ECO 353 ch. 3

8.7%

Consider a $10,000 one-year discount bond with a value today of $9,200. 𝑖=($10,000−$9,200)/$9,200

Present value

the value today of funds that will be received in the future.

Time value of money

the way that the value of a payment changes depending on when the payment is received

Face value

the amount to be repaid by the bond issuer (the borrower) at maturity

bid price

what a bond trader will pay you to buy your bond (you are seller)

asked price

what the bond trader will sell you his/her bond for (you are buyer)

Coupon

the annual fixed dollar amount of interest paid by the issuer of the bond to the buyer

Yield to maturity

the interest rate that makes the present value of the payments from an asset equal to the asset's price today.

Financial arbitrage

the process of buying and selling securities to profit from price changes over a brief period of time.

Compounding

the process of earning interest on interest, as savings accumulate over time

Discounting

the process of finding the present value of funds that will be received in the future (i.e., the opposite of compounding).

The rate of return (R)

the return on a security as a % of the initial price -For a bond, R equals the coupon payment plus the change in the price of a bond divided by the initial price

Interest-rate risk

the risk that the price of a financial asset will fluctuate in response to changes in market interest rates -Bonds with fewer years to maturity will be less affected by a change in market interest rates

Future value

the value at some future time of an investment made today.

Current yield

the value of the coupon expressed as a percentage of the current price

Coupon rate

the value of the coupon expressed as a percentage of the par value of the bond

8.8%

A simple loan for $500,000 that requires a payment of $700,000 in 4 years.

10.46%

A student loan of $2,500, which requires payments of $315 per year for 25 years. The payments start in 2 years. (need wolfram alpha)

examples of payments

-Additional earnings from college graduation -Dividends and capital gains from buying shares of stock -Rents from buying a rental property (e.g., apartment, house) -Coupon interest payments from buying a U.S. Treasury bond

Some Important Points about Discounting

1. Present value is also known as "present discounted value." 2. The further in the future a payment is to be received, the smaller its present value. 3. The higher the interest rate used to discount future payments, the smaller the present value of the payments. 4. The present value of a series of future payments is simply the sum of the discounted value of each individual payment.

additional earnings from college graduation

1. example of payments

Dividends and capital gains from buying shares of stock

2. example of payments

Rents from buying a rental property

3. example of payments

Coupon interest payments from buying a U.S. Treasury bond

4. example of payments

10.67%

A corporate bond with a face value of $1,000, a price of $975, a coupon rate of 10%, and a maturity of 5 years (need wolfram alpha)

11.1%

A discount bond with a price of $9,000, which has a face value of $10,000 and matures in 1 year.

50%

By 2008, the prices of many mortgage-backed securities had declined by ____ or more. Higher yields on these securities meant lower prices.

trillion

By early 2009, U.S. commercial banks had suffered losses of about $1 _______ on their investments

10%

For a $10,000 loan required to pay $11,000 in one year. Solving for i: 𝑖=($11,000−$10,000)/$10,000

worth less

Funds in the future are ______________ than funds in the present, so they have to be reduced, or discounted, to find their present value.

greater, less

If the inflation rate is _________ than the expected inflation rate, the real interest rate will be ________ than the expected real interest rate. borrowers+, lenders -

negative

It is possible for the nominal interest rate to be lower than the real interest rate. -This occurs when the inflation rate is _________

fixed-payment loan equation

Loan value=𝐹𝑃/((1+𝑖))+𝐹𝑃/(1+𝑖)2

debt instrument categories

Simple loans Discount bonds Coupon bonds Fixed-payment loans

tips

Since 1997, the U.S. Treasury has issued inflation indexed bonds called__________(Treasury Inflation Protection Securities). TIPS were an increasing percentage of all U.S. Treasury securities until 2009. How TIPS work: coupon rate reflects a real interest rate; and face value goes up at rate of inflation. So if face value starts at $1,000, and inflation rate for first year of bond is 5%, then at start of second year, face value is adjusted to $1,050.

yield to maturity

The current yield is not a good substitute for the _____ __ _________ for a short time to maturity because it ignores the effect of expected capital gains or losses.

expected real interest rate

The expected real interest rate (r) equals the nominal interest rate (i) minus the expected rate of inflation (pi^e).

smaller

The further in the future a payment is to be received, the _________ its present value.

smaller

The higher the interest rate used to discount future payments, the __________ the present value of the payments

opportunity cost

The interest rate on a loan should cover the ________________________ of supplying credit

present and future

The interest rate provides a link between the financial _______ and the financial _________.

discount bonds

Treasury bills are _____________________, not coupon bonds.

yields

Treasury bills quote ________

prices

Treasury notes and bonds quote _______

Equity

a claim to part ownership of a firm -Example: common stock issued by a corporation

Simple loan

a debt instrument in which the borrower receives from the lender an amount called the principal and agrees to repay the lender the principal plus interest on a specific date when the loan matures. (loan from bank)

Discount bond

a debt instrument in which the borrower repays the amount of the loan in a single payment at maturity but receives less than the face value of the bond initially.

fixed-payment loan

a debt instrument that requires the borrower to make regular periodic payments of principal and interest to the lender. -Example: You are repaying a $10,000 10-year student loan with a 9% interest rate, so your monthly payment is approximately $127

5%

a perpetuity with a coupon of $25 and a price of $500 has a yield to maturity of

Return

a security's total earnings -For a bond, its return is the coupon payment plus the change in its price

Deflation

a sustained decline in the price level.

credit market instruments

aka Debt instruments, fixed income assets

coupon bond

is a debt instrument that requires multiple payments of interest on a regular basis, and a payment of the face value at maturity.

perpetuity

does not mature. The price of a coupon bond that pays an infinite number of coupons equals: 𝑃=𝐶/𝑖

law of one price

identical products should sell for the same price everywhere.

response of fed

increasing the money supply that would lead to high inflation in the long run. -The expectation of high future inflation would lower the prices of bonds as a result of higher interest rates on those bonds.

inflation, default risk, waiting to spend

interest rates should compensate for 3 things:

Real interest rate

interest rates that are adjusted for changes in purchasing power.

Nominal interest rates

interest rates that are not adjusted for changes in purchasing power

Debt instruments

methods of financing debt, including simple loans, discount bonds, coupon bonds, and fixed payment loans

future

most financial transactions involve payments in the ____________

capital loss

occurs when the market price of an asset declines

capital gain

occurs when the market price of an asset increases.

discounting formula

𝑃𝑉=𝐹𝑉𝑛/(1+𝑖)𝑛

compounding equation

𝑃𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙 × (1 +𝑖)𝑛=𝐹𝑉𝑛

rate of return

𝑅=(Coupon+Capital gain)/(Purchase price)

one-year discount bond

𝑖=(𝐹𝑉−𝑃)/𝑃