Answer:
The correct answer is option (a) 0.8807
Explanation:
Solution
Given that:
We start from the liability of bond in 3 years.
Thus, the $100 liability can be an offset by Bond C.
The cash flow of Bond C and the payment of final coupon in year 3 is given as:
100 + (5%*100) = 105
Now,
the number of Bond C which will offset a liability of $100 which is = 100/105 = 0.9524 (All cash flows of Bond C is multiplied by this)
So, the remaining liability becomes
Time Liabilities cash flow Cash flow from Bond C Remaining liabilities
1 99 4.76 94.24
2 102 4.76 97.24
3 100 100.00
Thus,
The year 2 liability offset is $97.24
For Bond B, this can be the offset which contains a cash flow of $100 (which is a zero coupon bond)
The Bond number which are required for this offset is = 97.24/100 =0.974
The remaining cash flow is computed as follows:
Time = 1 ,2, 3
Liabilities cash flow = 99, 102, 100
Cash flow from Bond C =4.76, 4.76. 100.00
Remaining liabilities = 94.24, 97.24
Cash flow from Bond B = 0, 97.24
Remaining liabilities = 97.24
What this suggest is that The Bond A has to offset at approximately $94.24 in year 1.
The Cash flow from Bond A = 100 + (7%*100) = 107
Hence,
The number of Bond A's needed = 94.24/107 = 0.8807
