Econ 2035 Chapter 3
What is the price of a coupon bond that has annual coupon payments of $75, a par value of $1,000, a yield to maturity of 5%, and a maturity of two years?
$1,046.49
Suppose First National Bank makes a one-year simple loan of $1,000 at 7% interest to Harry's Restaurant. At the end of one year Harry's Restaurant will pay First National
$1,070
Which of the following represents the equation that would be used to determine the yield to maturity of a corporate bond with a face value of $1,000, price of $1,100, coupon rate of 5%, and maturity in three years?
$1,100 = $500/(1 + i) + $500/(1 + i)2 + 1,500/(1 + i)3
Which of the following represents the equation that would be used to determine the yield to maturity of a three-year fixed payment loan of $1,400 which has payments of $500 per year?
$1,400 = $500/(1 + i) + $500/(1 + i)2 + $500/(1 + i)3
$1 received n years from now has a value today of
$1/(1 + i)n
If you deposit $10,000 in a savings account at an annual interest rate of 6%, how much will you have in the account at the end of three years?
$11,910
If the annual interest rate is 8%, what would you expect to pay for a bond paying a lump sum of $10,000 in ten years?
$4,632
Suppose you put $500 in your savings account and earn 4% interest per year. How much will you have in your account after two years? Be sure to round off to the nearest cent.
$500 × 1.04 × 1.04 = $540.80
If you deposit $500 in a savings account at an annual interest rate of 5%, how much will you have in the account at the end of five years?
$638
At an interest rate of 6%, how much will need to be invested today to have $10,000 in 5 years?
$7,473
If the annual interest rate is 9%, what would you expect to pay for a bond paying a lump sum of $10,000 in two years?
$8,417
At an interest rate of 3%, what is the present value of $1,000 to be received five years from now?
$863
Suppose Matt's New Cars issues a bond in which they'll need to pay $10,000 in one year, which includes 4% interest. How much will they receive for the bond?
$9,615
What is the price of a coupon bond that has annual coupon payments of $85, a par value of $1,000, a yield to maturity of 10%, and a maturity of three years?
$962.70
The yield to maturity on a new one-year discount bond equals
(FV- P)/P
What is the yield on a discount basis for a U.S. Treasury bill that has a face value of $10,000, has a price of $9,500, and will mature in 180 days?
10.00%
What is the rate of return on a bond with a coupon of $55 that was purchased for $900 and sold one year later for $950?
11.67%
What is the rate of return on a bond with a coupon of $38 payable in one year that was purchased for $950 and sold one year later for $931?
2%
Suppose you have a fixed-rate mortgage with a nominal interest rate of 6% and the expected annual inflation rate over the life of the mortgage is 2%. What is the expected real interest rate?
4%
A one-year discount bond with a par value of $5,000 sold today, at issuance, for $4,750 has a yield to maturity of
5.26%.
What is the yield to maturity on a simple loan that requires payment of $500 plus $30 in interest one year from now?
6%
A one-year discount bond with a par value of $1,000 sold today, at issuance, for $943 has a yield to maturity of
6.04%
Suppose Matt's New Cars issues and sells a one-year discount bond for $9,259 and repays $10,000 at maturity. The interest rate on this bond would be
8%
A coupon bond has an annual coupon of $75, a par value of $1,000, and a market price of $900. Its current yield equals
8.33%
What is the yield to maturity of a consol with a coupon of $85 and a price of $944.44?
9.00%
What are examples of discount bonds?
A US savings bond, a US treasury bill, and a zero-coupon bond
What is a fixed payment loan?
A home mortgage
What aren't fixed payment loans?
A home mortgage, a car loan, and a student loan
What are three reasons that banks charge interest on loans?
Banks charge interest on loans to compensate for inflation, to compensate for default risk, and to compensate for the opportunity cost of waiting to spend your money.
How do payments on a fixed-payment loan differ from a coupon bond?
Borrowers that use a coupon bond make interest payments at regular intervals and repay the face value when the bond reaches maturity. Those that borrow using a fixed-payment loan makes periodic payments that are equal and include both interest and principal.
Explain the process by which prices of securities adjust so as to eliminate arbitrage profits.
In competing to buy securities where earning arbitrage profits is possible, traders force prices up to the level where arbitrage profits can no longer be earned.
Why isn't the current yield a good indicator of holding a bond?
It doesn't account for capital gains or losses
The total payment to a lender for a one-period simple loan is
P(1 + i)
How long does it take prices of securities to adjust so as to eliminate arbitrage profits?
Seconds
interest on simple loans and discount bonds is paid in a single payment, while issuers of coupon bonds and fixed-payment loans make multiple payments of interest and principal
Simple loans and discount bonds differ from coupon bonds and fixed-payment loans in that
A corporation issues a three-year bond with a coupon of $50 and a face value of $1,000. A year later, market interest rates have declined to 4%. What is the price of the bond a year after it was issued? Report your answer to the nearest dollar.
Since the price of the bond equals its present value, the price is $50 / 1.04 + $1,050 / (1.04)2 = $1,019.
A corporation issues a three year bond with a coupon of $50 and a face value of $1,000. Immediately after being issued, market interest rates decline to 4%. What is the price of the bond? Report your answer to the nearest dollar.
Since the price of the bond equals its present value, the price is $50 / 1.04 + $50 / (1.04)2 + $1,050 / (1.04)3 = $1,027.75.
Which type of bond would you purchase if you expected higher rates of inflation during the life of the bond?
TIPS
Suppose a firm receives $975 for a discount bond with a face value of $1,000 to be repaid in one year. What is the amount of interest on the bond? What is the interest rate on the bond? Report a percentage with two decimal places.
The amount of interest is $1,000 - $975 or $25. the interest rate is $25 / $975 which equals 2.56%.
What is true about a fixed payment loan?
The borrower is required to make regular periodic payments to the lender, the payments made by the borrower include both interest and principal, a home mortgage is an example of fixed payment loan
Suppose a bond has a coupon of $40, face value of $1,000, and current price of $950. What is the coupon rate? What is its current yield? Report a percentage with two decimal places
The coupon rate is $40 / $1,000 = 4.00%. The current yield is $40 / $950 = 4.21%.
Suppose a bond has a coupon of $75, face value of $1,000, and current price of $1,100. What is the coupon rate? What is its current yield? Report a percentage with two decimal places.
The coupon rate is $75 / $1,000 = 7.50%. The current yield is $75 / $1,100 = 6.82%.
Suppose you had $1,000 and were deciding between two investments. One pays 5% a year for two years while the other pays 8% the first year and 2% the second year. Which investment would provide a higher return?
The first investment which earned 5% a year for two years would result in $1,102.50 after two years. The second investment would result in $1,101.60. Thus, the first investment provides the higher return.
How are TIPS adjusted for inflation?
The principal is adjusted for inflation each period
What is the yield to maturity of a perpetuity with a coupon of $40 and a price of $800?
The yield to maturity equals $40 / $800 = 5%.
A one-year discount bond has a face value of $1,000 and price of $880. What is the yield to maturity on the bond? Report using percentages with two decimal places.
The yield to maturity is ($1,000 - $880) / $880 = 13.64%.
A one-year discount bond has a face value of $1,000 and a price of $925. What is the yield to maturity on the bond? Report using percentages with two decimal places.
The yield to maturity is ($1,000-$925) / $925 = 8.11%.
What is an example of a coupon bond?
a US Treasury note or bond
If an investor is certain that market interest rates will decline in the future, which of the following will she be most likely to purchase?
a fifty-year government bond
A debt instrument represents
a promise by a borrower to repay principal plus interest to a lender
If the current price of a bond is less than its face value
an investor will receive a capital gain by holding the bond until maturity.
The coupon rate is the
annual coupon payment divided by the face value of the bond
U.S. Treasury bonds
are subject to fluctuations in their market prices and are therefore risky investments.
As the housing bubble began to burst in 2006-2008, investors would only buy mortgage-backed securities at high yields to compensate for higher perceived default risk. As a result
banks suffered significant capital losses as the value of their holdings of mortgage-backed securities declined
The most common type of simple loan is a(an)
commercial loan from a bank
Why may investors buy a Treasury bill with a negative real interest rate?
concern about the high default risk of alternative investments
Debt instruments are also called
credit market instruments
Suppose a coupon bond with a par value of $1,000 is currently priced at $950 and has a coupon of $40. Which of the following is TRUE?
current yield > coupon rate
A sustained decrease in the price level is known as
deflation
A bond's price and its yield to maturity are inversely related because
discounting future payments at a higher rate reduces the present value of the payments.
On a coupon bond, the yield to maturity
equates the present value of all the bond's payments to its price today
Nominal interest rates are higher than real interest rates as long as
expected inflation is positive
Interest-rate risk can best be characterized as the risk that
fluctuations in the price of a financial asset in response to changes in market interest rates.
How can a bond have a negative rate of return?
if the rate of capital loss exceeds the current yield
What will result in a decrease in the price of an existing corporate bond?
increased default risk
What will lead to a higher interest rate on a loan?
increased perceived risk of default
A coupon bond involves
interest payments from the borrower to the lender periodically during the life of the loan and payment by the borrower to the lender of the face value of the loan at maturity.
Though Treasury bonds may have little default risk, what type of risk exists when current interest rates are low?
interest-rate risk
For simple loans, the yield to maturity
is always equal to the specified simple interest rate
An speculator who buys a fifty-year corporate bond
is probably expecting market interest rates to decrease in the future
Issuers of coupon bonds
make a single payment of principal when the bonds matures, but multiple payments of interest over the life of the bond
Which of the following is a consequence of extending the payback period of a student loan from 10 to 30 years?
more interest paid over the life of the loan
A discount bond involves
payment by the borrower to the lender of the face value of the loan at maturity
A simple loan involves
payment of interest by the borrower to the lender only at the time the loan matures
The price of a financial asset equals the
present value of all future payments.
A capital gain occurs when the
price of an asset increases
The amount of funds the borrower receives from the lender with a simple loan is called the
principal
The key to present value calculations is that they
provide a common unit for measuring funds at different times
Which of the following is the correct expression for the approximate expected real interest rate?
r = i - πe
Banks who held mortgage-backed securities "took a bath" during the financial crisis of 2007-2009 due to
rising yields in secondary markets which led to a decline in the price of mortgage-backed securities
The rate of return is equal to the
sum of the current yield and the actual rate of capital gain or loss.
A borrower and a lender agree on a mortgage interest rate. If inflation turns out to be less than expected
the actual real interest rate will exceed the expected real interest rate
With respect to U.S. Treasury bills
the asked price is always greater than the bid price
A discount bond resembles a simple loan in that
the borrower repays in a single paym
The current yield is equal to
the coupon divided by the market price of the bond
When the price of a coupon bond increases
the current yield declines
The rate of return is equal to
the current yield plus the rate of capital gains.
The yield to maturity is equal to
the interest rate at which the present value of an asset's returns is equal to its price today
If, while you are holding a coupon bond, its market price falls, you can be sure that
the interest rate on other similar bonds must have risen
For a specific change in the yield to maturity
the longer the time until a bond matures, the greater will be the change in its price.
If, while you are holding a coupon bond, the interest rates on other similar bonds fall, you can be sure that
the market price of your bond will rise
The expected real interest rate approximately equals
the nominal interest rate minus the expected rate of inflation
The bid price for a bond is
the price that you will receive from a securities dealer if you sell the bond
Compounding refers to
the process of earning interest on both the interest and the principal of an investment
If i is the yield to maturity of a fixed-payment loan
the value of the loan today equals the present value of the loan payments discounted at rate i
If the current price of a bond is greater than its face value
the yield to maturity must be less than the coupon rate
If the current price of a bond is equal to its face value
there is no capital gain or loss from holding the bond until maturity.
Which of the following types of mortgage loans became more common during the housing boom of the early-to-mid 2000s?
those with flawed credit histories
In comparing the yield to maturity on a Treasury bill with the yield on a discount basis on the same bill, we can say that the yield to maturity
will always be greater than the yield on a discount basis
Unless otherwise indicated, when economists or investors refer to the interest rate on a financial asset, they are referring to the
yield to maturity
