# 1 The cost of capital can be taken to be 14 per cent. 2 Cash flows will arise at year ends except…

1 The cost of
capital can be taken to be 14 per cent.

2 Cash flows will
arise at year ends except the initial payment to the government which occurs at
Time 0.

a Calculate the expected net present value (NPV) and
the standard deviation of the NPV for the project to buy the

English lignite mines if 900m is taken to be the
initial cash outflow.

b There is a chance that events will turn out to be
much worse than RJW would like. If the net present value of the

English operation turns out to be worse than negative
550m, RJW will be liquidated. What is the probability of

avoiding

1 The cost of
capital can be taken to be 14 per cent.

2 Cash flows will
arise at year ends except the initial payment to the government which occurs at
Time 0.

a Calculate the expected net present value (NPV) and
the standard deviation of the NPV for the project to buy the

English lignite mines if 900m is taken to be the
initial cash outflow.

b There is a chance that events will turn out to be
much worse than RJW would like. If the net present value of the

English operation turns out to be worse than negative
550m, RJW will be liquidated. What is the probability of

avoiding liquidation?

c If the NPV is greater than positive 100m then the
share price of RJW will start to rise rapidly in two or three

years after the purchase. What is the
probability of this occurring?

Q65;

1 (Examination
level) Alder plc is considering four projects,
for which the cash flows have been calculated as follows:

The appropriate rate of discount is judged to be 10
per cent for risk-free projects.

Accepting one of the projects does not exclude the
possibility of accepting another one, and each can only be

undertaken once.

Assume that the annual cash flows arise on the
anniversary dates of the initial outlay and that there is no inflation

or tax.

Required

a Calculate the net present value for each of the
projects on the assumption that the cash flows are not subject to

any risk. Rank the projects on the basis of these
calculations, assuming there is no capital rationing.

b Briefly explain two reasons why you might regard
net present value as being superior to internal rate of return

for project appraisal.

c Now assume that at Time 0 only 700,000 of capital
is available for project investment. Calculate the wisest allocation

of these funds to achieve the optimum return on the
assumption that each of the projects is divisible

(fractions may be undertaken). What is the highest
net present value achievable using the risk-free discount rate?

d A change in the law now makes the outcome of Project
D subject to risk because the cash flows depend upon the

actions of central government. The project will still
require an initial cash outflow of 150,000. If the government

licensing agency decides at Time 0 to permit Alder a
licence for a one-year trial production and sale of the

product, then the net cash in flow at the end of the
first year will be +50,000. If the agency decides to allow the

product to go on sale from time 0 under a four-year
licence without a trial run the cash inflow in at the end of

Year 1 will be +70,000. The probability of the
government insisting on a trial run is 50 per cent and the probability

of full licensing is 50 per cent. If the trial run
takes place then there are two possibilities for future cash flows. The first,
with a probability of 30 per cent, is that the product is subsequently given a
full licence for the remaining three years, resulting in a net cash flow of
+60,000 per year. The second possibility, with a probability of 70 per cent,
is that the government

does not grant a licence and production and sales
cease after the first year. If a full licence is granted at time 0 then there
are two possible sets of cash flows for the subsequent three years. First, the
product sells very well, producing an annual net cash flow of +80,000 this
has a probability of 60 per cent. Secondly, the product sells less well,
producing annual cash flows of +60,000 this has a probability of 40 per
cent. The management wish you to calculate the probability of this product
producing a negative net present value (assume a normal distribution). The
appropriate discount rate for a project of this risk class is 13 per cent.

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