You have negotiated a deal with the manufacturer to open an electric car

dealership in your hometown. The terms of the contract are such that you must

open the dealership immediately or in exactly one year. If you don't do either of

these things, you lose the right to open the dealership. The cost is $$5$ million

either now or one year from now. If you open immediately, you expect to

generate $$600,000$ in free cash flow in the first year and the cash flows are

expected to grow at $2$ percent each year in perpetuity. The cost of capital for this

investment is $12\%.$ If you wait, you will miss out on the first cash flow. If the

predicted volatility of returns to the dealership is $40\%,$ and the risk$-$free rate is

$3\mathrm{.}5\%,$ should you invest now or wait? Use the Black$-$Scholes calculator to solve

this problem.