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	Tax rate
First $4 of pre-tax profit	10%
Next $6 of pre-tax profit	15%
Next $8 of pre-tax profit	40%
Pre-tax profit greater than $18	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.

1. 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.

Suppose that the price of corn will follow the following distribution one year from now:

Corn Price	Probability
1.00	0.25
2.00	0.25
3.00	0.25
4.50	0.25

The following one-year call options are available on the price of corn.  The risk free rate is 5% compounded continuously:

Strike Price	Call Premium
1.50	1.24
2.00	0.85
2.50	0.55

The one year forward price of corn is 2.79 per bushel.

2. Given the information above, list at least 7of the possible hedging strategies that you can use to hedge against adverse fluctuations the price of corn (i.e. possible combinations of derivatives above that apply).  No calculations are required for this question, you’re answer should be a list. HINT: there are 10 in total.
3. Calculate the expected unhedged after-tax profit on the production and sale of corn.

4. Calculate the expected after-tax profit for all possible hedging strategies that you listed in part b. State which hedging strategy results in the highest expected profit.
5. Explain why reducing earnings volatility in a progressive tax environment can improve expected after-tax profit

Answer 1

Corn price	1	2	3	4.5
Selling price of ethanol	40	40	40	40
Less: Direct materials	10	20	30	45
Less: Fixed costs	12	12	12	12
Profit before Tax	18	8	-2	-17
Less: Tax	4.5	1	0	0
PAT	13.5	7	-2	-17

Maximum Profit will be earned at the corn price of 1$, ie, 13.5$
Workings
Tax Computation for Corn price of 1$
Slab	Value	Tax Rate	Tax
0-4	4	0.1	0.4
5 to 10	6	0.15	0.9
11 to 18	8	0.4	3.2
19 and above	0	0.5	0
			4.5
Tax Computation for Corn price of 2$
Slab	Value	Tax Rate	Tax
0-4	4	0.1	0.4
5 to 10	4	0.15	0.6
11 to 18	0	0.4	0
19 and above	0	0.5	0
			1

a) Hedging strategies possible

Strategy	Strike price	Actual Price	Profit
1	1.5	2	0.5
2	1.5	3	1.5
3	1.5	4.5	3
4	2	3	1
5	2	4.5	2.5
6	2.5	3	0.5
7	2.5	4.5	2

b) Expected unhedged after- Tax profit

Corn price per unit	2.625
Selling price of ethanol (10 gallons)	40
Less: Direct materials	26.25
Less: Fixed costs	12
Profit before Tax	1.75
Less: Tax	0.175
PAT	1.575

Working:

Corn price per unit	Probability	Expected value
1	0.25	0.25
2	0.25	0.5
3	0.25	0.75
4.5	0.25	1.125
Expected Price of corn	2.625
Forward price		2.79

d)

Expected after-tax profit for possible hedging strategies

Corn price per unit	1.5	2	2.5
Selling price of ethanol (10 gallons)	40	40	40
Less: Direct materials	15	20	25
Less: Fixed costs	12	12	12
Less: Option premium	12.4	8.5	5.5
Profit before Tax	0.6	-0.5	-2.5
Less: Tax	0.06	0	0
PAT	0.54	-0.5	-2.5