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	$	64
Number of shares		40,000
Total assets	$	8,200,000
Total liabilities	$	4,000,000
Net income	$	700,000

   

MHMM is considering an investment that has the same PE ratio as the firm. The cost of the investment is $800,000, and it will be financed with a new equity issue.

	The ROE on the investment would have to be percent

he offering to be $64 per share (assume the PE ratio remains constant), and the NPV of the investment would be

occur in this case. Market value dilution

occur in this case.

Accounting dilution

Answer 1

a). ROE₀ = Net Income₀ / Equity₀

= $700,000 / [$8,200,000 - $4,000,000] = $700,000 / $4,200,000 = 0.1667, or 16.67%

b). NI₁ = (ROE₀) x (TE₁) = 0.1667 x ($4,200,000 + $800,000) = $833,333.33

EPS₀ = NI₀ / Shares Outstanding = $700,000 / 40,000 = $17.50

Number of new shares = Cost of Investment / Current Share Price = $800,000 / $64 = 12,500

EPS after the stock offer:

EPS₁ = NI₁ / Shares Outstanding = $833,333.33 / (40,000 + 12,500) = $15.87

PE₀ = $64 / $17.50 = 3.657

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

P₁ = $64 = 3.657(EPS₁)

EPS₁ = $64 / 3.657 = $17.50

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

Net Income = $17.50 x 40,000 = $700,000

ROE₁ = Net Income / Cost of Investment = $700,000 / $800,000 = 87.50%

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 = -$800,000 + [$64(52,500) - $64(40,000)]

= -$800,000 + $800,000 = $0

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

BVPS₀ = Equity₀/Shares₀

= $4,200,000 / 40,000 = $105

BVPS₁ = Equity₁/Shares₁

= ($4,200,000 + $800,000) / (40,000 + 12,500) = $5,000,000 / 52,500 = $95.24

Accounting dilution still takes place, as book value per share still falls from $105.00 to $95.24, but no market dilution takes place because the firm is investing in a zero NPV project.