Question

Six months from now, Farmer Julie will harvest 20,000 bushels of corn. In doing so, she incurs costs of $100,000. The current spot price of corn is $5.50 per bushel, and the effective six-month interest rate is 2 percent. Julie has decided to hedge by purchasing put options on 20,000 bushels of corn with a strike price of $5.50 per bushel. The puts have a premium of $0.54 per bushel. What total profit would she earn if the market price of corn at harvest time is $4.90, $5.30, $5.70, and $6.10, respectively?

Answer 1

Formula sheet

A	B	C	D	E	F	G	H	I
2		Total corn	20000	Bushel
3		Spot Price	5.5	per Bushel
4		Effective six-month interest rate	0.02
5		Cost of Harvesting	100000
6		Premium of put option written	0.54	per Bushel
7		Exercise Price of Put Option	5.5
8		Period of put option	6	month
9
10		Calculation of total profit:
11
12		For put option buyer, gain occurs when asset price falls.
13		Put option gives option buyer the right to sell the Stock at a strike price.
14
15		Profit of put option buyer is given by following equation:
16		Profit of put option = Max(X-ST,0)-p
17		where ST is stock price at maturity, X is exercise price and p is premium paid to buy the put option.
18
19		Price at the maturity	4.9	5.3	5.7	6.1
20		Profit (Loss) from Put Option	=$D$2*(MAX($D$7-D19,0)-$D$6)	=$D$2*(MAX($D$7-E19,0)-$D$6)	=$D$2*(MAX($D$7-F19,0)-$D$6)	=$D$2*(MAX($D$7-G19,0)-$D$6)
21		Proceed from Sales of harvest	=D19*$D$2	=E19*$D$2	=F19*$D$2	=G19*$D$2
22		Cost of Harvesting	=$D$5	=$D$5	=$D$5	=$D$5
23		Interest Lost on premium of put option	=-$D$2*$D$6*$D$4	=-$D$2*$D$6*$D$4	=-$D$2*$D$6*$D$4	=-$D$2*$D$6*$D$4
24		Total Profit	=SUM(D20:D23)	=SUM(E20:E23)	=SUM(F20:F23)	=SUM(G20:G23)	=SUM(G20:G23)
25