Consider the commodities and financial assets listed in the following table:

Asset Spot Price Comments

Magnoosium $$2,970$ per ton Net convenience yield $=5\%$ per year

Oat bran $$0\mathrm{.}61$ per bushel Net convenience yield $=0\mathrm{.}7\%$ per month

Biotech stock index $$141\mathrm{.}9$ Dividend $=0$

Allen Wrench Company common stock $$59\mathrm{.}70$ Cash dividend $=$ $$4\mathrm{.}10$ per year

$5-$year Treasury note $$108\mathrm{.}938\%$ coupon

Westonian ruple $3\mathrm{.}27$ ruples $=$ $$114\%$ interest rate in ruples

The risk$-$free interest rate is $6\%$ a year, and the term structure is flat.

a$.$ Calculate the six$-$month futures price for each case.

c$.$ Suppose the producer sells $1,000$ tons of six$-$month magnoosium futures but after one$-$month magnoosium prices have fallen to $$2,200.$ Will the producer have to undertake additional futures market trades to restore its hedged position?

d$.$ Does the biotech index futures price provide useful information about the expected future performance of biotech stocks?

e$.$ Suppose Allen Wrench stock falls suddenly by $$14\mathrm{.}25$ per share. Investors are confident that the cash dividend will not be reduced. What happens to the futures price?

f$.$ Suppose interest rates suddenly fall to $4\%.$ The term structure remains flat. Determine the six$-$month futures price on the five$-$year Treasury note.