The firm’s overall cost of capital today is 6% . 1/3 + 12% . 2/3 = 10%. Because 4% + 3% . β = 10%, the beta is 2. The easy way is to recognize that the firmis sheltering $500 . 6% = $30 through interest payments.

If it refinanced with $1,000, it could now shelter $1,000 . 8% = $80. Uncle Sam would see an additional

$50 less in income, which means that the firm would pay $50 . 20% = $10 less in income tax next year.

Now you need to determine the appropriate discount rate for $10 in tax savings. For convenience, use the debt cost of capital: 8%. This means that our recapitalization increases firm value by $10/1.08 ≈ $9.26. (If you prefer to use the overall firm cost of capital, you would obtain $9.09.) The question intentionally gave additional irrelevant information about the firm’s future existence.