Rand Water is evaluating five possible projects to enhance the efficiency of its water treatment plant. It is permitted to spend R5 million on investment projects at Time 0. The cash flows for five...

Question 1
Rand Water is evaluating five possible projects to enhance the efficiency of its water treatment
plant. It is permitted to spend R5 million on investment projects at Time 0. The cash flows for five
proposed projects are:
Year
Project (R
Million) 0 1 2 3 4
A -1.5 0.5 0.5 1 1
B -2 0 0 0 4
C -1.8 0 0 1.2 1.2
D -3 1.2 1.2 1.2 1.2
E -0.5 0.3 0.3 0.3 0.3

The cost of capital is 12 per cent, all projects are divisible and none may be repeated. The projects
are not mutually exclusive.
Required:
I. Which projects should be undertaken to maximise NPV in the
presence of the capital constraint? (10)
II. If the division was able to undertake all positive NPV projects, what level of NPV could be
achieved? (5)
III. If you now assume that these projects are indivisible, how would you allocate the available
R5 million? (5)
Solutions:
Formula for NPV: -Initial investment + [(Cash Inflow1)/(1+r)
1
] + [(Cash Inflow2)/(1+r)
2
] + [(Cash
Inflow3)/(1+r)
3
]…..+ [(Cash Inflown)/(1+r)
n
]
I. Project A:
=> -$1,500,000 + ($500,000/1.12) + ($500,000/1.12
2
) + ($1,000,000/1.12
3
) +
($1,000,000/1.12
4
)
=> -$1,500,000 + $44,6428.57 + $398,596.94 + $711,780.25 + $635,518.08 =
$692,323.84
Project B:
=> -$2,000,000 + ($4,000,000/1.12
4
)
=> -$2,000,000 + $2,542,072.31 = $542,072.31
Project C:
=> -$1,800,000 + ($1,200,000/1.12
3
) + ($1,200,000/1.12
4
)
=> -$1,800,000 + $854,136.30 + $762,621.69 = -$183,242.01
Project D:
=> -$3,000,000 + ($1,200,000/1.12) + ($1,200,000/1.12
2
) + ($1,200,000/1.12
3
) +
($1,200,000/1.12
4
)
=> -$3,000,000 + $1,071,428.57 + $956,632.65 + $854,136.30 + $762,621.69 =
$644,819.22
Project E:
=> -$500,000 + ($300,000/1.12) + ($300,000/1.12
2
) + ($300,000/1.12
3
) +
($300,000/1.12
4
)
=> -$500,000 + $267,857.14 + $239,158.16 + $213,534.07 + $190,655.42 = $411,204.80
As you can see in the above calculations, Project A has the highest NPV and hence, this
should be undertaken.
II. NPV to be achieved with all positive NPV projects = $692,323.84 + $542,072.31 +
$644,819.22 + $411,204.80 = $2,290,420.17
III. If these projects are indivisible, we can’t undertake the projects as the available fund is
R5 million only whereas funds required to undertake the projects are R8.8 million.
Question 2
A project requires an immediate outflow of cash of R400 000 in return for the following probable
cash flows:
State of Economy Probability End of year 1 (Rands) End of year 2 (Rands)
Recession 0.3 100 000 150 000
Growth 0.5 300 000 350 000
Boom 0.2 500 000 550 000

Assume that the state of the economy will be the same in the second year as in the first. The
equired rate of return is 8 per cent. There is no tax or inflation.
Required:
I. Calculate the expected NPV. (10)

II. Calculate the standard deviation of NPV and the coefficient of variance of the NPV. Interpret
these results taking into consideration of the state of economy. (10)
Solutions:

I. Expected NPV = R142,181
II. Standard deviation of NPV = (62,328,649,841) 0.5 = R2,49,657
Coefficient of variation = SD/Expected value = 249657/142181 = 1.76
The COV indicates high deviation. This is revealed by the NPV for recession
and boom which are -R178,807 and R534,499.
Question 3

Mr Patel has approached you for an advice on how best to invest his savings. You have proposed
that he can invest all his savings in shares of Sanlam, or all his savings in Sasol. Alternatively, he could
diversify his investment between these two (share companies). There are three possible states of
the economy, boom, growth or recession, and the returns on Sanlam and Sasol depend on which
state will occur.

State of Economy
Probability of
growth
occu
ing Sanlam return (%) Sasol return (%)
Recession 0.3 40 10
Growth 0.4 30 15
Boom 0.3 -10 20

Required:
I. Calculate the expected return, variance and standard deviation for each share. (10)

II. Calculate the expected return, variance and standard deviation for the following diversifying
allocations of Mr Patel’s savings:

a) 50% in Sanlam, 50% in Sasol. (5)

) 10% in Sanlam, 90% in Sasol. (5)

III. Explain the relationship...