In: Finance
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 be LIBOR + 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 be LIBOR + 3% Hence B is better off by LIBOR-1% for using the swap. | |
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 be equally 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 of x and y that will satisfy the constraints imposed. |
From constraint (1), we have for FI that Cash Inflow – Cash Outflow = 0.2 => (y+L)-(x+L)=0.2 => y-x=0.2 (3) |
Gains from using Swap We determine the net cash outflow, |
Hence gain from using swap over doing |
Direct Gain (A) = Net cash outflow – Cost of direct floating rate loan for A = [(L+0.3)-x] – [L+0.2]=0.1-x |
Direct Gain (B) = Net cash outflow – Cost of 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 & 4 simultaneously to get : x=0.7-0.2=0.5 & y=0.7 Thus the swap payments 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% |