The Metallica Heavy Metal Mining (MHMM) Corporation wants to diversify its operations. Some recent financial information for the company is shown here:
Stock price $ 80 Number of shares 40,000 Total assets $ 8,800,000 Total liabilities $ 5,100,000 Net income $ 900,000
MHMM is considering an investment that has the same PE ratio as the firm. The cost of the investment is $640,000, and it will be financed with a new equity issue. (Do not round intermediate calculations.) The ROE on the investment would have to be ? percent (Round your answer to 2 decimal places (e.g., 32.16).) if we wanted the price after the offering to be $80 per share (assume the PE ratio remains constant), and the NPV of the investment would be ? (Leave no cells blank – be certain to enter “0” wherever required.). Accounting dilution occur in this case. Market value dilution occur in this case.
Answer
The total equity of the company is total assets minus total liabilities, or:
Equity = $8,800,000 – 5,100,000
Equity =$3,700,000
So, the current ROE of the company is:
ROE0= NI0/TE0
= $900,000 / $3,700,000
= 0.2432 or 24.32%
The new net income will be the ROE times the new total equity, or:
NI1= (ROE0)(TE1) =
0.2432($3,700,000+ 640,000)
= $1055488
The company’s current earnings per share are:
EPS0= NI0/Shares outstanding0
= $900,000/40,000 shares
. = $22.50
The number of shares the company will offer is the cost of the investment divided by the current share price, so:
Number of new shares
= $640,000/$80
= 8,000
The earnings per share after the stock offer will be:
EPS1= $1055488/48000 shares
= $21.98
The current P/E ratio is:
(P/E)0= $80/$22.50
=3.55
Assuming the P/E remains constant, the new stock price will be:
P1= 3.55($21.980)
= $78.15
The current book value per share and the new book value per share are:
BVPS0
= TE0/shares0
= ($8,800,000 – $5,100,00)/40,000 shares
= $92.5 per share
BVPS1
= TE1/shares1
= ($48,800,000 – $5,100,00+ 640,000)/48000 shares
= $90.42 per share
So the current and new market-to-book ratios are
:Market-to-book0
= 80/$92.5
= 0.864
Market-to-book1
= $78.15/$90.42
= 0.8643
The NPV of the project is the cost of the project plus the new market value of the firm minus thecurrent market value of the firm, or:
NPV = –$640,000 + [$78.15(48000) – $80(40,000)]
= – $88800
Accounting dilution takes place here because the market-to-book ratio is less than one. Marketvalue dilution has occurred since the firm is investing in a negative NPV project
