or the sinking fund price, whichever is lower. The firm can only repurchase a limited fraction of the bond issue at the sinking fund price. At best some indentures allow firms to use a doubling option, which allows repurchase of double the required number of bonds at the sinking fund price.

Bond refunding occurs when all three of the following are true:

1. Interest rates in the market are sufficiently less than the coupon rate on the old bond. 2. The price of the old bond is less than par. 3. The sinking fund has accumulated enough money to retire the bond issue.

three categories of bond maturities:

1. Short term (bills): maturities between one to five years (Instruments that mature in less than one year are considered Money Market Instruments.) 2. Medium term (notes): maturities between six to twelve years 3. Long term (bonds): maturities greater than twelve years

three main categories of United States Treasury securities available in the market.

1. Treasury Bills (short-term): maturities ranging from a few days to 52 weeks 2. Treasury Notes (medium-term): maturities ranging between 2 years and 10 years 3. Treasury Bonds (long-term): mature in 30 years

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.

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. Key Points *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. *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. *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. *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.

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.

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 bondholder.

Sinking 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. Key Points *Sinking fund provision of the corporate bond indenture requires a certain portion of the issue to be retired periodically. *A sinking fund reduces credit risk but presents reinvestment risk to bondholders. *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.

Straight bond

A straight bond is a bond with no embedded options (call or put options).

A bond pays a coupon rate equal to the LIBOR rate plus 0.30%. The coupon rate is recalculated every three months. What type of bond is this? A) A floating rate note B) A zero-coupon bond C) An inflation-linked bond D) A stepped-coupon bond

A) A floating rate note *Floating rate notes (FRNs, floaters) have a variable coupon that is linked to a reference rate of interest, such as LIBOR or Euribor. For example, the coupon may be defined as three month USD LIBOR + 0.20%. The coupon rate is recalculated periodically, typically every one or three months.

Asset-backed securities

An asset-backed security is a security that has value and income payments derived from and collateralized (or "backed") by a specified pool of underlying assets. The pool of assets is typically a group of small and illiquid assets that are unable to be sold individually.

Inflation Premium

An inflation premium is the part of prevailing interest rates that results from lenders compensating for expected inflation. Key Points *Investors seek this premium to compensate for the erosion in the value of their capital due to inflation. *Actual interest rates (without factoring in inflation) are viewed by economists and investors as being the nominal (stated) interest rate minus the inflation premium. *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. Equation: i = r + π

A US Treasury security matures in 7 years. What type of security is it? A) A money market instrument B) A note C) A bill D) A bond

B) A note *U.S. Treasury notes are medium-term instruments with maturities ranging between 2 years and 10 years.

Bond price formula

Bond price is the present value of all coupon payments and the face value paid at maturity. Equation: P= (C/1+i+C/(1+i)2+...+C/(1+i)N)+M/(1+i)^N =(∑ n=1NC/(1+i)n)+M/(1+i)^N =C(1−(1+i)−N/i)+M(1+i)^−N

A US Treasury security matures in 26 weeks. What type of treasury is it? A) A bank deposit B) A note c) A bond D) A bill

D) A bill *U.S. Treasury bills are short-term instruments with maturities ranging from a few days to 52 weeks

A bond makes only one payment—the payment of the face value on the maturity date. The bond is sold at a discount. What type of bond is this? A) Floating rate note B) Stepped-coupon bond C) Inflation-linked bond D) Zero-coupon bond

D) Zero-coupon bond *Zero-coupon bonds are those that pay no coupons and thus have a coupon rate of 0%. Such bonds make only one payment-the payment of the face value on the maturity date. Normally, to compensate the bondholder for the time value of money, the price of a zero-coupon bond will always be less than its face value on any date before the maturity date. The bondholder receives the full principal amount on the redemption date. An example of zero coupon bonds is Series E savings bonds issued by the U.S. government.

Default Risk

Default risk is the risk that a bond issuer will default on any type of debt by failing to make payments which it is obligated to make. Key Points *With default risk, the risk is primarily that of the bondholder and includes lost principal and interest, disruption to cash flows, and increased collection costs. *To reduce the bondholders' credit risk, the lender may perform a credit check on the prospective borrower and may require the issuer to take out appropriate insurance. *A company's bondholders may lose much or all their money if the company goes bankrupt. There is no guarantee of how much money will remain to repay bondholders.

Annuity formula

Equation: an¯|i=1−(1+i)−n/i

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.

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.

Liquidated

In law, liquidation is the process by which a company (or part of a company) is brought to an end and the assets and property of the company redistributed.

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.

In the bond market, firms raise debt financing directly from....

Investors *Issuers sell bonds or other debt instruments to investors in the bond market to fund the operations of their organizations. Firms like bonds because typically they help defray costs by going straight to investors.

Maturity Date

Maturity date refers to the final payment date of a loan or other financial instrument. Key Points *As long as all due payments have been made, the issuer has no further obligations to the bond holders after the maturity date. *The length of time until the maturity date is often referred to as the term or tenor or maturity of a bond. *In the market for United States Treasury securities, there are three categories of bond maturities: short term, medium term, and long term.

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)). Key Points *Nominal rate refers to the rate before adjustment for inflation; the real rate is the nominal rate minus inflation. *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)). *Simple equation between nominal rates and real rates: i = R - r.

Bonds: Other Features

Other important features of bonds include the yield, market price and putability of a bond. Key Points *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. *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. *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. Equation: P= (C/1+i+C/(1+i)^2+...+C/(1+i)^N)+M/(1+i)N =(∑ n=1NC/(1+i)n)+M/(1+i)N =C(1−(1+i)−N/i)+M(1+i)^−N Bond Price: Bond price is the present value of coupon payments and face value paid at maturity.

Par Value Maturity

Par value is stated value or face value, with a typical bond making a repayment of par value at maturity. Key Points *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. *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. *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.

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. Key Points *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. *A bond's price fluctuates throughout its life in response to a number of variables, including interest rates and time to maturity. *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).

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. Key Points *Payment frequency can be annual, semi-annual, quarterly, monthly, weekly, daily, or continuous. *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. *The more frequent a bond makes coupon payments, the higher the bond price, given equal coupon, par, and face.

Price Risk vs Reinvestment Risk

Price risk is positively correlated to changes in interest rates, while reinvestment risk is inversely correlated. Key Points *Price risk and reinvestment risk are both the uncertainty associated with the effects of changes in market interest rates. *Price risk and changes in interest rates are positively correlated. *Reinvestment risk and changes in interest rates are 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. Key Points *The market price of bonds will decrease in value when the generally prevailing interest rates rise and vice versa. *Unless you plan to buy or sell them in the open market, changing interest rates do not affect the interest payments to the bondholder. *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.

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.

Nominal Rates

Real and nominal: The relationship between real and nominal interest rates is captured by the formula. Equation: (1+r)(1+i)=(1+R)

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. Key Points *The issue of new, lower-interest debt allows the company to prematurely refund the older, higher-interest debt. *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. *The decision of whether to refund a particular debt issue is usually based on a capital budgeting (present value) analysis.

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. Key Points *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. *Two factors that have a bearing on the degree of reinvestment risk are maturity of the bond and the coupon interest rate.

The three steps of whether to make a refunding decision are as follows:

Step 1: Calculate the present value of interest savings (cash inflows): Interest savings = annual interest of old issue - annual interest of new issue Step 2: Calculate the net investment (net cash outflow at time 0). This involves computing the after-tax call premium, the issuance cost of the new issue, the issuance cost of the old issue, and the overlapping interest. The call premium is a cash outflow. Step 3: Finally, calculate the net present value of refunding.

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. Key Points *Coupon interest rate is usually fixed throughout the life of the bond. It can also vary with a money market index. *Not all bonds have coupons. Zero-coupon bonds are those that pay no coupons and thus have a coupon rate of 0%. *Based on different coupon rates, there are fixed rate bonds, floating rate bonds, and inflation linked bonds.

Bond Rating System

The credit rating is a financial indicator assigned by credit rating agencies; bond ratings below BBB-/Baa are considered junk bonds. Key Points *In investment, the bond credit rating assesses the credit-worthiness of a corporation's or government debt issues. *The credit rating is a financial indicator to potential investors of debt securities, such as bonds. These are assigned by credit rating agencies such as Moody's, *Standard & Poor's, and Fitch Ratings to have letter designations (such as AAA, B, CC) which represent the quality of a bond. *Bond ratings below BBB-/Baa are considered not to be investment grade and are colloquially called junk bonds.

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.

Resale 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.

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. Key Points *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. *The present value of coupon payments is the present value of an annuity of coupon payments. *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. Equation: PVA=PMTi⋅1−1/(1+i)n n is the number of periods and i is the per period interest rate.

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.

Bankruptcy and Bond Value

There is no guarantee of how much money will remain to repay bondholders in a bankruptcy, therefore, the value of the bond is uncertain. Key Points *When a business is unable to service its debt or pay its creditors, it or its creditors can file with a federal bankruptcy court for protection under either Chapter 7 or Chapter 11 of the Bankruptcy code. *If a company goes bankrupt, its bondholders will often receive some money back (the recovery amount). *In a bankruptcy involving reorganization or recapitalization, as opposed to liquidation, bondholders may end up having the value of their bonds reduced, often through an exchange for a smaller number of newly-issued bonds.

Insolvent

Unable to pay one's bills as they fall due.

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. Key Points *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. *Yield to maturity (YTM) = [(Face value/Present value)1/Time period] - 1. *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. *There are some variants of YTM: yield to call, yield to put, yield to worst. Equation: Yield to maturity (YTM) = (Face value/Present value)^1/Time period −1

Money market

a market for trading short-term debt instruments, such as treasury bills, commercial paper, bankers' acceptances, and certificates of deposit.

Recapitalization

a restructuring of a company's mixture of equity and debt.

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.

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.

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.

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.

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.

London Interbank Offer Rate (LIBOR)

the equivalent to the federal funds rate, or the interest rate one bank charges another for a loan.

Federal Funds Rate (FFR)

the rate at which depository institutions (banks) lend reserve balances to other banks on an overnight basis.

Quote

to name the current price, notably of a financial security.