Question

A firm uses corn as an input into their production of ethanol. You require 1 bushel of corn to produce one gallon of ethanol. Each gallon of ethanol sells for $4. Fixed costs are $12, and you can produce and sell 10 gallons of ethanol this year. Corporate taxes on profits follow a progressive pattern, and are as follows: Tax Bracket First $4 of pre-tax profit Next $6 of pre-tax profit Next $8 of pre-tax profit Pre-tax profit greater than $18 Tax rate 10% 15% 40% 50% For illustrative purposes, assume that all cash flows occur at the end of the year (i.e. assume that all corn is purchased and ethanal produced and sold at the end of the year). This way, there is no adjustment for time value of money required to calculate profit. a) If all of the above assumptions hold, what is the price of corn for which profits are maximized? Calculate the maximum profit you can earn. [8 Marks]

Answer 1

a) Selling price= 10 gallons * $4 = $40

- Fixed cost = $12

Profit before tax = $28

Maximum profit after tax:

Upto $4 @10% = 4-0.4=3.6

Upto $6 @15% = 6-0.9=5.1

Upto $8 @40% = 8-3.2=4.8

Upto $10 @50% = 10-5=5

Answer = 3.6+5.1+4.8+5= $18.5

b) Strategies are as follows

1. Covered call

2. Married put

3. Bull call spread

4. Bear put spread

5. Protective collar

6. Long straddle

7. Long strangle

8. Long call butterfly spread

9. Iron condor

10. Iron Butterfly