Finance Exam 2

Bonds

debt securities issued by a corporation or government entity to borrow money from the public on a long-term basis

Nike needs $500 million to expand its factories. Instead of borrowing from a bank, it sells investments to the public that promise regular interest payments and repayment later.

Coupons

the states interest payment made on a bond (assume level coupon bonds)

You invest $1,000 in a company, and it pays you $60 every year until your investment reaches its repayment date.

Face Value (Par Value)

the principal amount of a bond that is repaid at the end of the term. (Assume $1,000 face value unless expressly told)

You purchase an investment for $950 today. When it reaches its repayment date, the company gives you $1,000.

Coupon Rate

the annual coupon divided by the face value of a bond

You have a $1,000 investment that pays you $80 each year. The annual payment is 8% of its stated value.

Maturiry

the specified date on which the principal amount of a bond is paid

You purchase an investment in 2026, and the company promises to repay your original $1,000 in 2036.

Yield to Maturity (YTM)

The interest rate required in the market on a bond

You purchase an investment for $900. Considering all the payments you'll receive plus the final repayment, you'll earn about 7% annually if you hold it until the end.

Inverse relationship

Bond prices and interest rates have what?

Market interest rates increase from 5% to 8%. Your older investment becomes less attractive, causing its market price to fall.

Discount Bond

A bond that sells for less than face value

An investment will repay $1,000 in the future, but you can purchase it today for only $920.

Premium bond

a bond that sells for more than face value

An investment will repay $1,000 in the future, but investors are currently willing to pay $1,080 for it.

Current Yield

A bond’s annual coupon divided by its price

An investment pays you $60 per year and currently sells for $900. You divide $60 by $900 to get 6.67%.

coupon payments

Bonds have an annuity component which is what?

you receive $50 every year for the next 10 years. Each payment is the same amount and occurs at regular intervals.

Face value paid at maturity

bonds have a lump sum which is what?

After receiving regular payments for 10 years, you receive your original $1,000 back all at once at the end.

Coupon Rate > Current Yield > Yield to maturity

What is the yield relationship for a premium bond?

You have an investment paying 8% annually that currently sells for more than its stated value. Its returns are: 8% > 7% > 6%.

YTM>Current Yield> Coupon Rate

What is the yield relationship for a discount bond?

You have an investment paying 4% annually that currently sells for less than its stated value. Its returns are: 6% > 5% > 4%.

The greater the interest rate risk

The longer the time to maturity:

Two investments are identical except one ends next year and the other ends in 30 years. When market interest rates rise, the 30-year investment's price falls much more.

the greater the interest rate risk

The lower the coupon rate:

Two investments both end in 20 years. One pays 8% annually and the other pays 2%. When interest rates change, the one paying 2% experiences a larger price change.

the present value of the bonds remaining cash flows declines.

When interest rates rise, what happens

You have an investment paying 5%, but new investments start paying 8%. Yours becomes less attractive, so its market price falls.

the bond is worth more

when the interest rate falls, what happens

You have an investment paying 8%, but new investments only pay 5%. Yours becomes more attractive, so its market price rises.

nominal rates

Interest rates or rates of return that have not been adjusted for inflation.

Your savings account advertises that you'll earn 5% this year. That advertised percentage doesn't account for inflation.

real rates

Interest rates or rates of return that have been adjusted for inflation.

Your savings account earns 5%, but prices increase by 3%. Your purchasing power actually increases by roughly 2%.

upward sloping

downward sloping

long-term rates are higher than short-term rates:

short-term rates are higher than long-term rates:

Banks offer 3% for one-year borrowing and 5% for ten-year borrowing. In another economy, one-year borrowing might cost 6% while ten-year borrowing costs 4%.

U.S. Treasury Securities (Treasuries)

• Have no default risk

• Exempt from state income taxes (but not federal income taxes)

The federal government needs money to fund its operations, so it borrows money directly from investors and promises to repay them later.

Municipal securities (Munis)

issued by state and local governments to fund public projects

The city of Columbus needs money to build a new school, so the local government borrows money from investors to finance it.

Zero Coupon Bond

A bond that makes no coupon payments and is this initially priced at a deep discount (zeroes)

you pay $600 today and receive no payments along the way. Years later, you receive $1,000.

Common Stock

Equity without priority for dividends or in bankruptcy

You purchase 100 shares of Apple, giving you a small ownership stake in the company and the possibility of receiving distributions from its profits.

Dividends

payments by a corporation to shareholders, made in either cash or stock

Apple has a profitable year and decides to distribute $2 per share to its shareholders.

The capital contributed to the corporation by shareholders

Dividends paid to shareholders represent a return on what?

Investors provide money to a corporation by purchasing shares. The corporation later distributes some of its profits back to those investors.

Preferred Stock

stock with dividend priority over common stock, normally with fixed dividend rate, sometimes without voting rights.

A company has two types of shareholders. One group receives a fixed payment and gets paid before regular shareholders.

only that the holders of the preferred shares must receive a dividend before holders of common shares are entitled to anything

What does preference mean?

A struggling company doesn't have enough money to pay every shareholder. One class of shareholders must receive its promised payment before the other class gets anything.

ordinary perpetuity

If a dividend is always the same, the stock can be viewed as what?

You purchase an investment that promises to pay you $5 every year forever, with no ending date.

P_⁰ = D/R

The price of stock for zero coupon bond is given by:

(continued indefinitely)

payment / interest rate

present value of a perpetuity formula:

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.

• [P₀ = D₁/(R – g)]

Can be used to find the stock price at any point in time:

whats different about P_t = D_t+1/(R – g) compared to P₀ = D₁/(R – g)

• g: growth rate (Must be less than the discount rate)

• D₀: the dividend just paid

• D₁: the next dividend

Name the terms in [P₀ = D₁/(R – g)]:

nonconstant growth

Dividends grow at different rates for a limited time before eventuall growing at a constant rate forever

A young company increases its shareholder payments by 20% this year, 15% next year, 10% the following year, and eventually settles at 5% per year.

two-stage dividend growth

dividends grow at one rate for a certain number of years and then at another constant rate forever

A company's shareholder payments grow 15% annually for five years. After that, they grow 4% annually forever.

R has two components

• D₁/P₀ is the dividend yield

• g is the growth rate (Capital Gains Yield)

Required Return: R has how many components

Dividend Yield

A stock’s expected cash dividend divided by its current price.

You purchase a share for $100 and expect to receive a $4 cash payment over the next year. That portion of your return is 4%.

Capital Gains Yield

The dividend growth rate, or the rate at which the value of an investment grows (price appreciation and capital gains yield are interchangeable)

You purchase a share for $100 and its market value increases to $106. You earned 6% from the increase in price.

Dividend + Capital Gains Yield

Required Return formula:

R = D₁/P₀ + g

dividend growth model:

The ratio of a stock’s price per share to its earnings per share (EPS) over the previous year.

• Price at Time t = Benchmark PE Ratio x EPS_t

Price-to-Earnings (PE) Ratio:

A PE ratio that is based on estimated future earnings.

• Price at Time t = Benchmark PE Ratio x EPSt₊₁

• Forecasted prices are often called target prices

Forward PE Ratio:

Net Present Value (NPV)

The difference between an investments market value and its cost

how much value is created or added today by undertaking an investment

A new machine costs $100,000 today. All the future cash it will generate is worth $120,000 in today's dollars, meaning the investment adds $20,000 of value.

an investment should be accepted if the net present value is positive and rejected if negative

One project would add $15,000 of value to a company, while another would destroy $4,000 of value. Management accepts the first and rejects the second.

what is the net present value rule?

The length of time it takes to recover our initial investment

A restaurant spends $100,000 on new equipment. After four years, the equipment has generated enough cash to completely recover the original $100,000.

pack back is what?

payback period

The amount of time required for an investment to generate cash flows sufficient to recover its initial cost

A company spends $60,000 on equipment that generates $20,000 each year. It takes three years to recover the original investment.

An investment is acceptable if its calculated payback period is less than some prespecified number of years

A company only accepts projects that recover their original cost within four years. A proposed project takes three years, so management accepts it.

What is the payback period rule?

Discounted payback period

the length of time required for an investment’s discounted cash flows to equal its initial cost

A company spends $100,000 on equipment. Before determining how long it takes to recover the cost, it converts each future cash flow into today's dollars.

An investment is acceptable if its discounted payback is less than some prespecified number of years

A company requires projects to recover their cost within five years after adjusting future cash flows into today's dollars. A project takes 4.2 years, so it's accepted.

what is the discounted payback rule?

Internal Rate of Return (IRR)

The discount rate that makes the NPV of an investment zero

A company invests $100,000 in a project. When management evaluates the project's future cash flows using 12%, the value created is exactly $0.

Modified Internal Rate of Return (MIRR)

A more realistic version of IRR that assumes cash flows are reinvested at the company’s cost of capital.

A company evaluates a project's return while assuming money received during the project can be reinvested at the company's 8% cost of capital instead of the project's own return.

An investment is acceptable if the IRR exceeds the required return. Rejected otherwise

A company requires projects to earn at least 10%. A proposed project is expected to earn 14%, so management accepts it.

IRR Rules

Zero

Management keeps changing the percentage used to discount a project's cash flows. At exactly 11.4%, the project's value created becomes $0.

The IRR on an investment is the required return that results in what kind of NPV when it is used as the discount rate

Multiple Rates of Return

he possibility that more than one discount rate will make the NPV of an investment zero.

A project requires money upfront, produces cash, requires another large payment later, and then produces more cash. When analyzed, two possible returns appear: 8% and 23%.

Mutually Exclusive Investment Decision

A situation in which taking one investment prevents the taking of another.

Amazon has one piece of land. It can build either a warehouse or a manufacturing facility there, but choosing one means it cannot build the other.

Crossover Rate

the discount rate that makes the NPVs of two projects equal

A company compares two projects. One is better when the required return is low, while the other is better when it's high. At exactly 9%, both projects have the same value.