NPH wants to increase capacity by $40\%$ with a $$10$ million investment in plant and machinery. The firm wants to maintain the current debt$-$to$-$total$-$asset ratio in the capital structure of $40\%.$ It also wants to maintain the past dividend policy of distributing $45\%$ of last year$$s income as dividends. Last year$$s income was $$5$ million. How much external equity must NPH seek for the expansion?