Question $1$

GreenTech Innovations is considering buying a vacant lot that sells for $$3$ million. If the property is purchased, the company's plan is to spend another $$4$ million today to build a renewable energy plant on the property. The after$-$tax cash flows from the plant will depend critically upon whether the country imposes a carbon tax in this year's budget. If the tax is imposed, the plant is expected to produce after$-$tax inflows of $$950,000$ at the end of each of the next $15$ years. If the tax is not imposed, the plant is expected to produce after$-$tax cash inflows of $$1,800,000$ at the end of each of the next $18$ years. The energy sector has been lobbying vigorously against the tax, and projections are that there is a $60\%$ probability that it will not be imposed.

While the company does not have the option to delay construction, it does have the option to abandon the project $1$ year from now if the tax is imposed. If it abandons the project, it would sell the complete property $2$ years from now at a price of $$6\mathrm{.}5$ million. Wrapping$-$up costs of $$0\mathrm{.}85$ million would be incurred.

The project has an $11\%$ cost of capital.

a$)$ Draw a decision tree showing the decisions, outcomes and probabilities associated with the new project.

$[5$ marks$]$

$2$

b$)$ Calculate the joint probability and NPV of each path of decision tree. Assume the required rate of return is $17\%.$

$[20$ marks$]$

c$)$ Calculate the expected NPV of the entire project.

$[4$ marks$]$

d$)$ What is the value of the abandonment option?

$[3$ marks$]$

e$)$ Should the firm undertake the project?

$[2$ marks$]$