A beta factor will be estimated for Security Y from the following data.
Returns from the
market portfolio
Returns from Security
Y
%
%
1
+2
+3
2
–1
–2
3
–2
–2
4
+3
+5
EV of monthly return
+ 0.5
+ 1.0
Month
Required
(a)
(b)
Use this data to calculate:
(i)
the standard deviation of the monthly return from the market portfolio and
(ii)
the standard deviation of the monthly return from Security Y.
Calculate the correlation coefficient for the market returns and the returns from
Security Y. This is calculated as:
 m, y  Cov m, y
m x y
where:
m = the standard deviation of returns from the market portfolio

y
= the standard deviation of returns from Security Y
The formula for the covariance is:
Cov x, y  x  x y  y 
(c)

Use this data to calculate the beta factor for Security Y. You can use either of
the following formulas.

Cov m, y
Var m
Alternatively



 m, y x  y
m
Sodium Plc is a highly diversified company operating in a number of different
industries. Its shares are widely traded on the Stock Exchange and have a current
market price of Rs. 3.20.
Its dividend payments over the last five years are:
Year
DPS
2016
0.25
2015
0.23
2014
0.20
2013
0.19
2012
0.18
Sodium Plc is considering two investment opportunities: one is the Hotel and Tourism
(H&T) sector and the other is the Food and Beverages (F&B) sector. Both projects
have relatively short lives and their cash flows are as follows:
H&T
F&B
Year
Rs.’m
Rs.’m
1
85
190
2
170
180
3
150
200
The investment in Hotel and Tourism would cost Rs. 300 million while that in Food
and Beverages would cost Rs. 400 million.
The directors have discovered that industry beta for Hotel & Tourism and Food and
Beverages sectors are 1.2 and 2.2 respectively. They believe the investments being
considered are typical of projects in the relevant industries.
Sodium Plc industries beta is 1.6, treasury bill rate is 9% and the average return on
companies quoted on the stock exchange is 14%.
Required
(a)
(b)
(i)
Compute the net present values of both projects using the company’s
weighted average cost of capital as a discount rate.
(ii)
Compute the NPVs using a discount rate which takes account of the risk
associated with the individual projects.
(iii)
Advise the directors regarding the project to accept.
Enumerate the uses and limitations of the Capital Asset Pricing Model (CAPM)
Mushtaq Limited is considering two possible investment projects. Both the projects have a
life of one year only. The returns from new projects are uncertain and depend upon the
growth rate of the economy. Estimated returns at different levels of economic growth are
shown below:
Economic
Growth
(Annual Avg.)
Probability of
Occurrence
Returns (%)
Project 1
Project 2
Market
1%
0.25
20
22
30
3%
0.50
30
28
25
5%
0.25
40
40
40
Risk free rate of return is 10%.
Required
Evaluate the above projects using the Capital Assets Pricing Model.