Finance Midterm 2

Reinvestment Rate Risk

*short-term bonds and high coupon rate bonds have higher reinvestment risk* - Uncertainty concerning rates at which cash flows can be reinvested - Short-term bonds have more reinvestment rate risk than long-term bonds - High coupon rate bonds have more reinvestment rate risk than low coupon rate bonds

treasury securities= federal government debt

- Treasury Bills (T-bills) -lowest risk, low interest paid for • Pure discount bonds • Original maturity of one year or less - Treasury notes • Coupon debt • Original maturity between one and ten years - Treasury bonds • Coupon debt• Original maturity greater than ten years

Suppose a bond with a 10% coupon rate and semiannual coupons, has a face value of $1000, 20 years to maturity and is selling for $1197.93. - What is the semiannual coupon payment? - How many periods are there?

- What is the semiannual coupon payment? 50 - How many periods are there? 40

Debt

- a contract - Not an ownership interest - No voting rights - Interest is tax deductible - Creditors have legal recourse if interest or principal payments are missed - Excess debt can lead to financial distress and bankruptcy

change to BGN on calc

-2nd PMT, 2nd enter -remember to change back

Factors Effecting Required Return

-Default risk premium - bond ratings -Taxability premium - municipal versus taxable -Liquidity premium - bonds that have more frequent trading will generally have lower required returns -Maturity premium - longer term bonds will tend to have higher required returns.

Present value: multiple cash flows You are considering an investment that will pay you $1,000 in one year, $2,000 in two years and $3,000 in three years. • If you want to earn 10% on your money, how much would you be willing to pay?

= $4,815.92

If a T-bill promises to repay $10,000 in 12 months and the market interest rate is 7 percent, how much will the bill sell for in the market?

PV= $10,000 N= 1, since 12 mos I/Y= 7 CPT FV= -9345.79, you pay less now than what you are going to get in the future

$1,000 due on credit card• Payment = $20 month minimum • Rate = 1.5% per month

PV= 1,000 I/y= 1.5 PMT= -20 CPT N = 93.111 months = 7.75 years

callable bond

opportunity to lose return you bargained for

Suppose you win the Publishers Clearinghouse $10 million sweepstakes. The money is paid in equal annual installments of $333,333.33 over 30 years. If the appropriate discount rate is 5%, how much is the sweepstakes actually worth today?

ordinary annuity= end PMT= 333,333.33 I/Y= 5 N= 30 PV= 5,124,150.29

Suppose you want to borrow $20,000 for a new car. You can borrow at 8% per year, compounded monthly (8/12 = .66667% per month). If you take a 4 year loan, what is your monthly payment?

ordinary annuity= end n= 4 x 12 = 300 I/y = 8/12 = .67 PV= 20,0000 PMT= -488.26

The Fisher Effect defines

the relationship between real rates, nominal rates and inflation (1 + R) = (1 + r)(1 + h) R = nominal rate (Quoted rate) r = real rate h = expected inflation rate Approximation: R = r + h

Suppose you can earn 1% per month on $1 invested today. What is the APR?

1(12) = 12%

if we pay more than a thousand dollars, then we

better be compensated with higher coupon payments because we are only getting a 1000 back when the bond matures

higher coupon rate? A bond with a sinking fund versus one without

bond without

bonds vs. stocks

bonds are different than stocks because they have are a contractual arrangement "this is what you're going to get paid for a period of time" -this is what you are going to get paid for this period of time -very defined and finite features and rates required in the bond

Moody's uses

both capital and lower case

If given D1, do not need to

bring it forward a year -if given d0, you do need to find it

short term vs. long term bond- which of your payments should be more?

long-term

as the required rate of return goes up, the higher/lower the stock price

lower

the lower the risk, the lower or higher the coupon?

lower

constant growth model: what is price in year 5?

use year 6, use next year's dividend -separately calculate using growth rate

PMT on calc

used for equal payment -usually a monthly thing

maturity date

when this bond is going to be paid back -no matter what happens to the bond, up or down, when the price matures, you get a 1000

Suppose you are looking at the following possible cash flows: - Year 1 CF = $100;- Years 2 and 3 CFs = $200;- Years 4 and 5 CFs = $300.- The required discount rate is 7% • What is the value of the CFs at year 5? • What is the value of the CFs today?

year 5: CF 1: 100 FO1: 1 CF 2: 200 F02: 2 CF 3: 300 F03: 2 NPV= 874.17 today: NPV, click CPT on NFV =1,226.07

How to solve for future cash flow problems

you work back from how many years the problem is asking for -If you invest today, but the problem is asking for two years out, then you have to have an N of 2 on that original investment

Estimating Dividends Special Cases

• Constant dividend/Zero Growth- Firm will pay a constant dividend forever- Like preferred stock- Price is computed using the perpetuity formula • Constant dividend growth - Firm will increase the dividend by a constant percent every period • Supernormal growth - Dividend growth is not consistent initially, but settles down to constant growth eventually

Dividend Characteristics

• Dividends are not a liability of the firm until declared by the Board of Directors - A firm cannot go bankrupt for not declaring dividends • Dividends and Taxes - Dividends are not tax deductible for firm - Taxed as ordinary income for individuals - Dividends received by corporations have a minimum 70% exclusion from taxable income

NASDAQ

• NASDAQ OMX (merged 2007)• Computer-based quotation system• Multiple market makers• Electronic Communications Networks • Three levels of information- Level 1 - median quotes, registered representatives - Level 2 - view quotes, brokers & dealers- Level 3 - view and update quotes, dealers only • Large portion of technology stocks

NYSE operations

• Operational goal = attract order flow • NYSE DMMs: - Assigned broker/dealer • Each stock has one assigned DMM • All trading in that stock occurs at the "DMM's post" - Trading takes place between customer orders placed with the DMMs and "the crowd" - "Crowd" = Floor brokers and SLPs

The Stock Markets

• Primary vs. Secondary Markets - Primary = new-issue market - Secondary = existing shares traded among investors • Dealers vs. Brokers- Dealer: Maintains an inventor Ready to buy or sell at any time Think "Used car dealer"- Broker: Brings buyers and sellers together Think "Real estate broker"

Quoted Price versus Invoice Price

• Quoted bond prices = "clean" price - Net of accrued interest • Invoice Price = "dirty" or "full" price - Price actually paid- Includes accrued interest • Accrued Interest - Interest earned since last coupon payment is owed to bond seller at time of sale

Inflation and Interest Rates

• Real rate of interest =Change in purchasing power • Nominal rate of interest= Quoted rate of interest,= Change in purchasing power and inflation

New York Stock Exchange (NYSE)

•need a specliast for every exchange NYSE - Merged with Euronext in 2007 - NYSE Euronext merged with the American Stock Exchange in 2008 • Members (Historically) - Buy a trading license (own a seat) - Designated market makers, DMMs (formerly known as "specialists") - Floor brokers - Supplemental liquidity providers (SLPs)

You are considering preferred stock that pays a quarterly dividend of $1.50. If your desired return is 3% per quarter, how much would you be willing to pay?

$1.50/0.03 = $50

price risk

*longer the bond, higher the risk* *lower coupon rate, higher the risk* - Change in price due to changes in interest rates - Long-term bonds have more price risk than short-term bonds - Low coupon rate bonds have more price risk than high coupon rate bonds

Ordinary Annuity

*same stream of payments for a finite period* finite series of equal payments that occur at regular intervals - If the first payment occurs at the end of the period, it is called an ordinary annuity -bond

A taxable bond has a yield of 8% and a municipal bond has a yield of 6% • If you are in a 40% tax bracket, which bond do you prefer?

*take 1-tax rate times the percent for the taxable bond, compare that to the nontaxable bond 8%(1 - .4) = 4.8% -The after-tax return on the corporate bond is 4.8%, compared to a 6% return on the municipal

ARR Average Accounting Return

- Average net income/Average book value - Accept if AAR > Some specified target - Needed data usually readily available - Not a true rate of return - Time value of money ignored - Arbitrary benchmark - Based on accounting data not cash flows

Profitability index

- Benefit-cost ratio - Accept investment if PI > 1 - Cannot be used to rank mutually exclusive projects - May be used to rank projects in the presence of capital rationing

Security bonds

- Collateral - secured by financial securities - Mortgage - secured by real property, normally land or buildings

unsecured bonds

- Debentures - unsecured - Notes - unsecured debt with original maturity less than 10 years

bond

- Debt contract only get paid interest on a bond, I'm gonna pay your interest during the year and at the end of the contract I'm going to pay the bond $ back - Interest-only loan

Ordinary annuity versus Annuity due

- If the first payment occurs at the beginning of the period, it is called an annuity due - If the first payment occurs at the end of the period, it is called an ordinary annuity -most problems are ordinary

-high grade

- Moody's Aaa and S&P AAA - capacity to pay is extremely strong - Moody's Aa and S&P AA - capacity to pay is very strong

Low Grade

- Moody's Ba, B, Caa and Ca- S&P BB, B, CCC, CC- Considered speculative with respect to capacity to pay. The "B" ratings are the lowest degree of speculation.

Very Low Grade

- Moody's C and S&P C - income bonds with no interest being paid - Moody's D and S&P D - in default with principal and interest in arrears

Equity

- Ownership interest - Common stockholders vote to elect the board of directors and on other issues - Dividends are not tax deductible - Dividends are not a liability of the firm until declared. Stockholders have no legal recourse if dividends are not declared - An all-equity firm cannot go bankrupt

If we require a 10% real return and we expect inflation to be 8%, what is the nominal rate?

- R = (1.1)(1.08) - 1 = .188 = 18.8% - Approximation: R = 10% + 8% = 18%- Because the real return and expected inflation are relatively high, there is significant difference between the actual Fisher Effect and the approximation.

If you own a share of stock, you can receive cash in two ways

- The company pays dividends - You sell your shares, either to another investor in the market or back to the company

Effective Annual Rate (EAR)

- The interest rate expressed as if it were compounded once per year. - Used to compare two alternative investments with different compounding periods

How to tell the difference between present and future cash flow problems

-Future cash flow will be asking in future tense, asking for how the lump cash sum will be affected with the decisions you make in the upcoming years -"how much will the account be affecting in 5 years if..." -How much will you have in 5 years if you make no further deposits? -Suppose you plan to deposit $100 into an account in one year and $300 into the account in three years. How much will be in the account in five years if the interest rate is 8%? -If the fund pays 9% annually, how much will you have in two years?

Future Value with Multiple Cash Flows

-I start with a certain sum, I put this much in on an annual basis, How much is it going to be worth at some point in the future? -you have a lump of cash and either add to it or take away from it over time, you don't just leave the cash

Bond Markets

-Primarily over-the-counter transactions with dealers connected electronically -Extremely large number of bond issues, but generally low daily volume in single issues -Getting up-to-date prices difficult, particularly on small company or municipal issues -Treasury securities are an exception

Senority bonds

-Senior versus Junior -Subordinated: may have subordinated the bond to another lender as the first position to inventory

Annual Percentage Rate (APR) "Nominal"

-The interest rate charged per period multiplied by the number of periods per year - The annual rate quoted by law- APR = periodic rate X number of periods per year- Periodic rate = APR / periods per year

Present value: multiple cash flows - You are offered an investment that will pay • $200 in year 1,• $400 the next year,• $600 the following year, and • $800 at the end of the 4th year.• You can earn 12 percent on similar investments. • What is the most you should pay for this one?

-cash flow function Most you should pay: $1,432.93

You can afford $632 per month. Going rate = 1%/month for 48 months. How much can you borrow? (you can tell its an annuity problem because of equal payments)

-change to BGN N=48 I/Y= 1 PMT= -632 Find PV since you are looking for money today

coupon < YTM when

-discount bond YTM is higher than what it was issued at -paid less in order to get decreased yield price is less than par value

Suppose you invest $500 in a mutual fund today and $600 in one year. • If the fund pays 9% annually, how much will you have in two years? *Solve*

-future value: working towards the two years 1. solve for 500 PV= -500 N=2 (since you invested today) I/Y=9 =594.05 2. Solve for 600 PV= -600 N= 1 I/Y=9 = 654.00 3. add = $1,248.05

bond ratings- investment quality

-high grade -medium grade S&P and Moody's

would you expect a higher or lesser return on a sinking fund bond?

-higher return, lower risk -more security

The Bond Indenture *know components*

-how bond is structured Contract between issuing company and bondholders includes: - Basic terms of the bonds - Total amount of bonds issued - Secured versus Unsecured - Sinking fund provisions - Call provisions • Deferred call • Call premium - Details of protective covenants

Suppose stock is expected to pay a $0.50 dividend every quarter and the required return is 10% with quarterly compounding. What is the price?

-not calc .10/4 since quarters= 0.025 so .50/.025= 20

Amortization loan

-pay more of the interest when the loan first starts and less of the principal, eventually switch around -lender may require the borrower to repay parts of the loan amount over time -how its applied is different in how close you are to getting that loan paid off

coupon > YTM when

-premium bond price is more than par

stock- constant growth model

-present value of a stock having constant growth dividends *D1/R-G* D1= dividend at time 1, at end of first period (next period) R= required rate of return G= growth rate

Pure Discount Loans

-simplest form of a loan -the borrow receives money today and repays a single lump sum at some time in the future -pay something less, then get paid for full face amount at the end -have to trust, absolute assurance, government is good Treasury bills are excellent examples of pure discount loans. - Principal amount is repaid at some future date - No periodic interest payments - buying the earnings upfront

Yeild to maturity YTM

-the market required rate of return implied by the current bond price what you'd make according to what you pay for the bond according to cash flow of the bond

coupon rate

-the stated interest payment made on a bond only used to define the coupon payment *do not use the coupon rate in any of my calcs -essentially an APR

Suppose you invest $500 in a mutual fund today and $600 in one year. • If the fund pays 9% annually, how much will you have in two years? How much will you have in 5 years if you make no further deposits?

-use the $1,248.05 from two years now for your FV FV: $1,248.05 I/Y: 9 5 years - 2 years = 3 years so N= 3 = $1,616.26 in 5 years

What is the APR if the semiannual rate is .5%?

.5%(2) = 1%

What is the APR if the monthly rate is .5%?

.5(12) = 6%

If you deposit $100 in one year, $200 in two years and $300 in three years. How much will you have in three years at 7 percent interest? How much in five years if you don't add additional amounts?

1. 100 N= 2, PV= -100, I/Y=7 =114.49 2. 200, PV= -200, I/Y=7 =214.00 3. 300 N= 0, I/Y= 7, PV= -300 =300 4. add =628.49 How much in five years if you don't add additional amounts? 5-3= 2 years N = 2, I/Y= 7, use new sum as PV=628.49 FV= 719.56

Suppose you plan to deposit $100 into an account in one year and $300 into the account in three years. How much will be in the account in five years if the interest rate is 8%?

1. 100 PV= -100 I/Y= 8 N= 5 years - 1 year = 4 years, N = 4 =136.05 2. 300 PV= -300 I/Y = 8 N= 5 years - 3 years = 2 years, N = 2 = 349.92 3. add =$485.97

Which savings accounts should you choose - 5.25% with daily compounding.- 5.30% with semiannual compounding (Annual rate has been given, always been given, so look for effective rate)

1. Nom= 5.25, C/Y= 365 (all days of year) EFF=5.39 2. Nom=5.30, C/Y=2 (semi annual) EFF= 5.37 Choose first one

Coupon rate = 14% Semiannual YTM = 16% (APR) Maturity = 7 years *Transfer to semiannual*

1. Number of coupon payments: 14 = 2 x 7 years 2. Semiannual coupon payment: 1000 x .14= 140 140/2= $70 3. Semiannual yield: 16%/2 =8% -change back, 16

Coupon rate=10% Annual coupons Par=$1,000 Maturity=20years YTM=8%

1. PMT=100 2. N=20 I/Y=8 FV=1000 PMT=100 3. PV= -1196.36

payback period with non-constant cash flows 90,000 investment cash flows of 25,000, 25,000, 15,000

1. divide 15,000 by 90,000 to get a percent =16.67 2. divide 90,000 by 25,000 =3.6 3. add the percent

cash flows to stockholder programs

1. find cash flows add D and P for the period 2. CF function

Non constant growth- different growth rates finding the price of the stock Suppose a firm is expected to increase dividends by 20% in one year and by 15% in two years. After that dividends will increase at a rate of 5% per year indefinitely. If the last dividend was $1 and the required return is 20%, what is the price of the stock?

1. find dividends for each year D1: 1 x .20 = 1.20 D2: 1.20 x .15 = 1.38 D3: 1.38 x .5 = 1.449 once it becomes constant, you can stop in that year 2.

government bonds

1. municipal securities 2. treasury securities= federal government debt

Consider an investment that costs $100,000 and has a cash inflow of $25,000 every year for 5 years. The required return is 9% and required payback is 4 years. - What is the payback period? - What is the NPV? - What is the IRR? - Should we accept the project?

1. payback period investment/cash inflow 100,000/25,000= 4 2. NPV C0:-100,000 C01: 25,000 Fo1: 5 CF function: NPV =-2,758.72 3. IRR button IRR: 7.93

How do we determine what a bond should be valued at/YTM?

1. price risk 2. Reinvestment Rate Risk

• Couponrate=10% • Annual coupons Par=$1,000 Maturity=5 years YTM=11%

1. use coupon rate to find annual payment 10% of 1000= 100=PMT 2. Calc PMT=100 N=5 I/Y(YTM)=11 FV= 1000 =PV of -963.04

if you have a bond problem that isn't giving a future value, use

1000

all corporate bonds have a face value of

1000 -bonds always issue at a 1000, change from there so FV will always be 1000 in bond problems

What is the monthly rate if the APR is 12% with monthly compounding?

12%/12=1%

12 month at 6%

12= C/Y 6=NOM (APR) CPT, EFF= 6.17

Consider a bond with a 10% annual coupon rate, 15 years to maturity and a par value of $1000. The current price is $928.09. - Will the yield be more or less than 10%?

15 N 928.09 PV (enter as a negative) 100 PMT FV 1000 PV= 11%

What if the company starts increasing dividends by 3% per year beginning with the next dividend? The required return remains at 15%.

2(1.03)/.15-.03 = 17.17

Suppose TB Pirates, Inc. is expected to pay a $2 dividend in one year. If the dividend is expected to grow at 5% per year and the required return is 20%, what is the price?

2=D1 g=5 r=20 = 2/.20-.05= $13.33

how to clear ICOV

2nd ICONV (2) 2nd CE/C

Suppose if you put it in another account, you earn 3% per quarter. APR?

3 x 4 = 12%

investment cutoff for S&P

AAA - BBB AAA, AA, A, BBB Triple a= top of investment grade triple b= bottom of investment grade

standard quoting mechanism for interest earned or interest paid

APR

Which rate do you need to use in the time value of money calculations?

APR -only ever this

everything you hear quoted to you about interest rates will be quoted in

APR -only way interest rates are quoted -cannot be quoted in anything but APR

Suppose you can earn 1% per month on $1 invested today. - What is the APR? 1(12) = 12% - How much are you effectively earning?

APR= 12 C/Y= 12 EFF= 12.68

investment cutoff for Moody's

Aaa - Baa Aaa, Aa, A, Baa

payback period decision rule

Accept if the payback period is less than some preset limit.

What is the definition of an APR?

Annual percentage rate -rate quoted -rate we are charged -rate we use

non investment for S&P

BB, B, CCC, CC, C, D

non investment for Moody's

Ba, B, Caa, Ca, C

why does it say 100.641 as a price for a bond?

Bonds are priced at percent of par- 100% plus .641 beyond the value of the bond -a discount bond could be listed at something like 989

what would you have to do yeild to get the right answer above?

Bring back to a year, YTM is annual since its APR, must leave at annual even though the other two are semi-annual

Present value: multiple cash flows Your broker calls you and tells you that he has this great investment opportunity. If you invest $100 today, you will receive $40 in one year and $75 in two years. If you require a 15% return on investments of this risk, should you take the investment?

CF CF 1: 40 CF 2: 75 I: 15 CPT NPV: 91.49 Since he is asking for more than 91.49, don't take it

You are offered the opportunity to put some money away for retirement. You will receive five annual payments of $25,000 each beginning in 40 years. How much would you be willing to invest today if you desire an interest rate of 12%

CF 0= 0, goes for 39 years on the calc goes for 39 years F01= 39, same cash flow for 39 periods C02= 25,000 F02= 5 calc =1084.71

How to clear CF function?

CF2nd CE/C

You think you will be able to deposit $4,000 at the end of each of the next three years in a bank account paying 8 percent interest. You currently have $7,000 in the account. How much will you have in 3 years? How much in 4 years?

Change FV from previous problem to PV, solve for a one year FV with same interest PV= $21,803.58 I/Y= 8 N= 1 FV= $23,547.87

C/Y=

Compounding periods per year

Floating Rate Bonds

Coupon rate floats depending on some index value Examples - adjustable rate mortgages and inflation-linked Treasuries Less price risk with floating rate bonds - Coupon floats, so is less likely to differ substantially from the yield-to-maturity Coupons may have a "collar" - the rate cannot go above a specified "ceiling" or below a specified "floor"

A firm's stock is selling for $10.50. They just paid a $1 dividend and dividends are expected to grow at 5% per year. What is the required return?

D1: 1 x .05 = 1.05 1.05/1.50 =15% return

Gordon Growth Company is expected to pay a dividend of $4 next period and dividends are expected to grow at 6% per year. The required return is 16%. What is the current price?

D1: 4 G: 6 R: 16 4/.16-.06= $40

If a problem has daily compounding with APR given, what do you do?

Divide APR by 365

Features of Preferred Stock

Dividends - Must be paid before dividends can be paid to common stockholders - Not a liability of the firm - Can be deferred indefinitely - Most preferred dividends are cumulative • Missed preferred dividends have to be paid before common dividends can be paid • Preferred stock generally does not carry voting rights

Zero Growth

Dividends expected at regular intervals forever = perpetuity -used in constant, unchanged dividend amount P0 = D / R

Suppose you want to earn an effective rate of 12% and you are looking at an account that compounds on a monthly basis. What APR must they pay?

EFF = 12 C/Y = 12 NOM = 11.3866

Will the effective rate or APR (nom) always be bigger?

Effective -compound periods of any amount make a higher APR than quoted

EFF=

Effective annual rate- EAR

Suppose you invest $500 in a mutual fund today and $600 in one year. • If the fund pays 9% annually, how much will you have in two years? *Is this a future cash flow or present cash flow problem?*

Future cash flow

Coupon rate = 14% Semiannual YTM = 16% (APR) Maturity = 7 years *solve*

I/Y= 8 N= 14 PMT= 70 FV= 1000 PV= -917.56

medium grade

Moody's A and S&P A - capacity to pay is strong, but more susceptible to changes in circumstances - Moody's Baa and S&P BBB - capacity to pay is adequate, adverse conditions will have more impact on the firm's ability to pay

Call provision bond

More risk, more opportunity cost, lower return -bond issuer can take the bond back at a certain point, gives defined reasons for this

municipal securities

Municipal Securities - Debt of state and local governments - Varying degrees of default risk, rated similar to corporate debt - Interest received is tax-exempt at the federal level - Interest usually exempt from state tax in issuing state

What if an APR is quoted monthly?

Must change it to annual before you move on -annual

Zero Coupon Bonds

Make no periodic interest payments (coupon rate = 0%) Entire yield-to-maturity comes from the difference between the purchase price and the par value (capital gains) Cannot sell for more than par value Sometimes called zeroes, or deep discount bonds Treasury Bills and U.S. Savings bonds are good examples of zeroes

Suppose a bond with a 10% coupon rate and semiannual coupons, has a face value of $1,000, 20 years to maturity and is selling for $1,197.93. Solveeeee

N = 40 PMT = 50 PV= 1,197.93 FV= 1000 =4% (semiannual) 4 x 2 = 8- multiple times 2 since asking for YTM, bring it back to annual

You think you will be able to deposit $4,000 at the end of each of the next three years in a bank account paying 8 percent interest. You currently have $7,000 in the account. How much will you have in 3 years?

N= 3, I/Y= 8, PV= 7,000, PMT=4,000 FV= $21,803.58

Can you divide the above APR by 2 to get the semiannual rate?

NO. You need an APR based on semiannual compounding to find the semiannual rate.

NOM=

NOM (Nominal rate-APR)

Suppose if you put it in another account, you earn 3% per quarter. - What is the APR? 3(4) = 12% -How much are you effectively earning?

NOM = 12 C/Y =4 EFF = 12.5509

What decision rule should be the primary decision method?

NPV

Constant Growth Stock

One whose dividends are expected to grow forever at a constant rate, g. 0= today, present value d0= dividend just paid d1= next dividend, end of period 1 dt= dividend at that period, whichever one you put in

An investment offers a perpetual cash flow of $500 each year. The return you want is 8%. What is the value of the investment?

PV = PMT / r 500/8= $6,250

time value of money calculations

PV, FV

If we have a constant dividend, then we use what formula?

Perpetuity dividend/required rate of return

Perpetuity formula

Perpetuity formula: PV = PMT / r

What is the definition of an effective rate?

Rate that is realized after imputing the value of compounding -with compounding, the effective rate changes

stated interest rate

The interest rate expressed in terms of the interest payment made each period. Also known as the quoted interest rate.

Features of Common Stock

Voting Rights- Stockholders elect directors- Cumulative voting vs. Straight voting- Boards are often staggered, or "classified" - Proxy voting • Classes of stock - Founders' shares - Class A and Class B shares Other Rights (2 of 2) - Share proportionally in declared dividends - Share proportionally in remaining assets during liquidation - Preemptive right • Right of first refusal to buy new stock issue to maintain proportional ownership if desired

When a bond trades for less than it originally sold at, its called

a discount bond

Typically, compound periods will result in

a higher effective rate -if carried out for longer periods of time, the difference gets larger and larger

dividend growth model

a model that determines the current price of a stock as its dividend next period divided by the discount rate less the dividend growth rate

When a bond trades for more than it originally sold at, its called

a premium bond

protective covenants

measurable structures inside a bond -you cannot issue bonds if you fall below a specified financial metrics, cannot borrow anymore

convertible bonds

able to convert them into shares of stock

You are saving for a new house and you put $10,000 per year in an account paying 8%. The first payment is made *today*. How much will you have at the end of 3 years?

annuity due- BGN PMT: -10,000 I/Y: 8 N: 3 CPT FV: 35061.12

You want to have $1 million to use for retirement in 35 years. If you can earn 1% per month, how much do you need to deposit on a monthly basis if the first payment is made today

annuity due= made today, BGN FV= 1 mil N= 420 I/Y= 1 CPT PMT= -153.96

Coupon rate and YTM are the same only when

at issue, 1000

higher coupon rate? A callable bond versus a non-callable bond

callable bond

S&P only uses

capital letters

frequency should stay at 1 in CF when...

cash flows are different

Annuity due

change to BGN on calc -An annuity for which the cash flows occur at the beginning of the period - If the first payment occurs at the beginning of the period, it is called an annuity due -almost any type of an arrangement where we have to repay the same amount each period -paying rent in a lease

bond indenture

contract of the bond -paid usually 2 time a year in the US

how to get payment going to receive each year for the bond

coupon rate x bond value

higher coupon rate? Secured debt versus a debenture

debenture

if I/Y goes up with all other things equal, the present value must

decrease visa versa -yield maturity goes up, price goes down

as interest rates go up, bond values... why?

decrease, inverse If a new issue bond is less than an old issue bond, I can buy for greater cash flow

APR is always yearly, so if asked in a problem for monthly compounding, what do you do?

divide APR by 12

d stands for

dividend

What is the value of a stock that is expected to pay a constant dividend of $2 per year if the required return is 15%?

dividend/required rate of return 2/15= 13.33

Which rate should you use to compare alternative investments or loans?

effective -gives you actual return as opposed to quoted

all else remaining the same, the more the compound periods there are, the greater the difference

effective and APR

To compute NOM

enter the EFF and C/Y values, move to NOM and press CPT

To compute EFF

enter the NOM and C/Y values, move to EFF and press CPT

d1 to dt

expected dividends

Suppose you desposit $100 today in an account paying 8 percent. In one year, you will deposit another $100. How much will you have in two years?

first year: 100 second year: 100 x 1.08 for 108. 100 + 108 = 208 208 x 1.08 = 224.64

How does inflation affect interest rates?

generally higher the inflation, higher interest rates -inflation rates high give us an abnormal yield curve, higher interest rates at first then lower later

if you pay less for the bond at face value, the return...

goes up (return value to ownership AKA YTM) -cash flow stays the same, collecting same amount per year

put bonds

have the right to sell the bond back before maturity -CD bonds with a bank

the greater the growth rate the higher/lower the stock price

higher -makes a large difference on the price of the stock today

Perpetuity

infinite series of equal payments -same stream of payments for an infinte period -preferred stock

yeild curve is made up of

interest rate risk premium, inflation premium, real rate

structured notes

pays according to some other index -with a floor and ceiling -looking to define ways that structure your return

You know the payment amount for a loan and you want to know how much was borrowed. - Do you compute a present value or a future value?

present value, you have to take the money at some point

As interest rates increase

present values decrease

P stands for

price

coupon rate = YTM only when

price = par 1000 issuing

annual percentage rate is always the

quoted rate and effective rate

Suppose Big D, Inc. just paid a dividend of $.50. It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk, how much should the stock be selling for?

required rate of return= .02 growth rate= .15 1. Find D1, period ahead .50 x .02 = .01 .01 + .5= .51=D1 2. .51/R-G .51/.15-.02 = 3.92

r

required return, interest rate, or risk

The sooner you take to get your money back, the less

risk you take, the longer, the more -measured by the yield curve

higher coupon rate? Subordinated debenture versus senior debt

subordinated debenture

Payback Period

the amount of time required for an investment to generate cash flows sufficient to recover its initial cost =investment/cash inflow= number of years - Length of time until initial investment is recovered - Accept if payback < some specified target - Doesn't account for time value of money - Ignores cash flows after payback - Arbitrary cutoff period - Asks the wrong question Compute: - Estimate the cash flows - Subtract the future cash flows from the initial cost until initial investment is recovered. - A "break-even" type measure

the longer it takes me to get paid back, if the interest rates don't change,

the bond price is gonna change

sinking fund

the company/issuer of bond is putting away money every year to be able to fully repay the bond at maturity

Net Present Value (NPV)

the difference between an investment's market value and its cost - Difference between market value (PV of inflows) and cost - Accept if NPV > 0 - No serious flaws - Preferred decision criterion

Internal Rate of Return

the discount rate that makes the NPV of an investment zero - Discount rate that makes NPV = 0 - Accept if IRR > required return - Same decision as NPV with conventional cash flows - Unreliable with:• Non-conventional cash flows • Mutually exclusive projects - MIRR = better alternative

band ratings are only concerned with what possibility?

the possibility of default -the risk of a change in the value of a bond resulting in an interest rate change

what happens if yield to maturity goes up?

the present value goes down -interest rates and value of bonds (PV) are inverse

face value

the principal amount of a bond that is repaid at the end of the term -repaid at maturity -1,000 -par value