RJW plc is a quoted firm which operates ten lignite mines in Wales. It has total assets of £50m and the value of its shares is £90m. RJW plc's directors perceive a great opportunity in the UK government's privatization drive. They have held preliminary discussions with the government about the purchase of the 25 lignite mines in England. The purchase price suggested by the Treasury is £900m.
For two months the directors have been engaged in a fund-raising campaign to persuade City financial institutions to provide £500m of new equity capital for RJW and £400m of fixed interest rate debt capital in the form of bank loans.
You are a senior analyst with the fund management arm of Klein-Ben Wensons and last week you listened attentively to RJW's presentation. You were impressed by their determination, acumen and track record but have some concerns about their figures for the new project.
RJW's projections are as follows, excluding the cost of purchasing the mines:
Table 1: Cash flows for the English lignite mines: RJW's estimate

You believe the probability of RJW's projections being correct to be 50 per cent (or 0.5). You also estimate that there is a chance that RJW's estimates are over-cautious. There is a 30 per cent probability of the cash flows being as shown in Table 2 (excluding the cost of purchasing the mines).
Table 2: A more optimistic forecast

On the other hand, events may not turn out as well as RJW's estimates. There is a 20 per cent probability that the cash flows will be as shown in Table 3.
Table 3: A more pessimistic scenario (excluding purchase cost of mines)

Assume
1. The cost of capital can be taken to be 14 per cent.
2. Cash flows will arise at year ends except the initial payment to the government which occurs at Time 0.
Required
a. Calculate the expected net present value (NPV) and the standard deviation of the NPV for the project to buy the English lignite mines if £900m is taken to be the initial cash outflow.
b. There is a chance that events will turn out to be much worse than RJW would like. If the net present value of the English operation turns out to be worse than negative £550m, RJW will be liquidated. What is the probability of avoiding liquidation?
c. If the NPV is greater than positive £100m then the share price of RJW will start to rise rapidly in two or three years after the purchase. What is the probability of this occurring?

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5 and all subsequent years Time t Sales (Sm) (cash inflows) Less operating costs (m) (cash outflows) Net cash flows (Em) 1,250 1,105 145 1,300 1,150 150 1,320 1,190 130 1,350 1,200 1,070 130 1,200 150 5 and all subsequent years Time t 0 Sales (Em) (cash inflows) Less operating costs (Em) (cash outflows) 1,360 ,416.7 1,473.33 1,496 1,190 1,225 260 276.7 283.33 271 1,530 1,100 1,140 1,250 Net cash flows (Em) 280 Timer 5 and all subsequent years Sales (Em) (cash inflows) Less operating costs (Em)(cash outflows) 1,166.67 ,267 ,266.67 1,144 1,070 105 1150 1.165 -21 1,170 1,150 Net cash flows (Em) 96.67 7 116.67 20