Periodic discount rate - Revision history

imported>Doug Williamson: Categorise.

2018-02-22T12:03:26Z

Categorise.

← Older revision		Revision as of 12:03, 22 February 2018
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	*[[Periodic yield]]		*[[Periodic yield]]
	*[[Yield]]		*[[Yield]]

			[[Category:Corporate_finance]]

imported>Doug Williamson: Mend broken mathtype equations.

2016-12-14T12:27:47Z

Mend broken mathtype equations.

← Older revision		Revision as of 12:27, 14 December 2016
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	d = (End - Start) / End		d = (End - Start) / End

	~~''or''~~		= (1.03 - 1) / 1.03

	d = ~~<math>\frac{(End - Start)}{End}</math>~~


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

	= 0.029126		= 0.029126
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	The periodic discount rate (d) is:		The periodic discount rate (d) is:

	= ~~<math>\frac{~~(End - Start)}{End~~}</math>~~		= (End - Start) / End


	= ~~<math>\frac{~~(1.00 - 0.97)}{1.00~~}</math>~~		= (1.00 - 0.97) / 1.00

	= 0.030000		= 0.030000
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	'''''Solution'''''		'''''Solution'''''

	The periodic discount rate (d) is ~~defined as~~:		The periodic discount rate (d) is:

	d = ~~<math>\frac{~~(End - Start)}{End~~}</math>~~		d = (End - Start) / End


	d = ~~<math>\frac{~~End}{End~~}</math>~~ - ~~<math>\frac{~~Start}{End~~}</math>~~		d = (End / End) - (Start / End)


	d = 1 - ~~<math>\frac{~~Start}{End~~}</math>~~		d = 1 - (Start / End)


	''Rearranging this relationship:''		''Rearranging this relationship:''

	1 - d = ~~<math>\frac{~~Start}{End~~}</math>~~		1 - d = (Start / End)


	End = ~~<math>\frac{~~Start}{(1-d)~~}</math>~~		End = Start / (1 - d)


	''Substituting the given information into this relationship:''		''Substituting the given information into this relationship:''

	End = ~~<math>\frac{~~0.97}{(1 - 0.030000)~~}</math>~~		End = 0.97 / (1 - 0.030000)


	= ~~<math>\frac{~~0.97}{0.97~~}</math>~~		= 0.97 / 0.97


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	As before, the periodic discount rate (d) is defined as:		As before, the periodic discount rate (d) is defined as:

	d = ~~<math>\frac{~~(End - Start)}{End~~}</math>~~		d = (End - Start) / End


	d = 1 - ~~<math>\frac{~~Start}{End~~}</math>~~		d = 1 - (Start / End)


	''Rearranging this relationship:''		''Rearranging this relationship:''

	~~<math>\frac{~~Start}{End~~}</math>~~ = 1 - d		(Start / End) = 1 - d

imported>Doug Williamson: Standardise headings with examples

2015-12-02T12:09:14Z

Standardise headings with examples

← Older revision		Revision as of 12:09, 2 December 2015
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	~~__NOTOC__~~
	Periodic discount rate is a cost of borrowing - or rate of return - expressed as:		Periodic discount rate is a cost of borrowing - or rate of return - expressed as:

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	====Example 1~~====~~		==Calculating periodic discount rate from start and end cash==

			Given the cash amounts at the start and end of an investment or borrowing period, we can calculate the periodic discount rate.


			<span style="color:#4B0082">'''Example 1: Discount rate of 2.91%'''</span>

	GBP 1 million is borrowed.		GBP 1 million is borrowed.
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	=~~===~~Example 2~~====~~		<span style="color:#4B0082">'''Example 2: Discount rate of 3%'''</span>

	GBP 0.97 million is borrowed or invested		GBP 0.97 million is borrowed or invested
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	====Example 3~~====~~		==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.		GBP 0.97 million is borrowed.
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	====Example 4~~====~~		==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.		An investment will pay out a single amount of GBP 1.00m at its final maturity after one period.
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	====Periodic yield====		==Periodic yield==

	The periodic discount rate (d) is also related to the [[periodic yield]] (r), and each can be calculated from the other.		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)~~:'''''~~		====Conversion formulae (d to r and r to d)====

	r = d / (1 - d)		r = d / (1 - d)

imported>Doug Williamson: Layout.

2015-11-21T17:29:42Z

Layout.

← Older revision		Revision as of 17:29, 21 November 2015
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	Where:		''Where:''

	r = periodic interest rate or yield		r = periodic interest rate or yield

imported>Doug Williamson: Link with periodic yield.

2015-11-01T10:02:40Z

Link with periodic yield.

← Older revision		Revision as of 10:02, 1 November 2015
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	= '''GBP 0.97m'''		= '''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

imported>Doug Williamson at 14:37, 28 October 2015

2015-10-28T14:37:43Z

← Older revision		Revision as of 14:37, 28 October 2015
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	The periodic discount rate (d) is:		The periodic discount rate (d) is:

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

	Which can also be expressed as:		Which can also be expressed as:
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	''Substituting the given information into this relationship:''		''Substituting the given information into this relationship:''

	End = <math>\frac{0.97}{(1 - 0.030000}</math>		End = <math>\frac{0.97}{(1 - 0.030000)}</math>

imported>Doug Williamson: Expand example

2015-10-28T14:13:34Z

Expand example

← Older revision		Revision as of 14:13, 28 October 2015
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	__NOTOC__		__NOTOC__
	A cost of borrowing - or rate of return - expressed as:		Periodic discount rate is a cost of borrowing - or rate of return - expressed as:

	*The excess of the amount at the end over the amount at the start		*The excess of the amount at the end over the amount at the start
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	==Example 1==		====Example 1====

	GBP 1 million is borrowed.		GBP 1 million is borrowed.

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

	~~''or''~~		Which can also be expressed as:

	d = (End - Start) / End		d = (End - Start) / End

			''or''

	= (1.03 - 1) / 1.03		d = <math>\frac{(End - Start)}{End}</math>


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

	= 0.029126		= 0.029126
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	==Example 2==		====Example 2====

	GBP 0.97 million is borrowed or invested		GBP 0.97 million is borrowed or invested

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	The periodic discount rate (d) is:		The periodic discount rate (d) is:

	= (End - Start) / ~~End~~		= <math>\frac{(End - Start)}{End}</math>


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

	= 0.030000		= 0.030000
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	==Example 3==		====Example 3====

	GBP 0.97 million is borrowed.		GBP 0.97 million is borrowed.

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	Calculate the amount repayable at the end of the period.		Calculate the amount repayable at the end of the period.

	~~===~~Solution~~===~~
			'''''Solution'''''

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

	d = (End - Start) / ~~End~~		d = <math>\frac{(End - Start)}{End}</math>

	~~d = (End / End) - (Start / End)~~

	d = 1 - (Start / ~~End)~~		d = <math>\frac{End}{End}</math> - <math>\frac{Start}{End}</math>


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


	''Rearranging this relationship:''		''Rearranging this relationship:''

	~~(Start / End) =~~ 1 - d		1 - d = <math>\frac{Start}{End}</math>

	~~Start = End x (1 - d)~~

	Start / (1 - d) ~~= End~~		End = <math>\frac{Start}{(1-d)}</math>

	~~End = Start / (1 - d)~~

			''Substituting the given information into this relationship:''

			End = <math>\frac{0.97}{(1 - 0.030000}</math>

	~~''Substituting the given information into this relationship:''~~

	~~End~~ = ~~GBP~~ 0.~~97m / (1 -~~ 0.~~030000)~~		= <math>\frac{0.97}{0.97}</math>

	~~= GBP 0.97m / 0.97~~

	= '''GBP 1.00m'''		= '''GBP 1.00m'''


	==Example 4==		====Example 4====

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

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

	~~===~~Solution~~===~~
			'''''Solution'''''

	As before, the periodic discount rate (d) is defined as:		As before, the periodic discount rate (d) is defined as:

	d = (End - Start) / ~~End~~		d = <math>\frac{(End - Start)}{End}</math>


	d = 1 - (Start/ ~~End)~~		d = 1 - <math>\frac{Start}{End}</math>


	''Rearranging this relationship:''		''Rearranging this relationship:''

	(Start / ~~End)~~ = 1 - d		<math>\frac{Start}{End}</math> = 1 - d


	Start = End x (1 - d)		Start = End x (1 - d)
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	''Substitute the given data into this relationship:''		''Substitute the given data into this relationship:''

	Start = ~~GBP~~ 1.~~00m~~ x (1 - 0.030000)		Start = 1.00 x (1 - 0.030000)

	= '''GBP 0.97m'''		= '''GBP 0.97m'''

imported>Doug Williamson: Expand example

2015-10-28T10:11:32Z

Expand example

← Older revision		Revision as of 10:11, 28 October 2015
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	d = (End amount - start amount) / End amount		d = (End amount - start amount) / End amount

			''or''

			d = (End - Start) / End


	= (1.03 - 1) / 1.03		= (1.03 - 1) / 1.03
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	The periodic discount rate (d) is:		The periodic discount rate (d) is:

	(End ~~amount~~ - ~~start amount~~) / End ~~amount~~		= (End - Start) / End

	= (1.00 - 0.97) / 1.00		= (1.00 - 0.97) / 1.00

	= 0.030000		= 0.030000
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	The periodic discount rate (d) is defined as:		The periodic discount rate (d) is defined as:

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

			d = (End / End) - (Start / End)

	d = 1 - (Start ~~amount~~ / End ~~amount~~)		d = 1 - (Start / End)


	''Rearranging this relationship:''		''Rearranging this relationship:''

	(Start ~~amount~~ / End ~~amount~~) = 1 - d		(Start / End) = 1 - d

	Start ~~amount~~ = End ~~amount~~ x (1 - d)		Start = End x (1 - d)

	Start ~~amount~~ / (1 - d) = End ~~amount~~		Start / (1 - d) = End

	End ~~amount~~ = Start ~~amount~~ / (1 - d)		End = Start / (1 - d)


	''Substituting the given information into this relationship:''		''Substituting the given information into this relationship:''

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

	= GBP 0.97m / 0.97		= GBP 0.97m / 0.97
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	As before, the periodic discount rate (d) is defined as:		As before, the periodic discount rate (d) is defined as:

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

	d = 1 - (Start ~~amount~~ / End ~~amount~~)		d = 1 - (Start/ End)


	''Rearranging this relationship:''		''Rearranging this relationship:''

	(Start ~~amount~~ / End ~~amount~~) = 1 - d		(Start / End) = 1 - d

	Start ~~amount~~ = End ~~amount~~ x (1 - d)		Start = End x (1 - d)


	''Substitute the given data into this relationship:''		''Substitute the given data into this relationship:''

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

	= '''GBP 0.97m'''		= '''GBP 0.97m'''

imported>Doug Williamson: Add links.

2015-10-27T11:06:02Z

Add links.

← Older revision		Revision as of 11:06, 27 October 2015
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	*[[Effective annual rate]]		*[[Effective annual rate]]
			*[[Certificate in Treasury Fundamentals]]
			*[[Certificate in Treasury]]
	*[[Discount rate]]		*[[Discount rate]]
	*[[Nominal annual rate]]		*[[Nominal annual rate]]
	*[[Periodic yield]]		*[[Periodic yield]]
	*[[Yield]]		*[[Yield]]

imported>Doug Williamson: Layout

2015-10-26T15:04:33Z

Layout

← Older revision		Revision as of 15:04, 26 October 2015
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	Rearranging this relationship:		''Rearranging this relationship:''

	(Start amount / End amount) = 1 - d		(Start amount / End amount) = 1 - d
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	Substituting the given information into this relationship:		''Substituting the given information into this relationship:''

	End amount = GBP 0.97m / (1 - 0.030000)		End amount = GBP 0.97m / (1 - 0.030000)
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	Rearranging this relationship:		''Rearranging this relationship:''

	(Start amount / End amount) = 1 - d		(Start amount / End amount) = 1 - d
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	Substitute the given data into this relationship:		''Substitute the given data into this relationship:''

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