Assignment
1 A) Amagolo village consist of a total of 1800 households. A market research firm gathered data in an attempt to investigate the loyalty of these households for a particular brand of toilet soap X, Y and Z sold in the village shops. A customer survey at the end of Dec.2014 revealed the following brands switching patterns.
|
|
|
TO
|
|
X
|
Y
|
Z
|
|
FROM
|
X
|
400
|
150
|
150
|
|
Y
|
100
|
350
|
50
|
|
Z
|
60
|
180
|
360
|
Required
i. Determine the transition matrix for the above Markov process
ii. Determine the steady state distribution of the usage of the three types of toilet soap.
B) Solve the following using Simplex method
Maximize Z=4X+6Y
X-Y≤11
X+Y≤27
2X+5Y≤90
X, Y≥0
c) Electromechanical equipment has purchase price of Kshs 80,000. Its running cost per year and the sales values are given as follows
|
Year
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
|
Running cost (sh 000)
|
22
|
23
|
24
|
26
|
30
|
38
|
41
|
46
|
|
Resale value (Sh 000)
|
50
|
40
|
28
|
22
|
20
|
15
|
13
|
10
|
Determine the best replacement time
2 A) Big Ltd. is contemplating acquiring small Ltd. to consolidate its market share. The following financial data is available about the two companies;
|
|
Orange limited
|
Rainbow limited
|
|
Annual sales (million)
|
Sh. 375
|
Sh.45
|
|
Net income (million)
|
Sh. 30
|
Sh.3.75
|
|
Ordinary shares outstanding (million)
|
7.5
|
1.5
|
|
Earnings per share
|
Sh.4
|
Sh.2.5
|
|
Market price per share
|
Sh.42
|
Sh.18
|
Both companies are in 30% income bracket
Required
i. Maximum exchange ratio Big Ltd should agree to if it expects no dilution in its EPS
ii. Premium the shareholders of small would receive at an exchange ratio obtained in (i) above
iii. Big Ltd post acquisition EPS if the two companies agree at an offer price of Kshs 2.1
iv. Big Ltd EPS if every 50 shares of rainbow Ltd are exchanged for one 12% debentures of Kshs 1000 per value
B ) An investor is evaluating six portfolios with the following characteristics;
|
portfolio
|
Expected return %
|
Standard deviation %
|
|
A
|
19
|
8
|
|
B
|
25
|
12
|
|
C
|
16
|
6
|
|
D
|
32
|
16
|
The expected return on the market portfolio is 12% with an accompanying standard deviation of 4%. The risk free rate of interest is 5%
Required
a. Using the capital market line, advice the investor on which of the above portfolios are efficient and inefficient
b. In the case of an inefficient portfolio on (a) above, state what the standard deviation should be for efficiency to be achieved with the given expected return.