A Young Investment Banker Meets One of Its Clients, SOSO $$\begin{array} { c c c } & AU\$ & \$ \\\hline 1 \text { year } & 10 \% & 6 \% \\2 \text { year } & 11 \% & 7 \%\end{array}$$

A young investment banker meets one of its clients, SOSO Inc. that is based in Sydney, Australia.
Current market conditions are the following:
FX Spot rate: AU$/$ =2.
Interest rate (zero-coupon):
$$\begin{array} { c c c } & AU\$ & \$ \\\hline 1 \text { year } & 10 \% & 6 \% \\2 \text { year } & 11 \% & 7 \%\end{array}$$ Quote in U.S.$ cents for options (strike price: 50 cents per AU$).
$\begin{array}{lcc} & \text { PUT } A U \$ & C A L L A U \$ \\\hline 1 \text { year } & 2.5 & 2 \\\text { 2 year } & 3.5 & 3\end{array}$
For example a PUT AU$, traded in Chicago, gives the right to sell 1 Australian dollar (AU$) at
50 cents in a year. Its current price is 2.5 cents per AU$.
SOSO would like to issue a bond paying a fixed annual coupon of 6 AU$ and to be reimbursed in a year 100 AU$ or 50$ at the bearer's choice.
a. Assuming that the bond is actually issued at 105 AU$, what is the implicit price of the option linked to that bond? Would you recommend that bond to an investor?
b. If the market was efficient, what is the normal issue price for such a bond?
After many thoughts, SOSO agrees to issue instead a dual-currency bond with an annual coupon in AU$ and a nominal to be reimbursed in US$ with the following characteristics:
- Issue Price: 100 AU$.
- Reimbursement Price: 50$
- Maturity: 2 years.
- Annual Coupon: C AU$.
c. Under current market conditions, at what level should Coupon C on the dual-currency
bond be set?