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
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
Arnold Kling -- AP Economics
"Corporate Finance: Leverage and the Modigliani-Miller Theorem" (undated)
Google search strategy:
Modigliani Miller theorem