VIPSolutionsGive step-by-step solution with explanation and final answer:Mrs. Smith is an orange juice distributor who, in January, signed a contract to deliver 60,000 pounds of frozen orange juice to Churchill Downs on Kentucky Derby Day (first Saturday of May). Mrs. Smith plans to buy the orange juice from a local distributor in May. With the small profit margins, Mrs. Smith is afraid she might incur a loss if orange juice prices increase. Explain how Mrs. Smith could lock in her orange juice costs with a May frozen orange juice futures contract trading in January at FO = $.90/lb. The contract size is 15,000lbs. Show the net costs at the futures expiration date, from closing the futures position and buying 60,000lbs of frozen orange juice on the spot market at possible prices of $.90/lb, and $1.0/lb . How much cash or risk - free securities would Mrs. Smith have to deposit to satisfy the initial margin requirement of 5% ?
Question:
Give step-by-step solution with explanation and final answer:
Mrs. Smith is an orange juice distributor who, in January, signed a contract to deliver 60,000
pounds of frozen orange juice to Churchill Downs on Kentucky Derby Day (first Saturday of
May). Mrs. Smith plans to buy the orange juice from a local distributor in May. With the
small profit margins, Mrs. Smith is afraid she might incur a loss if orange juice prices increase.
Explain how Mrs. Smith could lock in her orange juice costs with a May frozen orange juice
futures contract trading in January at FO = $.90/lb. The contract size is 15,000lbs. Show
the net costs at the futures expiration date, from closing the futures position and buying
60,000lbs of frozen orange juice on the spot market at possible prices of $.90/lb, and $1.0/lb
. How much cash or risk - free securities would Mrs. Smith have to deposit to satisfy the
initial margin requirement of 5% ?
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Asked by: Sampangi Swetha
Created at: 2025-09-13 01:23:44
Asked by: Sampangi Swetha
Created at: 2025-09-13 01:23:44
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# Step-by-Step Solution
## **Step 1: Understanding the Scenario**
- **Mrs. Smith** needs to deliver **60,000 lbs** of frozen orange juice in May.
- She fears **price increases** in orange juice by that time.
- She can lock in her purchase price using **May orange juice futures**.
- **Futures contract details:**
- **Current (January) futures price (F₀): $0.90/lb**
- **Contract size: 15,000 lbs**
- **Spot prices in May** could be:
- $0.90/lb (unchanged)
- $1.00/lb (increased)
---
## **Step 2: Hedging With Futures Contracts**
**To hedge:**
- Mrs. Smith needs to buy orange juice in May.
- She should **buy (long) May futures contracts in January** to lock in the price.
**How many contracts?**
\[
\text{Number of contracts} = \frac{60,000~\text{lbs}}{15,000~\text{lbs/contract}} = 4~\text{contracts}
\]
---
## **Step 3: Net Cost at Futures Expiration**
### **Case 1: Spot Price in May = $0.90/lb**
#### a) Futures position:
- Futures price at expiration = Spot price = $0.90/lb
- Futures were bought at $0.90/lb in January, so **no gain/loss on futures**.
#### b) Buy orange juice in spot market:
- Cost = $0.90/lb × 60,000 lbs = **$54,000**
#### **Net cost = $54,000**
---
### **Case 2: Spot Price in May = $1.00/lb**
#### a) Futures position:
- Futures price at expiration = $1.00/lb
- She **bought futures at $0.90/lb**, so **gain = $1.00 - $0.90 = $0.10/lb** on 60,000 lbs = **$6,000 total gain**
#### b) Buy orange juice in spot market:
- Cost = $1.00/lb × 60,000 lbs = $60,000
#### c) **Net cost after futures gain:**
\[
\text{Net cost} = \$60,000 - \$6,000 = \$54,000
\]
---
### **Conclusion:**
**By hedging with futures, Mrs. Smith locks in her cost at $0.90/lb or $54,000, regardless of spot price changes.**
---
## **Step 4: Initial Margin Requirement**
- **Initial margin requirement = 5% of the contract value.**
### **Contract Value:**
- For 1 contract = 15,000 lbs × $0.90/lb = $13,500
- For 4 contracts = 4 × $13,500 = $54,000
### **Margin Required:**
\[
\text{Initial margin} = 5\% \times \$54,000 = \$2,700
\]
---
## **Final Answers**
### **1. Hedging with Futures**
- Mrs. Smith should **buy 4 May orange juice futures contracts** at $0.90/lb in January.
- At contract expiration, regardless of spot market price ($0.90/lb or $1.00/lb), her **net cost to buy the 60,000 lbs will be $54,000** ($0.90/lb).
### **2. Initial Margin Requirement**
- Mrs. Smith must deposit **$2,700** in cash or risk-free securities to satisfy the initial margin requirement (5% of $54,000).
---
**Summary Table**
| Spot Price in May | Cost to Buy Orange Juice | Gain/Loss on Futures | Net Cost |
|-------------------|-------------------------|----------------------|----------|
| $0.90/lb | $54,000 | $0 | $54,000 |
| $1.00/lb | $60,000 | +$6,000 | $54,000 |
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