Benchmark Metrics, Inc. $($BMI$),$ an all$-$equity financed firm, reported EPS of $$5\mathrm{.}82$ in $2008.$ Despite the economic downturn, BMI is confident regarding its current investment opportunities. But due to the financial crisis, BMI does not wish to fund these investments externally. The Board has therefore decided to suspend its stock repurchase plan and cut its dividend to $$0\mathrm{.}84$ per share $($vs$.$ almost $$2$ per share in $2007),$ and retain these funds instead. The firm has just paid the $2008$ dividend, and BMI plans to keep its dividend at $$0\mathrm{.}84$ per share in $2009$ as well. In subsequent years, it expects its growth opportunities to slow, and it will still be able to fund its growth internally with a target $44\%$ dividend payout ratio, and reinitiating its stock repurchase plan for a total payout rate of $63\%.($All dividends and repurchases occur at the end of each year.$)$

Suppose BMI's existing operations will continue to generate the current level of earnings per share in the future. Assume further that the return on new investment is $15\%,$ and that reinvestments will account for all future earnings growth $($if any$).$ Finally, assume BMI's equity cost of capital is $10\%.$

a$.$ Estimate BMI's EPS in $2009$ and $2010($before any share repurchases$).$

b$.$ What is the value of a share of BMI at the start of $2009($end of $2008)?$ Hint: Make sure to round all intermediate calculations to at least four decimal places.