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Homework answers / question archive / 1)Please define the term standard deviation
1)Please define the term standard deviation. And why do you think we can use standard deviation to measure risk?
2)Consider the following information for two all-equity firms, Firm A and Firm B: Firm A Firm B Shares outstanding 2,400 7,200 Price per share $48 $36 Firm A estimates that the value of the synergistic benefit from acquiring Firm B is $7,020. Firm B has indicated that it would accept a cash purchase offer of $42 per share. Should Firm A proceed? (Find NPV of a merger)
1)
Standard deviation
The standard deviation basically measures the dispersion of the sample data from the mean point . While the typical definition may seem to be perplexing , standard deviation shows how much the data set can deviate from the mean. Thus standard deviation is the measure of a central tendency in the data set of values .
The typical uses of standard deviation are as follows
|
No |
Uses |
Description |
|
1 |
Shows the range of deviation in a data set |
The Std dev shows the range of variability in the data set by a percentage % of the mean . |
|
2 |
Helps to determine the central tendency and CV |
The central tendency along with the Coefficient of variation can be determined |
|
3 |
Measures the maximum positive and negative deviations in a data set |
The maximum positive returns and the minimum or loss zones in the financial data set can be predicted |
|
4 |
Makes Sample and Population Estimation possible by sample data set |
Large estimates on population data can be estimated using a small sample data set |
|
5 |
Shows the Confidence Intervals |
Shows the confidence intervals of acceptance from 95-99% |
Measures of Risk
Standard deviation is the most widely accepted measure for the rik of a financial portfolio or an asset class. Portfolios having higher std dev have the higher risk factor as the range of variation is higher than that of an asset with low standard deviation .
Therefore risk averse investors prefer assets and portfolio with low standards deviation as they have low deviations from the mean and hence provides a stable set of returns .
2)
Given Information
|
Firm |
Firm A |
Firm B |
|
No of Shares outstanding |
2,400 |
7,200 |
|
Price per share |
$48 |
$36 |
Firm A’s estimated value pf synergistic benefits = $7,020
Firm B’s expectation of cash price offer = $42
Premium asked by Firm B per share = 42 – 36 =$6
Total premium for Firm B = 7200*6 = $43,200
Synergistic benefit accruing to Firm A = 7020 -43200= -$36,180
As the Firm B’s premium is more than the synergistic benefits to be derived by Firm A from the transaction resulting in negative value for Firm A.
So, Firm A should not proceed with the transaction.
NPV of merger = Pre-merger market value of Firm B + Synergistic Benefit – Acquisition cost of Firm B
=> NPV of merger = 7200*36 + 7020 – 7200*42 = -$36,180
