1 A. Look up the US Treasury yield curve online.
i. What is the promised yield for a 1-month T-bill?
ii. For a 6-month T-bill?
iii. A 1-year T-bill?
iv. A 5-year T-bond?
v. A 10-year T-bond?
iv. A 20-year T-bond?
iiv. A 30-year T-bond?
iiiv. On what date did you look up these yields?
ix. On what Web site did you find these yields?
B. Is this yield curve flat, rising, or inverted?
C. Many introductory finance textbooks say, at the beginning of bond valuation problems, "Assume the yield curve is flat." Another way of putting this is "Assume the term structure of interest rates is flat." How would this assumption make the questions easier for students of introductory finance to solve?
2 Fill in the missing items in the following table, using the Law of One Price. Assume all these bonds have the same risk, the yield curve is flat, and any coupon payments are paid annually.
|
Bond #
|
1
|
2
|
3
|
4
|
|
|
1-year
strip bond
|
2-year
strip bond
|
2-year
6% coupon bond
|
2-year
7% coupon bond
|
|
Time 0 cash flow (i.e., Purchase
Price for the bond)
|
-950
|
?
|
?
|
?
|
|
Time 1 cash flow
|
+1000
|
0
|
+60
|
+70
|
|
Time 2 cash flow
|
0
|
+1000
|
+1060
|
+1070
|
|
Yield
|
?
|
?
|
5.50%
|
?
|
3 A. You are considering two investments from the bonds listed in question 8.2. Show that the cash flows from the following two investments would be identical.
i. 60 units of Bond #1 + 1060 units of Bond #2, and
ii. 1000 units of Bond #3.
B. How many units of Bond #1 and #2 would you need to replicate the cash flows of 1000 units of Bond #4?
C. i. If the yield of Bond #3 is 5.5%, what would it cost to buy 1000 units of Bond #3?
ii. What would it cost to buy 60 units of Bond #1?
iii. From part A. above, infer the value of 1060 units of Bond #2.
iv. What is the value of one unit of Bond #2? Yield of Bond #2?
D. What's the value of 1000 units of Bond #4? Yield?
E. What have you learned about the Law of One Price from questions 8.2 and 8.3?
4 Assume the yield curve on "plain vanilla" default-free bonds is flat at 5%, and you are thinking of buying a default-free bond. Specifically, you're thinking of buying a bond issued by Risklessco, a company considered to be default-free by all major bond rating firms.
You will select one of the following three bonds, all identical except for the special features listed:
|
|
Face Value
|
Maturity
|
Coupon Rate (Paid Annually)
|
Yield to Maturity
|
Special Features
|
Price
|
|
A
|
1000
|
20 years
|
5.5%
|
5%
|
None
|
?
|
|
B
|
1000
|
20 years
|
5.5%
|
5%
|
Callable
|
Par
|
|
C
|
1000
|
20 years
|
5.5%
|
3.5%
|
Callable and Convertible into Risklessco Stock
|
?
|
A. Why is the yield on bonds A and B 5%? Why is the yield on bond C different?
B. What would be the price of Bond A?
C. If bond C is considered identical to bond B except for the conversion privilege, what is the value of the conversion privilege? Does the conversion privilege benefit the issuer of the bond or the purchaser? Is this consistent with the price you calculated for bond C?
D. Who does the callability provision benefit, the issuer or the purchaser? Is this consistent with the price you calculated for bond A?