Perpetuity - Revision history

imported>Doug Williamson: Add link.

2021-06-12T13:25:31Z

Add link.

← Older revision		Revision as of 13:25, 12 June 2021
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	== See also ==		== See also ==
	* [[Annuity]]		* [[Annuity]]
			* [[Consol]]
	* [[Discounted cash flow]]		* [[Discounted cash flow]]
	* [[Dividend growth model]]		* [[Dividend growth model]]

imported>Doug Williamson: Layout.

2021-06-12T12:45:32Z

Layout.

← Older revision		Revision as of 12:45, 12 June 2021
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	2. ''Fixed perpetuity''		2. ''Fixed perpetuity.''

	A fixed perpetuity is a periodic cash flow starting one period in the future, then carrying on for ever thereafter.		A fixed perpetuity is a periodic cash flow starting one period in the future, then carrying on for ever thereafter.
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	3. ''Growing perpetuity''		3. ''Growing perpetuity.''

	A growing perpetuity is an infinite series of cash flows, modelled to grow by a constant proportionate amount every period.		A growing perpetuity is an infinite series of cash flows, modelled to grow by a constant proportionate amount every period.
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	4. ''Declining perpetuity''		4. ''Declining perpetuity.''

	Growth can be negative, in other words, decline.		Growth can be negative, in other words, decline.

imported>Doug Williamson: Add links.

2021-04-08T13:19:40Z

Add links.

← Older revision		Revision as of 13:19, 8 April 2021
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	1.		1. ''Valuation.''

	A series of cash flows modelled to carry on for an infinite amount of time in the future.		A series of cash flows modelled to carry on for an infinite amount of time in the future.


	2. '''Fixed perpetuity'''		2. ''Fixed perpetuity''

	A fixed perpetuity is a periodic cash flow starting one period in the future, then carrying on for ever thereafter.		A fixed perpetuity is a periodic cash flow starting one period in the future, then carrying on for ever thereafter.
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	3. '''Growing perpetuity'''		3. ''Growing perpetuity''

	A growing perpetuity is an infinite series of cash flows, modelled to grow by a constant proportionate amount every period.		A growing perpetuity is an infinite series of cash flows, modelled to grow by a constant proportionate amount every period.
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	4. '''Declining perpetuity'''		4. ''Declining perpetuity''

	Growth can be negative, in other words, decline.		Growth can be negative, in other words, decline.
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	== See also ==		== See also ==
	* [[Annuity]]		* [[Annuity]]
			* [[Discounted cash flow]]
	* [[Dividend growth model]]		* [[Dividend growth model]]
	* [[Growing annuity]]		* [[Growing annuity]]
	* [[Growing perpetuity]]		* [[Growing perpetuity]]
			* [[Growing perpetuity factor]]
	* [[Irredeemable]]		* [[Irredeemable]]
	* [[Perpetuity due]]		* [[Perpetuity due]]
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	==~~Student article~~==		==The Treasurer articles==
	[[Media:2013_10_Oct_-_The_real_deal.pdf\| The real deal, The Treasurer]]		[[Media:2013_10_Oct_-_The_real_deal.pdf\| The real deal, The Treasurer]]

imported>Doug Williamson: Layout.

2020-04-20T00:44:20Z

Layout.

← Older revision		Revision as of 00:44, 20 April 2020
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	''Real rates of corporate decline often lead to miscalculation, overpaying for acquisitions and disastrous losses.''		''Real rates of corporate decline often lead to miscalculation, overpaying for acquisitions and disastrous losses.''

	''Read this article to discover how to avoid the most common errors and add value for your organisation.''		''Read this article to discover how to avoid the most common errors, and add value for your organisation.''

	[[Category:Corporate_finance]]		[[Category:Corporate_finance]]
	[[Category:Long_term_funding]]		[[Category:Long_term_funding]]

imported>Doug Williamson: Layout.

2017-12-31T14:09:51Z

Layout.

← Older revision		Revision as of 14:09, 31 December 2017
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	* [[Perpetuity factor]]		* [[Perpetuity factor]]
	* [[Simple annuity]]		* [[Simple annuity]]


	==Student article==		==Student article==

imported>Doug Williamson: Update links.

2017-12-31T14:09:25Z

Update links.

← Older revision		Revision as of 14:09, 31 December 2017
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	* [[Annuity]]		* [[Annuity]]
	* [[Dividend growth model]]		* [[Dividend growth model]]
			* [[Growing annuity]]
	* [[Growing perpetuity]]		* [[Growing perpetuity]]
	* [[Irredeemable]]		* [[Irredeemable]]
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	* [[Perpetuity factor]]		* [[Perpetuity factor]]
	* [[Simple annuity]]		* [[Simple annuity]]
	* [[Growing annuity]]



	==Student article==		==Student article==

imported>Doug Williamson: Update cost of capital to 5%.

2017-12-31T12:23:41Z

Update cost of capital to 5%.

← Older revision		Revision as of 12:23, 31 December 2017
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	Time 1 cash flow = $10m, continuing at the same amount each period thereafter in perpetuity.		Time 1 cash flow = $10m, continuing at the same amount each period thereafter in perpetuity.

	Periodic cost of capital = 10%		Periodic cost of capital = 5%

	The present value of the fixed perpetuity is:		The present value of the fixed perpetuity is:

	= $10m x (1 / 0.10)		= $10m x (1 / 0.05)

	= $10m x 10		= $10m x 20

	= $'''~~100~~'''m		= $'''200'''m


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	Time 1 cash flow = $10m, growing by a constant percentage amount each period thereafter in perpetuity.		Time 1 cash flow = $10m, growing by a constant percentage amount each period thereafter in perpetuity.

	Periodic cost of capital = 10%.		Periodic cost of capital = 5%.

	Periodic growth rate = 2%		Periodic growth rate = 2%
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	= A<sub>1</sub> x 1 / (r - g)		= A<sub>1</sub> x 1 / (r - g)

	= $10m x (1 / (0.10 - 0.02) )		= $10m x (1 / (0.05 - 0.02) )

	= $10m x (1 / 0.08)		= $10m x (1 / 0.03)

	= $10m x 12.5		= $10m x 33.3

	= $'''~~125~~'''m		= $'''333'''m


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	Time 1 cash flow = $10m, declining by a constant percentage amount each period thereafter in perpetuity.		Time 1 cash flow = $10m, declining by a constant percentage amount each period thereafter in perpetuity.

	Periodic cost of capital = 10%.		Periodic cost of capital = 5%.

	Periodic growth rate = -(2)% negative = -0.02		Periodic growth rate = -(2)% negative = -0.02
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	= A<sub>1</sub> x 1 / (r - g)		= A<sub>1</sub> x 1 / (r - g)

	= $10m x (1 / (0.10 - -0.02) )		= $10m x (1 / (0.05 - -0.02) )

	= $10m x (1 / 0.12)		= $10m x (1 / 0.07)

	= $10m x 8.33		= $10m x 14.3

	= $'''~~83.3~~'''m		= $'''143'''m


	The negative rate of growth in the cash flow has reduced the total present value substantially.		The small negative rate of growth in the cash flow has reduced the total present value very substantially.



	The growing perpetuity concept is applied in many contexts.		The growing / declining perpetuity concept is applied in many contexts.

	For example, the Dividend growth model for share valuation.		For example, the Dividend growth model for share valuation.

imported>Doug Williamson: Add declining perpetuity example.

2017-12-31T12:19:29Z

Add declining perpetuity example.

← Older revision		Revision as of 12:19, 31 December 2017
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	The modest rate of growth in the cash flow has added substantially to the total present value.		The modest rate of growth in the cash flow has added substantially to the total present value.




			4. '''Declining perpetuity'''

			Growth can be negative, in other words, decline.

			For a declining perpetuity, the present value formula is the same as the growing perpetuity, but the growth rate (g) is entered as a negative number as follows:


			<span style="color:#4B0082">'''Example 3: Declining perpetuity valuation'''</span>

			Time 1 cash flow = $10m, declining by a constant percentage amount each period thereafter in perpetuity.

			Periodic cost of capital = 10%.

			Periodic growth rate = -(2)% negative = -0.02


			The present value of the declining perpetuity is:

			= A<sub>1</sub> x 1 / (r - g)

			= $10m x (1 / (0.10 - -0.02) )

			= $10m x (1 / 0.12)

			= $10m x 8.33

			= $'''83.3'''m


			The negative rate of growth in the cash flow has reduced the total present value substantially.

imported>Doug Williamson: Add case study link.

2017-12-31T09:47:47Z

Add case study link.

← Older revision		Revision as of 09:47, 31 December 2017
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	* [[Simple annuity]]		* [[Simple annuity]]
	* [[Growing annuity]]		* [[Growing annuity]]



			==Student article==
			[[Media:2013_10_Oct_-_The_real_deal.pdf\| The real deal, The Treasurer]]

			''Real rates of corporate decline often lead to miscalculation, overpaying for acquisitions and disastrous losses.''

			''Read this article to discover how to avoid the most common errors and add value for your organisation.''

	[[Category:Corporate_finance]]		[[Category:Corporate_finance]]
	[[Category:Long_term_funding]]		[[Category:Long_term_funding]]

imported>Doug Williamson: Add examples.

2017-08-20T15:00:24Z

Add examples.

← Older revision		Revision as of 15:00, 20 August 2017
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	r = periodic cost of capital		r = periodic cost of capital


			<span style="color:#4B0082">'''Example 1: Fixed perpetuity valuation'''</span>

			Time 1 cash flow = $10m, continuing at the same amount each period thereafter in perpetuity.

			Periodic cost of capital = 10%

			The present value of the fixed perpetuity is:

			= $10m x (1 / 0.10)

			= $10m x 10

			= $'''100'''m



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	where g = the periodic rate of growth of the cash flow.		where g = the periodic rate of growth of the cash flow.


			<span style="color:#4B0082">'''Example 2: Growing perpetuity valuation'''</span>

			Time 1 cash flow = $10m, growing by a constant percentage amount each period thereafter in perpetuity.

			Periodic cost of capital = 10%.

			Periodic growth rate = 2%


			The present value of the growing perpetuity is:

			= A<sub>1</sub> x 1 / (r - g)

			= $10m x (1 / (0.10 - 0.02) )

			= $10m x (1 / 0.08)

			= $10m x 12.5

			= $'''125'''m


			The modest rate of growth in the cash flow has added substantially to the total present value.