This document presents a comic summary of an academic article that proposes an algorithm for renegotiating debt through equivalent equations and transaction costs. The comic outlines how John, a debtor, and Sarah, a creditor, use the algorithm to restructure John's debt into three hypothetical scenarios with different payment schemes that account for inflation, interest rates, and transaction costs. The goal of the debt restructuring model is to balance the needs of both the debtor to defer payments and the creditor to receive additional interest and fees.

1. AN ALGORITHM TO RENEGOTIATE DEBT THROUGH EQUIVALENT EQUATIONS AND
TRANSACTION COSTS: A PROPOSAL FOR THE FIELD OF FINANCIAL EDUCATION
STUDENTS OF THE UCC BUSINESS SCHOOL PRESENT: A COMIC ADAPTATION OF
PUBLISHED AT INTERNATIONAL ELECTRONIC
JOURNAL OF MATHEMATICS EDUCATION
BY ARTURO GARCÍA SANTILLÁN
“DO YOU KNOW
WHAT IS A DEBT
RESTRUCTURING?”
“FREQUENTLY, THE SHADOW OF FINANCIAL INSOLVENCY IS PRESENT IN
COUNTRIES, COMPANIES AND PEOPLE WHO CONTRACT THE OBLIGATION
OF A LOAN OR OTHER DEBT.”
“DEBT RESTRUCTURING IS ONE OF THE MOST
EFFECTIVE FINANCIAL TOOLS TO FACE THIS.”
“THE DEBTOR SHOULD CONSIDER APPROACHING
HIS CREDITOR BEFORE THAT THE CREDITOR
ATTEMPTS COLLECTION BY JUDICIAL MEANS.”
“IT IS IMPORTANT TO REACH AN AGREEMENT
WHERE DEBT RESTRUCTURING CAN BE CARRIED
OUT WITH NEW PAYMENT SCHEMES SUITABLE TO
THE DEBTOR´S CASH FLOW.”

2. “CONSIDERING THAT THE CREDITOR DOES NOT RECOVER
HIS CAPITAL IN THE TERMS PREVIOUSLY AGREED UPON,
IT IS NECESSARY TO INCLUDE THE TRANSACTION COSTS,
WICH ARE THE COSTS OF TRANSFERRING PROPERTY
RIGHTS, IN THIS CASE IT WOULD BE THE PROPERTY OF
THE BORROWED CAPITAL.”
AN HYPOTHETICAL CASE OF DEBT RESTRUCTURE
“JOHN, THE DEBTOR,
AND SARAH, THE CREDI-
TOR, SEEK TO DEBT
RESTRUCTURE.”
“THEY REACHED AN AGREE-
MENT TO RESTRUCTURE THE
PROMISSORY NOTES THAT HAVE
EXPIRED AND ALSO THOSE THAT
HAVE NOT YET EXPIRED.”
*THE AGREEMENT ALSO STIPULATE AN INFLATION RATE OF 3.8% PER YEAR
AND A 2.5% FOR TRANSACTION COSTS.
”THE AGREEMENT STIPULATES A NOMINAL
INTEREST RATE OF 13.5% CAPITALIZABLE
EVERY 28 DAYS FOR BOTH, DOCUMENTS
THAT HAVE ALREADY EXPIRED AND DOCU-
MENTS THAT HAVE NOT YET EXPIRED.”
THIS WAS THE ORIGINAL JOHN’S DEBT WITH SARAH:
PROMISSORY
NOTES
1
2
3
4
5
6
7
8
9
10
11
12
13
EXPIRED AND
NOT EXPIRED
bfd
bfd
bfd
bfd
bfd
fd
afd
afd
afd
afd
afd
afd
afd
YEAR
2019
2019
2019
2019
2019
2019
2020
2020
2020
2020
2020
2020
2020
DAYS TO
FOCAL DATE
297
190
140
111
60
0
21
87
121
161
221
290
321
TOTAL:
AMOUNT
K DLS.
$17.50
$20.00
$17.00
$18.00
$19.00
$15.00
$11.50
$12.00
$14.00
$22.00
$19.50
$17.00
$15.00
$217.50

3. “TO DEVELOP THE FINANCIAL MODELING OF
DEBT RESTRUCTURING IT IS NECESSARY TO
CONVERT NOMINAL INTEREST RATE IN ITS
EFFECTIVE RATE AND IN ITS REAL
INTEREST RATE”
VODadjusted = ∑
1...j VOD
PN”1bfd1...j
bff
[( )*(VOD+itce)]+
VOD
PN”fd
[( )*(VOD+itce)]+ ∑
1...j VOD
PN”afd1...j
aff
[( ) *(VOD+itce)]
Eir = 1+( *m) -1 *100 and Rir = *100
t
m
Nir
t[ ] [ ](Eir-Inf)
(1+Inf)
“SUBSEQUENTLY, FROM REVALUATING
THE ORIGINAL DEBT AND EVALUATING
THE NEW SCHEME OF PAYMENT, IT IS
POSSIBLE TO CALCULATE THE AMOUNT
OF EACH EQUIVALENT PAYMENT FOR
THE NEW PAYMENT SCHEME.”
“IF TRANSACTION COST IS AGREED, THE MATHEMATICAL MODEL MUST BE RESTRUCTURED BASED ON THE PRORATED FUNCTION
ACCORDING TO THE AMOUNT OF EACH RESTRUCTURED PROMISSORY NOTE IN RELATION TO THE TOTAL DEBT REVALUED.
BASED ON THIS MATHEMATICAL
MODEL SARAH PROPOSES TO JOHN
THREE HYPOTHETICAL SCENARIOS
FOR THE NEW PAYMENT SCHEME IN
DEBT RESTRUCTURING.
Y1...j =
VOD
VNSP
=
∑
1...j
PN 1...j.bfd 1+( *m) + PNfd +∑
1...j
t
m
(1+ *m)
PN 1...j.afd
∑
bfd
1...j
bfd afd
Eir
t[ ] t
m
Rir
t
X 1...j.bfd 1+( *m) + Xfd + ∑
1...j
t
m
(1+ *m)
X 1...j.afd
afd
Eir
t[ ] t
m
Rir
t

4. PROMISSORY
NOTES
1
2
3
4
5
6
7
8
9
10
11
12
EXPIRED AND
NOT EXPIRED
bfd
fd
afd
afd
afd
afd
afd
afd
afd
afd
afd
afd
YEAR
2019
2019
2019
2019
2019
2020
2020
2020
2020
2020
2021
2021
DAYS TO
FOCAL DATE
15
0
35
60
120
180
240
270
300
330
390
450
TOTAL:
AMOUNT
K DLS.
$19.64
$19.64
$19.64
$19.64
$19.64
$19.64
$19.64
$19.64
$19.64
$19.64
$19.64
$19.64
$235.63
PROMISSORY
NOTES
1
2
3
4
5
6
7
8
9
10
11
EXPIRED AND
NOT EXPIRED
bfd
bfd
fd
afd
afd
afd
afd
afd
afd
afd
afd
YEAR
2019
2019
2019
2019
2019
2020
2020
2020
2020
2020
2021
DAYS TO
FOCAL DATE
28
15
0
35
60
120
180
210
240
270
480
TOTAL:
AMOUNT
K DLS.
$12.50
$10.00
$9.00
$8.00
$7.00
$8.50
$7.50
$6.00
$6.50
$10.50
$157.50
$243.00
SCENARIO A
SCENARIO B
“SARAH PROPOSES 12 EQUAL PAYMENTS TO
LIQUIDATE THE DEBT. IN THIS SCENARIO
JOHN WOULD HAVE TO COVER 12 EQUAL
PAYMENTS OF $19.64 (THOUSANDS OF
DOLLAR) TO ACQUIT THE DEBT. ”
“THE PROPOSAL IS TO MAKE 10
DIFFERENT PAYMENTS AND AN
AMOUNT AT THE END FOR THE
DIFFERENCE.
IN THIS CASE JOHN WOULD COVER
SMALL PAYMENT DURING 2019
AND 2020, KNOWING THAT ON
2021 HE WILL RECEIVE AN IMPOR-
TANT AMOUNT THAT WILL ALLOW
HIM TO LIQUIDATE THE DEBT.

5. PROMISSORY
NOTES
1
2
3
4
5
6
7
8
EXPIRED AND
NOT EXPIRED
afd
afd
afd
afd
afd
afd
afd
afd
YEAR
2019
2019
2019
2020
2020
2020
2020
2021
DAYS TO
FOCAL DATE
50
110
160
222
270
321
470
511
TOTAL:
AMOUNT
K DLS.
$27.5
$27.5
$27.5
$27.5
$27.5
$32.27
$32.27
$32.27
$234.30
SCENARIO C
SARAH PROPOSES 8 PAYMENTS, 5 WITH SIMI-
LAR AMOUNTS OF $27.5 AND THE THREE-RE-
MAINING WITH SIMILAR AMOUNTS.
AS THE PREVIOUS CASES, THIS DIFFERENTIAL
INTEGRATES THE TRANSACTION COST AND
THE AMOUNTS DERIVED FROM THE
ADJUSTMENTS MADE IN VOD OF ALL THE PRO-
MISSORY NOTES THAT ARE RESTRUCTURED IN
THE NEW PAYMENT SCHEME.
“THE PROPOSAL OF THE EQUIVA-
LENT EQUATION MODEL HAS THE
PURPOSE OF SEEKING BALANCE
BETWEEN THE PARTIES.”
“THE DEBTOR SEEKS A DEFERRAL OVER
TIME, ALLOWING A BETTER MANAGE-
MENT OF HIS CASH FLOW AND GENERA-
TING BETTER SOLVENCY, IN ORDER TO
PAY HIS COMMITMENTS.”
“ON THE OTHER HAND, THE CREDITOR
WOULD REQUEST AND ADDITIONAL
BENEFIT, BEING IN THIS CASE THE MO-
RATORIUM INTEREST ACCRUED AND
TRANSACTION COST IN HIS FAVOR”.
“THIS MODEL IS NOT THE ONLY OPTION TO RENE-
GOTIATE DEBT; IT IS AT LEAST A SCHEME WHICH
SEEKS TO SET UP A MUTUAL BALANCE BETWEEN
THE NEEDS OF BOTH DEBTORS AND CREDITORS.”
THIS COMIC WITH AN ACADEMIC PURPOSE WAS MADE BY RAQUEL ALCÁNTARA MENDOZA AND FRANCISCO AMEZCUA PAREDES