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