Spencer Hahn

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Chapter 12 Problem

• In a good economy the cost to produce orange juice from fresh oranges is \$.75/gallon, and producing orange juice from concentrate has a cost of \$.40/gallon.
• In a bad economy the cost to produce orange juice from fresh oranges is \$.50/ gallon, due to increase in demand for concentrate in bad economies the cost to produce orange juice from concentrate rises to \$.45/gallon.
• The risk neutral probabilities for these states are both (.5).
• The price of orange juice is \$1.50/gallon for the juice made from fresh oranges, and \$1.35/gallon for the juice made from concentrate in a good economy.
• In a bad economy fresh orange juice continues to sell for \$1.50/gallon, when the juice from concentrate sells for \$1.15/gallon.

Assume that the fixed cost for both operations are identical. Furthermore in each scenario a minimum of 100,000 gallons of orange juice must be produced. If the firm wants to produce an additional 100,000 gallons of orange juice it will cost an additional \$70,000 to do so.

Which scenario would be most lucrative for a firm to engage in?
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Explanation:
Cost of Producing OJ from fresh oranges (Scenario 1)
\$.625/gallon = .5*(.75) + .5*(.50)

Cost of producing OJ from concentrate (Scenario 2)
.425/gallon = .5*(.4) + .5*(.45)

Profit in (Scenario One) for one period:
Good Economy —> 100,000*(1.5 - .625/gallon) = \$87,500
Bad Economy —> 100,000*(1.5 - .625/gallon) = \$87,500

Profit in (Scenario 2) for one period:
Good Economy —> 100,000*(1.35 -.425/gallon) = \$92,500
Bad Economy —> 100,000*(1.15 - .425/gallon) = \$72,500

After one period the firm is faced with a decision to pay \$70,000 to produce an additional 100,000 gallons of orange juice.

In a BAD economy it is more lucrative to make orange juice from fresh oranges (Scenario 1) because \$105,000 > \$75,000:
\$87,500*2(periods) - \$70,000 (for producing additional 100,000 gallons) = \$105,000

\$72,500*2(periods) - \$70,000 (producing additional 100,000 gallons) = \$75,000

In a GOOD economy it would make more sense to produce orange from concentrate (Scenario 2) because \$105,000< \$135,000

Scenario 1 (GOOD Econ)
\$87,500*2(periods) - \$70,000 (for producing additional 100,000 gallons) = \$105,000

Scenario 2 (GOOD Econ)
\$92,500*2(periods) - \$70,000 (for producing additional 100,000 gallons) = \$135,000

Chapter 21 Problem:

Spencer's Shot-glasses manufactures premium design-to-order shot-glasses. Currently, Spencer, CEO of Spencer's Shot-glasses is considering selling the company. Ronnie's Glassblowing (UK) is interested in the purchase of Spencer's Shot-glasses. Currently the British pound is converting at 1.32 US Dollars, but over the course of the year is expected to reach 1.50 \$/Pound. When the conversion rate is 1.32 Spencer's Shot-glasses is worth 2 million dollars, and when the conversion rate is 1.50\$/pound Spencer's Shot-glasses is worth 2.5 million dollars.

To avoid buying when the Pound is weaker compared to the dollar Ronny is considering entering into a forward contract with Spencer's Shot-glasses. If the forward rate is 1.38 \$/Pound and Spencer's Shot-glasses is worth 2.1 million dollars, should Ronny enter into the contact?
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Explanation:
Ronny should enter into the forward contract because the cost to acquire Spencer's Shot-glasses for 2.1 million dollars is less than the average price which would be 2.25 million dollars.

2,100,000 < (2,500,000 + 2,000,000)/2
2,100,000 < 4,500,000/2
2,100,000 < \$2,250,000

Chapter 22 Problem: Determining the future/forward price with convenience yields

Pork Bellies are currently at \$.78/pound, assume that the convenience yield is 4% per year. If the risk free rate is 5% per year, what is the future/forward price of pork bellies 1 year from now?

1> Fo =
So * (1 + Rf Rate)
(1 + Conv. Yield)

2> Fo =
\$.78 * (1 + .05)
(1 + .04)

3> Fo =
\$ .819
1.04

4> Fo = \$.7875/ pound

Thus, the one year future price of Pork Bellies is now \$.7875/pound.

Chapter 23 Problem: MacAuley/ Modified Duration.

Calculate both the MacAuley and Modified duration based on the following data. Starting value of the bond is \$500, when the face value (ending value) of the bond is \$550. The bond is set to mature in 4 years with an annual coupon rate of 11%. The Yield to maturity on the bond is 10%.

MacAuley Duration = ((.11/1.1) + (2*(.11/1.12)) + (3* (.11/1.13)) + (4*(550/1.14))) / 500

MacAuley Duration = .1 + .181818 + .247934 + 1502.629602

MacAuley Duration = 3.006319

Modified Duration =
MacAuley Duration
__Risk Free Rate __ +1
Num of times compounded

Modified Duration = 3.006319/ 1.11

Modified Duration = 2.708395

page revision: 10, last edited: 02 Mar 2009 23:03