Problem 1

In 1989, a couple purchased a house, financing $155,000 of the purchase with an 11% mortgage (monthly compounded) over 30 years. On the anniversary date of their mortgage in 1999, rates had fallen to 9%. If they refinance their home at this time with a new 20 year loan, they will incur prepayment penalties and closing costs which are equal to 5% on the new mortgage. Assume that the couple can finance both the new mortgage and the prepayment/closing costs at the 9% rate. Assume the couple makes monthly payments. Should they refinance their home?

Problem 2

The following table records current prices for zero-coupon bonds of various maturities (all securities have a face value of $100):

Bond
Maturity 
(in years)
Price 
(in $)
A
1
95.24
B
2
89.85
C
3
83.96

Use the prices to value a bond with a coupon rate of 5% per year, $100,000 face value, and three years remaining to maturity (annual coupon payments).

Problem 3

The following table records current spot rates for zero-coupon bonds of various maturities:
Bond
Maturity 
(in years)
Spot Rate 
(in % per year)
A
1
5.00
B
2
5.50
C
3
6.00

Use the spot rates to derive (a) the forward rate between year 1 and 2, (b) the forward rate between year 2 and 3, and (c) the forward rate between year 1 and 3. The forward rates should all be expressed on an annual basis.

Problem 4

You are interested in purchasing a new car. The list price is $58,000 and the manufacturer provides financing over five years at 5.5% per year, compounding monthly with repayments to be made monthly. One dealer has offered you a $4,000 discount and has offered to provide financing (over five years) at 6% per year, compounding monthly with repayments to be made monthly. The question is which terms are more attractive?

Problem 5

You own government bonds with a face value of $2 million. The bonds mature 6 years and 3 months from today and have a coupon rate of 12%, paid semi-annually. The next coupon will be paid in three months. The current yield on these bonds is 6% per year compounded semi-annually. How much are the bonds worth if sold today?

The next two questions are more advanced and include material beyond what we plan to ask in the quiz.

Problem 6

A 3-year coupon bond has payments as follows:
Bond Cash Flow at Year (in $)
Year 1
Year 2
Year 3
8
8
108

This 8% coupon bond is currently trading at par ($100).

(a) What is the annually compounded yield of the bond?
(b) Compute the Macaulay duration and the DV01 of the bond.
(c) Using the DV01, how much do you expect this bond's price to rise if the yield on the bond declines by 10 basis points compounded annually?

Problem 7

A financial institution has raised $1 million by selling a number of 2-year zero-coupon bonds to individuals. These bonds have a yield-to-maturity of 6%. The institution has used the proceeds to buy a number of long-term coupon bonds. These bonds have a Macaulay duration of 12 years and a yield-to-maturity of 7%. Use the concept of duration to explain how this institution is exposed to changes in interest rates. In particular, what happens to the value of the zero-coupon bonds, the long-term bonds, and the value of the firm as a whole, if the yields on these bonds change by 50 basis points (half of one percent)? [Hint: Use the duration as an approximation for percentage price changes.]