Factoring and Periodic yield: Difference between pages

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The sale or transfer by a supplier of legal title to accounts receivable (invoices).
__NOTOC__
Periodic yield is a rate of return - or cost of borrowing - expressed as the proportion by which the amount at the end of the period exceeds the amount at the start.  


The supplier sells or transfers title to the receivables to a third party known as a factor.


The arrangement can be either with or without recourse.
<span style="color:#4B0082">'''Example 1'''</span>


GBP 1 million is borrowed or invested.


Factoring is often a convenient - but relatively expensive - form of finance for weaker corporate credits.
GBP 1.03 million is repayable at the end of the period.  


The supplier sells its invoices, at a discount, to the factor. The factor then becomes responsible for collecting the debt.


A factoring agreement between the factor and a client sets out the terms on which a factoring arrangement is made.
The periodic yield (r) is:


r = (End amount / Start amount) - 1


As noted above, factoring arrangements can be with or without recourse.
Which can also be expressed as:


Recourse factoring allows the factor to recover from the supplier/borrower any losses caused by bad debts.
r = (End / Start) - 1


''or''


== See also ==
r = <math>\frac{End}{Start}</math> - 1


* [[Factors]]
 
* [[Confidential factoring]]
= <math>\frac{1.03}{1}</math> - 1
* [[Domestic factoring]]
 
* [[Export factoring]]
= 0.03
* [[Import factoring]]
 
* [[Internal factoring]]
= '''3%'''
* [[International factoring]]
 
* [[Invoice discounting]]
 
* [[Recourse]]
<span style="color:#4B0082">'''Example 2'''</span>
* [[Securitisation]]
 
GBP  0.97 million is borrowed or invested.
 
GBP 1.00 million is repayable at the end of the period.
 
 
The periodic yield (r) is:
 
r = <math>\frac{End}{Start}</math> - 1
 
 
= <math>\frac{1.00}{0.97}</math> - 1
 
= 0.030928
 
= '''3.0928%'''
 
 
''Check:''
 
Amount at end = 0.97 x 1.030928 = 1.00, as expected.
 
 
<span style="color:#4B0082">'''Example 3'''</span>
 
GBP  0.97 million is invested.
 
The periodic yield is 3.0928%.
 
Calculate the amount repayable at the end of the period.
 
 
'''''Solution'''''
 
The periodic yield (r) is defined as:
 
r = <math>\frac{End}{Start}</math> - 1
 
 
''Rearranging this relationship:''
 
1 + r = <math>\frac{End}{Start}</math>
 
 
End = Start x (1 + r)
 
 
''Substituting the given information into this relationship:''
 
End = GBP 0.97m x (1 + 0.030928)
 
= '''GBP 1.00m'''
 
 
<span style="color:#4B0082">'''Example 4'''</span>
 
An investment will pay out a single amount of GBP 1.00m at its final maturity after one period.
 
The periodic yield is 3.0928%.
 
Calculate the amount invested at the start of the period.
 
 
'''''Solution'''''
 
As before, the periodic yield (r) is defined as:
 
r = <math>\frac{End}{Start}</math> - 1
 
 
''Rearranging this relationship:''
 
1 + r = <math>\frac{End}{Start}</math>
 
 
Start = <math>\frac{End}{(1 + r)}</math>
 
 
''Substitute the given data into this relationship:''
 
Start = <math>\frac{1.00}{(1  +  0.030928)}</math>
 
 
= '''GBP 0.97m'''
 
 
''Check:''
 
Amount at start = 0.97 x 1.030928 = 1.00, as expected.
 
 
====Effective annual rate====
 
The periodic yield (r) is related to the [[effective annual rate]] (EAR), and each can be calculated from the other.
 
 
'''''Conversion formulae (r to EAR and EAR to r):'''''
 
EAR = (1 + r)<sup>n</sup> - 1
 
r = (1 + EAR)<sup>(1/n)</sup> - 1
 
 
Where:
 
EAR = effective annual rate or yield
 
r = periodic interest rate or yield, as before
 
n = number of times the period fits into a calendar year
 
 
====Periodic discount rate====
 
The periodic yield (r) is also related to the [[periodic discount rate]] (d), and each can be calculated from the other.
 
 
'''''Conversion formulae (r to d and d to r):'''''
 
d = r / (1 + r)
 
r = d / (1 - d)
 
 
Where:
 
d = periodic discount rate
 
r = periodic interest rate or yield
 
 
==See also==
 
*[[Effective annual rate]]
*[[Discount rate]]
*[[Nominal annual rate]]
*[[Nominal annual yield]]
*[[Periodic discount rate]]
*[[Yield]]
*[[Forward yield]]
*[[Zero coupon yield]]
*[[Par yield]]
 
 
===Other resources===
[[Media:2013_09_Sept_-_Simple_solutions.pdf| The Treasurer students, Simple solutions]]

Revision as of 22:14, 22 November 2015

Periodic yield is a rate of return - or cost of borrowing - expressed as the proportion by which the amount at the end of the period exceeds the amount at the start.


Example 1

GBP 1 million is borrowed or invested.

GBP 1.03 million is repayable at the end of the period.


The periodic yield (r) is:

r = (End amount / Start amount) - 1

Which can also be expressed as:

r = (End / Start) - 1

or

r = <math>\frac{End}{Start}</math> - 1


= <math>\frac{1.03}{1}</math> - 1

= 0.03

= 3%


Example 2

GBP 0.97 million is borrowed or invested.

GBP 1.00 million is repayable at the end of the period.


The periodic yield (r) is:

r = <math>\frac{End}{Start}</math> - 1


= <math>\frac{1.00}{0.97}</math> - 1

= 0.030928

= 3.0928%


Check:

Amount at end = 0.97 x 1.030928 = 1.00, as expected.


Example 3

GBP 0.97 million is invested.

The periodic yield is 3.0928%.

Calculate the amount repayable at the end of the period.


Solution

The periodic yield (r) is defined as:

r = <math>\frac{End}{Start}</math> - 1


Rearranging this relationship:

1 + r = <math>\frac{End}{Start}</math>


End = Start x (1 + r)


Substituting the given information into this relationship:

End = GBP 0.97m x (1 + 0.030928)

= GBP 1.00m


Example 4

An investment will pay out a single amount of GBP 1.00m at its final maturity after one period.

The periodic yield is 3.0928%.

Calculate the amount invested at the start of the period.


Solution

As before, the periodic yield (r) is defined as:

r = <math>\frac{End}{Start}</math> - 1


Rearranging this relationship:

1 + r = <math>\frac{End}{Start}</math>


Start = <math>\frac{End}{(1 + r)}</math>


Substitute the given data into this relationship:

Start = <math>\frac{1.00}{(1 + 0.030928)}</math>


= GBP 0.97m


Check:

Amount at start = 0.97 x 1.030928 = 1.00, as expected.


Effective annual rate

The periodic yield (r) is related to the effective annual rate (EAR), and each can be calculated from the other.


Conversion formulae (r to EAR and EAR to r):

EAR = (1 + r)n - 1

r = (1 + EAR)(1/n) - 1


Where:

EAR = effective annual rate or yield

r = periodic interest rate or yield, as before

n = number of times the period fits into a calendar year


Periodic discount rate

The periodic yield (r) is also related to the periodic discount rate (d), and each can be calculated from the other.


Conversion formulae (r to d and d to r):

d = r / (1 + r)

r = d / (1 - d)


Where:

d = periodic discount rate

r = periodic interest rate or yield


See also


Other resources

The Treasurer students, Simple solutions