Lesson 13 of 25 · 6 min

The forced-sale multiple on this facility

The multiple is 3.333… and it was knowable in March, before any price had moved.

The forced-sale multiple is how many dollars of collateral must be sold per dollar of shortfall. It equals 1 ÷ (1 − threshold). On this facility the threshold is 0.70, so the multiple is 1 ÷ 0.30 = 3.333…, or 10/3.

forced-sale multiple = 1 ÷ (1 − t)

forced-sale multiple: The factor that turns a shortfall into a sale. Dimensionless.
t: The maintenance threshold as a decimal. 0.70 on this facility.
1 − t: The fraction of each dollar sold that closes gap. 0.30 here.

Apply it to the 60 percent shortfall: $241,972.67 × 10/3 = $806,575.57, which is the sale the previous lesson already computed by dividing by 0.30. The two routes are the same arithmetic. What the multiple adds is that the factor does not depend on the shortfall, the book, or the prices. It depends on the threshold alone.

That is why it was knowable on 2 April, the statement date, with the book still at $6,032,795 and headroom at 55.99 percent. Nothing about the March close is an input. A 75 percent threshold would have printed 4. An 80 percent threshold would have printed 5. This facility printed 3.333… on the day it was signed, and every subsequent shortfall is multiplied by that same factor. The stress finds how large the gap is; the agreement already found how many dollars of sale each dollar of gap requires.

The multiple is a property of the agreement. A stress finds the shortfall. It does not find the multiple.

Key terms

Forced-sale multiple: One divided by one minus the maintenance threshold. On this facility, 1 ÷ 0.30 = 3.333….
Threshold-only input: A quantity that does not take prices, balances or haircuts as inputs. The multiple is one.
3.333…: The repeating decimal 10/3. The exact multiple at a 70 percent threshold, not a rounded 3.3.

Worked example

The factor, applied and then stripped back

Threshold 70 percent. Shortfall $241,972.67 on the 60 percent book.

Multiple: 3.333…
Sale: $806,575.57
Sale divided by the shortfall: 3.333…
Multiple at a 75 percent threshold: 4
Inputs required from the March statement: The threshold only

The shortfall came from the stress. The 3.333… came from the agreement. Multiplying them is the whole of the sale.

Check yourself

This facility's threshold is 70 percent of market value. What is the forced-sale multiple, and which March figures does the multiple use?

Saved in this browser only. No account, nothing sent anywhere.

Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.