Question

On January 4, 2019, the DJIA opened at 10,097.90. The divisor at that time was .147621194. In January 2019, Boeing was the highest-priced stock in the DJIA and Cisco was the lowest. The closing price for Boeing on January 3, 2019, was $340.90, and the closing price for Cisco was $43.47. Suppose the next day the other 29 stock prices remained unchanged and Boeing increased 3.2 percent. What would the new DJIA level be

Answer 1

The question is incomplete. The complete question is :

On January 4, 2019, the DJIA opened at 10,097.90. The divisor at that time was .147621194. In January 2019, Boeing was the highest-priced stock in the DJIA and Cisco was the lowest. The closing price for Boeing on January 3, 2019, was $340.90, and the closing price for Cisco was $43.47. Suppose the next day the other 29 stock prices remained unchanged and Boeing increased 3.2 percent. What would the new DJIA level be :

1. DIJA if Boeing increases 3.2 percent

2. DIJA if Cisco increases 3.2 percent

Solution :

On 3 Jan 2019, Boeing = $ 340.90,  Cisco = $ 43.47

DJIA = 10,097.90

Divisor = 0.147621194

Index value = $\frac{\text{value of all shares}}{\text{divisor}}$

Then the value of shares,

$10097=\frac{\text{value of all shares}}{\text{0.147621194}}$

Value of all shares = 10097 x 0.147621194

                               = 1490.664

The other 29 stock prices remain unchanged, then we add the increased value of a stock to total value after divide by divisor, then we get the Index value.

The new DJIA level :

1. When Boeing increases 3.2 %

 Increases in the value of Boeing = $340.90 \times 3.2\%$

                                                        = 1501.5728

The new DJIA level = $\frac{1501.5728}{0.1476211}$

                                = 10171.80

2. When Cisco increases 3.2 %

Increases in the value of Cisco = $43.47 \times 3.2\%$

                                                        = 1.39104

Total value of the shares = 1490.664 + 1.39104

                                         = 1492.055

The new DJIA level = $\frac{1492.055}{0.1476211}$

                                = 10107.32