8.2 The Law of One Price implies that financial instruments with the same risk and the same cash flows at the same time should have the same price.

You are given the following table containing incomplete information on four different bonds. Assume that all these bonds have the same risk, and any coupon payments are paid annually.

Note that you can find an optional webcast that shows calculations for a similar example with three strip bonds and three-year coupon bonds. See About FNCE/ECON 300: Optional Webcasts: Law of One Price or link from the Lesson 8 Reading and Learning Objectives. (20 marks total)

Bond #	1	2	3	4
	1-year strip bond	2-year strip bond	2-year 6% coupon bond	2-year 7% coupon bond
Purchase price ($xxxx.xx)	950.00
Time 1 cash flow	+1000.00	0	+60.00	+70.00
Time 2 cash flow	0	+1000.00	+1060.00	+1070.00
Yield to maturity (xx.xx%)			5.50%

1. What is the yield to maturity on Bond #1? (2 marks)
2. What is the price of Bond #3? (2 marks)
3. You are considering two investments from the bonds listed in the table.

Portfolio 1: 60 units of Bond #1 + 1060 units of Bond #2

Portfolio 2: 1000 units of Bond #3.

Show that the future cash flows from these two portfolios would be identical, in amount and timing. (2 marks)

4. Based on the information in the given table,

i. What would it cost to buy 1000 units of Bond #3? (1 mark)

ii. What would it cost to buy 60 units of Bond #1? (1 mark)

iii. From part c. above and your answers in part d.i and ii, infer the value of 1060 units of Bond #2. (2 marks)

iv. What is the value of one unit of Bond #2? (1 mark)

v. What is the implied yield of Bond #2? (2 marks)

5. How many units of Bond #1 and #2 would you need to replicate the future cash flows of 1000 units of Bond #4? (2 marks)
6. Using your answer to part e above, determine the following

i. Whats the value of 1000 units of Bond #4? (2 marks)

ii. Whats the yield of Bond 4? (2 marks)

7. Fill in the missing information in the given table: (1 mark)

Bond #	1	2	3	4
	1-year strip bond	2-year strip bond	2-year 6% coupon bond	2-year 7% coupon bond
Purchase price ($xxxx.xx)	950.00
Time 1 cash flow	+1000.00	0	+60.00	+70.00
Time 2 cash flow	0	+1000.00	+1060.00	+1070.00
Yield to maturity (xx.xx%)			5.50%