Homework Assignment #1

Homework Assignment #1
ECO 3223, Summer A 2015
Instructions: Answer each of the following questions, showing your work where appropriate.
Due: Monday, May 18th at the beginning of class
1. In 2012, there were 314 million people living in the United States.
a. If the U.S. population grows at a constant rate of 3% per year, what will the population be in
2020?
b. If the population grows at a constant rate of 3% per year, what would the population have
been in 2006?
c. Suppose that the U.S. population has been growing at 3% per year, but at the beginning of
2015, the growth rate falls to 1.5% per year and remains there. What will the population be
in 2020?
d. At what rate would the population need to grow between 2012 and 2020 in order for there
to be 440 million people living in the U.S. in 2020?
2. Suppose that you own a zero coupon bond that will mature in 4 years. The face value of the
bond is $10,000.
a. If the (nominal) interest rate is currently 3% and is expected to remain at 3% for the next 4
years, what is the present value of your bond?
b. Assuming that you are right about future interest rates, what will the bond’s value be in 2
years?
c. If the (nominal) interest rate is currently 3%, but is expected to rise to 10% after 2 years
(and remain at 10% after that), what is the present value of the bond?
d. Assuming that you are right about future interest rates, what will the bond’s value be in 2
years?
3. Consider a 5 year coupon bond with a 15% coupon rate and $1000 face value. Coupon
payments are made once each year, at the end of the year.
a. If the (nominal) interest rate is 8% at the time the bond is issued and is expected to remain
at 8% for the next 5 years, what will be the present value of the bond at the time it is
issued?
b. If the (nominal) interest rate is 8% at the time the bond is issued, but is expected to fall to
4% after 2 years (and remain there), what will be the present value of the bond at the time
it is issued?
c. What price would you expect to pay for this bond at the time it is issued if the interest rate
stays at 8%? What price would you expect to pay for this bond at the time it is issued if the
interest rate is expected to fall to 4% after 2 years?
4. Consider a newly issued 2 year coupon bond with a 4.5% coupon rate and a $10,000 face
value. Coupon payments are made once each year, at the end of the year.
a. What is the bond’s (nominal) yield to maturity if it sells for $9600?
b. At what price would a 2-year zero coupon bond with a $10,000 face value have to sell in
order to offer an equivalent yield to maturity?
c. What is the coupon bond’s (nominal) yield to maturity if it sells for $9400?
d. In that case, at what price would a 2-year zero coupon bond with a $10,000 face value have
to sell in order to offer an equivalent yield to maturity?
5. Suppose that you purchase a 2 year coupon bond at the time it is issued for $1100. The face
value of the bond is $1000, with annual coupon payments of $80.
a.
b.
c.
d.
What is the bond’s “coupon rate”?
What is the bond’s “current yield”?
What is the bond’s (nominal) “yield to maturity”?
If you hold the bond for 1 year and sell it for $1035 (after collecting the first coupon
payment), what is your “holding period rate of return”?
6. Describe the difference between a bond’s “yield to maturity” and its “holding period rate of
return”. Under what conditions would they be the same for a coupon bond?
7. Consider a 2 year, zero coupon bond with a face value of $1000.
a.
b.
c.
d.
If the bond sells for $940, what is its (nominal) yield to maturity?
If the bond sells for $960, what is its (nominal) yield to maturity?
If the bond sells for $980, what is its (nominal) yield to maturity?
In general, how are bond prices and bond yields related, all else equal? Explain.
8. Suppose you win $10 million in the Florida State Lottery. You are given the choice between
receiving your winnings in $1 million increments paid every year (at the end of the year) for
10 years or receiving 3 million immediately and the balance ($7 million) in 10 years.
a. Which payment scheme should you take if the per-annum interest rate is 6%? Assume that
the price of goods and services is not expected to rise significantly over the next 10 years.
Why?
b. Would you make a different choice if the interest rate were higher? Explain.
9. What is the difference between an “annuity” and a “coupon bond”? How much would you
expect to pay for a 20 year annuity that makes annual payments of $1000 if the interest rate
is expected to average 3.5% over that period? How much would you expect to pay for a 20
year, $10,000 (face value) bond that makes annual coupon payments of $1000 if the interest
rate is expected to average 3.5% over that period?
10. Suppose that you buy a 3 year, $10,000 (face value) coupon bond with a 7% coupon rate for
$10,000 at the time it is issued. Coupon payments are made once each year, at the end of
the year.
a. What is the (nominal) yield to maturity offered by the bond?
b. At the end of 1 year (after collecting the first coupon payment), you decide to sell the bond.
If the nominal interest rate is 7% at the end of one year, what price will the bond sell for?
What will be your holding period rate of return?
c. If, instead, the nominal interest rate is 10% at the end of one year, what price will the bond
sell for? What will be your holding period rate of return in that case?
d. Suppose, instead, that you hold the bond for 2 years (and collect 2 coupon payments)
before you decide to sell it. If the nominal interest rate is 10% at the end of 2 years, what
price will the bond sell for? What will be your holding period rate of return?
11. Suppose you take out a $12,000 fixed payment loan to purchase a car. The loan is to be
repaid in monthly installments over a term of 3 years. If your loan is obtained at an annual
nominal interest rate of 6.5%, and interest is compounded monthly, how much will your
monthly payments be?
12. Describe the difference between the “nominal interest rate” offered on a loan and the expost “real interest rate”? In general, how is the ex-post real interest rate related to the
nominal interest rate?
13. Suppose you buy a 3 year, zero coupon bond with a face value of $1000 at the time it is
issued.
a. If you buy the bond for $920, what is its nominal yield to maturity?
b. What is the bond’s ex-ante real yield to maturity, if the inflation rate is expected to average
2% per year over the next 3 years?
c. Suppose that after 2 years, you sell the bond for $990. What nominal holding period rate of
return have you earned?
d. What was your real holding period rate of return if the inflation rate was 2% over the two
years that you held the bond?