Bus 170 exam 3

What is the formula for the valuation of a perpetuity?

PMT/ Discount rate

Nominal interest rate vs. Effective interest rate-

The nominal interest rate (INOM) , also called the annual percentage rate (APR) , is the quoted, or stated, rate that credit card companies, student loan officers, auto dealers, and other lenders tell you they are charging on loans. The one that requires monthly payments is charging more than the one with quarterly payments because it will receive your money sooner. So to compare loans across lenders, or interest rates earned on different securities, you should calculate effective annual rates as described here.*The effective annual rate , abbreviated EFF% , is also called the equivalent annual rate (EAR) . This is the rate that would produce the same future value under annual compounding as would more frequent compounding at a given nominal rate.If a loan or an investment uses annual compounding, its nominal rate is also its effective rate. However, if compounding occurs more than once a year, the EFF% is higher than INOM .

The "Real Risk Free Rate," abbreviated r*-

The real risk-free rate of interest, r* , is the interest rate that would exist on a riskless security if no inflation were expected. It may be thought of as the rate of interest on short-term U.S. Treasury securities in an inflation-free world. The real risk-free rate is not static—it changes over time, depending on economic conditions, especially on

The London Interbank Offered Rate (LIBOR) is

a benchmark interest rate at which major global banks lend to one another in the international interbank market for short-term loans. LIBOR, which stands for London Interbank Offered Rate, serves as a globally accepted key benchmark interest rate that indicates borrowing costs between banks. The rate is calculated and published each day by the Intercontinental Exchange (ICE).

An annuity is

a contract between you and an insurance company in which you make a lump-sum payment or series of payments and, in return, receive regular disbursements, beginning either immediately or at some point in the future.

The call date is

a day on which the issuer has the right to redeem a callable bond at par, or at a small premium to par, prior to the stated maturity date. The call date and related terms will be stated in a security's prospectus.

Yield to call (YTC) is

a financial term that refers to the return a bondholder receives if the bond is held until the call date, which occurs sometime before it reaches maturity. This number can be mathematically calculated as the compound interest rate at which the present value of a bond's future coupon payments and call price is equal to the current market price of the bond. Yield to call applies to callable bonds, which are debt instruments that let bond investors redeem the bonds—or the bond issuer to repurchase them—on what is known as the call date, at a price known as the call price. By definition, the call date of a bond chronologically occurs before the maturity date.

Face value is

a financial term used to describe the nominal or dollar value of a security, as stated by its issuer. For stocks, the face value is the original cost of the stock, as listed on the certificate. For bonds, it is the amount paid to the holder at maturity, typically in $1,000 denominations. The face value for bonds is often referred to as "par value" or simply "par."

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. Bonds are used by companies, municipalities, states, and sovereign governments to finance projects and operations. Owners of bonds are debtholders, or creditors, of the issuer. Bond details include the end date when the principal of the loan is due to be paid to the bond owner and usually includes the terms for variable or fixed interest payments made by the borrower.

The internal rate of return is

a metric used in financial analysis to estimate the profitability of potential investments. The internal rate of return is a discount rate that makes the net present value (NPV) of all cash flows equal to zero in a discounted cash flow analysis. IRR calculations rely on the same formula as NPV does.

A Treasury Bill (T-Bill) is

a short-term U.S. government debt obligation backed by the Treasury Department with a maturity of one year or less. Treasury bills are usually sold in denominations of $1,000. However, some can reach a maximum denomination of $5 million in non-competitive bids.1 These securities are widely regarded as low-risk and secure investments.

A call provision

a stipulation on the contract for a bond—or other fixed-income instruments—that allows the issuer to repurchase and retire the debt security. Call provision triggering events include the underlying asset reaching a preset price and a specified anniversary or other date being reached.

Treasury inflation-protected securities (TIPS) are

a type of Treasury security issued by the U.S. government. TIPS are indexed to inflation in order to protect investors from a decline in the purchasing power of their money. As inflation rises, TIPS adjust in price to maintain its real value.1

A debenture is

a type of bond or other debt instrument that is unsecured by collateral. Since debentures have no collateral backing, debentures must rely on the creditworthiness and reputation of the issuer for support. Both corporations and governments frequently issue debentures to raise capital or funds.

liquidity premium

additional value demanded by investors when any given security cannot be easily and efficiently sold or otherwise converted into cash for its fair market value. When the liquidity premium is high, the asset is said to be illiquid, Investors of illiquid assets require compensation for the added risk of investing their funds in assets that may not be able to be sold for an extended period, especially since valuations can fluctuate with market effects in the interim.

A loan that is to be repaid in equal amounts on a monthly, quarterly, or annual basis is called an

amortized loan .

Annuity due

an annuity whose payment is due immediately at the beginning of each period. A common example of an annuity due payment is rent, as landlords often require payment upon the start of a new month as opposed to collecting it after the renter has enjoyed the benefits of the apartment for an entire month.

Perpetuity

an annuity with an extended life. Because the payments go on forever, you can't apply the step-by-step approach.

A floating interest rate is

an interest rate that moves up and down with the market or an index. It can also be referred to as a variable interest rate because it can vary over the duration of the debt obligation. This contrasts with a fixed interest rate, in which the interest rate of a debt obligation stays constant for the duration of the loan's term.

Senior debt is

borrowed money that a company must repay first if it goes out of business. Each type of financing has a different priority level in being repaid if the company goes out of business. If a company goes bankrupt, the issuers of senior debt, which are often bondholders or banks that have issued revolving credit lines, are most likely to be repaid, followed by junior debt holders, preferred stock holders and common stock holders, possibly by selling collateral held for debt repayment.

Interest earned on the interest earned in prior periods, is called

compound interest

convertible bonds are

corporate bonds that can be converted by the holder into the common stock of the issuing company.

Secured debt is

debt backed or secured by collateral to reduce the risk associated with lending. If the borrower on a loan defaults on repayment, the bank seizes the collateral, sells it, and uses the proceeds to pay back the debt. Assets backing debt or a debt instrument are considered as a form of security, which is why unsecured debt is considered a riskier investment than secured debt.

Fixed-Income securities are

debt instruments that pay a fixed amount of interest—in the form of coupon payments—to investors. The interest payments are typically made semiannually while the principal invested returns to the investor at maturity. Bonds are the most common form of fixed-income securities. Companies raise capital by issuing fixed-income products to investors.

Finding present values is called

discounting

Treasury bonds (T-bonds) are

government debt securities issued by the U.S. Federal government that have maturities greater than 20 years. T-bonds earn periodic interest until maturity, at which point the owner is also paid a par amount equal to the principal. Treasury bonds are part of the larger category of U.S. sovereign debt known collectively as treasuries, which are typically regarded as virtually risk-free since they are backed by the U.S. government's ability to tax its citizens.

The increasing onset of demand for longer-maturity bonds and the lack of demand for shorter-term securities lead to

higher prices but lower yields on longer-maturity bonds, and lower prices but higher yields on shorter-term securities, further inverting a down-sloped yield curve.

A normal yield curve

is one in which longer maturity bonds have a higher yield compared to shorter-term bonds due to the risks associated with time

An inverted yield curve

is one in which the shorter-term yields are higher than the longer-term yields, which can be a sign of an upcoming recession.

When investors expect longer-maturity bond yields to become even lower in the future, many would purchase _______ bonds to lock in yields before they decrease further.

longer-maturity

A long-term bond generally offers a maturity risk premium in the form of a higher built-in rate of return to compensate for the added risk of interest rate changes over time. The larger duration of longer-term securities means higher interest rate risk for those securities. To compensate investors for taking on more risk, the expected rates of return on longer-term securities are typically higher than rates on shorter-term securities. This is known as the

maturity risk premium.

A sunk cost refers to

money that has already been spent and which cannot be recovered. In business, the axiom that one has to "spend money to make money" is reflected in the phenomenon of the sunk cost. A sunk cost differs from future costs that a business may face, such as decisions about inventory purchase costs or product pricing. Sunk costs are excluded from future business decisions because the cost will remain the same regardless of the outcome of a decision.

Basis points (BPS)

refers to a common unit of measure for interest rates and other percentages in finance. One basis point is equal to 1/100th of 1%, or 0.01%, or 0.0001, and is used to denote the percentage change in a financial instrument. The relationship between percentage changes and basis points can be summarized as follows: 1% change = 100 basis points and 0.01% = 1 basis point.

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. Zero-coupon bonds are the only fixed-income security to have no investment risk since they issue no coupon payments.

If interest is not earned on interest, we have

simple interest . The formula for FV with simple interest is FV= PV+PV(I) (N). Most financial contracts are based on compound interest, but in legal proceedings, the law often specifies that simple interest must be used

The payback period refers to

the amount of time it takes to recover the cost of an investment. Simply put, the payback period is the length of time an investment reaches a break-even point.

A coupon or coupon payment is

the annual interest rate paid on a bond, expressed as a percentage of the face value and paid from issue date until maturity. Coupons are usually referred to in terms of the coupon rate (the sum of coupons paid in a year divided by the face value of the bond in question).

The maturity date is

the date on which the principal amount of a note, draft, acceptance bond or other debt instrument becomes due. On this date, which is generally printed on the certificate of the instrument in question, the principal investment is repaid to the investor, while the interest payments that were regularly paid out during the life of the bond, cease to roll in. The maturity date also refers to the termination date (due date) on which an installment loan must be paid back in full.

A project's IRR is

the discount rate that forces the PV of its inflows to equal its cost. This is equivalent to forcing the NPV to equal zero. The IRR is an estimate of the project's rate of return, and it is comparable to the YTM on a bond.

Call premium

the dollar amount over the par value of a callable debt security that is given to holders when the security is redeemed early by the issuer. The call premium is also called the redemption premium. In options terminology, the call premium is the amount that the purchaser of a call option must pay to the writer.

Yield refers to

the earnings generated and realized on an investment over a particular period of time. It's expressed as a percentage based on the invested amount, current market value, or face value of the security. It includes the interest earned or dividends received from holding a particular security. Depending on the valuation (fixed vs. fluctuating) of the security, yields may be classified as known or anticipated.

Par value is

the face value of a bond. Par value is important for a bond or fixed-income instrument because it determines its maturity value as well as the dollar value of coupon payments. The market price of a bond may be above or below par, depending on factors such as the level of interest rates and the bond's credit status. Par value for a bond is typically $1,000 or $100 because these are the usual denominations in which they are issued.

The prime rate is

the interest rate that commercial banks charge their most creditworthy corporate customers. The federal funds overnight rate serves as the basis for the prime rate, and prime serves as the starting point for most other interest rates.

A hurdle rate is

the minimum rate of return on a project or investment required by a manager or investor. It allows companies to make important decisions on whether or not to pursue a specific project. The hurdle rate describes the appropriate compensation for the level of risk present—riskier projects generally have higher hurdle rates than those with less risk. In order to determine the rate, the following are some of the areas that must be taken into consideration: associated risks, cost of capital, and the returns of other possible investments or projects.

Interest rate risk is

the potential for investment losses that result from a change in interest rates. If interest rates rise, for instance, the value of a bond or other fixed-income investment will decline. The change in a bond's price given a change in interest rates is known as its duration.

net present value (NPV)

the present value of the project's free cash flows discounted at the cost of capital. The NPV tells us how much a project contributes to shareholder wealth; the larger the NPV, the more value the project adds—and added value means a higher stock price.* Thus, NPV is the best selection criterion.

Capital budgeting

the process a business undertakes to evaluate potential major projects or investments. Construction of a new plant or a big investment in an outside venture are examples of projects that would require capital budgeting before they are approved or rejected. As part of capital budgeting, a company might assess a prospective project's lifetime cash inflows and outflows to determine whether the potential returns that would be generated meet a sufficient target benchmark. The capital budgeting process is also known as investment appraisal.

Opportunity Cost-

the rate of return you could earn on an alternative investment of similar risk.

Default risk is

the risk that a lender takes on in the chance that a borrower will be unable to make the required payments on their debt obligation. Lenders and investors are exposed to default risk in virtually all forms of credit extensions. A higher level of default risk leads to a higher required return, and in turn, a higher interest rate.

Federal funds rate is

the target interest rate set by the Federal Open Market Committee (FOMC) at which commercial banks borrow and lend their excess reserves to each other overnight

Yield to maturity (YTM) is

the total return anticipated on a bond if the bond is held until it matures. Yield to maturity is considered a long-term bond yield but is expressed as an annual rate. In other words, it is the internal rate of return (IRR) of an investment in a bond if the investor holds the bond until maturity, with all payments made as scheduled and reinvested at the same rate.

Time Lines

will help you visualize what's happening in a particular problem.

discount rate

First, the discount rate refers to the interest rate charged to the commercial banks and other financial institutions for the loans they take from the Federal Reserve Bank through the discount window loan process, and second, the discount rate refers to the interest rate used in discounted cash flow (DCF) analysis to determine the present value of future cash flows.

Ordinary Annuities

If the payments occur at the end of each year, the annuity is an ordinary (or deferred) annuity. Ordinary annuities are more common in finance; so when we use the term annuity in this book, assume that the payments occur at the ends of the periods unless otherwise noted. When the payments are equal and are made at fixed intervals, the series is an annuity .

What should be the decision if Projects S and L are independent?

In this case, both should be accepted because both have positive NPVs and thus add value to the firm. However, if they are mutually exclusive, Project L should be chosen because it has the higher positive NPV and thus adds more value than S. Here is a summary of the NPV decision rules: Independent projects. If NPV exceeds zero, accept the project. Mutually exclusive projects. Accept the project with the highest positive NPV. If no project has a positive NPV, reject them all.

Independent vs Mutually exclusive projects

Independent projects are projects whose cash flows are not affected by one another. If Walmart was considering a new store in Boise and another in Atlanta, the projects would be independent—and if both had positive NPVs, Walmart should accept both. Mutually exclusive projects, on the other hand, are projects where if one project is accepted, the other must be rejected. A conveyor belt system to move goods in a warehouse and a fleet of forklifts used for the same purpose would be mutually exclusive—accepting one implies rejecting the other.