Periodic discount rate and Redemption value: Difference between pages

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Periodic discount rate is a cost of borrowing - or rate of return - expressed as:
The amount of the cash payment or equivalent consideration to the holder, on the redemption of a security.


*The excess of the amount at the end over the amount at the start
*Divided by the amount at the end


 
== See also ==
==Calculating periodic discount rate from start and end cash==
* [[Face value]]
 
* [[Par]]
Given the cash amounts at the start and end of an investment or borrowing period, we can calculate the periodic discount rate.
* [[Premium]]
 
* [[Redemption]]
 
* [[Security]]
<span style="color:#4B0082">'''Example 1: Discount rate of 2.91%'''</span>
* [[Spens clause]]
 
* [[Undated]]
GBP 1 million is borrowed.
 
GBP 1.03 million is repayable at the end of the period.
 
 
The periodic discount rate (d) is:
 
d = (End amount - Start amount) / End amount
 
Which can also be expressed as:
 
d = (End - Start) / End
 
= (1.03 - 1) / 1.03
 
= 0.029126
 
= '''2.9126%'''
 
 
<span style="color:#4B0082">'''Example 2: Discount rate of 3%'''</span>
 
GBP 0.97 million is borrowed or invested
 
GBP 1.00 million is repayable at the end of the period.
 
 
The periodic discount rate (d) is:
 
= (End - Start) / End
 
 
= (1.00 - 0.97) / 1.00
 
= 0.030000
 
= '''3.0000%'''
 
 
==Calculating end cash from periodic discount rate==
 
We can also work this relationship in the other direction.
 
Given the cash amount at the start of an investment or borrowing period, together with the periodic discount rate, we can calculate the end amount.
 
 
<span style="color:#4B0082">'''Example 3: End amount from periodic discount rate'''</span>
 
GBP  0.97 million is borrowed.
 
The periodic discount rate is 3.0000%.
 
Calculate the amount repayable at the end of the period.
 
 
'''''Solution'''''
 
The periodic discount rate (d) is:
 
d = (End - Start) / End
 
 
d = (End / End) - (Start / End)
 
 
d = 1 - (Start / End)
 
 
''Rearranging this relationship:''
 
1 - d = (Start / End)
 
 
End = Start / (1 - d)
 
 
''Substituting the given information into this relationship:''
 
End = 0.97 / (1 - 0.030000)
 
 
= 0.97 / 0.97
 
 
= '''GBP 1.00m'''
 
 
==Calculating start cash from periodic discount rate==
 
We can also work the same relationship reversing the direction of time travel.
 
Given the cash amount at the end of an investment or borrowing period, again together with the periodic discount rate, we can calculate the start amount.
 
 
<span style="color:#4B0082">'''Example 4: Start amount from periodic discount rate'''</span>
 
An investment will pay out a single amount of GBP 1.00m at its final maturity after one period.
 
The periodic discount rate is 3.0000%.
 
Calculate the amount invested at the start of the period.
 
 
'''''Solution'''''
 
As before, the periodic discount rate (d) is defined as:
 
d = (End - Start) / End
 
 
d = 1 - (Start / End)
 
 
''Rearranging this relationship:''
 
(Start / End) = 1 - d
 
 
Start = End x (1 - d)
 
 
''Substitute the given data into this relationship:''
 
Start = 1.00 x (1 - 0.030000)
 
= '''GBP 0.97m'''
 
 
==Periodic yield==
 
The periodic discount rate (d) is also related to the [[periodic yield]] (r), and each can be calculated from the other.
 
 
====Conversion formulae (d to r and r to d)====
 
r = d / (1 - d)
 
d = r / (1 + r)
 
 
''Where:''
 
r = periodic interest rate or yield
 
d = periodic discount rate
 
 
 
==See also==
 
*[[Effective annual rate]]
*[[Certificate in Treasury Fundamentals]]
*[[Certificate in Treasury]]
*[[Discount rate]]
*[[Nominal annual rate]]
*[[Periodic yield]]
*[[Yield]]


[[Category:Corporate_finance]]
[[Category:Corporate_finance]]
[[Category:Intercompany_funding]]
[[Category:Investment]]
[[Category:Long_term_funding]]
[[Category:Identify_and_assess_risks]]
[[Category:Manage_risks]]
[[Category:Risk_frameworks]]
[[Category:Financial_products_and_markets]]

Latest revision as of 22:59, 19 April 2020

The amount of the cash payment or equivalent consideration to the holder, on the redemption of a security.


See also