1 Why has the

development of powerful computers helped the more widespread adoption of

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

development of powerful computers helped the more widespread adoption of

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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