Executives at XYZ Corporation realize that they have too much liquid assets. They want to use this cash to buy a company that has decent returns to maximize their asset utilization.  They find two companies they can buy, and want to decide if they should acquire company A or Company B. The expected returns from both companies depending on the state of the economy are shown in the table below. Each state of the economy is equally likely to happen.State of the economyReturn on company A(%)Return on company B (%)Worse than expected7.3%-4.7%Expected11.5%5.4%Better than expected16.6%24.3% Calculate the expected rate of return, and standard deviation of each company. Critically evaluate the importance of the standard deviation factor in comparing investments.

Question
Asked Nov 9, 2019

Executives at XYZ Corporation realize that they have too much liquid assets. They want to use this cash to buy a company that has decent returns to maximize their asset utilization.  They find two companies they can buy, and want to decide if they should acquire company A or Company B. The expected returns from both companies depending on the state of the economy are shown in the table below. Each state of the economy is equally likely to happen.

State of the economy

Return on company A(%)

Return on company B (%)

Worse than expected

7.3%

-4.7%

Expected

11.5%

5.4%

Better than expected

16.6%

24.3%

 

  1. Calculate the expected rate of return, and standard deviation of each company. 
  2. Critically evaluate the importance of the standard deviation factor in comparing investments. 
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Expert Answer

Step 1

Expected return can be calculated using excel as below:

B
E
State of the economy Return on company A(% ) Return on company B (% ) Probability Expected Return on A Expected Return for B
Worse than expected
-D2 *B2
=D3 *B3
-D2 C2
-D3 C3
0.073
0.115
-0.047
- 1/ 3
3 Expected
- 1 / 3
0.054
Better than expected
4
=D4*B4
0.166
=D4*C4
0.243
- 1/3
Expected Return for A
-SUM(E2E4)
Expected Return for B
=SUM(F2:F4)
6
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B E State of the economy Return on company A(% ) Return on company B (% ) Probability Expected Return on A Expected Return for B Worse than expected -D2 *B2 =D3 *B3 -D2 C2 -D3 C3 0.073 0.115 -0.047 - 1/ 3 3 Expected - 1 / 3 0.054 Better than expected 4 =D4*B4 0.166 =D4*C4 0.243 - 1/3 Expected Return for A -SUM(E2E4) Expected Return for B =SUM(F2:F4) 6

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Step 2
A.
C
D
Е
Expected Expected
company company BProbability Return on Return for
Return on Return on
State of
the
(%)
в
economy A(%)
1
A
Worse than
7.30%
-4.70%
33.33%
2.43%
-1.57%
2 expected
з Еxpected
Better than
4 expected
11.50%
33.33%
5.40%
3.83%
1.80%
16.60%
33.33%
5.53%
8.10%
24.30%
11.80%
Expected Return for A
8.33%
Expected Return for B
6
n
help_outline

Image Transcriptionclose

A. C D Е Expected Expected company company BProbability Return on Return for Return on Return on State of the (%) в economy A(%) 1 A Worse than 7.30% -4.70% 33.33% 2.43% -1.57% 2 expected з Еxpected Better than 4 expected 11.50% 33.33% 5.40% 3.83% 1.80% 16.60% 33.33% 5.53% 8.10% 24.30% 11.80% Expected Return for A 8.33% Expected Return for B 6 n

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Step 3

Standard&nb...

L
M
R
Pro Expected Return of Expected Retarn (r (A) E(RA)^ 2
(r(B) E(RB
2
State of the economy Return on company A() rA) Return on company B (0)r (B)abili
AE(RA)
ty
of B. E(RB)
(r(A)-E(RA ) ^2 P
r(B)-E(RB) 2 P
Worse than expected
0.073
0.115
- 02 L2
Q3 L3
- 02 12
- 03 L3
K2-SNS3)2
-K3-SNS3) 2
-0.047
|0.054
- 02-5MS3)2
0.083333333333333(3-SMS3) 2
3 Expected
- 1/3 0.118
Better than expected
0.166
- 14-SMS3)2
K4-SNS32
0.243
-04 " L4
Q4*L4
-1/3
- SUMP2:P4 )
|-SUMRR)
-SORT(R5)
-SQRT P5)
Standard deviation
i
m
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L M R Pro Expected Return of Expected Retarn (r (A) E(RA)^ 2 (r(B) E(RB 2 State of the economy Return on company A() rA) Return on company B (0)r (B)abili AE(RA) ty of B. E(RB) (r(A)-E(RA ) ^2 P r(B)-E(RB) 2 P Worse than expected 0.073 0.115 - 02 L2 Q3 L3 - 02 12 - 03 L3 K2-SNS3)2 -K3-SNS3) 2 -0.047 |0.054 - 02-5MS3)2 0.083333333333333(3-SMS3) 2 3 Expected - 1/3 0.118 Better than expected 0.166 - 14-SMS3)2 K4-SNS32 0.243 -04 " L4 Q4*L4 -1/3 - SUMP2:P4 ) |-SUMRR) -SORT(R5) -SQRT P5) Standard deviation i m

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