Discount rate and Periodic discount rate: Difference between pages

From ACT Wiki
(Difference between pages)
Jump to navigationJump to search
imported>Doug Williamson
(Link with Periodic discount rate page.)
 
imported>Doug Williamson
(Layout)
 
Line 1: Line 1:
1.
__NOTOC__
A cost of borrowing - or rate of return - expressed as:


The quoted market rate for traded instruments quoted at a discount.
*The excess of the amount at the end over the amount at the start
*Divided by the amount at the end


The market discount rate is quoted based on a percentage of the ''maturity amount''.


==Example 1==
GBP 1 million is borrowed.


<span style="color:#4B0082">'''Example 1: Discount rate calculation'''</span>
GBP 1.03 million is repayable at the end of the period.


The maturity amount for an investment is £10m.


The gain for the single period from the start to the final maturity is £2m.
The periodic discount rate (d) is:
 
d = (End amount - start amount) / End amount
 
= (1.03 - 1) / 1.03
 
= 0.029126
 
= '''2.9126%'''
 
 
==Example 2==
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:
The periodic discount rate (d) is:


(d) = Gain / End amount
(End amount - start amount) / End amount
 
= (1.00 - 0.97) /  1.00
 
= 0.030000
 
= '''3.0000%'''
 
 
==Example 3==
GBP  0.97 million is borrowed.


= 2 / 10
The periodic discount rate is 3.0000%.


= '''20%'''
Calculate the amount repayable at the end of the period.


===Solution===
The periodic discount rate (d) is defined as:


In the US the market discount rate is sometimes known as the ''discount yield''.
d = (End amount - start amount) / End amount


This is different from a [[yield]] or interest rate, which is conventionally quoted based on a percentage of the ''starting amount''.
d = 1 - (Start amount / End amount)




<span style="color:#4B0082">'''Example 2: Yield calculation'''</span>
''Rearranging this relationship:''


The starting amount for an investment is £8m.
(Start amount / End amount) = 1 - d


The gain for the single period from the start to the final maturity is £2m.
Start amount = End amount x (1 - d)


The periodic yield (r) is:
Start amount / (1 - d) = End amount


(r) = Gain / Start amount
End amount = Start amount / (1 - d)


= 2 / 8


= '''25%'''
''Substituting the given information into this relationship:''


End amount = GBP 0.97m / (1 - 0.030000)


Notice that the discount rate and the yield calculated above both relate to exactly the same deal.
= GBP 0.97m / 0.97


£8m is invested now, and £10m is repaid at the end of one period.
= '''GBP 1.00m'''


The discount rate of 20% and the yield of 25% both summarise the same deal, using different conventional bases.


==Example 4==
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%.


2.  
Calculate the amount invested at the start of the period.


Cost of capital.
===Solution===
As before, the periodic discount rate (d) is defined as:


The yield used to calculate [[discount factor]]s and present values.
d = (End amount - start amount) / End amount


d = 1 - (Start amount / End amount)


3.


The rate used to discount future liabilities of a Defined benefit pension scheme in order to calculate the present value of the liabilities, often for the purpose of comparing them with the market value of the scheme’s assets. 
''Rearranging this relationship:''


Historically it was common to use the blended rate of investment return expected on the actual assets in the scheme, but typically now a market rate is used, such as the government bond or AA corporate bond yield for a fixed income security with a similar duration to that of the underlying liabilities.
(Start amount / End amount) = 1 - d


Start amount = End amount x (1 - d)


4.


In the US, the interest rate that member banks pay the Federal Reserve when the banks use securities as collateral.  The discount rate acts as a benchmark for interest rates issued. 
''Substitute the given data into this relationship:''


Other central banks also have similar discount rates.
Start amount = GBP 1.00m x (1 - 0.030000)


= '''GBP 0.97m'''


== See also ==
* [[CertFMM]]
* [[Cost of capital]]
* [[Discount]]
* [[Discount basis]]
* [[Discount instruments]]
* [[Discounted cash flow]]
* [[Interest rate]]
* [[Monetary policy]]
* [[Nominal annual discount rate]]
* [[Periodic discount rate]]
* [[Periodic rate]]
* [[Yield]]




===Other links===
==See also==
[http://www.treasurers.org/node/8837 Students: Triumph with timelines, The Treasurer, March 2013]


[[Category:Corporate_finance]]
*[[Effective annual rate]]
*[[Discount rate]]
*[[Nominal annual rate]]
*[[Periodic yield]]
*[[Yield]]

Revision as of 15:04, 26 October 2015

A cost of borrowing - or rate of return - expressed as:

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


Example 1

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

= (1.03 - 1) / 1.03

= 0.029126

= 2.9126%


Example 2

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 amount - start amount) / End amount

= (1.00 - 0.97) / 1.00

= 0.030000

= 3.0000%


Example 3

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 defined as:

d = (End amount - start amount) / End amount

d = 1 - (Start amount / End amount)


Rearranging this relationship:

(Start amount / End amount) = 1 - d

Start amount = End amount x (1 - d)

Start amount / (1 - d) = End amount

End amount = Start amount / (1 - d)


Substituting the given information into this relationship:

End amount = GBP 0.97m / (1 - 0.030000)

= GBP 0.97m / 0.97

= 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 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 amount - start amount) / End amount

d = 1 - (Start amount / End amount)


Rearranging this relationship:

(Start amount / End amount) = 1 - d

Start amount = End amount x (1 - d)


Substitute the given data into this relationship:

Start amount = GBP 1.00m x (1 - 0.030000)

= GBP 0.97m


See also

Retrieved from ‘https://wiki.treasurers.org/w/index.php?title=Discount_rate&oldid=37283’