Given: Two companies- Levico and Unlecal-- are identical in every way
except their capital
structures. Each company projects $96 million in earnings before
interest each year for perpetuity, with each company distributing all
earnings as dividends. Levico's perpetual debt has a market value of
$275 million and a cost of 8 percent annually. Levico has 4.5 million
shares outstanding currently at $100 per share. Unlecal has zero debt
and 10 million shares outstanding, currently worth $80 per share.
Neither firm pays taxes. Is Levico's stock a better buy than Unleco's
stock, and why? Sorry, gotta show the math. At first I thought this
was a WACC calculation but without beta I cannot see how to get CAPM,
and so it must not be a simple WACC.

Hi!!

Unlecal is an all-equity firm (that is an unlevered firm), then its
value is equal to the market value of its outstanding shares:

Unlecal has 10 million shares of common stock outstanding, worth $80
per share, then the value of Unlecal is $800 million (= 10 million
shares * $80 per share).

Recall Modigliani-Miller Proposition I without taxes:
- In the absence of taxes, the value of a levered firm equals the
value of an otherwise identical unlevered firm. VL = VU (Value of
levered firm equals value of unlevered firm)
- The cost of capital does not change if the capital structure changes.

See for further reference:
"WWWFinance-Capital Structure and Payout Policies: Campbell R. Harvey":
http://www.duke.edu/~charvey/Classes/ba350/capstruc/capstruc.htm


Since Levico is a levered firm identical to Unlecal in every way
except its capital structure and neither firm pays taxes, the value of
the two firms should be equal. This means that Levico´s value should
be $800 million also.

Now we must take a look into the Levico´s capital structure:
Levico has 4.5 million outstanding shares, worth $100 per share, then
the market value of Levico?s equity is $450 million; and, according to
the problem´s statement, the market value of Levico?s debt is $275
million.
Recall that the market value of a levered firm equals the market value
of its debt plus the market value of its equity. Therefore, the
current Levico´s market value is:
MVL = B + S
    = $275 million + $450 million
    = $725 million	
Note that to hold MM Proposition I, the market value of Levico?s
equity needs to be $525 million instead its current market value of
$450 million.

Since Levico?s market value is less than Unlecal?s market value and,
according to MM Proposition I, they have the same value, Levico is
relatively underpriced and an investor will prefer to buy Levico´s
stock.


I hope that this helps you. Feel free to request for a clarification
if you need it.

Regards, 
livioflores-ga

Thank you very much! A well written, clearly understandable answer.

Here is my take:

Levco : Earnings = 96 Million
        Interest Expense = 0.08 * 96 Million
                         = 7.68 Million.
        Cash Flow to Equity Holders = 88.32 Million
        EPS = $19.63 = Dividends
Thus Dividend return is 20% Anually

Unecal : Earnings = 96 Million
         Cash Flow to Equity Holders = 96 Million
         EPS = $9.6 = Dividends
Thus Dividend return is 10% Anually

The shares in either company will not rise because of lack of Retained
Earnings which means growth = ROE * RE = 0 thus the only way for
equity holders to make money is through the dividends.

Finance_guru-ga, this is excellent info for a supporting argument. I
appreciate the input! Many thanks!

Oops, but for Levco isn't it:

Levco : Earnings = 96 Million
        Interest Expense = 0.08 * $275 Million (perpetual debt market value)
                         = $22 Million.
        Cash Flow to Equity Holders = $74 Million
        EPS = $16.44 = Dividends
Thus Dividend return is ~16% Anually

Yes

Sorry about the mis calculation ..