Benchmark$$ Metrics, Inc.$($BMI$),$ an$$ all$-$equity financed$$ firm, reported EPS of

$ $5\mathrm{.}08$$$5\mathrm{.}08$

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{.}69$$$0\mathrm{.}69$

per share$($vs$.$ almost

$ $2$$$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{.}69$$$0\mathrm{.}69$

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

$41\%41\%$

dividend payout$$ ratio, and reinitiating its stock repurchase plan for a total payout rate of

$60\%60\%.$

$($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

$15\%15\%,$

and that reinvestments will account for all future earnings growth$($if any$).$ Finally, assume$$ BMI's equity cost of capital is

$10\%10\%.$

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