Spark Electricity plc is considering building a plant that is planned to cost $500$ million and an estimated building period of $12$ months. When the plant enters into operation after its completion it will produce a perpetual stream of cash flows. There are a number of factors leading to substantial uncertainty as to whether the plant should be given the go$-$ahead now or wait one year and then decide whether to build or not then.The cash flows expected to be generated by the project differ over these two options. In the case that the project is undertaken immediately, the plant will produce $50$ million for sure in its first year of operation. However, subsequent annual cash flows will depend on the state of the economy: in the good state, the plant will generate $75$ million each year, whereas in the bad state the total annual cash flows generated are forecasted to be $10$ million.In the case that management decides to delay the project by one year, the first year initial cash flows of $50$ million will be irretrievably lost. The perpetual cash flows will start two years from today and will be $($a$)$ either $75$ million in the good state of nature, or $($b$)10$ million in the bad state of nature.The risk free interest rate is $6\%$ per annum and investing $1$ in the market portfolio is forecasted to generate either $1\mathrm{.}40$ in the good state, or $0\mathrm{.}90$ in the case that the bad state emerges. After computing the project's NPV$,$ analyse whether or not the firm's management should build now or wait one year to take the decision.