First Midterm
1. Consider a transaction between a seller of coins and a buyer of coins. Suppose there are two types of coins: a high quality coin and a low quality coin. The coin seller's valuation of the coins is lower than the coin buyer's valuation, as summarized in the table below. Assume both the seller and the buyer know the table.
a. If neither the coin seller nor the coin buyer knows the quality of coins (i.e., they know that there is one high quality coin and one low quality coin, but not which of the tow is high quality), what is the range of possible market prices?
b. If only the seller knows the quality while the buyer does not, what is the range of possible market prices?
|
Quality of coin
|
# of coins
|
Value to the buyer
|
Value to the seller
|
|
High
|
1
|
$30,000
|
$20,000
|
|
Low
|
1
|
$2,800
|
$1,200
|
2. Suppose the nominal interest rate before tax payments is 8%, the after-tax real interest rate is 2% and the expected inflation rate is 2%. Find the tax rate on the interest income.
3. Consider a consol with coupon payment $200. Assume the after-tax real interest rate is 5%, tax rate on interest is 50%, the expected inflation rate is 5%, and they will be constant forever. Calculate the present value of this consol.
4. Assume a firm's total revenue is $6,000, total expense is $5,000, and dividends payment is $100. Calculate the retained earning. If this firm wants to invest $2000 and uses all the retained earning for investment, the retained earning will be insufficient to finance. How much does this firm need to borrow in that case?
5. Consider a two-year coupon bond with a face value of $2,000 and a coupon rate of 10%. If the bond's price is $1,800, what is the current yield on the bond?
6. Suppose the liquidity effect is smaller than the expected inflation rate and the adjustment of the expected inflation is slow. What will happen to the interest rate if the rate of money supply growth decreases? Draw a diagram of how the interest rate responds over time to the decreased rate of money supply growth.
7. Calculate the growth rate of real wage per hour between 1992 and 2002 from the following table. (CPI is Consumer Price Index.)
|
Year
|
Nominal Wage per Hour
|
CPI
|
|
1992
|
$20
|
120
|
|
2002
|
$25
|
135
|
8. Consider a one-year discount bond with a face value of $2,000. Suppose you purchase it for $1,500 and it matures in 240 days. Compute the discount yield on this bond and the yield to maturity on this bond.
9. Consider a two-year coupon bond with a face value of $2,000 and a coupon rate of 10%. If the bond's price is $1,800, what is the current yield on the bond?
10. Suppose you purchased a two-year coupon bond one year ago for $1,500. The bond has a face value of $1,200 and a coupon rate of 10%. If the bond is now worth $1,400, what return on the bond did you earn in the past year?
11. Consider a two-year coupon bond with a coupon of $200 and a coupon rate of 20%. Suppose the nominal interest rate is 15% for the first year and 20% for the second year. Find the price of this bond.
12. Consider a two-year coupon bond with a coupon of $110 and a face value of $1210. Assume the after-tax real interest rate for the first year is 4%, the after-tax real interest rate for the first year is 5%, the expected inflation rate for the first year is 6%, the tax rate on the interest income for the first year is 0%, and the tax rate on the interest income for the second year is 50%. If the price of this bond is $1,100, what should the expected inflation rate for the second year be?
13. Consider a CD and a tax-free municipal bond. Assume the rate on the CD is 15% and the rate on the tax-free municipal bond is 5%. Calculate the tax rate such that the CD and the tax-free municipal bond are indifferent in terms of after-tax rate.
14. Draw diagrams representing the bond market and the loanable funds market in equilibrium. On your diagram, explain what would happen to the price of bonds, the interest rate, the quantity of bonds and the quantity of loanable funds if the expected inflation rate increases.
15. Draw diagrams representing the bond market and the loanable funds market in equilibrium. On your diagram, explain what would happen to the price of bonds, the interest rate, the quantity of bonds and the quantity of loanable funds if wealth increases and the government deficit shrinks simultaneously.
16. Draw diagrams representing the bond market and the loanable funds market in equilibrium. On your diagram, explain what would happen to the price of bonds, the interest rate, the quantity of bonds and the quantity of loanable funds in a business cycle contraction.