Mr Smart has c75 000 invested in relatively risk-free assets returning 10 per cent per year. He has been approached by a friend with a ‘really good idea’ for a business venture. This would take the whole of the c75 000. Market research has revealed that it is not possible to be exact about the returns of the project, but that the following can be inferred from the study:

■ There is a 20 per cent chance that returns will be c10 000 per year.

■ There is a 60 per cent chance that returns will be c30 000 per year.

■ There is a 20 per cent chance that returns will be c50 000 per year.

■ If returns are c10 000 per year, there is a 60 per cent chance that the life of the project will be five years and a 40 per cent chance that it will be seven years.

■ If returns are c30 000 per year, there is a 50 per cent chance that the life of the project will be five years and a 50 per cent chance that it will be seven years.

■ If returns are c50 000 per year, there is a 40 per cent chance that the life of the project will be five years and a 60 per cent chance that it will be seven years.

Assume that cash flows happen at the end of each year.

(a) Calculate the worst likely return and the best likely return on the project, along with the probabilities of these events happening.

(b) Calculate the expected net present value of the investment.