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)

Current price = cash flow year 1/(1 + yield to maturity)^1

Here, current price = $950 and cash flow year 1 = $1000

Using these values in the above formula, we get:

950 = 1000/(1 + yield to maturity)^1

Rearranging values, we get,

Yield to maturity on bond 1 = (1000/950) 1 = 5.26%

2. What is the price of Bond #3?

Price of bond 3 = cash flow year 1/(1 + yield to maturity)^1 + cash flow year 2/(1 + yield to maturity)^2

Here, cash flow year 1 = $60, cash flow year 2 = $1060 and yield to maturity = 5.50%

Using these values in the above formula, we get,

Price of bond 3 = 60/(1 + 5.50%)^1 + (1,060)/(1 + 5.50%)^2 = $1009.23 (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

Cash flow year 1 = total units of bond 1*cash flow year 1 from bond 1 + total units of bond 2*cash flow year 1 from bond 2 = 60*1000 + 1060*0 = $60,000

Cash flow year 2 = total units of bond 1*cash flow year 2 from bond 1 + total units of bond 2* cash flow year 2 from bond 2 = 60*0 + 1060*1000 = $1,060,000

Portfolio 2: 1000 units of Bond #3.

Cash flow year 1 = total units of bond 3*cash flow year 1 = 1000*60 = $60,000

Cash flow year 2 = total units of bond 3*cash flow year 2 = 1000*1060 = $1,060,000

As you can see from the above calculations that the future cash flow from these two portfolios would be identifical, in amount and timing. A cash flow of $60,000 in year 1 and cash flow of $1,060,000 in year 2 would occur with both of the portfolios.

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)

total cost to buy 1000 units of bond 3 = total units of bond 3*price of bond 3 = 1000*1009.23 = $1,009,231.60

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

total cost to buy 60 units of bond 1 = total units of bond 1*price of bond 1 = 60*950 = $57,000

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)

the value of 1,060 units of bond 2 is inferred as below:

value of 60 units of bond 1 + value of 1060 units of bond 2 = value of 1000 units of bond 3 (using law of one price)

therefore, substituting values in the above equation, we get

57000 + value of 1060 units of bond 2 = 1,009,231.60

Rearranging values, we get,

Value of 1060 units of bond 2 = 1,009,231.60 57000 = $952,231.60

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

value of one unit of bond 2 = value of 1060 units of bond 2/1060 units = 952,231.60/1060 = $898.33

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

implied yield of bond 2 = yield to maturity of bond 3 = 5.50%

the same can be calculated below:

value of one unit of bond 2 = cash flow year 0/(1 + yield)^1 + cash flow year 1/(1 + yield)^2

898.33 = 0/(1 + yield)^1 + 1000/(1 + yield)^2

Rearranging the values, we get,

Yield = (1000/898.33)^(1/2) 1 = 5.51% which is close to 5.50%

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%

I only need help answering part e, f, g please. All of the information that I was given is posted.