Solid Corporation secured a project to supply Toyota with $30,000$ kilograms of machine parts annually for $5$ years and the company needs an initial investment of $$2$ million to purchase a special equipment to manufacture the parts. The annual fixed costs are estimated to be

$$850,000,$ while the variable costs are $$40$ per kilogram. The equipment purchased will be depreciated over $5$ years using simplified straight$-$line method. At the end of the project, the equipment can be sold to a used$-$parts dealer for $$250,000.$ The selling price for the machine parts is set at $$90$ per kilogram, and the company requires an initial net working capital of

$$200,000,$ which will remain constant annually and can be recovered in full at the end of the project. The required rate of return is $12\%$ and the tax rate is $18\%.$

a$)$ Calculate the OCF for this project.

b$)$ Calculate the NPV$.$ Is the project viable?

c$)$ What is the sensitivity of the project OCF to changes in the quantity supplied?

d$)$ What is the sensitivity of NPV to changes in quantity supplied?

e$)$ What is the minimum level of output below which you would not want to operate? Why?