Question 1 [10 marks] HydroGen will issue a 30-year bond on 15 June 2021, paying coupon semiannually at j2=3% p.a. Future payments of coupon and return of capital will depend on the viability of the business. You have studied the firm and believe there is a constant probability of default in each half-year period of 2% and that, if the firm defaults, no further payments will be forthcoming.

a. [2 marks] Draw a detailed contingent cash flow diagram, from an investors perspective, that illustrates the payments of the bond over its 30 potential years. Assume a face value of $100.

b. [2 marks] For a valuation date of 15 June 2021, write out the equation of value you would use to value the HydroGen bond. Simplify your mathematical expression for price as far as possible. No numerical solution is required; only algebra is required. Today (9 June 2021) HydroGen has decided to buy infrastructure for its business from overseas. To remove exchange rate risk from the transaction, HydroGen enters into a forward contract with a counterparty, contracting to pay AUD$5 million on 15 November, in consideration for adequate foreign currency to pay for the infrastructure. Currently, HydroGen can borrow/lend for periods up to 180 days at 2.6% p.a. (simple interest).

c. [2 marks] Draw a carefully labelled cash flow diagram, from HydroGens perspective, that illustrates and explains how HydroGen could replicate the forward AUD$5 million purchase of the foreign currency. Use a forward exchange rate of f5 and a spot exchange rate of s. You are thinking of buying a European call option, expiring in one months time, on shares in HydroGen. You want to know how much such an option will cost, and decide to price it using a simple (binomial) model. Your model assumes a monthly price increase of 7% on the current price or a price decrease of 4% on the current price. The current price of one HydroGen share is $10. The strike price for the European call option is $10.50. No dividends are expected from HydroGen over the next few months. You can borrow money today for month at a rate of j12=3.6% p.a.

d. [2 marks] Draw a carefully labelled cash flow diagram, from your perspective, that illustrates and explains how you could replicate the payoffs of the European call option described above.

e. [2 marks] Write out the algebra your model generateshow replicates the cash flows associated with the option payoffs and the payment for the option. You are not required to solve these equations; algebraic expressions and accompanying written explanations are all that is required.