Question

The Metallica Heavy Metal Mining (MHMM) Corporation wants to diversify its operations. Some recent financial information for the company is shown here:

Stock price	$	40
Number of shares		30,000
Total assets	$	9,800,000
Total liabilities	$	4,700,000
Net income	$	420,000

   
The company 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 XXXX (Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) if we wanted the price after the offering to be $40 per share (assume the PE ratio remains constant), and the NPV of the investment would be $ XXXX(Leave no cells blank - be certain to enter "0" wherever required.).

Please answer all questions

Answer 1

The current ROE of the company is:

ROE₀= Net income₀ / Equity₀

ROE₀= $ 420,000/$5,100,000

ROE₀= 8.24%

The new net income will be the ROE times the new total equity, or:

NI₁ = (ROE₀)(TE₁)

NI₁= .0824 * ($5,100,000 + 640,000)

NI₁= $ 472976

The company’s current earnings per share are:

EPS₀ = Net income₀ /Shares outstanding₀

EPS₀= $420,000 / 30,000 shares

EPS0= $14.00

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/$40

Number of new shares = 16,000

The earnings per share after the stock offer will be:

EPS₁= $472,976/46,000 shares

EPS1= $10.28

The current PE ratio is:

PE0= $40/$14

PE0= 2.86

Using the PE ratio to find the necessary EPS after the stock issue, we get:

P1 = $40 = 2.86(EPS₁)

EPS₁= $14.00

The additional net income level must be the EPS times the new shares outstanding, so

Net income = $14.00(30,000 shares)

Net income = $420,000

And the new ROE is:

ROE1= $420,000/$640,000

ROE1= .65625, or 65.63%

Next, we need to find the NPV of the project. The NPV of the project is the cost of the project plus the new market value of the firm minus the current market value of the firm, or:

NPV = –$640,000 + [$40(46,000) – $40(30,000)]

NPV = $0

The current book value per share and the new book value per share are:

BVPS0= Equity0/Shares0

BVPS0= $5,100,000/20,000 shares

BVPS0= $170.00 per share

BVPS1= Equity1/Shares1

BVPS1= (5,100,000 + 640,000)/46,000 shares

BVPS1= $124.78 per share

Accounting dilution still takes place, as book value per share still falls from $170.00 to $124.78, but no market dilution takes place because the firm is investing in a zero NPV project