MAC 718 Midterm

Maturity date

periods or end of timeline # of years, or an explicit date

Discount rates are ______ and they vary by _______ and _________

personal; person and project

Always remember: "To what are you discounting?"

"At the point of retirement, what is this cash flow stream worth to you?" t=1 t0 -> DF always 1

What are some of the "phrases" that trigger future value?

-"end" -"at maturity" -"account balance at maturity"

What are some of the "phrases" that trigger present value?

-"today" -"right now" -"good deal" -"worth today" -"how much would you pay today?"

In the PV function for a perpetuity, the r denominator tells you what?

-About the other things you could've done with your money (other opportunities) -contextualizes the value of $10 payments as time goes on

Bond Pricing Theorems

-Bonds of similar risk (and maturity) will be priced to yield about the same return, regardless of the coupon rate. -If you know the price of one bond, you can estimate its YTM and use that to find the price of the second bond. -This is a useful concept that can be transferred to valuing assets other than bonds.

Price 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.

What is the discount rate?

-Compensation I require/rate of return (ROR) on investment for parting with my money i) Lost opportunity (risk-free) ii) Uncertainty (Risky) Key point here: you can't compare money from different time periods

What is a firm worth?

-Conceptually, a firm should be worth the present value of the firm's cash flows. -The tricky part is determining the size, timing, and risk of those cash flows.

Interest-Only Loan

-Consider a five-year, interest-only loan with a 7 percent interest rate. The principal amount is $10,000. Interest is paid annually. ◦ What would the stream of cash flows be? Years 1-4: Interest payments of .07(10,000) = 700 Year 5: Interest + principal = 10,700 -This cash flow stream is similar to the cash flows on corporate bonds, and we will talk about them in greater detail later.

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

How long does it take the project to "pay back" its initial investment, taking the time value of money into account?

-Decision rule: Accept the project if it pays back on a discounted basis within the specified time. -By the time you have discounted the cash flows, you might as well calculate the NPV.

Factors Affecting Required Return

-Default risk premium—remember bond ratings -Taxability premium—remember municipal versus taxable -Liquidity premium—bonds that have more frequent trading will generally have lower required returns (remember bid-ask spreads) -Anything else that affects the risk of the cash flows to the bondholders will affect the required returns.

Disadvantages and advantages of the payback period method

-Disadvantages: Ignores the time value of money, Ignores cash flows after the payback period, Biased against long-term projects, Requires an arbitrary acceptance criteria, A project accepted based on the payback criteria may not have a positive NPV -Advantages: Easy to understand and Biased toward liquidity

Treasury Securities

-Federal government debt -T-bills—pure discount bonds with original maturity less than one year -T-notes—coupon debt with original maturity between one and ten years -T-bonds—coupon debt with original maturity greater than ten years

Corporate Bonds

-Greater default risk relative to government bonds -The promised yield (YTM) may be higher than the expected return due to this added default risk

The Payback Period Method

-How long does it take the project to "pay back" its initial investment? -Payback Period = number of years to recover initial costs -Minimum Acceptance Criteria: set by management -Ranking Criteria: set by management

The Internal Rate of Return

-IRR: the discount rate that sets NPV to zero -Minimum Acceptance Criteria: Accept if the IRR exceeds the required return -Ranking Criteria: Select alternative with the highest IRR -Reinvestment assumption: All future cash flows are assumed to be reinvested at the IRR Disadvantages: -Does not distinguish between investing and borrowing -IRR may not exist, or there may be multiple IRRs -Problems with mutually exclusive investments Advantages: -Easy to understand and communicate

Zero Coupon Bonds

-Make no periodic interest payments (coupon rate = 0%) -The entire yield to maturity comes from the difference between the purchase price and the par value -Cannot sell for more than par value -Sometimes called zeroes, deep discount bonds, or original issue discount bonds (OIDs) -Treasury bills and principal-only Treasury strips are good examples of zeroes

Inflation-Linked Bonds

-Most government bonds face inflation risk -TIPS (Treasury inflation-protected securities), however, eliminate this risk by providing promised payments specified in real, rather than nominal, terms

Accepting positive NPV projects benefits stockholders.

-NPV uses cash flows -NPV uses all the cash flows of the project -NPV discounts the cash flows properly

The Net Present Value (NPV) Rule

-Net Present Value (NPV) =Total PV of future CFs + Initial investment -Estimating NPV: 1. Estimate future cash flows: How much? And when? 2. Estimate discount rate 3. Estimate initial costs -Minimum Acceptance Criteria: Accept if NPV > 0 -Ranking Criteria: Choose the highest NPV

A bond is a legally binding agreement between a borrower and a lender that specifies the:

-Par (face) value -Coupon rate -Coupon payment -Maturity date

"Market" for bonds

-People who issue debt will be a player in this market -when looking at the supply/demand graph in class exemplifying the bond market, it is important to remember that everyone is coming to the market with their own PERSONAL discount rates; the price balances everyone out -the DR average (line over DR for mathematical/1st derivative) is like the average between the people who have bonds and the people who want bonds

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 -Makes getting up-to-date prices difficult, particularly on a small company or municipal issues -Treasury securities are an exception

Bond Valuation

-Primary Principle: Value of financial securities = PV of expected future cash flows -Bond value is, therefore, determined by the present value of the coupon payments and par value. -Interest rates are inversely related to present values (i.e., bond prices).

Loan Amortization

-Pure discount loans are the simplest form of loan. The borrower receives money today and repays a single lump sum (principal and interest) at a future time. -Interest-only loans require an interest payment each period, with full principal due at maturity. -Amortized loans require repayment of principal over time, in addition to required interest.

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 -The ex ante nominal rate of interest includes our desired real rate of return plus an adjustment for expected inflation.

What drives the Discount Factor?

-T and R (separated on purpose; have different meanings)

With an in-class example, the PV of a bond went from $1197 to $1193. How is this possible when the piece of paper/legal document did not change?

-The piece of paper didn't change, BUT the bond is worth less to you as you progress through the timeline based on the bond market and prevailing economic conditions

What is "r?"

-The required rate of return -What I need to make up for the fact that I lost opportunity and am facing risk 0r (required rate of return) = risk free and risky

Information needed for valuing pure discount bonds:

-Time to maturity (T) = Maturity date - today's date -Face value (F) -Discount rate (r)

Pure Discount Loans

-Treasury bills are excellent examples of pure discount loans. The principal amount is repaid at some future date, without any periodic interest payments. -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 / 1.07 = 9,345.79

What is EAR and when do I need to use it?

-Two different saving accounts with different compounding frequencies (not interests) -> you must use compounding 4x > compounding 1x EAR excel: Effect: APR -> EAR Nominal: EAR -> APR

Reinvestment Rate 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.

Consider a bond with a 10% annual coupon rate, 15 years to maturity, and a par value of $1,000. The current price is $928.09.

-Will the yield be more or less than 10%? -N = 15; PV = -928.09; FV = 1,000; PMT = 100 -CPT I/Y = 11%

What is a sneaky risk associated with bonds that's not listed?

-You need to assess the value of bond paper @ T1 given (based on the d.r. and the economic environment at the time of purchase) -sneaky risk; many reasons why value can move (one big risk: default) -borrower: person issuing the bond! If George Washington couldn't pay you back, they'd be in default

What is some important information that is not on the bond contract?

-buyer -> has to w/possession (bearer bond); whoever holds the bond at the time, is the legal owner -YTM -key: most bonds are usually electronic now

When is price risk relevant?

-essence of price risk: what happens when the interest rates go up and down -there is increased price risk when the slope is steeper (change in price/change in interest) -when interest rates change (specifically, when interest rates rise) -also relevant when you expose yourself to changing interest rates by engaging with long-term bonds -low coupon rate bonds have more price risk than high coupon rate bonds (if you have to sell early, more cash flows are exposed to the rate change with low coupon rate bonds) -early sales (if you sell bond before maturity), you are exposed to price risk because it is based on what the market is doing -PV based on YtM

What does the coupon rate of a bond tell me?

-when used in excel, this is the payment argument (PMT) in PV function -percentage of face value of a bond that you'll be getting back to make up for not having that money

Why don't the dollars across the timeline match?

1. Lost opportunities -I could've done something else with my money -Giving up other opportunities and there's a need to be compensated for that 2. Uncertainty -Will you give me my money back? -Might default -Default risk is the uncertainty here -Recession and inflation -Compensation needs to account for this -Can't match cash flows across the timeline

What is the par for a bond?

100! 100% of face value

If the year in the problem says "2001," start at ___________; timelines always start at _________ for proper counting

2000; 0

Current yield

=annual coupon / price

How to find periodic coupon rate for a bond?

=coupon rate/m **coupon rates usually quoted annually** **m is # of times per year; DO NOT ASSUME per timeline**

Yield to maturity

=current yield + capital gains yield

Independent projects:

Accepting or rejecting one project does not affect the decision of the other projects. -Must exceed a MINIMUM acceptance criteria

Compounding frequency

Can compare APRs and PPRs when on the same compounding frequency (APR -> EAR)

Annuity and PMT

Annuity is where you would use PMT argument in FV function

The Bond-Pricing Equation

Bond value = C x [1-1/(1+R)^t]/R + F/(1+R)^t Bond value = Present value of the coupons + Present value of the face amount

How to find coupon amount for a bond?

C=F*CR face value*coupon rate/dollar amount -usually quoted annual, but remember that this is not what you get every period!! must divide by m!!!

Which function can one use in excel for the first payment of an annuity?

COUNT function!

Coupon Rate for a bond

CR = C$/F$ coupon dollar amount scaled by face value

Formula for compounding an investment m times a year for T years provides for future value of wealth:

FV = C0 x (1+r/m)^mT

The Multiperiod Case Future Value Formula

FV = PV x (1+r)^t

Who is the borrower for a bond? Why would entities distribute bonds?

Entity distributing bond (whoever is giving out the piece of paper) Need $!!!

One-Period Case Future Value Formula

FV= PV x (1+r) Where PV is present value (i.e., the value today), and r is the appropriate interest rate.

Growing perpetuity

Formula: PV= C/(r-g) **must assume g<r** r>g-> what does this mean? r= all opportunities g= just that example r must include g A stream of cash flows that grows at a constant rate forever Example: The expected dividend next year is $1.30, and dividends are expected to grow at 5 percent forever. If the discount rate is 10 percent, what is the value of this promised dividend stream?

Perpetuity

Formula: PV= c/r A constant stream of cash flows that lasts forever Example: What is the value of a British consol that promises to pay £15 every year for ever? The interest rate is 10 percent.

Annuity

Formula: PV=(c-r)[1-(1/(1+r))^T] A stream of constant cash flows that lasts for a fixed number of periods Example: If you can afford a $400 monthly car payment, how much car can you afford if interest rates are 7 percent on 36-month loans?

Growing annuity

Formula: PV=(c/r-g)[1-((1+g/(1+r))^T] A stream of cash flows that grows at a constant rate for a fixed number of periods Example: A defined-benefit retirement plan offers to pay $20,000 per year for 40 years and increase the annual payment by 3 percent each year. What is the present value at retirement if the discount rate is 10 percent? Example 2: You are evaluating an income-generating property. Net rent is received at the end of each year. The first year's rent is expected to be $8,500, and rent is expected to increase 7 percent each year. What is the present value of the estimated income stream over the first five years if the discount rate is 12 percent?

If continuous compounding is involved, your asset is

Increasing in value

The PV of a bond is also called the

Market price

Does IRR or NPV win?! For example, if the IRR is higher and NPV is lower, which would you utilize?

NPV always wins

If the present value is less than the cost of an investment, should you purchase it?

No! If the present value is less than the cost, you should not purchase it.

Mutually exclusive projects:

Only ONE of several potential projects can be chosen, e.g., acquiring an accounting system. -RANK all alternatives, and select the best one.

For bonds, you can assume that ____________________

P = PV = [(C.F.)/(1+r)^T]

"The Magic Formula"

P ≈ PDV = (Cash Flows)/(Discount Rate) -Where P is the sticker price -≈ approximately equal to -PDV equals present discounted value (PDV); what it should be worth; price does not equal value; p does not equal PDV (PV) -Discount Rate: what I could have done with my money (shrinking=discounting) -Cash Flows: stocks that pay dividends, bonds with interest payments/coupons, annuity with monthly dispersals, small businesses' profits, etc.

Full "Magic Formula"

P ≈ PV = (Cash Flows)/(Discount Factor) = (FV)/(1+r)^T

APR is the annualized

PPR (EFFECT function)

How is APR quoted?

PPR is what you are compounding/discounting; EAR is for comparing Only use EAR when you have to compare across different periods

With compounding and discounting, you will always use

PPR, but be sure to watch the way it's quoted (might already be in PPR)

One-Period Case Present Value Formula

PV=(C1)/(1+r) Where C1 is cash flow at date 1, and r is the appropriate interest rate. We could also write the formula as: PV=(FV1)/(1+r)

Who is the lender for a bond? Why would one buy a bond?

Person receiving/buying the bond! investment + coupons are another incentive (coupons are the payment for parting with your money/other opportunities)

Pv0

Present value at time t=0

Net Present Value

The NPV of an investment is the present value of the expected cash flows, less the cost of the investment. If the present value of the cash inflow is greater than the cost. In other words, the Net Present Value is positive, so the investment should be purchased. NPV = -Cost + PV

Par (face) value for a bond

The amount that's borrowed -10k by default in US (m=2)

What happens when you part with your money?

The longer I part with my money, the less it's worth to me today. This is true even though the discount rate is the same. Eventually, all projects are worth nothing. Here, the denominator is getting bigger (mathematical explanation)

Nota bene

The only time you can compare across the timeline is if the interest rate is 0 (dollars today versus dollars tomorrow)

Future Value (FV)

The total amount due at the end of the investment is called the

Key note about bond prices and market interest rates

They move in opposite directions. The market price is the PV of a bond.

What is the purpose of a discount factor?

To determine the present value of a future value of a cash flow

How does one find the periodic interest rate?

To find this, you need to know how many periods there are

Why might sellers lower the discount rate for a project (specifically a capital budgeting project)?

To make the project appear more attractive/appealing/desirable

Discount bond

When coupon rate < YTM, price < par value -called a discount bond because the PV is less than what you're paying -don't apply capital gains/losses to coupons -capital gain -people would buy because it's cheap and sellers would sell because they're desperate for $ -would become a discount bond if the bond market interest rates increase (more opportunities to invest $)

Par Bond

When coupon rate = YTM, price = par value -no

Premium bond

When the coupon rate > YTM, price > par value -capital loss -people would buy if they have no other good opportunities (coupons help make this a little more appealing) -would become a premium bond if the bond market interest rates decrease

The IRR is

a type of discount rate that sets the NPV= 0 -IRR is about the project -discount rate is about me -To use IRR effectively, you need to know if you're investing or borrowing

Yield to maturity is the rate implied

by the current bond price.

C=F*CR

controls coupon

r=Ytm

controls discount -CF in amount I paid back -face -> stream of earnings for bonds

If the question mark is at the end of the timeline,

don't fill in the PMT argument for the function

If you're discussing capital budgeting and you want to use IRR effectively, you need to know if you're ______________ or ____________.

investing; borrowing

Investors with lots of opportunities might have a _______ discount rate because of more opportunities

larger Timeline: Investor A 10% $100 -$300k+ -> accredited investor -> can invest in risky opportunities with a high rate of return -examples of general opportunities: stocks, bonds, commodities, venture capital, hedge funds, private equity, etc.

If interest rates are higher, does one need more or less money in the bank for retirement?

less money

To convert from APR to PPR, by what do you divide?

m **remember that m is ALWAYS number of times per year, not per period**

What is m??

number of times per year; NOT per timeline m=1 annual m=2 semiannual As you increase, overall increase

If there is a question mark at the beginning of the timeline, you are finding

present value

Dirty price

price actually paid = quoted price plus accrued interest

The IRR is specific to the _____, while the hurdle rate/required rate of return is about _______

project; me/my company

Clean price

quoted price

Accept the IRR exceeds the

required rate/hurdle rate

An investor with fewer opportunities will have a ______ discount rate

smaller Timeline: Investor B 8% $100

If you are calculating the PV of an annuity on excel, you MUST use

the PMT function!!

Always use and trust ______________ for any interest rates or compound rates changing

the cash flow table

Yield to Maturity

the required market interest rate on the bond -always quoted annually; must divide by m to use in formulas -YTM is a discount rate!!!! remember opportunity cost here -if the fed changes interest rates, it changes my opportunity cost. while the paper doesn't move, my perception of the value/market price of that paper changes over time. -Ytm = interest rate I use to see what the bond is worth

The yield to maturity

the required market interest rate on the bond.

Consider two otherwise identical bonds. The long-maturity bond will have much more __________ with respect to changes in the ________.

volatility; discount rate

Consider two otherwise identical bonds. The low-coupon bond will have more __________ with respect to changes in the _____________.

volatility; discount rate