# 1 Why has the development of powerful computers helped the more widespread adoption of scenario…

1 Why has the
scenario analysis?

2 Suggest reasons
why probability analysis is used so infrequently by major international
corporations.

3 The flatter the
line on the sensitivity graph, the less attention we have to pay to that
variable. Is the executive who made this statement correct in all cases?

4 If one project has
a higher standard deviation and a higher expected return than another, can we
use the mean-variance rule?

5 What does it mean
if a project has a probability of a negative NPV of 20 per

1 Why has the
scenario analysis?

2 Suggest reasons
why probability analysis is used so infrequently by major international
corporations.

3 The flatter the
line on the sensitivity graph, the less attention we have to pay to that
variable. Is the executive who made this statement correct in all cases?

4 If one project has
a higher standard deviation and a higher expected return than another, can we
use the mean-variance rule?

5 What does it mean
if a project has a probability of a negative NPV of 20 per cent when (a) the
risk-free discount rate is used, (b) the risk-adjusted discount rate is used?

Q56;

1 What is the
probability of an outcome being within 0.5 of a standard deviation from the
expected outcome?

2 Calculate
the NPV of the following project with a discount rate of 9 per cent.

Now examine the impact on NPV of raising the discount
rate by the following risk premiums:

a 3 percentage points;

b 6 percentage points.

Q57;

1* (Examination
level)
Cashion International are considering a project that is susceptible to risk. An
initial investment of

90,000 will be followed by three years each with the
following most likely cash flows (there is no inflation or tax):

The initial investment consists of 70,000 in
machines, which have a zero scrap value at the end of the three-year life

of the project and 20,000 in additional working
capital which is recoverable at the end. The discount rate is 10 per cent.

a Draw a sensitivity graph showing the sensitivity of
NPV to changes in the following:

sales price;

labour costs;

material costs;

discount rate.

b For the four variables considered in (a) state the
break-even point and the percentage deviation from most likely levels before
break-even NPV is reached (assuming all other variables remain constant). (An
Excel spreadsheet version of these calculations is available in the
Lecturers-only section at www.pearsoned.co.uk/arnold)

Q58;

1* Use
the data in question 2 to calculate the NPV in two alternative scenarios:

Q59;

1 (Examination
level)
A company is trying to decide whether to make a 400,000 investment in a new
product area. The

project will last 10 years and the 400,000 of
machinery will have a zero scrap value. Other best estimate forecasts are:

sales volume of 22,000 units per year;

sales price 21 per unit;

variable direct costs 16 per unit.

There are no other costs and inflation and tax are
not relevant.

a The senior management team have asked you to
calculate the internal rate of return (IRR) of this project based on these
estimates.

b To gain a broader picture they also want you to
recalculate IRR on the assumption that each of the following variables changes
adversely by 5 per cent in turn:

sales volume;

sales price;

variable direct costs.

c Explain to the management team how this analysis
can help to direct attention and further work to improve the likelihood of a
successful project implementation.

(An Excel spreadsheet version of these
calculations is available at www.pearsoned.co.uk/arnold)

Q60;

1 Project W may
yield a return of 2m with a probability of 0.3, or a return of 4m with a
probability of 0.7. Project X may earn a negative return of 2m with a
probability of 0.3 or a positive return of 8m with a probability of 0.7. Project
Y yields a return of 2m which is certain. Compare the mean return and risk of
the projects.

2 The returns from a
project are normally distributed with a mean of 220,000 and a standard
deviation of 160,000. If the project loses more than 80,000 the company will
be made insolvent. What is the probability of insolvency?

3 (Examination
level)
Toughnut plc is considering a two-year project that has the following
probability distribution of

returns:

The events in each year are independent of other
years (that is, there are no conditional probabilities). An outlay of

15,000 is payable at Time 0 and the other cash flows
are receivable at the year ends. The risk-adjusted discount rate

is 11 per cent.

Calculate

a The expected NPV.

b The standard deviation of NPV.

c The probability of the NPV being less than zero
assuming a normal distribution of return (bell shaped and symmetrical about
the mean).

d Interpret the figure calculated in (c).

Q61;

1 A project with an
initial outlay of 1m has a 0.2 probability of producing a return of 800,000
in Year 1 and a 0.8 probability of delivering a return of 500,000 in Year 1.
If the 800,000 result occurs then the second year could return

either 700,000 (probability of 0.5) or 300,000
(probability of 0.5). If the 500,000 result for Year 1 occurs then either

600,000 (probability 0.7) or 400,000 (probability
0.3) could be received in the second year. All cash flows occur on

anniversary dates. The discount rate is 12 per cent.

Calculate the expected return and standard deviation.

(An Excel spreadsheet version of the
calculation is available at www.pearsoned.co.uk/arnold)

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