Please write out in detail every formula and step in the part of this question about calculations, I have questions about how to use the formulas in several of them. Thank you for your help.

Newtownabbot Council is considering refurbishing and re-launching a theatre which it has wholly owned and operated for thirty years. The required work has been costed for a 10 year development plan which is based upon a shift towards providing a much higher quality of service than in the past. The refurbished theatre would provide facilities that would be much more attractive to touring companies and artists and, it is hoped, to the theatre-going public.

The impact of the development is uncertain as the theatre has experienced decline in recent years and it is feared that local people have got out of the theatre-going habit. Three scenarios have been presented in the development plan, each based upon a view taken on likely demand after completion of the refurbishment work.

The cost of refurbishment would be 1.5m. The three scenarios are based upon high, medium and low expectations of increased demand. The net annual contribution of each is shown in the table below along with an assessment of probability which has been undertaken by a senior management group within the council.

Demand level Increase in contribution Probability %

High 250,000 25

Medium 200,000 40

Low 150,000 35

The council is risk averse and has decided to use expected value in its investment appraisal. It is normal practice for the council to calculate both net present value (NPV) and the internal rate of return (IRR) of proposed investments and to use a discount rate of 6% for schemes which have commercial element, such as this one.

Required

(a) What does it mean when the council is described as risk averse and how will expected values help in this context?

(15 Marks)

(b) Calculate the expected value of the annual contribution due to the refurbishment work.

(5 Marks)

(c) Using the expected value figure from above calculate the net present value and the internal rate of return of the proposed refurbishment scheme.

(40 Marks)

(d) Perform a sensitivity analysis to show how sensitive the project is to changes in the following variables:

Initial cost

Discount rate

(25 Marks)

(e) Discuss the advantages and disadvantages of sensitivity analysis.

(15 Marks)