FINANCE MIDTERM 2

What is the price of a 10-year bond with a semi-annual coupon of 10% if the market rate of interest (the discount rate) is 13%?

$834 N= 10 * 2 = 20 I/YR= 13/2 = 6.5 PMT= 100/2= 50 FV= 1,000 Solve for PV= 1834.72

EXAM QUESTION

- Interest rate on short term treasuries DECREASE - Long-term treasuries DECREASE - Interest rates relatively low ALL OF THESE ARE CORRECT FOR: graph w/ two horizontal lines the top (1 year ago) and the bottom (Last Close)

Key Features of a Bond

- Par Value: face amount of the bond, which is paid at maturity (assume $1,000) - Coupon Interest Rate: stated interest rate (generally fixed) paid by the issuer - Multiply by par value to get dollar payment of interest - Maturity Date: years until the bond must be paid - Issue Date: when the bond was issued - Yield to Maturity: rate of return earned on a bond held until maturity ("promised yield")

Long-Term Debt -- Banks vs. Bonds

- Relative to bank borrowing, selling bonds to the public allows the firm to broaden it's investor base, and may provide more attractive financing terms

What is quantitative easing?

-After the Financial Crisis of 2008, the Federal Reserve had an aggressive "quantitive easing" program by purchasing by over $1 trillion in Treasury Securities - INCREASE the money supply lowered interest rates & contributed the economic recovery

Why is it important to consider effective rates of return?

-An investment w/ monthly payments if different from one w/ quarterly payments -Must put each return on an EEF% basis to compare rates of return -Must use EEF% for comparisons -EEF% rates at various compounding periods: EAR annually = 10.00% EAR quarterly = 10.38% EAR monthly = 10.47% EAR daily(365) = 10.52%

Bonds & Borrowing

-Bond: financial security issued by the firm & represents a loan to the firm by an investor (such as an individual or another firm) - It is a LEGAL OBLIGATION: the firm must pay the stated interest & repays the principal bond when it matures -Corporate bonds typically have a denomination of $1,000 - The firm is under legal obligation to pay interest on the bond for a stated # of years and when the bond "matures", repay the investor the initial $1,000 -Interest Rates b/t securities (bonds) may differ due to: - Inflation - Risk - Liquidity - Maturity - 4 General categories of bonds: 1) Short-Term Treasury Securities 2) Long-Term Treasury Securities 3) Short-Term Corporate Securities 4) Long-Term Corporate Securities

Treasury v.s Corporate Debt

-The U.S. gov. sells Treasury Bonds to finance gov. deficits -Corporations sells corporate bonds to acquire needed cash: -The interest rate U.S. gov. bonds & corp. bonds will be different -The interest rate ca be attributable one or more factors (called premiums)

All else being equal, what is the relationship b/t movements in interest rates & stock prices?

-There is an INVERSE relationship b/t interest rates & stock prices - An INCREASE in interest rates RAISES borrowing costs for both corps. & consumers, which leads to LOWER spending and DECREASED corporation profits - A DECREASE in corporate earnings will lead to a DECREASE in stock prices - A DECREASE in interest rates will DECREASE in borrowing costs, leading to an INCREASE spending and corporate profits, which in turn INCREASE the stock prices

Are the Yield Curves for corporate bonds above or below the yield curve for Treasury Bonds?

-Yield curves for corporate bonds are drawn above the yield curve for Treasury Bonds -Corporate bonds have more risk than Treasury Securities (corp. bonds HAVE A DEFAULT RISK) & consequently will have HIGHER rates for given maturity

When is each Interest Rate Used?

-iNOM: written into contracts, quoted by banks & brokers (not used un calculations or shown on time lines) -iPER: used in calculations & shown on time lines (if m=1, iNOM = iPER = EAR) -EAR: used to compare returns on investments w/ different payments per year (used in calculations when annuity payments don't match compounding periods)

Present/Future Value Problems-- Have 4 Variables

1) Present value of an amount 2) Number of periods 3) Interest Rate 4) Future Value of an amount

Four General Factors that Affect the Level of Interest Rates

1) Production Opportunities: better opportunities mean more expected profits-- greeter expected profits means that firms would pay more for money from investors and lenders - Better production means higher interest rates b/c the demand for loans INCREASES 2) Savers Time Preferences for Current versus Future Consumption: affects how much money savers are willing to provide firms - If individuals save less (& consume more), there will be less money available to invest in firms-- this would INCREASE the cost of borrowing (INCREASE interest rates) 3) Inflation: savers must have a greater return than expected inflation - Any increase in inflation INCREASES interest rates (& a decrease in inflation REDUCES interest rates) 4) Risk: the greater the risk, the greater the return required by investors - An increase in risk INCREASES thee cost of borrowing (interest rates) to firms

What is a basis point?

100 basis points = 1%

Assume that you are evaluating 3 different 10 year bonds that have the following ratings: Bond #1 AAA Bond #2 A Bond #3 BBB Bond number ____ would be expected to that the highest yield-to-maturity; Bond number ____ would be expected to have the lowest yield-to-maturity.

3 ; 1

A 10-year, 10% semi-annual coupon bond with a price of $1,135.90 can be called in 4 years for $1,050. What is the yield-to-call?

3.568 N= 4 * 2 = 8 PV= - 1,135.90 PMT= 50 (10% of a $1,000 bond but semi so divide again) FV= 1,050 (PV -, PMT AND FV +) SOLVE FOR I/YR

If sales grow at 20% per year, how long before sales double? Solve w/ Rule of 72

72/20 = 4

EEF% EXAMPLE -- for 10% semiannual investment EEF%= (1 + iNOM / m) ^m - 1

= (1 + .10 / 2) ^2 - 1 = 10.25%

What is a bond?

A bond is a type of financial security that represents a loan to the firm by an investor; it is a legal obligation - the firm must pay the investor

For a given company,

A debenture would have a higher interest rate than a secured bond

What is the difference between a private placement of bonds and a public offering of bonds?

A public offering of bonds means that the company must abide by financial disclosure laws; private placements do not have to abide by these laws.

Annuity Due

A series of equal payments at fixed intervals for a specified number of periods, w/ payment occurring at the BEGINNING of the period

Ordinary Annuity

A series of equal payments at fixed intervals for a specified number of periods, w/ payment occurring at the END of a period

What is a sinking fund?

A sinking fund is a provision that requires the firm to pay off a certain percentage of the total bond issue each year, rather than paying the entire bond issue when the bonds mature.

Perpetuity

An annuity that goes on indefinitely FORMULA= payment per period/interest rate per period

What would increase the general level of interest rates?

An increase in the U.S. budget deficit &&& An increase in the rate of inflation

The required rate of return on a long-corporate bond includes:

An inflation premium, default risk premium, maturity risk premium and liquidity premium

Annual VS. Semi-Annual Compounding Invest $1,000 for 1 year at 10%

Annual= 1,000 (1.10) = $1,100 Semiannual= (1.05)(1.05) = $1,102.50 (earned interest) Semi- money put into your account during the year- earn interest on that 10% stated (nominal rate) 5% periodic rate 10.25% EEF% (1,102.50-1,000)/1000

A bond has a coupon interest rate of 3%; the market rate of interest is currently 5%. The bond will sell:

At a discount (less than $1,000)

All else being equal, which of the following provisions would INCREASE the interest rate on a bond?

Call provision

Term Loan (Bank Borrowing)

Contract b/t borrower and lender (financial institution) for a series of interest and principal payments on a specific dates - Generally 3 to 15 years - May be secured - Generally amortized in equal installments offer speed, flexibility & low insurance costs

A bond will a call provision will likely be called if interest rates ______ after the bond was issued.

Decrease

All else being equal, an increase in interest rates will _____ stock prices.

Decrease

If market interest rates go up after a bond has been issued, the bond's price will

Decrease

What do bond ratings measure?

Default Risk

What do bond ratings measure?

Default risk

The additional return on a bond required by an investor to compensate the investor of the risk of not receiving interest and principal on a corporate bond is called

Default risk premium

Why are interest rates different on various types of bonds?

Differences in interest rates can attributable to different risk premiums that attach to the bond. The premiums increase the interest on the bond.

Rule of 72

Divide 72 by growth rate for approx. # of years to double

The rate targeted by the federal reserve is the _____; it is a _____ term rate.

Fed funds; short

What are protective covenants?

Protective covenants protect the interests of the bondholders, and include positive covenants (things the company must do) and negative covenants (things the company cannot do).

Bonds

Represents a legal obligation for the firm to pay interest and the par value of the bond when the bond matures (also called maturity value) - When bonds are initially sold to an investor, the investor is lending money to the firm in exchange for the firm's promise to pay interest for a certain number of years and the par value of the bond at maturity - If a firm can't meet its legal payment obligations, the firm could be forced into bankruptcy - Corporate bonds generally have a standard par value (denomination) of $1,000 - Investor receives the stated interest payment on the bond each year, and will generally receive the par value at maturity (until the bond is "called")

Determinants of Interest Rates

r = r* + IP + DRP + LP + MRP r = required return on a debt security (nominal) r* = real risk-free rate of interest (determined by the interaction of supply & demand fed funds) IP = inflation premium DRP = default risk premium LP = liquidity premium MRP = maturity risk premium

Nominal Interest Rates VS. Real Interest Rates

r* = represents the "real" risk-free rate of interest (BASE RATE) r = represents any nominal (observed) interest rate r* to r -- additional premiums will be added depending on the type of credit

PERPETUITY EXAMPLE-- Value of perpetuity that pays $100 w/ the relevant interest rate being 8%?

$100/.08= $1,250

What is the Federal Funds Rate?

-The Federal Reserve targets the fed funds rate (basically a proxy for r*) -A very short term interest rate, which is the overnight borrowing rate b/t banks

Interest Rates- Why so important?

-Business Finance Perspective: interest rates are extremely important b/c they affect the cost of borrowing -Major source of funding for firms -If the cost of borrowing money (interest rates INCREASE, firms will borrow LESS) -w/ less money, firms will spend less, which in turn lowers economic growth & has a negative effect on employment -Interest rates affect firm profitability, individual wealth, consumer & corporate spending, economic growth, stock prices & the standard of living -When interest rates DECREASE, generally fosters economic expansion through an INCREASE in borrowing

AMORTIZATION-- Where does the money go?

-Constant payments -Declining interest payments -Declining balance

Interest Rates- Base Rates

-Determined by the interaction of supply (savers of money) and demand (borrowers of money) -Suppliers of Money: Federal Reserve (controls the money supply) & savers (individuals & few firms) -Demanders of Money: Federal Government (finance deficits), borrowers- could include individuals, firms & gov. -BASE RATE(r*): is what borrowers must pay savers for using their money (also referred to ask the real, risk-free rate of interest) -An INCREASE in supply for a given demand, DECREASES interest rates -An INCREASE in demand for a given supply, INCREASES interest rates

What are the risks of foreign investing?

-Example of Exchange Rate- U.S. investor wanting to invest in the Japanese stock market will need yen- the Japanese currency -When the U.S. investor sells their Japanese stocks, they will need to change the yen received when the stock is sold back into the U.S. -Making an investment in a foreign country is subject to not only the change in value of foreign investment, but also the change in the value of the U.S. dollar relative to the foreign country (differences in inflation, movements in interest rates b/t the countries, & differences in economic growth)

Does the Yield Curve historically slope up, down, or flat?

-Generally slopes upward (long term rates are higher than short term rates) -Exceptions have occurred in the early 1980's

Since 2008, what has been the policy of the Federal Reserve?

-Generally, keep interest rates @ historically, relatively low levels -However, from late 2015 through 2018, as a result of an improving economy & at least some expectation of an increased risk of inflation, the federal reserve increased interest rates -Summer of 2019, the Federal Reserve reduced the fed funds rate to contract growing concerns over a global economic slowdown & the effect of tariffs on the U.S. economy

What does the shape of the Yield Curve indicate about expected inflation over time?

-Generally, more inflation in the long-term, maturity risk attaches to long-term bonds only - As a result, in the U.S. long-term interest rates are usually HIGHER than short-term interest rates (if inflation were expected to DECREASE, the yield curve would slope down)

Policy goal of the Federal Reserve

-Goal: balance economic growth w/ an acceptable level of inflation -Tries to accomplish this goal through targeting the Fed. Funds Rate @ a rate that they believe will provide appropriate economic growth w/ an acceptable level of inflation

Which of the following would INCREASE the general level of interest rates?

-INCREASE in Federal Budget Deficit (INCREASE) -INCREASE in savings by individuals (DECREASE) -INCREASE in demand for borrowing by corporations (INCREASE) -DECREASE in demand for Treasury Bonds by foreign investors (INCREASE) -INCREASE in the money supply (DECREASE)

Why does the Federal Reserve targets the fed funds rate?

-If the Federal Reserve changes the Fed. Funds Rate, there is generally a rippling affect for changes in other interest rates (such as the interest rates on bonds, saving deposits, mortgage rates)

Interest Rate Premiums

-Inflation Premium: additional return needed to cover inflation, ALL bonds are subject to inflation, so an inflation premium would attach to ALL BONDS -Default Risk Premium: additional return needed to compensate investor for possibility of NOT receiving inters and/or principal - Attaches to CORPORATE BONDS ONLY, there is a slight chance that a corporation will not be able to meet it's required obligation of paying interest & principal - Treasury securities DO NOT have a default risk-- the Federal gov. has the ability to print more money to pay any debt (if Fed. prints too much money, there would be significant detrimental economic consequences if the Fed. gov. defaulted on it's debt) -Liquidity Premium: additional return needed to compensate investor for not being able to sell the security -Treasury securities are viewed as very liquid-- very easy to buy & very easy to sell (so there is NO liquidity premium attached to TREASURY SECURITIES) -Corporate bonds are viewed as being at least slightly less liquid, so liquidity premium DOES attach to CORPORATE BONDS -Maturity Risk Premium: additional return needed to compensate investor for changes is the price of the bond resulting from market interest rate changes -Mathematical risk that attaches to LONG-TERM BONDS

Multi-Period Compounding

-Interest on an invested amount of money may be paid more than one year - Annual compounding paying interest once a year -Other common periods that interest is paid -Semi-annually, quarterly, monthly, daily -For a stated interest rate- the greater the # of compounding periods, the greater the final wealth -When solving problems-- remember to use the appropriate interest rate for the period & the total # pf compounding periods

Classifications of Interest Rates

-Nominal Rate(iNOM): "quoted or stated rate" or "Annual Percentage Rate (APR)"-- annual rate that ignores compounding effects - Stated in contracts (periods must be given) -Periodic Rate(iPER): amount of interest charged each period, monthly, or quarterly iPER= iNOM/m (m= # compounding periods per year) -Effective (or equivalent) Annual Rate (EAR = EEF% = Annual Percentage Yield)- the annual rate of interest actually being earned, taking into account compounding EEF%= (1 + iNOM / m) ^m - 1

What Premium(s) Attach to

-Short-Term Treasury Securities-- INFLATION -Long-Term Treasury Securities--INFLATION, MATURITY RISK -Short-Term Corporate Securities-- INFLATION, LIQUIDITY, DEFAULT RISK -Long-Term Corporate Securities-- INFLATION, LIQUIDITY, DEFAULT RISK, MATURITY RISK

Yield Curve & Term Structure of Interest Rates

-Term Structure: relationship b/t interest rates (or yields) and maturities; w/ default risk held constant -Yield curve is a graph of the term structure b/t short term and long term interest rates for securities w. equal default risk but different maturities

Assume the following bonds: 1) Treasury bond w/ 10-year maturity 2) AAA rated bond w/ a 10-year maturity 3) BBB rated bond w/ 10-year maturity The _____ will have the highest yield; the _____ will have the lowest yield.

BBB rated bond; Treasury bond

SOLVING FOR PRESENT VALUE OF ANNUITY DUE-- 3 year annuity due of $100 at 10%

BEGIN MODE N= 3 I/YR= 10 PMT= -100 FV= 0 SOLVE FOR PV= -273.55

SOLVING FOR FUTURE VALUE OF ANNUITY DUE-- 3 year annuity due of $100 at 10%

BEGIN MODE!!! N= 3 I/YR= 10 PV= 0 PMT= -100 SOLVE FOR FV= 364.10

If a bond is selling at a discount and market interest rates remain constant, what would happen to the price of a bond as it approaches maturity?

Increase

From 2015 through 2018 the Federal Reserve _____ interest rates; in 2019 the Federal Reserve _____ interest rates.

Increased; decreased

What are interest rate premiums?

Interest rate premiums are the additional return (increase the interest rate) that an investor must receive to be compensated for some type of risk

Correct Statement:

Long-term bonds have more interest rate (price) risk than short-term bonds

Which would be an explanation for the Treasury yield curve to slope up?

Long-term treasury bonds have more inflation and maturity risk than short-term Treasuries

More risk...

More return

SOLVING FOR PAYMENT- COMPOUND INTEREST 40 year old starts saving for retirement, plans to save $3/day, at the end of the year she invests the accumulated savings ($1,095) in an online stock account, stock account has an expected annual return of 12% 20 Year old--FV= 1,487,262 40 Year old--FV= 146,001 How much the 40 year old deposit annually to catch the 20 year old?

N= 25 I/YR= 12 PV= 0 FV= 1,487,262 SOLVE FOR PV= -11,154.42

SOLVING FOR FV- COMPOUND INTEREST 40 year old starts saving for retirement, plans to save $3/day, at the end of the year she invests the accumulated savings ($1,095) in an online stock account, stock account has an expected annual return of 12%

N= 25 I/YR= 12 PV= 0 PMT= -1,095 SOLVE FOR FV= 146,001 (1.3 MIL LESS THAN STARTING AT 20)

What is the Present Value (PV) of $100 due in 3 years if I/YR= 10%?

N= 3 I/YR= 10 PMT= 0 FV= 100 SOLVE FOR PV= -75.13

What is the Future Value (FV) of an initial $100 after 3 years , if I/YR = 10%?

N= 3 I/YR= 10 PV= -100 PMT= 0 SOLVE FOR FV= 133.10

SOLVING FOR I-- What interest rate would cause $100 to grow to $125.97 in 3 years?

N= 3 PV= -100 PMT= 0 FV= 125.97 SOLVE FOR I/YR= 8

SOLVING FOR PRESENT VALUE OF ANNUITY-- What's the PV of a 3 year ordinary annuity of $100 at 10%?

N= 3 I/YR= 10 PMT= 100 FV= 0 SOLVE FOR PV= -248.69

SOLVING FOR FUTURE VALUE (FV) OF ANNUITY-- What's the FV of a 3 year ordinary annuity of $100 at the end of each period @ 10%

N= 3 I/YR= 10 PV= 0 PMT= -100 SOLVE FOR FV= 331

SOLVING FOR FUTURE VALUE OF COMPOUND INTEREST- 20 year old starts saving for retirement, plans to save $3/day, at the end of the year she invests the accumulated savings ($1,095) in an online stock account, stock account has an expected annual return of 12% How much money will she have when she is 65 years old?

N= 45 I/YR= 12 PV= 0 PMT= -1,095 SOLVE FOR FV= 1,487,262

SOLVING FOR FUTURE VALUE-- MULTI-PERIOD COMPOUNDING What is the future value of $500 assuming 12% interest compounded semiannually for 5 years?

N= 5yrs * 2 (semi) = 10 I/YR= 12/2 (semi) = 6 PV= -500 PMT= 0 SOLVE FOR FV= 895.40

Loan Amortization (all inputs are given & remember FV=0 b/c the reason for amortizing the loan & making payments is to retire the loan) Construct an amortization schedule for a $1,000, 10% annual rate loan w/ 3 equal payments

STEP 1: FIND THE REQUIRED ANNUAL PAYMENT N= 3 I/YR= 10 PV= -1,000 FV= 0 SOLVE FOR PMT= 402.11 STEP 2: FIND THE INTEREST PAID IN YEAR 1 INTt = BEG BALt (i) INTt = 1,000 (.10) = $100 STEP 3: FIND THE PRINCIPAL REPAID IN YEAR 1 PRIN = PMT - INT PRIN = 402.11 - 100 = $302.11 STEP 4: FIND THE ENDING BALANCE AFTER YEAR 1 END BAL = BEG BAL - PRIN END BAL = $1,000 - $302.11 = $697.89

If the firm enters bankruptcy, what is the order of payment between senior debt holders, and common stockholders?

Senior debt holders, subordinated debt holders, preferred stockholders, common stock holders

The rights of a bond holder are stated in

The bond indenture

BOND PRICE QUOTE Price: 107.34 Coupon: 2.950 Maturity: 15-Jan-2020 YTM: 1.251 Current Yield: 2.748 Rating: A Callable: No Why is the YTM (Yield-to-Maturity) less than the coupon rate?

The bond's price is higher than the maturity value, which lowers the return on the bond from 2.950% to 1.251%.

What is a call provision on a bond?

The call provision allows the company the option to buy back the bond from the investor before it matures.

What are nominal interest rates?

They are observed interest rates

What is the policy goal of the Federal Reserve?

To balance economic growth w/ an acceptable level of inflation

Interest Rate

The cost of borrowing money -If firms or individuals borrow money, they generally incur a legal obligation to pay back the amount of the loan plus "interest"

Corporate bond ratings indiciate

The default risk of the bond to an investor.

The additional return on a bond needed by an investor to cover inflation is called

The inflation premium

What is the conversion premium on a bond?

The percentage increase in the company's stock price that must occur to make converting the bond into stock attractive.

The nominal interest rate on a bond is equal to

The real risk-free interest rate plus one or more interest rate premiums

Future Value

The value in the future cash flows which earns interest at a stated interest rate

Present Value

The value of cash flows discounted at a stated interest (discount) rate

What is the yield curve?

The yield curve shows the relationship between short-term and long-term interest rates for securities with equal default risk

Historically, does the yield curve slope up, down or is it flat?

Up

Why does the Federal Reserve target the fed funds rate?

When the fed funds rate changes, there is generally a rippling effect for changes in interest rates in other financial market

A bond is callable and is currently selling at $105.23. Will the bond likely be called by the company?

Yes

Can the effective rate ever be equal to the nominal rate?

Yes but only if annual compounding is used (m = 1) -If m > 1 the EEF% will always be greater than the nominal rate

You are an investor with a 5 year investment time period; preservation of your initial investment is a top priority. Which of the following is your optimum investment?

a AAA grade a bond that matures in 5 years

BOND PRICE QUOTE Price: 107.34 Coupon: 2.950 Maturity: 15-Jan-2020 YTM: 1.251 Current Yield: 2.748 Rating: A Callable: No Select the correct statement. a) the price of the bond is $107.34 b) the interest paid on the bond is $2.95 annually c) the price of the bond is $1,073.40 d) the amount received at maturity by the bondholder is $100

c) the price of the bond is $1,073.40