We know the following borrowing conditions $($see below$)$ available to A plc and B plc$.$ For different reasons, B plc prefers flexibility and A plc prefers certainty. Hence, both A plc and B plc want to swap their liabilities. A swap dealer arranges an interest rate swap for the two companies on the following terms: $1$ million notional$$ two$-$year term with semi$-$annual payments. Design a swap deal so that the quality spread differential can be distributed evenly among A plc$,$ B plc and the swap dealer. Annual borrowing fixed rate Annual borrowing floating rate A plc $4\mathrm{.}89\%$ LIBOR $+1\mathrm{.}83\%$ B plc $3\mathrm{.}82\%$ LIBOR $+1\mathrm{.}66\%$

Borrowing conditions

For A Annual borrowing fixed is $4\mathrm{.}89\%$

For A Annual borrowing floating is LIBOR $+1\mathrm{.}83\%$

For B Annual borrowing fixed is $3\mathrm{.}82\%$

For B Annual borrowing floating is LIBOR $+1\mathrm{.}66\%$

$($a$)$ Produce a diagram which illustrates the above interest rate swap. Clearly specify the interest rate value of all cash flows in the swap and show the effective borrowing costs to both A plc and B Plc after the swap.

$($b$)$ Calculate the net cash payments made by A plc and B plc in their swap deals with the swap dealer if the annual pound LIBOR rate on each of the four payment dates is: $3\%,5\%,$ and $7\%.$