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% |
"Our Prices Start at $11.99. As Our First Client, Use Coupon Code GET15 to claim 15% Discount This Month!!"
![](https://writinghelpe.com/wp-content/uploads/2022/08/save.jpg)