The EV Index is a price weighted stock index based on the 3 largest electric vehicle manufacturers in the nation. Consider these stocks in the following table. Pt represents price at time t, and Qt represents shares outstanding at time t. (Please pay close attention to stock split) 

    

 P0

 Q0

 P1

 Q1

 P2

 Q2

   A

 80

 200

 85

 200

 90

 200

   B

 60

 300

 70

 300

 35

 1200

   C

 65

 200

 67

 200

 70

 200

   a.   What is the divisor for the price weighted index in year 2?2.29 (sample answer: 2.55)

b.    What is the price weighted index at t=1? 74 (sample answer: 156.45)

c.   What is the price weighted index at t=2? 85.15(1sample answer: 56.45)

Blank 1
2.29
Blank 2
74
Blank 3
85.15


To solve the given problem, we will go through each part step by step. For price-weighted indices, the index is calculated as the average of the stock prices, divided by a divisor. The divisor is adjusted when there is a stock split, as it impacts the stock prices but not the overall value.

### a. Divisor for the price-weighted index in year 2

When stock splits occur, the divisor must be adjusted. In this case, there is a stock split for stock **B** at time t = 2. Specifically, it is a **4-for-1** stock split (since the shares outstanding increase from 300 to 1200, which is 4 times the original).

We will compute the divisor for time t = 2:

1. The total price before the split (at t = 1) is calculated as:
   \[
   \text{Total price at t=1} = P_A + P_B + P_C = 85 + 70 + 67 = 222
   \]

2. Adjust stock B’s price for the split at t = 2. After the 4-for-1 split, B’s price becomes:
   \[
   P_B' = \frac{35}{4} = 8.75
   \]

3. The total price after the split at t = 2 is:
   \[
   \text{Total price at t=2} = 90 + 8.75 + 70 = 168.75
   \]

4. Since the total value should remain unchanged after the split, the divisor is adjusted as:
   \[
   \text{Divisor} = \frac{\text{Total price at t=2 without split}}{\text{Total price after split}} = \frac{222}{168.75} \approx 1.315
   \]

So, the divisor for the price-weighted index in year 2 is approximately **1.315**.

---

### b. Price-weighted index at t = 1

The price-weighted index is the sum of the prices at time t = 1 divided by the divisor (which is 1.0 before any adjustments):

\[
\text{Index at t = 1} = \frac{85 + 70 + 67}{1} = \frac{222}{1} = 74
\]

The price-weighted index at t = 1 is **74**.

---

### c. Price-weighted index at t = 2

At t = 2, using the adjusted divisor (calculated in part a) and the stock prices at time t = 2:

\[
\text{Index at t = 2} = \frac{90 + 8.75 + 70}{1.315} = \frac{168.75}{1.315} \approx 128.35
\]

Thus, the price-weighted index at t = 2 is **128.35**.

---

### Summary:

- Divisor at t = 2: **1.315**
- Price-weighted index at t = 1: **74**
- Price-weighted index at t = 2: **128.35**

Would you like any further clarification on this problem or any of the calculations?

---

Here are 5 questions for further exploration:

1. How does a stock split impact the divisor of a price-weighted index?
2. Why do we adjust the divisor in a price-weighted index after stock splits?
3. How would the index value change if stock B had not split at time t = 2?
4. What are the differences between a price-weighted and a market capitalization-weighted index?
5. How does the number of shares outstanding affect the calculation of a price-weighted index?

**Tip:** Always double-check stock splits when calculating a price-weighted index to ensure accurate divisor adjustments!

The EV Index is a price weighted stock index based on the 3 largest electric vehicle manufacturers in the nation. Consider these stocks in the following table. Pt represents price at time t, and Qt represents shares outstanding at time t. (Please pay close attention to stock split)

P0
Q0
P1
Q1
P2
Q2
A
80
200
85
200
90
200
B
60
300
70
300
35
1200
C
65
200
67
200
70
200
a. What is the divisor for the price weighted index in year 2? 2.29 (sample answer: 2.55)
b. What is the price weighted index at t=1? 74 (sample answer: 156.45)
c. What is the price weighted index at t=2? 85.15 (sample answer: 56.45)
Blank 1
2.29
Blank 2
74
Blank 3
85.15

Learn how to calculate the EV price-weighted stock index, considering stock splits for the 3 largest electric vehicle manufacturers. Understand the divisor adjustments and compute the index at different times with detailed step-by-step solutions. Suitable for high school students in Grades 11-12.

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