On $30$th January $2022$ sterling money market interest rates were as follows:

$91-$day interest rate spread $0\mathrm{.}84\%0\mathrm{.}88\%$

$182-$day interest rate spread $0\mathrm{.}91\%0\mathrm{.}95\%$

Sterling Three$-$Month Interest Rate Futures $500,000($CME$)$

Price

March $($delivery day $16$st March$)99\mathrm{.}0257$

June $($delivery day $18$th June$)98\mathrm{.}8657$

September $($delivery day $21$th September$)98\mathrm{.}8057$

Assume that the day$-$count convention for transactions in UK money markets is actual days$/365.$

The delivery days for the futures contracts are $16$st March, $18$th June and $21$th September.

a$)$MNS Plc plans to deposit $104,000,000$ for $91$ days, starting $91$ days from $30$th January.

Critically discuss the terms of a money market hedge and estimate the forward rate that the company could establish

via those money market transactions.

b$)$ Assume MNZ Plc had entered a Forward Rate Agreement with an investment bank to fix the forward deposit rate at the level implied by the money market hedge. Show how the FRA is settled if$,$ on the settlement date, three$-$month $$LIBOR is $1\mathrm{.}46\%$

c$)$ Critically devise a hedge of the interest rate risk using sterling futures and assess how well it works if three$-$month $$LIBOR in $91$ days is $1\mathrm{.}46\%$ and the futures contract price is $98\mathrm{.}49.$

d$)$ Critically discuss the factors that MNZ Plc need to consider in deciding:

i$.$ whether to hedge the deposit rate on the forthcoming cash flow

ii$.$ whether to enter a FRA or trade futures contracts to hedge the deposit rate.