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VIPSolutions · Accepted Answer

## Objective

Given:
- Your firm needs **140,000 bushels of corn** in December 202- You want to lock costs (using) based on the **closing price of the day** (from Table 23.1, which is not shown but we'll assume you have the December futures price).
- In part (b), December spot price is given as **$3.17 per bushel**.

---

## a. Lock-In Total Cost Using Futures

**Available Data/Information:**
- Quantity needed: $ Q = 140,000 $ bushels
- December futures closing price (assume from Table 23.1): Let $ P_f $ (You will need to plug in the value from your table; I'll use a placeholder for calculation steps.)

**Formula:**
$$
\text{Total Cost} = Q \times P_f
$$

**Calculation Steps:**
1. Write down the formula:  
   $$
   \text{Total Cost} = 140,000 \times P_f
   $$
2. Substitute $ P_f $ with the December futures price from Table 23.1.  
   (For example, if $ P_f = \$3.20 $,  
   $$
   \text{Total Cost} = 140,000 \times 3.20 = \$448,000
   $$
   )

---

## b. Profit or Loss on the Futures Position

**Available Data/Information:**
- Spot price in December: $ P_s = \$3.17 $ per bushel
- Futures price locked in: $ P_f $ (from Table 23.1)
- Quantity: $ Q = 140,000 $ bushels

**Formula:**
$$
\text{Profit/Loss per bushel} = |P_f - P_s|
$$
$$
\text{Total Profit/Loss} = Q \times |P_f - P_s|
$$

**Calculation Steps:**
1. Write down the formula:  
   $$
   \text{Total Profit/Loss} = 140,000 \times |P_f - 3.17|
   $$
2. Substitute $ P_f $ with the closing price from Table 23.1.  
   (For example, if $ P_f = 3.20 $:  
   $$
   \text{Total Profit/Loss} = 140,000 \times |3.20 - 3.17| = 140,000 \times .03 = \$4,200
   $$
   )

---

## **Final Answers (Summary/Crux):**

**a.** The total cost you lock in by using the futures price is:  
$$
\boxed{140,000 \times \text{[December futures price from Table 23.1]}}
$$
(For example, if futures price is \$3.20: \$448,000)

**b.** The profit or loss on your futures position if the spot price is \$3.17 per bushel in December is:  
$$
\boxed{140,000 \times |\text{[December futures price from Table 23.1]} - 3.17|}
$$
(For example, if futures price is \$3.20: \$4,200)

---

**Final Answer:**  
- a. The total cost is **140,000 × December futures price** (from Table 23.1), rounded to the nearest dollar.
- b. The profit or loss is **140,000 × |December futures price – 3.17|**, rounded to the nearest dollar.  
*Plug in the exact futures price from your Table 23.1 to get the specific dollar amounts.*

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