Williams and hannah corporations are identical firms except williams
is more levered.  Both will remain in business for one more year. The
companies' eceonomist agree that the probability of a recession next
year is 20% and the probability of a continuation of the current
expansion is 80%.  If the expansion continues, each firm will
generate earnings before interest and taxes (EBIT) of $2 million.  If
a recession occurs, each firm will generate earnings bfore interest
and taxes of $0.8 million.  Steinberg's debt obligation requires the
firm to pay $750,000 at the end of the year.  Williams's debt
obligation requires the firm to pay 1 million at the end of the year. 
Neither firm pays taxes.  Assume a one-period model, risk neutrality,
and an annual discount rate of 15 percent

a. Assuming there is no costs of bankruptcy, what is the market value
of each firm's debt and equity?

b. What is the value of each firm?

c. Hannah's CEO recently states that Hannah's value should be higher
than William's since the firm has less debt, therefore less bankruptcy
risk.  Is this assuption true?

---

Request for Question Clarification by omnivorous-ga on 29 Nov 2006 16:04 PST

Bladehulk --

I assume that this sentence should read:

>HANNAH'S debt obligation requires the firm to pay $750,000 at the end of the year.

I'll calculate this problem on that basis and if we need to correct
anything, we can do it after I post the Answer.

Best regards,

Omnivorous-GA

Bladehulk ?

The firm?s valuation is determined by expected future cash flows and
we have probabilities for a recession and for an expansion that allow
it to be calculated.

The calculations take into account the .20 probability of $800,000 in
EBIT, providing an expected cash flow in a recession of $160,000.  The
.80 probability of $2,000,000 gives an expected cash flow in an
expansion of $1.6 million.  So, both firms have the same expected cash
flow of $1.76 million ? but Williams will use $1 mllion of it to pay
off debt, while Hannah uses only $750,000.

You can see line-by-line calculations, including NPV assumptions, here:
Williams and Hannah Corporations
http://www.mooneyevents.com/williamshannah.xls


a.	As a result, the value of Williams equity is net cash flow * the
NPV factor for one year or $660,870.  The value of Williams debt also
needs be reduced by the NPV factor, so it is $869,565.  Of course the
debt value will rise with time during the year until it reaches the
full $1,000,000, assuming that we don?t face the recession case.

Hannah?s equity value is higher at $878,261 because the raw cash flow
after the bonds are paid is almost 33% higher.  Its debt is worth only
$652,174 today, though it should be worth the full $750,000 in a year
(even facing a recession).

b.	The value of each firm is the discounted value of the TOTAL
expected cash flow of $1,760,000, which is $1,530,435.

This value is made up of different equity amounts for each Williams
and Hannah but you?ll see that both lines 12 + 13 (for Williams) and
lines 24+25 (Hannah) total $1,530,435.

c.  Some time ago, each firm divided up the debt-equity pie.  Williams
went for higher leverage and the result now is that its equity is
worth less.  Hannah?s CEO is reaping that ?bankruptcy avoidance? award
already with an equity value that is almost 33% higher.

Merton Miller, who taught at the University of Chicago?s Graduate
School of Business when I was there and is a very funny guy, explains
the irrelevance of borrowing in the capital structure this way:

"Say you have a pizza, and it is divided into four slices. If you cut
it into eight slices, you still have the same amount of pizza. We
proved that! Rigorously!"

Merton Miller was referring to what is known in finance as the
Modigliani-Miller theorem, which says that the value of the firm is
determined by the cash flow and is independent of the financing used. 
Miller got a Nobel Prize for that work (but little for the pizza
analogy).

Arnold Kling -- AP Economics
"Corporate Finance: Leverage and the Modigliani-Miller Theorem" (undated)
http://arnoldkling.com/econ/saving/corpfin.html

Google search strategy:
Modigliani Miller theorem

Best regards,

Omnivorous-GA