Q$4.$ Suppose that a firm entered several years ago into a cross$-$currency swap where it is paying $8\%$ per

annum in Australian dollars $($AUD$)$ and receiving $4\%$ per annum in U$.$S$.$ dollars $($USD$).$ The principals in

the two currencies are AUD $20$ million and USD $12$ million. Payments are exchanged every year, with

one having just taken place. The swap will last $2$ more years. At present, the USD interest rates are $7\%$ for

all maturities and the AUD rates are $9\%$ for all maturities $($both with continuous compounding$).$ The

current exchange rate is AUD $1=$ USD $0\mathrm{.}62.$

a$.$ What is the current value of the swap $($in USD million$)$ for the company?

b$.$ What AUD foreign exchange rate would make the swap have zero value $($keeping interest rates at

current values$)?$ What USD interest rates would make the swap have zero value $($keeping constant

both the AUD interest and foreign exchange rates$)?$

$(3$ points$)$