Six months from now, Farmer Pam will harvest 10,000 bushels of corn. In doing so, she...

Six months from now, Farmer Pam will harvest 10,000 bushels of corn. In doing so, she incurs costs of $42,000. The current spot price of corn is $4.70 per bushel, and the effective six-month interest rate is 4 percent. Pam has decided to hedge with a collar by purchasing $4.50-strike puts and selling $4.90-strike calls on 10,000 bushels of corn. The puts have a premium of $0.21 per bushel, while the calls have a premium of $0.38 per bushel. What total profit would Pam earn if the market price of corn at harvest time is $4.10, $4.50, $4.90, and $5.30, respectively?

Answers: a. $1,984; $1,984; $3,984; $7,984

b. $2,016; $6,016; $8,016; $8,016

c. $–1,000; $3,000; $7,000; $11,000

d. $4,768; $4,768; $8,768; $8,768

e. $6,900; $6,900; $6,900; $6,900

Please provide formulas for answer, thank you.

Expert Solution


Cost of purchasing put(Long) Strike $4.50	$0.21
Amount received for call(Short) Strike $4.90	$0.38
Net Amount received per bushel	$0.17	(0.38-0.21)
Six months effective interest rate=4%=	0.04
Future Value of $0.17 after 6 months	$0.1768	(0.17*(1+0.04)
Future Value of total net premium received	$1,768	(10000*0.18)
Cost of harvesting 10000 bushel after 6 months	$42,000

P	A	B	C=A+B	D=C*10000	E	F	G=P*10000	H=D+E+F+G
Market Price at harvest time	Payoff per bushel for long put (strike$4.50)	Payoff per bushel for Short call (Strike $4.90)	Net Payoff per Bushel after six months	Net Pay off for 10000 bushel	Value of net premium received	Total Cost of haevesting	Amount received for selling corn	Total Profit Earned
$4.10	$0.40	$0	$0.40	$4,000	$1,768	($42,000)	$41,000	$4,768.00
$4.50	$0	$0	$0.00	$0	$1,768	($42,000)	$45,000	$4,768.00
$4.90	$0	$0	$0.00	$0	$1,768	($42,000)	$49,000	$8,768.00
$5.30	$0	($0.40)	($0.40)	($4,000)	$1,768	($42,000)	$53,000	$8,768.00
Put gives the buyer right to sell at strike price ($4.50). Hence , if price at expiration is lower than strike price , the buyer of put makes profit. In this case payoff =(4.50-4.10)=$0.40
Call gives the buyer right to buy at strike price. If market price is higher than strike price, the buyer of call makes profit and the seller makes loss. Hence loss=(5.3-4.9)=$0.40

Market Price at harvest time	Total Profit
$4.10	$4,768.00
$4.50	$4,768.00
$4.90	$8,768.00
$5.30	$8,768.00

Answer:
d.$4768,$4768,$8768,$8768

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