Bradford Services Inc. $($BSI$)$ is considering a project with a cost of $$9$ million and an expected life of $3$ years. There is a $20\%$ probability of good conditions, in which case the project will provide a cash flow of $$10$ million at the end of each of the next $3$ years. There is a $60\%$ probability of medium conditions, in which case the annual cash flows will be $$3$ million, and there is a $20\%$ probability of bad conditions with a cash flow of $-$$$1$ million per year. BSI uses an $11\%$ cost of capital to evaluate projects like this.

c$.$ Now assume that the project cannot be shut down. However, expertise gained by taking it on would lead to an opportunity at the end of Year $3$ to undertake a venture that would have the same cost as the original project, and the new project's cash flows would follow whichever branch resulted for the original project. In other words, there would be a second $$9$ million cost at the end of Year $3$ followed by cash flows of either $$10$ million, $$3$ million, or $-$$$1$ million for the subsequent $3$ years. Use decision$-$tree analysis to estimate the value of the project, including the opportunity to implement the new project at Year $3.$ Assume that the $$9$ million cost at Year $3$ is known with certainty and should be discounted at the risk$-$free rate of $7\%.$ Enter your answer in millions. For example, an answer of $$1\mathrm{.}23$ million should be entered as $1\mathrm{.}23,$ not $1,230,000.$ Round your answer to two decimal places.

d$.$ Now suppose the original project $($no abandonment option or additional growth option$)$ could be delayed a year. All the cash flows would remain unchanged, but information obtained during that year would tell the company exactly which set of demand conditions existed. Use decision$-$tree analysis to estimate the value of the project if it is delayed by $1$ year. $($Hint: Discount the $$9$ million cost at the risk$-$free rate of $7\%$ because the cost is known with certainty.$)$ Enter your answer in millions. For example, an answer of $$1\mathrm{.}23$ million should be entered as $1\mathrm{.}23,$ not $1,230,000.$ Round your answer to two decimal places.

e$.$ Go back to part c$.$ Instead of using decision$-$tree analysis, use the Black$-$Scholes model to estimate the value of the growth option. The risk$-$free rate is $7\%,$ and the variance of the project's rate of return is $0\mathrm{.}23.$ Enter your answer in millions. For example, an answer of $$1\mathrm{.}23$ million should be entered as $1\mathrm{.}23,$ not $1,230,000.$ Round your answer to two decimal places.