Page 180 - AFM Integrated Workbook STUDENT S18-J19

Chapter 9

Question 1

The finance director of Maximo Co has estimated that the average annual
return on one of its projects is $5 million, and that there is an annual standard
deviation of $2 million, based on a normal distribution of returns.

Required:

Assuming a 95% confidence level, calculate the Value at Risk for one
year, and also the total Value at Risk over the project’s 8 year life.

Solution

Shaded area is 0.4500 Mean =$5m

From the normal distribution table, 0.4500 corresponds (approximately) to a
distance of 1.64 standard deviations from the mean,

i.e. 1.64 × $2 million = $3.28 million.

Therefore, on an annual basis, there is a 95% chance that the return will be at
least $5 million – $3.28 million = $1.72 million (and hence only a 5% chance
that the return will fall below this level).

Over the project’s 8 year life, the mean of the cash flows will be 8 × $5 million =
$40 million, and the 8 year Value at Risk will be √8 × $3.28 million = $9.28
million.

Therefore, over the full 8 year life of the project, there is a 95% chance that the
return will be at least $40 million – $9.28 million = $30.72 million (and hence
only a 5% chance that the return will fall below this level).

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