Discounted payback - Revision history

imported>Doug Williamson: Add link.

2019-09-04T15:07:49Z

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	== See also ==		== See also ==
			* [[Investment appraisal]]
	* [[Payback]]		* [[Payback]]
	* [[Present value]]		* [[Present value]]

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

imported>Doug Williamson: Removed hence and replaced with .. at future Times 1 to 6 years respectively.

2015-05-30T16:03:15Z

Removed hence and replaced with .. at future Times 1 to 6 years respectively.

← Older revision		Revision as of 16:03, 30 May 2015
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	and will then pay out annual amounts of $10m, $20m, $30m, $40m, $50m and $60m,		and will then pay out annual amounts of $10m, $20m, $30m, $40m, $50m and $60m,

	at Times 1 to 6 years ~~hence~~ respectively.		at future Times 1 to 6 years respectively.

	The relevant cost of capital is 10% per year.		The relevant cost of capital is 10% per year.

imported>Doug Williamson: Standardise appearance of page

2015-03-21T17:00:22Z

Standardise appearance of page

← Older revision		Revision as of 17:00, 21 March 2015
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	~~For example a~~ proposal requires an initial investment of $100m at Time 0 years, and will then pay out annual amounts of $10m, $20m, $30m, $40m, $50m and $60m at Times 1 to 6 years hence respectively.		'''Example'''

			A proposal requires an initial investment of $100m at Time 0 years,

			and will then pay out annual amounts of $10m, $20m, $30m, $40m, $50m and $60m,

			at Times 1 to 6 years hence respectively.

	The relevant cost of capital is 10% per year.		The relevant cost of capital is 10% per year.
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	<u>Discounted cash flows:</u>		<u>Discounted cash flows:</u>

	Time 0: $(100)m x 1.10<sup>0</sup> ~~= $(100)m.~~		'''Time 0:''' (100) x 1.10<sup>0</sup>

	~~Time 1: $10m x 1.10<sup>-1</sup>~~ = $~~9.09m~~.		= $(100)m.

	~~Time 2: $20m x 1.10<sup>-2</sup> = $16.53m.~~

	Time 3: ~~$30m~~ x 1.10<sup>-3</sup> ~~= $22.54m.~~		'''Time 1:''' 10 x 1.10<sup>-1</sup>

	Time 4: ~~$40m~~ x 1.10<sup>-4</sup> = $27.32m.		= $9.09m.


			'''Time 2:''' 20 x 1.10<sup>-2</sup>

			= $16.53m.


			'''Time 3:''' 30 x 1.10<sup>-3</sup>

			= $22.54m.


			'''Time 4:''' 40 x 1.10<sup>-4</sup>

			= $27.32m.


			'''Time 5:''' 50 x 1.10<sup>-5</sup>

			= $31.05m.

	~~Time 5: $50m x 1.10<sup>-5</sup> = $31.05m.~~


	<u>Cumulative discounted cash flows:</u>		<u>Cumulative discounted cash flows:</u>

	Time 0: $(~~100~~)m.		'''Time 0:''' (100).


			'''Time 1:''' (100) + 9.09

			= $(90.91)m.


			'''Time 2:''' (90.91) + 16.53

			= $(74.38)m.


			'''Time 3:''' (74.38) + 22.54

			= $(51.84)m.


	Time 1: $(~~100~~)m + ~~$9.09m = $(90.91)m~~.		'''Time 4:''' (51.84) + 27.32

	~~Time 2: $(90.91)m + $16.53m~~ = $(74.38)m.		= $(24.52)m.

	~~Time 3: $(74.38)m + $22.54m = $(51.84)m.~~

	Time 4: ~~$(51.84)m + $27.32m = $~~(24.52)m.		'''Time 5:''' (24.52) + 31.05

	~~Time 5: $(24.52)m + $31.05m~~ = +$6.53m.		= +$6.53m.

imported>Doug Williamson: Spacing.

2014-07-29T20:15:03Z

Spacing.

← Older revision		Revision as of 20:15, 29 July 2014
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	For example a proposal requires an initial investment of $100m at Time 0 years, and will then pay out annual amounts of $10m, $20m, $30m, $40m, $50m and $60m at Times 1 to 6 years hence respectively. The relevant cost of capital is 10% per year.		For example a proposal requires an initial investment of $100m at Time 0 years, and will then pay out annual amounts of $10m, $20m, $30m, $40m, $50m and $60m at Times 1 to 6 years hence respectively.

			The relevant cost of capital is 10% per year.


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	* [[Present value]]		* [[Present value]]

	[[Category:~~Investment_Appraisal~~]]		[[Category:Corporate_finance]]

imported>Doug Williamson: Spacing and reduce Fog Factor by splitting up long sentences. Categorise the page.

2014-07-29T20:09:50Z

Spacing and reduce Fog Factor by splitting up long sentences. Categorise the page.

← Older revision		Revision as of 20:09, 29 July 2014
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	A variant of the payback method of investment appraisal ~~in which~~ amounts of money arising in different time periods are discounted to their present values.		Discounted payback is a variant of the [[payback]] method of investment appraisal.

			Under discounted payback, the amounts of money arising in different time periods are discounted to their present values.


	For example a proposal requires an initial investment of $100m at Time 0 years, and will then pay out annual amounts of $10m, $20m, $30m, $40m, $50m and $60m at Times 1 to 6 years hence respectively. The relevant cost of capital is 10% per year.		For example a proposal requires an initial investment of $100m at Time 0 years, and will then pay out annual amounts of $10m, $20m, $30m, $40m, $50m and $60m at Times 1 to 6 years hence respectively. The relevant cost of capital is 10% per year.


	The cumulative discounted net cash flow and discounted payback period are calculated as follows:		The cumulative discounted net cash flow and discounted payback period are calculated as follows:

	<u>Discounted cash flows:</u>		<u>Discounted cash flows:</u>

	Time 0: $(100)m x 1.10<sup>0</sup> = $(100)m.		Time 0: $(100)m x 1.10<sup>0</sup> = $(100)m.

	Time 1: $10m x 1.10<sup>-1</sup> = $9.09m.		Time 1: $10m x 1.10<sup>-1</sup> = $9.09m.

	Time 2: $20m x 1.10<sup>-2</sup> = $16.53m.		Time 2: $20m x 1.10<sup>-2</sup> = $16.53m.

	Time 3: $30m x 1.10<sup>-3</sup> = $22.54m.		Time 3: $30m x 1.10<sup>-3</sup> = $22.54m.

	Time 4: $40m x 1.10<sup>-4</sup> = $27.32m.		Time 4: $40m x 1.10<sup>-4</sup> = $27.32m.

	Time 5: $50m x 1.10<sup>-5</sup> = $31.05m.		Time 5: $50m x 1.10<sup>-5</sup> = $31.05m.


	<u>Cumulative discounted cash flows:</u>		<u>Cumulative discounted cash flows:</u>

	Time 0: $(100)m.		Time 0: $(100)m.

	Time 1: $(100)m + $9.09m = $(90.91)m.		Time 1: $(100)m + $9.09m = $(90.91)m.

	Time 2: $(90.91)m + $16.53m = $(74.38)m.		Time 2: $(90.91)m + $16.53m = $(74.38)m.

	Time 3: $(74.38)m + $22.54m = $(51.84)m.		Time 3: $(74.38)m + $22.54m = $(51.84)m.

	Time 4: $(51.84)m + $27.32m = $(24.52)m.		Time 4: $(51.84)m + $27.32m = $(24.52)m.

	Time 5: $(24.52)m + $31.05m = +$6.53m.		Time 5: $(24.52)m + $31.05m = +$6.53m.


	The initial investment has paid back by the end of 5 years, so the payback period to the nearest whole year is 5 years.		The initial investment has paid back by the end of 5 years, so the payback period to the nearest whole year is 5 years.
	~~It is also possible to calculate a more refined estimate using interpolation between 4 years and 5 years, by assuming that the cash flows arise evenly over the course of the 5th year.~~

	This method removes some of the problems of the simple payback method~~, but~~ still leaves significant problems and simplifying assumptions.		It is also possible to calculate a more refined estimate using interpolation between 4 years and 5 years. Interpolation assumes that the cash flows arise evenly over the course of the 5th year.


			This method removes some of the problems of the simple payback method. But it still leaves significant problems and simplifying assumptions.


	== See also ==		== See also ==
	* [[Payback]]		* [[Payback]]
	* [[Present value]]		* [[Present value]]


			[[Category:Investment_Appraisal]]

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2012-10-23T14:19:25Z

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A variant of the payback method of investment appraisal in which amounts of money arising in different time periods are discounted to their present values.

For example a proposal requires an initial investment of $100m at Time 0 years, and will then pay out annual amounts of $10m, $20m, $30m, $40m, $50m and $60m at Times 1 to 6 years hence respectively. The relevant cost of capital is 10% per year.

The cumulative discounted net cash flow and discounted payback period are calculated as follows:

Discounted cash flows:
Time 0: $(100)m x 1.100 = $(100)m.
Time 1: $10m x 1.10-1 = $9.09m.
Time 2: $20m x 1.10-2 = $16.53m.
Time 3: $30m x 1.10-3 = $22.54m.
Time 4: $40m x 1.10-4 = $27.32m.
Time 5: $50m x 1.10-5 = $31.05m.

Cumulative discounted cash flows:
Time 0: $(100)m.
Time 1: $(100)m + $9.09m = $(90.91)m.
Time 2: $(90.91)m + $16.53m = $(74.38)m.
Time 3: $(74.38)m + $22.54m = $(51.84)m.
Time 4: $(51.84)m + $27.32m = $(24.52)m.
Time 5: $(24.52)m + $31.05m = +$6.53m.

The initial investment has paid back by the end of 5 years, so the payback period to the nearest whole year is 5 years.
It is also possible to calculate a more refined estimate using interpolation between 4 years and 5 years, by assuming that the cash flows arise evenly over the course of the 5th year.

This method removes some of the problems of the simple payback method, but still leaves significant problems and simplifying assumptions.

== See also ==
* [[Payback]]
* [[Present value]]