Chapter 20, Problem 21E

To determine

Find the price relatives for the four stocks making up the Boran index in Exercise 20.

Find the January Year 3 and March Year 3 Boran indexes by using the weighted aggregates of price relatives.

Answer to Problem 21E

The price relatives for the four stocks for January Year 3 are givrn below:

Year	Year 1 Base	January Year 3	$\text{Price relative in Period }t$
Oil	31.50	22.75	72.2
Computer	65	49	75.4
Steel	40	32	80
Real Estate	18	6.50	36.1

The price relatives for the four stocks for March Year 3 are given below:

Year	Year 1 Base	March Year 3	$\text{Price relative in Period }t$
Oil	31.50	22.50	71.4
Computer	65	47.50	73.1
Steel	40	29.50	73.8
Real Estate	18	3.75	20.8

The Boran index for January Year 3 by using the weighted aggregates of price relatives is 73.5.

The Boran index for March Year 3 by using the weighted aggregates of price relatives is 70.10.

Explanation of Solution

Calculation:

The data shows that the price per share for Year 1, Year 2, and Year 3.

The price relatives for the four stocks for January Year 3 are obtained below:

Year	Year 1 Base	January Year 3	$\begin{array}{l}\text{Price relative in Period }t\\ =\frac{\text{Price in period }t}{\text{Base period price}}\left(100\right)\end{array}$
Oil	31.50	22.75	$\frac{\text{22}\text{.75}}{\text{31}\text{.50}}\left(100\right)=72.2$
Computer	65	49	$\frac{\text{49}}{\text{65}}\left(100\right)=75.4$
Steel	40	32	$\frac{\text{32}}{\text{40}}\left(100\right)=80$
Real Estate	18	6.50	$\frac{\text{6}\text{.50}}{\text{18}}\left(100\right)=36.1$

The price relatives for the four stocks for March Year 3 are obtained below:

Year	Year 1 Base	March Year 3	$\begin{array}{l}\text{Price relative in Period }t\\ =\frac{\text{Price in period }t}{\text{Base period price}}\left(100\right)\end{array}$
Oil	31.50	22.50	$\frac{\text{22}\text{.50}}{\text{31}\text{.50}}\left(100\right)=71.4$
Computer	65	47.50	$\frac{47.50}{\text{65}}\left(100\right)=73.1$
Steel	40	29.50	$\frac{\text{29}\text{.50}}{\text{40}}\left(100\right)=73.8$
Real Estate	18	3.75	$\frac{\text{3}\text{.75}}{\text{18}}\left(100\right)=20.8$

The Boran index for January Year 3 and March Year 3 by using the weighted aggregates of price relatives is obtained below:

$\begin{array}{c}{I}_t=\frac{{\displaystyle \sum P_{it}{Q}_i}}{{\displaystyle \sum P_{i0}{Q}_i}}\left(100\right)\\ I_{\text{January Year 3}}=\frac{22.75\left(100\right)+49\left(150\right)+32\left(75\right)+6.50\left(50\right)}{31.50\left(100\right)+65\left(150\right)+40\left(75\right)+18\left(50\right)}\left(100\right)\\ =\frac{\text{12,350}}{\text{16,800}}\left(100\right)\\ =73.5\end{array}$

Thus, the Boran index for January Year 3 by using the weighted aggregates of price relatives is 73.5.

The Boran index for March Year 3 by using the weighted aggregates of price relatives is obtained below:

$\begin{array}{c}{I}_t=\frac{{\displaystyle \sum P_{it}{Q}_i}}{{\displaystyle \sum P_{i0}{Q}_i}}\left(100\right)\\ I_{\text{March Year 3}}=\frac{22.50\left(100\right)+47.50\left(150\right)+29.50\left(75\right)+3.75\left(50\right)}{31.50\left(100\right)+65\left(150\right)+40\left(75\right)+18\left(50\right)}\left(100\right)\\ =\frac{\text{11,775}}{\text{16,800}}\left(100\right)\\ =70.10\end{array}$

Thus, the Boran index for March Year 3 by using the weighted aggregates of price relatives is 70.10.