Finance-Theory · Unit 2 · Video 1 · Interactive Practice

Thirty Cents on the Dollar: Why Nobody Could Price Fannie Mae's Paper

IKey Formulas

Formula	Name	Auction example
$\dfrac{P}{V}$	Price per dollar of worth, "cents on the dollar" ( $P$ = price paid, $V$ = worth)	iPod: $\dfrac{45}{150} = 0.30$ , thirty cents on the dollar
$1 - \dfrac{P}{V}$	Discount, when $P \lt V$	iPod: $1 - 0.30 = 0.70$ , a $70\%$ discount
$\dfrac{P}{V} - 1$	Premium, when $P \gt V$	Book: $\dfrac{60}{45} - 1 = \dfrac{1}{3} \approx 0.33$ , a third above retail

Key Insight: What a buyer will pay depends on what the buyer can find out. Both rooms saw only the size of a wrapped box, so each bid measured the packaging: the iPod worth about $150 fetched thirty cents on the dollar, the $45 book a third above retail. Fannie Mae and Freddie Mac paper in September 2008, with its payments and its issuer's survival both unknown, sold for less than thirty cents on the dollar, and how much less nobody could say.

IIPrice Against Worth — Cents on the Dollar

Each sale is a point $(V, P)$ ; the slope of its ray from the origin is $P/V$ , the price per dollar of worth.

iPod price $45 Book price $60

IIIThe Bid Follows the Box

If each bid measures only the wrapping, moving the contents changes every ratio and no bid.

IVThe Secondary Market — One Stock of Capital, a Pile of Promises

Selling each mortgage returns the bank's capital, so one stock of capital funds loan after loan while promises pile up.

Secondary market Cycle 0.0

💡 Each sheet in the stack is a promise to be made good. When housing turned down, the lenders behind the mortgages came under severe pressure, but every promise owed to the holders still had to be honored.

VQuiz Questions

Problem 1 · Thirty Cents on the Dollar

Given: the smaller box held an iPod with a retail value of about $150, and the winning bid was $45 — find the price per dollar of worth, $P/V$ .

✅ Correct!

45/150 = 0.30

: the room paid thirty cents for each dollar of worth, a

70\%

discount.

❌ That is the discount, not the price.

0.70

is the share of the worth the room did not pay,

1 - 0.30

❌ Wrong denominator. A $45 bid is 45 cents on the dollar only for an item worth $100. This one was worth about $150, so divide by 150.

❌ Upside down.

150/45 \approx 3.33

is dollars of worth per dollar paid. Price per dollar of worth puts the price on top.

Show solution

Price per dollar of worth divides what the room paid by what the item was worth:

\frac{P}{V} = \frac{45}{150} = 0.30

The room paid thirty cents on the dollar. The discount is the rest of the dollar:

1 - \frac{P}{V} = 1 - 0.30 = 0.70 = 70\%

This is the number the video carries forward to Fannie Mae's paper.

Problem 2 · A Third Above Retail

Given: the larger box held a book on hedge funds that retails for $45, and it sold for $60 — find the premium: by what percentage did the price exceed the worth?

✅ Correct! A $15 excess over a $45 worth is one third: the book fetched a third more than its retail price.

❌ Wrong base.

15/60 = 25\%

divides the $15 excess by the price. A premium measures the excess against the worth, $45.

❌ That is the whole price, not the excess.

60/45 \approx 1.33

is the price per dollar of worth; the premium is what remains after subtracting the 1 that matches the worth.

❌ That is the gap in dollars. The book sold for $15 more than its worth; as a percentage, that $15 must be divided by the $45 worth.

Show solution

The premium is the price per dollar of worth, minus the one dollar that matches the worth:

\frac{P}{V} - 1 = \frac{60}{45} - 1 = \frac{4}{3} - 1 = \frac{1}{3} \approx 33.3\%

Equivalently, divide the excess by the worth: $\dfrac{60 - 45}{45} = \dfrac{15}{45} = \dfrac{1}{3}$ . Dividing by the price instead, $15/60 = 25\%$ , measures the excess against the wrong base.

Problem 3 · Swap the Contents

Given: the rooms saw only the boxes, so suppose each bid belongs to its box, $45 for the smaller and $60 for the larger, whatever is inside. Swap the contents: the iPod (worth about $150) goes into the larger box and the book (worth $45) into the smaller — find each item's price per dollar of worth.

The iPod, now in the larger box

The book, now in the smaller box

✅ Correct! Both bids stay at $45 and $60; only the worth inside each box moved. The iPod now fetches $15 more than the book, so the price ranking matches the worth ranking, and nobody bidding could have told either arrangement from the other.

❌ The bid stayed with the box.

0.30

is the iPod's ratio as auctioned, when the smaller box's $45 bid was on it. In the larger box it draws the $60 bid: divide 60 by 150.

❌ The worth inside changed.

1.33

was the larger box's ratio while it held the $45 book. The $60 bid now sits over the iPod's $150 worth.

❌ Upside down.

150/60 = 2.50

is dollars of worth per dollar paid. Put the price on top.

❌ The bid stayed with the box.

1.33

is the book's ratio as auctioned, under the larger box's $60 bid. In the smaller box it draws $45, against its own $45 worth.

❌ The worth inside changed.

0.30

was the smaller box's ratio while it held the $150 iPod. The $45 bid now sits over the book's $45 worth.

Show solution

Each bid belongs to its box, so the prices stay where they were; only the worth under each price changes.

\text{iPod in the larger box:}\quad \frac{P}{V} = \frac{60}{150} = 0.40

\text{book in the smaller box:}\quad \frac{P}{V} = \frac{45}{45} = 1.00

As auctioned the ratios were $0.30$ and $1.33$ , and the ranking by price inverted the ranking by worth. Swapped, the iPod fetches $15 more than the book and the two rankings agree. The bids are identical in both arrangements because, on the video's reading, they measured the boxes, not the contents.

Problem 4 · Paper Nobody Could Price

Given: a holder owns Fannie Mae paper that promises to pay $10 million, quoted in cents per dollar promised. In September 2008 paper like it sells for considerably less than thirty cents on the dollar — find a sale price consistent with that conclusion, and the lower limit the argument puts on the price.

Which sale price fits the conclusion?

What lower limit does the argument put on the price?

✅ Correct! $2.0 million is 20 cents per dollar promised, below thirty cents, and the argument names no lower figure: the price is bounded from above only.

❌ That is the discount taken as the price. $7.0 million is 70 cents on the dollar, far above thirty.

❌ On the line, not below it. $3.0 million is exactly thirty cents on the dollar, the iPod's ratio. The paper sells for less than that.

❌ Divided instead of multiplied.

10/0.30 \approx 33.3

is more than the promise itself. A price quoted in cents on the dollar is that fraction of the $10 million.

❌ No second discount of fixed size. Nothing says the ignorance stacks by another 70%. It pushes the price below thirty cents by an amount nobody in the room could name.

❌ Unknown is not worthless. The argument never says the paper pays nothing; it says nobody could tell what it pays. Its conclusion is an inequality, not a figure.

Show solution

A price quoted in cents per dollar promised is that fraction of the $10 million promise. In millions of dollars:

0.20 \times 10 = 2.0, \qquad 0.30 \times 10 = 3.0, \qquad 0.70 \times 10 = 7.0

Only $2.0 million lies below the thirty-cent line; $3.0 million sits exactly on it, and $7.0 million mistakes the $70\%$ discount for the price. The conclusion itself is open-ended:

\frac{\text{price}}{\text{amount promised}} \lt 0.30

No lower figure is attached, because the buyer does not know what the paper pays, the seller does not know whether the issuer survives, and each knows the other is in the dark.

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