Question

On october 28, 2015, the djia opened at 17,581.43. The divisor at that time was 0.14967727343. In october 2015, goldman sachs was the highest priced stock in the djia and cisco was the lowest. The closing price for goldman sachs on october 27, 2015, was $186.31, and the closing price for cisco was $29.05. Suppose the next day the other 29 stock prices remained unchanged and goldman sachs increased 5 percent. What would the new djia level be? Now assume only cisco increased by 5 percent. Find the new djia level.

Answer 1

Answer: The new DJIA level if Goldman Sachs rises by 5% is 17643.67.

The new DJIA level if Cisco rises by 5% is 17591.13.

The DJIA index is calculated as follows:

$DJIA Index = \frac{Total of one stock of all the components of the index}{Divisor}$

We can find the total of one stock of all the index components in October as follows:

$17,581.43 = \frac{Total of one stock of all the components of the index}{0.14967727343}$

$17,581.43 * 0.14967727343 = Total of one stock of all the components of the index$

$Total of one stock of all the components of the index = 2631.540505$

a. New DJIA level if Goldman Sachs rises by 5%

$Total of one stock of all the components of the index = 631.540505$

If Goldman Sachs rises by 5%, the numerator of the DJIA will be

$Total of one stock of all the components of the index = 2631.540505- 186.31 + (186.31 * 1.05)$

$Total of one stock of all the components of the index = 2631.540505- 186.31 + 195.6255$

$Total of one stock of all the components of the index = 2640.856005$

$New DJIA level = \frac{2640.856005}{0.14967727343}$

$New DJIA level = 17643.66724$

B. New DJIA level if Cisco rises by 5%

$Total of one stock of all the components of the index = 2631.540505$

If Cisco rises by 5%, the numerator of the DJIA will be

$Total of one stock of all the components of the index = 2631.540505- 29.05 + (29.05 * 1.05)$

$Total of one stock of all the components of the index = 2631.540505- 186.31 + 30.5025$

$Total of one stock of all the components of the index = 2632.993005$

$New DJIA level = \frac{2632.993005}{0.14967727343}$

$New DJIA level = 17591.13421$