Finance-Theory · Unit 4 · Video 3 · Interactive Practice

Last in Line: Chapter 11 and How Lehman's Equity Hit Zero

IKey Relations

Relation	Name	What it says
$E = \max(V - D,\; 0)$	Equity is the residual claim	Shareholders receive the value of the assets $V$ less everything owed to creditors $D$ , and never less than nothing: the last tier is paid only out of what the tiers above it did not need
$S = \min(V,\; D_S)$ $J = \min\big(\max(V - D_S,\; 0),\; D_J\big)$	The waterfall	Senior claims $D_S$ are filled to the brim before a single dollar reaches the junior claims $D_J$ , and the shareholders stand below both
$R = \dfrac{P_1 - P_0}{P_0}$	Return on a holding	Ending value minus beginning value, over beginning value
$R = \dfrac{0 - 62}{62} = -100\%$	Lehman equity, end-2007 to September 2008	Carrying the ending value as exactly zero gives the limiting case, and $E \ge 0$ makes $-100\%$ the floor: the stake is all a shareholder can lose

Key Insight: Nothing inside the firm had changed — the bankers, the traders and the asset managers were as capable the week after the filing as the week before. What the court enforces is the order of payment; whether anybody is paid at all waits on the one number nobody had, the value of the assets; and what carried the equity to zero was that counterparties were no longer prepared to do business with the firm.

IIThe Order of Payment

Everything depends on one number nobody had: what are the assets worth?

Assets marked at $60bn

IIIFrom $62 to Zero

Take the return the way you would take any other: ending value minus beginning, over beginning.

September 2008 price $0.00

IVCounterparties, Concern, and the Value of the Business

A firm nobody will deal with is not a business, and the value of that business goes to zero.

Trigger Round 0

💡 That the panic at Bear Stearns was set off by a rumour rather than by large exposures actually coming due is Andrew Lo's characterisation of the episode, not an established finding. The damage underneath it was real: Bear's hedge funds, invested in subprime mortgages, CDOs and credit default swaps, had gone under in the summer of 2007.

VQuiz Questions

Problem 1 · The Return on the Holding

Given: Lehman closed 2007 at $62 a share; nine months later the stock was essentially worthless. Carrying the ending value as exactly zero, what is the return on that holding?

✅ Correct!

\frac{0 - 62}{62} = -1

, the whole stake. And because equity is

\max(V - D, 0)

, no share price can take the return below that.

❌ That is the fall in dollars, not the return. The holding fell by $62, but the return divides that fall by what was put in:

-62 / 62 = -1

, not

-0.62

❌ The subtraction runs the other way. It is ending minus beginning,

0 - 62

, not

62 - 0

. A positive return would mean the shareholders ended richer.

❌ Only the denominator can undo the calculation, and the denominator is the beginning value. That value is $62, not zero, so the quotient is perfectly well defined.

Show solution

Apply the definition with $P_0 = 62$ and $P_1 = 0$ :

R = \frac{P_1 - P_0}{P_0} = \frac{0 - 62}{62} = \frac{-62}{62} = -1 = -100\%

Two points worth keeping. First, the ending value was essentially zero rather than exactly zero, and carrying it as exactly zero is what makes the answer exactly $-100\%$ ; at $0.25 a share the return would be $-99.60\%$ , which is still $-100\%$ to the nearest whole percent.

Second, $-100\%$ is a floor, not a coincidence. A shareholder's claim is $E = \max(V - D, 0)$ , so it stops at zero however far the assets fall short of the debts: the creditors' shortfall stays with the creditors.

Problem 2 · Who Is Paid, and How Much

Given: a firm in Chapter 11 whose assets are marked at $60bn, against senior claims of $40bn and junior claims of $40bn. How is the $60bn distributed?

✅ Correct! The senior tier fills to its brim first, and only the $20bn left over reaches the junior tier — a 50% recovery there, and nothing below it.

❌ The shortfall is not billed to the shareholders. Equity is

\max(V - D, 0)

: the claim stops at zero, so the $20bn the creditors are short is the creditors' loss, not a debt owed by the shareholders.

❌ That splits the assets pro rata and ignores priority. Paying every creditor

60/80 = 75\%

is what would happen if the two tiers ranked equally. They do not: the senior claim is satisfied in full before the junior claim is paid anything.

❌ The tiers are not equal shares. Priority means the assets run down the stack in order, and the shareholders are last: they receive something only once every creditor is satisfied.

Show solution

Run the waterfall with $V = 60$ , $D_S = 40$ , $D_J = 40$ , in $bn.

Senior tier:

S = \min(V,\; D_S) = \min(60,\; 40) = 40

Junior tier — only what the senior tier left behind:

J = \min\big(\max(60 - 40,\; 0),\; 40\big) = \min(20,\; 40) = 20

a recovery of $20/40 = 50\%$ on the junior claims.

Shareholders:

E = \max(V - D,\; 0) = \max(60 - 80,\; 0) = 0

Note what the junior tier shows: it is part paid, not wiped out. At this mark many creditors lose money and some are left whole, which is exactly the middle of the range that was open in September 2008.

Problem 3 · A Lower Mark

Given: the same firm — senior claims $40bn, junior claims $40bn — but the assets are now marked at $55bn.

What fraction of the junior claims is repaid?

What do the shareholders receive?

✅ Correct! $15bn reaches a $40bn junior claim —

37.5\%

— and the tier below it stays empty, with no liability attached.

❌ Check which tier the $55bn reaches. The senior claim takes $40bn of it in full; what is left for a $40bn junior claim is $15bn. Paying every creditor

55/80 = 68.75\%

would be the answer only if the two tiers ranked equally.

❌ The shareholders are below both creditor tiers. The junior claim is still $25bn short, so nothing reaches them — and

E = \max(V - D, 0)

stops at zero rather than turning into a debt they owe.

Show solution

With $V = 55$ , $D_S = 40$ , $D_J = 40$ , in $bn:

S = \min(55,\; 40) = 40 \qquad J = \min\big(\max(55 - 40,\; 0),\; 40\big) = 15

The junior recovery rate is

\frac{J}{D_J} = \frac{15}{40} = 0.375 = 37.5\%

and the residual claim is

E = \max(55 - 80,\; 0) = 0

The $25bn the junior creditors do not receive is their loss. It is not charged back to the shareholders, whose claim is a right to a residual and never an obligation to make one up — which is why $-100\%$ is the worst return a share can produce.

Why $68.75\%$ is wrong: that is $55/80$ , the recovery every creditor would get if the $55bn were divided pro rata across all $80bn of claims. Priority is exactly what replaces that split: the senior tier is filled to its brim first, and the junior tier gets only the remainder.

Problem 4 · Where the Value Went

Given: in the week after the filing the firm's investment bankers, proprietary traders and asset managers were as experienced and as knowledgeable as they had been the week before, and the desks were where they had always been. Which statement best accounts for the value of the business reaching zero?

✅ Correct! The change sat outside the firm, in what everybody else was now prepared to do with it: once no counterparty will deal with you, you are not a business, and the value of that business is zero.

❌ Nothing happened to the people. They were as smart, as savvy and as experienced the week after as the week before. That is precisely what makes the destruction of value worth explaining.

❌ That is not what the filing does. Chapter 11 freezes the claims and enforces the order in which they are settled — in the ordinary case the firm's own managers stay on as debtor in possession. It settles who is repaid first, not what the business is worth.

❌ The causation runs the other way. Concern about viability drove the counterparties away, and their leaving took the value of the business — and with it the share price — down. There is a chicken-and-egg quality to it, but the price is the reading, not the cause.

Show solution

Split the destruction of value into its tangible and intangible parts. The tangible part — the buildings, the equipment, the securities — is the smaller share. The large part is intangible: the brand, and the viability of the business itself.

Viability is not a property the firm holds on its own books. The magnitude of the exposures created general concern about it; once that concern is general, counterparties stop wanting to do business with the firm; and when everybody stops wanting to do business with you, you are not a business. There is a loop in this: the concern damages the firm, and the damage justifies the concern.

The same mechanism had already taken down Bear Stearns earlier that year, with one change at the start — on Lo's account the panic there was set off by what appears to have been a rumour rather than by large exposures actually coming due. Lehman's exposures were much larger, so the concern about its viability had real exposures behind it, but the route to zero was the same one.

Solved: 0 / 4