Alder plc is considering four projects, for which the cash flows have been calculated as follows:

The appropriate rate of discount is judged to be 10 per cent for risk-free projects.
Accepting one of the projects does not exclude the possibility of accepting another one, and each can only be undertaken once.
Assume that the annual cash flows arise on the anniversary dates of the initial outlay and that there is no inflation or tax.
Required
a. Calculate the net present value for each of the projects on the assumption that the cash flows are not subject to any risk. Rank the projects on the basis of these calculations, assuming there is no capital rationing.
b. Briefly explain two reasons why you might regard net present value as being superior to internal rate of return for project appraisal.
c. Now assume that at Time 0 only £700,000 of capital is available for project investment. Calculate the wisest allocation of these funds to achieve the optimum return on the assumption that each of the projects is divisible (fractions may be undertaken). What is the highest net present value achievable using the risk-free discount rate?
d. A change in the law now makes the outcome of Project D subject to risk because the cash flows depend upon the actions of central government. The project will still require an initial cash outflow of £150,000. If the government licensing agency decides at Time 0 to permit Alder a license for a one-year trial production and sale of the product, then the net cash in flow at the end of the first year will be +£50,000. If the agency decides to allow the product to go on sale from time 0 under a four-year license without a trial run the cash inflow in at the end of Year 1 will be +£70,000. The probability of the government insisting on a trial run is 50 per cent and the probability of full licensing is 50 per cent.
If the trial run takes place then there are two possibilities for future cash flows. The first, with a probability of 30 per cent, is that the product is subsequently given a full license for the remaining three years, resulting in a net cash flow of +£60,000 per year. The second possibility, with a probability of 70 per cent, is that the government does not grant a license and production and sales cease after the first year.
If a full license is granted at time 0 then there are two possible sets of cash flows for the subsequent three years. First, the product sells very well, producing an annual net cash flow of +£80,000 - this has a probability of 60 per cent. Secondly, the product sells less well, producing annual cash flows of +£60,000 - this has a probability of 40 per cent.
The management wish you to calculate the probability of this product producing a negative net present value (assume a normal distribution). The appropriate discount rate for a project of this risk class is 13 per cent.

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Points in time (yearly intervals) Project 0 T0 Project ends after 1 year Project ends after 2 years. Project ends after 2 years. -£500,000 +600,000 -£200,000 200,000 +£150,000 £700,000 0 Elmillion -150,000 +560,000 +0,000 +0,000 +, Project ends after 4 years