Question

As a portfolio manager, you have a portfolio with one liability of a single payment 5 years from now of $7,500 and five bonds, which mature 10 years from now at par ($1,000 each) with annual interest payments of $100 each. Assuming that the bond sold at par, and the nominal interest rate remains at about 10 percent, you should be able to make the balloon payment with the interest on the bonds for 5 years ($500 times 5 = $2,500, not including the interest from receiving the interest) plus redeeming the bonds ($1,000 times 5 = $5,000). Your calculation are simple, and you sleep in blissful ignorance. What is the fallacy in this calculation?

Answer 1

Answer:

Liability on bonds

1. The interest on any bond are paid periodically, hence liability arises for paying interest periodically (here annually)
2. The redemption value liability on bond is created on expiry of the term of the bond (here 10 years from now)

In the above question, the liabilities created at the end of each year are mentioned below:

End of Year	Interest liability ($)	Liability at redemption ($)	Total liability ($)
1	100 per bond for 5 bonds = 500	0	500
2	100 per bond for 5 bonds = 500	0	500
3	100 per bond for 5 bonds = 500	0	500
4	100 per bond for 5 bonds = 500	0	500
5	100 per bond for 5 bonds = 500	0	500
6	100 per bond for 5 bonds = 500	0	500
7	100 per bond for 5 bonds = 500	0	500
8	100 per bond for 5 bonds = 500	0	500
9	100 per bond for 5 bonds = 500	0	500
10	100 per bond for 5 bonds = 500	1000 per bond for 5 bonds =5,000	5,500

The simple calculations made in the question are false The interest cannot be paid as a balloon payment at the end of five years and the bonds cannot be redeemed after end of 5^th year where the full term of 10 years.