Problem 1)
Part 1
The farmer can hedge perfectly by selling the September wheat forward. For selling 60,000 bushels he
Part 2
No matter what the exchange rate is, the revenue of the farmer is $3.41*60,000=$204,600
from the forward sale. Commodity contracts are typically not cash-settled, but you can
compute notional gains/losses:
Quantity
60000
Futures price
$3.41
Wheat spot price
$3.25
$3.35
$3.45
Notional gain on futures
$9,600
$3,600
-$2,400
Hypothetical revenue
$195,000
$201,000
$207,000
from spot sale
Total
$204,600
$204,600
$204,600
Part 3
There are slightly different ways of doing this. First, compute the present value of the farmer's
salary as of January 1st, using a monthly discount rate of 0.4% (4.8%/12):
$30,879.13
To this you have to add the $150,000 the farmer can leave in his bank account in January. Then
the total costs from these two items in January are:
$180,879.13
The future value as of September 30 is then:
$187,495.94
To this you have to add the opportunity costs of leasing the land, assuming the lease payment
for the land would be due at the end of September:
$192,495.94
breakeven rate for the wheat price is found by dividing $192,495.94 by 60,000 bushels to
obtain the break even price per bushel:
$3.208
Hence, for a wheat price below $3.208 the farmer does not break even anymore.
Part 4
The farmer could also store the wheat and wait until December. Compute the gain from this
as of September 30. Then you have to compare the $204,600 the farmer makes from selling
in September with the present value from selling in December, minus the present
value of the storage costs. This gives:
Present value of sale in December
$208,389.31
PV of storage costs
$3,571.39
Total
$204,817.92
Net (deduct opportunity costs)
$217.92
Hence, selling in December and storing in the months from September to December gives the farmer
a small gain of $217.92.
Part 5
In this case the answer is clear without calculations from part 4: the farmer can store an addtional 40,000
bushels at no costs, hence the profit margin must be bigger than in part 4, where the storage costs where
needs to sell 60,000/5,000 = 12 September wheat contracts.
This is the total dollar amount the farmer could make from not growing wheat
. Hence the