a$)[15]$ Suppose you are a furniture making company that needs to purchase timber on a

regular basis. Timber generates a fixed percentage convenience yield of $3\%$ of its current

market price and a $2\%$ storage cost $[$both figures are compounded quarterly and are not

annualized$].$ You know that the risk$-$free rate is $8\%$ compounded annually and current spot

price is $$1000$ per $100$ logs$.$ Use discrete quarterly compounding to find a $9-$month Forward

price of $100$ logs$.$

b$)[20]$ Suppose you observe a share of stock traded in the market at a price of $$80.$ This stock

has just paid out dividends of $$1$ per share. The company will continue paying out dividends

in the next $5$ quarters. The company plans to increase the amount of dividends by $5\%$ per

quarter. Suppose you want to buy a $17-$months Forward on this stock. Find the equilibrium

forward price if the risk$-$free rate is flat $10\%$ per year $($continuously compounded$).$

c$)[15]$ If currently the price of forward from $($b$)$ is $$83,$ how can you obtain an arbitrage profit?

Clearly explain your strategy and demonstrate the cash and asset flows.