Q$3.$ United Healthcare, a health maintenance organization, is expected to have earnings growth of $30\%$ for the next five years and $6\%$ after that. The dividend payout ratio will be only $10\%$ during the high growth phase, but will increase to $60\%$ in steady state. The stock has a beta of $1\mathrm{.}65$ currently, but the beta is expected to drop to $1\mathrm{.}10$ in steady state. $($The Treasury bond rate is $6\mathrm{.}5\%.)$

a$.$ Estimate the price$/$book value ratio for United Healthcare, given the inputs as given.

b$.$ Estimate PB ratios given the growth rates in high growth period ranging from $10\%$ to $50\%,$ with a $10\%$ incremental interval.

c$.$ United Healthcare trades at a price$/$book value ratio of $7\mathrm{.}00.$ How long would extraordinary growth have to last $($at a $30\%$ annual rate$)$ to justify this PBV ratio?