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**CFA Practice Question**

A Value-weighted index is based on the following information:

stock A is worth $5, 500 000 shares

Stock B is worth $22, 2.5 million shares

Stock C is worth $18, 1.5 million shares

December 31, 2011: stock A is worth $10; stock B is worth $15, stock C is worth $20

December 31, 2010 (base value date):

stock A is worth $5, 500 000 shares

Stock B is worth $22, 2.5 million shares

Stock C is worth $18, 1.5 million shares

December 31, 2011: stock A is worth $10; stock B is worth $15, stock C is worth $20

Calculate the Index value on December 31, 2011. (Base value = 100)

A. 116.5517

B. 85.7988

C. None of these

**Explanation:**New Index Value = Current Market Value/Base Value x Beginning Index Value

2010:

5 x .5 = 2.5 million

22 x 2.5 = 55 million

18 x 1.5 = 27 million

Total = 84.5 million at base value 100

2011:

10 x 0.5 = 5 million

15 x 2.5 = 37.5 million

20 x 1.5 = 30 million

Total = 72.5 million

New Index Value = 72.5/84.5 x 100 = 85.798817

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**User Contributed Comments**
3

User |
Comment |
---|---|

djread |
exact same as a CPI calc |

schweitzdm |
The first formula given does not match with the final formula used for calculating the answer in this explanation. |

tung |
schweitzdm: why? current market value is 72.5, and base value is 84.5. I don't see why they don't match. |