The all-equity firm Metallica Heavy Metal Mining (MHMM) Corporation wants to diversify its operations

Given,

Total Assets = $8,700,000

Total Liabilties = $3,600,000

Total Equity = $8,700,000-$3,600,000 = $5,100,000

Number of Shares = 30,000

Current Market Price = $50

Net Income = $600,000

So,

Return on Equity (ROE) = Net Income / Total Equity = $600,000/$5,100,000 = 11.76%

Current Earning per Share (EPS) = Net Income / Number of Shares = $600,000/30,000 = $20

Current Price to Earnings (P/E) Ratio = Current Market Price / Earning per Share = $50/$20 = 2.5

Additional Shares to be issued for raising $640,000 at price of $50 = $640,000/$50 = 12,800

Now,

Price to Earnings (P/E) Ratio = Market Price / Earning per Share

2.5 = $50 / Earning per Share

Earning per Share =$50/2.5 = $20

So,

Net Income = $20*12,800 = $256,000

1) Revised Return on Equity (ROE) = $256,000/$640,000 = 40%

2) NPV of New Investment:

NPV = Cost of New Project + New Market Value - Old Market Value of Firm

= -$640,000+ ($50*(30,000+12,800) - ($50*30,000)

= -$640,000+$2,396,800 - $1,680,000

NPV = $76,800