Your company operates a steel plant. On average, revenues from the plant are $$30$ million per year. All of the plant's costs are variable costs, and are consistently $89\%$ of revenues. $($This includes the energy costs associated with powering the plant which represent one quarter of the plant's costs, or an average of $$6\mathrm{.}68$ million per year.$)$ Suppose the plant has an asset beta of $1\mathrm{.}25,$ the risk$-$free rate is $4\%,$ and the market risk premium is $5\%.$ The tax rate is $35\%,$ and there are no other costs.

a$.$ Estimate the value of the plant today assuming no growth.

b$.$ Suppose you enter a long$-$term contract which will supply all of the plant's energy needs for a fixed cost of $$3$ million per year $($before tax$).$ What is the value of the plant if you take this contract?

c$.$ How would taking the contract in $($b$)$ change the plant's cost of capital? Explain.