You are valuing a private company for sale and have made the following estimates of cashflows and expected growth rates:

$1$ Run by the existing management $($which is not entirely efficient$),$ your annual cash flows would be $ $10$ million next year and grow $4\%$ a year thereafter. If the management were replaced, you expect cashflows next year to be $ $12$ million a year, still growing at $4\%$ a year.

$2$ The market unlevered beta for the firm is $0\mathrm{.}8,$ based upon comparable firms that are publicly traded. However, the average correlation of these firms with the market is $0\mathrm{.}40.$ The firm has no debt; you have estimated an optimal debt ratio of $20\%$ at which point the pre$-$tax cost of debt would be $6\%.($Both private firms and public corporations get taxed at a $40\%$ tax rate$)$

$3$ The riskfree rate is $5\%$ and the market risk premium is $4\%.$

Imagine you are selling $40\%$ of the firm to another private individual $($who will not be diversified$).$Provide the estimate of the beta $($total beta$)$ to be used in the discount rate. Remember the firm has no debt.

Answers

$0\mathrm{.}32$

$0\mathrm{.}8$

$2\mathrm{.}0$

$4\mathrm{.}0$