Class 20
Bankruptcy, Spring, 2009
Interest Rates
Randal C. Picker
Leffmann Professor of Commercial Law
The Law School
The University of Chicago
773.702.0864/[email protected]
Copyright © 2005-09 Randal C. Picker. All Rights
One-Period Present Value

Numbers
10%
interest rate
From Today to Tomorrow

$1 today is worth $1.10 one year from now
From

July 28, 2017
Tomorrow to Today
$1.10 one year from now is worth $1 today
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One-Period Present Value

Formulas
FV  PV 1 r 
FV
PV 
1 r
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Two-Period Present Value

Numbers
From
Today to Tomorrow to The Period
After Tomorrow

$1 today—present value—is worth $1.10
one year from now, is worth 1.21 two years
from now
From

July 28, 2017
Two Years from Now to Today
A future value of $1.21 two years from now
is worth $1 today
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Two-Period Present Value

Formulas
FV  PV 1 r11  r2 
FV
PV 
1 r11 r2 
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Two-Period Stream

Question
What
is $1.10 one year from now + $1.21
two years from now worth today?

We have done this already!
$1.10
one year from now is worth $1 today
$1.21 two years from now is worth $1 today
Together, they are worth $2 today
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6
Two-Period Stream Again

Question
What
is $1 one year from now + $1 two
years from now worth today?

Answer
$1/1.1
July 28, 2017
+ $1/1.21 = 1.735
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N-Period Stream

Assumptions
Stream
will pay fixed amount C in every
period
One-period interest rate r is same in every
period

What is the formula that tells us the present
value of a stream of N periodic payments of
C?
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N-Period Stream

Formula
C 
1 
PV 
1
N 

r  1  r 
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Applying the Formula

Do The Numbers in our Prior Example
 What
is $1 one year from now + $1 two years
from now worth today? $1.735
 C = 1; N = 2; r = .1
 C/r = 10
C 
1 
 1.1*1.1 = 1.21
PV 
1
N 

 1/1.21 = 0.826
r  1  r 
 1 – 0.826 = .1735
 10 * 0.1735 = 1.735
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A Real Example

Buying the Used Truck
 We
start with the PV—the amount of the debt—
and we find C
 PV = 6,395 + 330.75 – 300 = 6425.75
 N = 68 (payments every two weeks for 136 weeks)
 Interest rate is 21% annually
 But we need an interest rate for each two-week
period
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A Real Example
Two

Tries
Just Divide
• r = .21/26 = 0.008077

Compounded 2-Week Rate
• Find r such that the compounded two-week rate
results in the annual rate
– (1+r)^26 = 1 + .21 = 1.21
– That gives r = .007358494
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A Real Example

Resetting
C 
1 
PV 
1
N 

r  1  r 
PV = 6425.75
 N = 68
 r1 = 0.008077 or r2 = .007358494
 At r1, C = 123.18, with total interest of 68*C – PV =
1950.61
 At r2, C = 120.44, with total interest of 68*C – PV =
1764.29
 Note that (1950.61 + 1764.29)/2 = 1857.45
 The figure in the case is 1859.49

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Till

Core Facts
Borrowing
in the way just described
Default and C13 filing
Debt amount: $4894.89
 Collateral Value: $4000
 Sec 506(a) bifurcation [but not after 2005]

Plan:
July 28, 2017
Keep truck and meet 1325(a)(5)(B)
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1325

Confirmation of plan
(a)
Except as provided in subsection (b), the
court shall confirm a plan if-(1) the plan complies with the provisions of
this chapter and with the other applicable
provisions of this title;
 (2) [omitted]
 (3) the plan has been proposed in good faith
and not by any means forbidden by law;

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1325 (cont.)

Confirmation of plan (cont.)
(a)

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(cont.)
(4) the value, as of the effective date of the
plan, of property to be distributed under the
plan on account of each allowed unsecured
claim is not less than the amount that would
be paid on such claim if the estate of the
debtor were liquidated under chapter 7 of
this title on such date;
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Pre-2005 1325(a)(5)

Confirmation of plan (cont.)
 (a)

(cont.)
(5) with respect to each allowed secured claim
provided for by the plan-• (A) the holder of such claim has accepted the plan;
• (B) (i) the plan provides that the holder of such claim retain
the lien securing such claim; and (ii) the value, as of the
effective date of the plan, of property to be distributed
under the plan on account of such claim is not less than
the allowed amount of such claim; or
• (C) the debtor surrenders the property securing such claim
to such holder;
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Post-2005 1325(a)

Confirmation of plan (cont.)
 (a)

(cont.)
(5) with respect to each allowed secured claim
provided for by the plan-• (A) the holder of such claim has accepted the plan;
• (B) (i) the plan provides that
– (I) the holder of such claim retain the lien securing such claim until
the earlier of—
– (aa) the payment of the underlying debt determined under
nonbankruptcy law; or
– (bb) discharge under section 1328; and
– (II) if the case under this chapter is dismissed or converted without
completion of the plan, such lien shall also be retained by such
holder to the extent recognized by applicable nonbankruptcy law;
and
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Post-2005 1325(a)
• (ii) the value, as of the effective date of the plan,
of property to be distributed under the plan on
account of such claim is not less than the
allowed amount of such claim; and
• (iii) if—
– (I) property to be distributed pursuant to this subsection is in the
form of periodic payments, such payments shall be in equal monthly
amounts; and
– (II) the holder of the claim is secured by personal property, the
amount of such payments shall not be less than an amount
sufficient to provide to the holder of such claim adequate protection
during the period of the plan; or
• (C) the debtor surrenders the property securing such claim
to such holder;
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Post-2005 1325(a)

Hanging Paragraph
 For
purposes of paragraph (5), section 506 shall not
apply to a claim described in that paragraph if the
creditor has a purchase money security interest
securing the debt that is the subject of the claim, the
debt was incurred within the 910-day preceding the
date of the filing of the petition, and the collateral for
that debt consists of a motor vehicle (as defined in
section 30102 of title 49) acquired for the personal use
of the debtor, or if collateral for that debt consists of
any other thing of value, if the debt was incurred during
the 1-year period preceding that filing.
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What Interest Rate

Consider Five Rates
The

Possibly the rate the US gov’t borrows at?
The

July 28, 2017
risk-free rate
cost of funds rate
The rate that the creditor in question
borrows at
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What Interest Rate
The

formula rate
Start with the prime rate—that is, the rate
that banks offer to their best borrowers—and
adjust upwards depending on the risks
associated with this borrower
The
contract rate
The coerced loan rate

July 28, 2017
What rate would the creditor get on a new
loan to a similarly situated debtor?
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Choosing

Key Questions
What
does the Code require?
Independent of that, which of these is right?
What are the likely consequences of the
choice?
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