# Companies A and B have been re

Companies A and B have been required the following rates perannum on a $10 million notional:

Fixed rate Floating rate

Company A 2.0% p.a. LIBOR + 0.3% p.a.

Company B 3.0% p.a. LIBOR + 1.3% p.a.

a)Under which assumption Company A and B may find it useful toenter a swap?

b)In that case, design a swap that will net a bank, acting asintermediary, 0.2% per annum and that will appear equallyattractive to both companies.

How does your answer to question b) modify if A is availableto receive 1/3 of the amount that is shared between A and B (i.e.,the overall gain minus the intermediary fee is split into threeparts, one for A and two for B)?

Plus: when B-A(float) equals to B-A(fixed) how to determine Band A chose floating or fixed markets?

Answer:

Fixed | Floating | |||

A | 0.3% | LIBOR + | 2% | |

B | 1.3% | LIBOR + | 3% | |

Company A | External vendor | B | ||

Pay | 0.30% | LIBOR+2% | ||

Hence net rate of borrowing = | (LIBOR + 2%) – 0.30% = | LIBOR +1.7% | If A borrowed directly, i.e. w/o the swap, its rate would beLIBOR + 2% Hence A is better off by 0.3% for using the swap. | |

Company B | External vendor | A | ||

Pay | 1.3% | LIBOR+3% | ||

Hence net rate of borrowing = | (LIBOR + 3%) – 1.3% = | LIBOR -1% | If B borrowed directly, i.e. w/o the swap, its rate would beLIBOR + 3% Hence B is better off by LIBOR-1% for using theswap. | |

We now consider the case with a financial intermediary | ||||

We have the following constraints: | ||||

1 | Net gain to financial intermediary is 0.2%. | |||

2 | Net gain to A must equal net gain to B since deal must beequally attractive to both companies. |

External lender <…………….. | A | FI | B | ……………………..>External lender | |

0.30% | <………………………… | <………………………… | LIBOR+3% | ||

X | Y | ||||

…………………………> | …………………………> | ||||

LIBOR | LIBOR |

We need to find the values ofx and y that will satisfy the constraints imposed. |

From constraint (1), we have for FI thatCash Inflow – Cash Outflow = 0.2 => (y+L)-(x+L)=0.2 =>y-x=0.2 (3) |

Gains from using Swap We determine the netcash outflow, |

Hence gain from using swap over doing |

Direct Gain (A) = Net cash outflow – Costof direct floating rate loan for A = [(L+0.3)-x] –[L+0.2]=0.1-x |

Direct Gain (B) = Net cash outflow – Costof direct fixed rate loan for B = [y+L+3-L]-1.3=y-0.7 |

To satisfy (2), we must have |

Gain (A) = Gain (B) => 0.1-x = y -0.7=> y+x = 0.8 (4) |

We can then solve equations 3 & 4simultaneously to get : x=0.7-0.2=0.5 & y=0.7 Thus the swappayments will be as follows: |

Company A |

• Pay 0.3%% to outside lender |

• Pay LIBOR to FI |

• Receive 0.7% from FI |

Hence net rate of borrowing for A=0.3% +LIBOR -0.7%=LIBOR-0.4% |

Company B |

• Pay LIBOR+0.3% to outside lender |

• Pay 0.5% to FI |

• Receive LIBOR from FI |

Hence net rate of borrowing for B:=LIBOR+0.3% + 0.5%-LIBOR = 0.8% |