A business plans to borrow approximately $$40$ million in short$-$term funding through the issue of commercial paper in three months$$ time. The business does not have a view on what is likely to happen to interest rates over the next three months, but it would be very satisfied if it could obtain its funding at the current yield. We have the following data:

Time Commericlal paper yields $90-$day bank$-$accepted bills futures price

Totday $6\mathrm{.}00\%$ p$.$a $93\mathrm{.}75$

In $3$ months $7\mathrm{.}00\%$ p$.$a $93\mathrm{.}25$

a$)$ Using the above data, show how $90-$day bank$-$accepted bills futures contracts can be used to hedge the interest rate risk to which the business is exposed.

b$)$ Draw a timeline to show the calculation and timing of all transactions and cash flows $($ignore transaction costs and margin requirements$).$ Your timeline should consist of three points in time $($t$=0,$ t$=90$ days, and t$=180$ days$).$ You may benefit from drawing one timeline for the planned borrowing of funds in the commercial paper market, drawing a second timeline for the cash flows associated with the futures hedge, and drawing a third timeline that shows the NET cash flows from the first two timelines.

c$)$ What is the effective cost of funds achieved with this hedging strategy? What would the cost of funds have been had the hedge not been put in place? Explain your answer, showing your calculations.