Cinnamon, a manufacturer of industrial freezers, has recently developed a newhighly energy$-$efficient freezer, the HC$.$ Market research has shown that demand for the HC may be high $(4,800$ units per year$)$ or low $(4,250$ units per year$).$ Theprobability of high demand is $40\%.$ The firm is now considering whether or not to go ahead with a project to produce and sell the HC for a period of four years.Each HC will be sold for $$1,400.$ The variable production costs will be $$900$ perHC.Cinnamon already owns a factory that can be used for the HC project. IfCinnamon does not go ahead with the project the factory could be sold now for $$0\mathrm{.}7$ million.The project would require machinery to be bought now at a cost of $$4\mathrm{.}3$ million.At the end of four years the value of the machinery will be zero. For the purposes of tax, the firm can claim depreciation $($capital allowances$)$ on the machinery at $25\%$ per year. Assume Cinnamon will have enough taxable capacity from other projects to take advantage of any additional tax breaks from the HC project. All cash flows are assumed to occur at the end of the year except for those that would occur now. Cinnamon's cost of capital is $16\%$ and the tax rate is $40\%.($a$)$ If demand for the HC is high, what is the net present value $($NPV$)$ of theproject? What is the NPV if demand is low?$(12$ marks$)($b$)$ Calculate the probability of high demand at which the expected value of theNPV is zero. Should the firm undertake the project? Explain.$(4$ marks$)($c$)$ Cinnamon discovers that because of the environmentally friendly nature of the project, it can claim a $100\%$ capital allowance for the machinery in year $1$instead of claiming $25\%$ in each year. By how much does this change theexpected NPV of the project? Should the firm undertake the project? Explain.$(6$ marks$)($d$)$ Cinnamon used a market research firm to estimate the demand for the HC$,$ atan agreed price of $$100,000.$ Cinnamon has paid the market research firm$$70,000$ to date. By how much does this information change the expected NPV of the project? Explain.