8.3 A. You are considering two investments from the bonds listed in question 8.2

Question

8.3   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?

Explanation / Answer

A) i. 60 units of Bond #1 + 1060 units of Bond #2

Year 1 cash flow - 60 * 1000 + 0 * 1060 = $60000

Year 2 cash flow = 60 * 0 + 1000 * 1060 = $1060000

ii. 1000 units of Bond #3

Year 1 cash flow = 60 * 1000 = $60000

Year 2 cash flow =1000 * 1060 = $1060000

B) Cash flow in year 1 = 1000 * 70 = $70000

Cash flow in year 2 = 1000 * 1070 = $10700000

This can be replicated by using 70 units ob Bond # 1 and 1070 units of Bond # 2.

C) Price of bond #3 with a yield of 5.5% =PV(5.5%,2,60,1000) = $1009.2316

i) For 1000 bonds, value would be = 1000 * 1009.23 = $1,009,231.60

ii) For 60 units of bond # 1, cost would be = 60 * 950 = $57,000

iii) From part A, the value of 1060 units of bond # 2 = 1,009,231.60 - 57,000 = $952,231.60

iv) Value of 1 unit of bond#2 = 952,231.60/1060 = $898.33

Yield of bond#2 =RATE(2,0,-898.33,1000) = 5.50%

D) Value of 1000 unit of bond#4 = 70 * 950 + 1070 * 898.33 = $1,027,714.92 (From part B above)

Value of 1 unit of bond # 4 = 1,027,714.92/1000 = $1027.715

Yield =RATE(2,70,-1027.715,1000) = 5.50%

E) From the law of one price mechanism, we have learnt, that the bonds or financial instruments that are giving similar cash flows in the future should have the same price today.

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