Gamma Tube Company plans to undertake a $7.5 million capital improvement program and is considering how much debt to use. It feels that it could obtain debt financing at the following interest rates (assume that this debt is perpetual):

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Next $1.5 millic !xt $1 million The company has made projections of its net cash flows (exclusive of new financing)

during a period of adversity such as a recession. In a recession, it expects a net cash flow of $3 million with a standard deviation of $2 million (assume a normal distribution). Its beginning cash balance is $1 million. If the company is willing to tolerate only a 5 percent probability of running out of cash during a recession, what is the maximum proportion of the $7.5 million capital improvement program that can be financed with debt? (Ignore any tax considerations.)

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