Question

Six months from now, Farmer Sam will harvest 20,000 bushels of corn. In doing so, he incurs costs of $93,000. The current spot price of corn is $4.90 per bushel, and the effective six-month interest rate is 6 percent. Sam has decided to hedge with a collar by purchasing $4.70-strike puts and selling $5.10-strike calls on 20,000 bushels of corn. The puts have a premium of $0.36 per bushel, while the calls have a premium of $0.63 per bushel. What total profit would Sam earn if the market price of corn at harvest time is $4.30, $4.70, $5.10, and $5.50, respectively?

Answer 1

Formula sheet

A	B	C	D	E	F	G	H	I	J	K
2		Total corn	20000	Bushel
3		Spot Price	5.5	per Bushel
4		Effective six-month interest rate	0.06
5		Cost of Harvesting	93000
6		Premium of put option bought	0.36	per Bushel
7		Exercise Price of Put Option	4.7	per Bushel
8		Premium of call option sold	0.63	per Bushel
9		Exercise Price of Call Option	5.1	per Bushel
10
11
12		Calculation of total profit:
13
14		For put option buyer, gain occurs when asset price falls.
15		Put option gives option buyer the right to sell the Stock at a strike price.
16
17		Profit of put option buyer is given by following equation:
18		Profit of put option = Max(X-ST,0)-p
19		where ST is stock price at maturity, X is exercise price and p is premium paid to buy the put option.
20
21		Call option gives option buyer the right to by the Stock at a strike price at a specified time in future.
22
23		Profit of Call option buyer is given by following equation:
24		Profit of Call option = Max(ST-X,0) -c
25		where ST is stock price at maturity, X is exercise price and c is premium paid to buy the Call option.
26
27		Profit of Call option seller is given by following equation:
28		Profit of Call option seller = -(Max(ST-X,0) -c)
29		where ST is stock price at maturity, X is exercise price and c is premium paid to buy the Call option.
30
31		Price at the maturity	4.3	4.7	5.1	5.5
32		Profit (Loss) from Put Option Bought	=$D$2*(MAX($D$7-D31,0)-$D$6)	=$D$2*(MAX($D$7-E31,0)-$D$6)	=$D$2*(MAX($D$7-F31,0)-$D$6)	=$D$2*(MAX($D$7-G31,0)-$D$6)	=$D$2*(MAX($D$7-G31,0)-$D$6)
33		Profit (Loss) from Call Option Sold	=-$D$2*(MAX(D31-$D$9,0)-$D$8)	=-$D$2*(MAX(E31-$D$9,0)-$D$8)	=-$D$2*(MAX(F31-$D$9,0)-$D$8)	=-$D$2*(MAX(G31-$D$9,0)-$D$8)	=-$D$2*(MAX(G31-$D$9,0)-$D$8)
34		Proceed from Sales of harvest	=D31*$D$2	=E31*$D$2	=F31*$D$2	=G31*$D$2	=G31*$D$2
35		Cost of Harvesting	=-$D$5	=-$D$5	=-$D$5	=-$D$5	=-$D$5
36		Interest on premium	=$D$8*$D$2*$D$4-$D$2*$D$6*$D$4	=$D$8*$D$2*$D$4-$D$2*$D$6*$D$4	=$D$8*$D$2*$D$4-$D$2*$D$6*$D$4	=$D$8*$D$2*$D$4-$D$2*$D$6*$D$4	=$D$8*$D$2*$D$4-$D$2*$D$6*$D$4
37		Total Profit	=SUM(D32:D36)	=SUM(E32:E36)	=SUM(F32:F36)	=SUM(G32:G36)	=SUM(G32:G36)
38