Financial Exercises 5: Investment Timing - Versionsgeschichte

Wikimeister am 24. Januar 2013 um 17:12 Uhr

2013-01-24T17:12:46Z

← Nächstältere Version		Version vom 24. Januar 2013, 19:12 Uhr
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	''by Clemens Werkmeister''		''by Clemens Werkmeister''

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Wikimeister am 12. Januar 2012 um 15:24 Uhr

2012-01-12T15:24:16Z

← Nächstältere Version		Version vom 12. Januar 2012, 17:24 Uhr
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	c. Calculate the present values of felling in years 11 to 15.<br/>		c. Calculate the present values of felling in years 11 to 15.<br/>
	d. Given your calculations, what is the best year for felling the trees?<br/>		d. Given your calculations, what is the best year for felling the trees?<br/>


	=== 2. Timing of [[Ersatzproblem\|replacement]] (the case of perpetual investment chains) ===		=== 2. Timing of [[Ersatzproblem\|replacement]] (the case of perpetual investment chains) ===
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	b. Calculate the NPVs if the wine is sold after year 1, 2, …, 5. Which is the best year to put the wine into market?<br/>		b. Calculate the NPVs if the wine is sold after year 1, 2, …, 5. Which is the best year to put the wine into market?<br/>
	c. Since the barrels that guarantee the extraordinary flavour of Jim Wean’s wines are scarce and hard to get, they are reused. What does this mean for the best age of marketing Jim Wean’s wines? Compare the annuities.<br/>		c. Since the barrels that guarantee the extraordinary flavour of Jim Wean’s wines are scarce and hard to get, they are reused. What does this mean for the best age of marketing Jim Wean’s wines? Compare the annuities.<br/>


	=== 4. Comparing investment proposals with different lifetimes ===		=== 4. Comparing investment proposals with different lifetimes ===

Wikimeister: /* 3. Life cycles of single investments and investment chains */

2012-01-12T15:23:50Z

3. Life cycles of single investments and investment chains

← Nächstältere Version		Version vom 12. Januar 2012, 17:23 Uhr
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	Jim Weam produces premium wine whose extraordinary flavour depends on the old barrels he uses. The cost of grapes and processing are 150 € per barrel. Handling and preparing the barrel every other year of maturing costs 10 €. While maturing in barrels up to five years, the wine price increases. The following table lists the expected revenues per barrel if the wine is sold after x years of maturing:<br/>		Jim Weam produces premium wine whose extraordinary flavour depends on the old barrels he uses. The cost of grapes and processing are 150 € per barrel. Handling and preparing the barrel every other year of maturing costs 10 €. While maturing in barrels up to five years, the wine price increases. The following table lists the expected revenues per barrel if the wine is sold after x years of maturing:<br/>

			{\|align="left" border="1" cellpadding="3" cellspacing="0"
	{\|align="~~center~~" border="1" cellpadding="3" cellspacing="0"
	\|- align="center"		\|- align="center"
	\|years of maturing\|\| cash flows if sold in year\|\| annual costs until sale		\|years of maturing\|\| cash flows if sold in year\|\| annual costs until sale
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	\|0\|\|600 \|\|		\|0\|\|600 \|\|
	\|}		\|}
	<br>		<br style="clear:left;"/>

			a. Forecast the cash flows for every year until the sales year.<br/>
	a. Forecast the cash flows for ~~each~~ year until the sales year.<br/>
	b. Calculate the NPVs if the wine is sold after year 1, 2, …, 5. Which is the best year to put the wine into market?<br/>		b. Calculate the NPVs if the wine is sold after year 1, 2, …, 5. Which is the best year to put the wine into market?<br/>
	c. Since the barrels that guarantee the extraordinary flavour of Jim Wean’s wines are scarce and hard to get, they are reused. What does this mean for the best age of marketing Jim Wean’s wines? Compare the annuities.<br/>		c. Since the barrels that guarantee the extraordinary flavour of Jim Wean’s wines are scarce and hard to get, they are reused. What does this mean for the best age of marketing Jim Wean’s wines? Compare the annuities.<br/>


	=== 4. Comparing investment proposals with different lifetimes ===		=== 4. Comparing investment proposals with different lifetimes ===

Wikimeister: /* 1. Timing of a single investment */

2012-01-12T15:22:31Z

1. Timing of a single investment

← Nächstältere Version		Version vom 12. Januar 2012, 17:22 Uhr
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	Ten years ago, John Walden planted Nordman fir trees. The plan is to fell them and sell them as christmas trees. For reasons of efficiency, it is best to fell the complete lot. But John can decide whether to harvest the trees early or to wait and get higher revenues for larger trees. The following table contains the expected revenues for felling the trees in the given year. Walden assumes a 10 % cost of capital.<br/>		Ten years ago, John Walden planted Nordman fir trees. The plan is to fell them and sell them as christmas trees. For reasons of efficiency, it is best to fell the complete lot. But John can decide whether to harvest the trees early or to wait and get higher revenues for larger trees. The following table contains the expected revenues for felling the trees in the given year. Walden assumes a 10 % cost of capital.<br/>

			{\|align="left" border="1" cellpadding="3" cellspacing="0"
	{\|align="~~center~~" border="1" cellpadding="3" cellspacing="0"
	\|- align="center"		\|- align="center"
	\|year\|\| alternative cash flows		\|year\|\| alternative cash flows
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	\|0\|\|180		\|0\|\|180
	\|}		\|}

			<br style="clear:left;"/>
	<br>		<br>

	a. Calculate the additional annual cash flow and the opportunity cost of capital for deferring the felling to years 11 to 15. Calculate the difference between additional cash flows and opportunity costs (the economic value added) for years 11 to 15. <br/>		a. Calculate the additional annual cash flow and the opportunity cost of capital for deferring the felling to years 11 to 15. Calculate the difference between additional cash flows and opportunity costs (the economic value added) for years 11 to 15. <br/>
	b. Calculate for years 11 to 15 the percentage change of revenues compared to the previous year.<br/>		b. Calculate for years 11 to 15 the percentage change of revenues compared to the previous year.<br/>
	c. Calculate the present values of felling in years 11 to 15.<br/>		c. Calculate the present values of felling in years 11 to 15.<br/>
	d. Given your calculations, what is the best year for felling the trees?<br/>		d. Given your calculations, what is the best year for felling the trees?<br/>


	=== 2. Timing of [[Ersatzproblem\|replacement]] (the case of perpetual investment chains) ===		=== 2. Timing of [[Ersatzproblem\|replacement]] (the case of perpetual investment chains) ===

Wikimeister am 5. Januar 2012 um 09:07 Uhr

2012-01-05T09:07:21Z

← Nächstältere Version		Version vom 5. Januar 2012, 11:07 Uhr
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	<br>		<br>

	(a) Calculate the additional annual cash flow and the opportunity cost of capital for deferring the felling to years 11 to 15. Calculate the difference between additional cash flows and opportunity costs (the economic value added) for years 11 to 15. <br/>		a. Calculate the additional annual cash flow and the opportunity cost of capital for deferring the felling to years 11 to 15. Calculate the difference between additional cash flows and opportunity costs (the economic value added) for years 11 to 15. <br/>
	(b) Calculate for years 11 to 15 the percentage change of revenues compared to the previous year.<br/>		b. Calculate for years 11 to 15 the percentage change of revenues compared to the previous year.<br/>
	(c) Calculate the present values of felling in years 11 to 15.<br/>		c. Calculate the present values of felling in years 11 to 15.<br/>
	(d) Given your calculations, what is the best year for felling the trees?<br/>		d. Given your calculations, what is the best year for felling the trees?<br/>


	=== 2. Timing of [[Ersatzproblem\|replacement]] (the case of perpetual investment chains) ===		=== 2. Timing of [[Ersatzproblem\|replacement]] (the case of perpetual investment chains) ===
	John Walden plans to reuse the area for the next generation of christmas trees of the same kind. Hence, the same expected revenues apply again after the life cycle of the trees.<br/>		John Walden plans to reuse the area for the next generation of christmas trees of the same kind. Hence, the same expected revenues apply again after the life cycle of the trees.<br/>
	(a) Calculate the annuity of the revenues over the different lifetimes (11 to 15 years).<br/>		a. Calculate the annuity of the revenues over the different lifetimes (11 to 15 years).<br/>
	(b) At what age is it best to fell the christmas trees in this case?<br/>		b. At what age is it best to fell the christmas trees in this case?<br/>


Zeile 63:		Zeile 63:


	(a) Forecast the cash flows for each year until the sales year.<br/>		a. Forecast the cash flows for each year until the sales year.<br/>
	(b) Calculate the NPVs if the wine is sold after year 1, 2, …, 5. Which is the best year to put the wine into market?<br/>		b. Calculate the NPVs if the wine is sold after year 1, 2, …, 5. Which is the best year to put the wine into market?<br/>
	(c) Since the barrels that guarantee the extraordinary flavour of Jim Wean’s wines are scarce and hard to get, they are reused. What does this mean for the best age of marketing Jim Wean’s wines? Compare the annuities.<br/>		c. Since the barrels that guarantee the extraordinary flavour of Jim Wean’s wines are scarce and hard to get, they are reused. What does this mean for the best age of marketing Jim Wean’s wines? Compare the annuities.<br/>

Wikimeister: /* 4. Comparing investment proposals with different lifetimes */

2012-01-05T09:06:18Z

4. Comparing investment proposals with different lifetimes

← Nächstältere Version		Version vom 5. Januar 2012, 11:06 Uhr
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	=== 4. Comparing investment proposals with different lifetimes ===		=== 4. Comparing investment proposals with different lifetimes ===
	A ski resort plans to install a new lift and is analyzing two different proposals. Proposal A requires an initial investment of 5 million Euro and annual maintenance cost of 900,000 Euro. The corresponding figures for proposal B are 3 million Euro of initial investment and 1.2 million Euro of annual maintenance cost. Proposal A has to be replaced after nine years, proposal B after six years.<br/>		A ski resort plans to install a new lift and is analyzing two different proposals. Proposal A requires an initial investment of 5 million Euro and annual maintenance cost of 900,000 Euro. The corresponding figures for proposal B are 3 million Euro of initial investment and 1.2 million Euro of annual maintenance cost. Proposal A has to be replaced after nine years, proposal B after six years.<br/>
	(a) Calculate the NPV and the annuity (equal annual cost – EAC) of the lift proposals.<br/>		a. Calculate the NPV and the annuity (equal annual cost – EAC) of the lift proposals.<br/>
	(b) Which is the better project if you expect to quit operations after the economic lifetime of the lift?<br/>		b. Which is the better project if you expect to quit operations after the economic lifetime of the lift?<br/>
	(c) What happens if we assume annual revenues of 2 million Euro, independent of the kind of lift?<br/>		c. What happens if we assume annual revenues of 2 million Euro, independent of the kind of lift?<br/>
	(d) Which lift would you buy if you plan to use similar lifts for at least 18 years?<br/>		d. Which lift would you buy if you plan to use similar lifts for at least 18 years?<br/>

Wikimeister am 5. Januar 2012 um 08:54 Uhr

2012-01-05T08:54:48Z

← Nächstältere Version		Version vom 5. Januar 2012, 10:54 Uhr
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	=== 1. Timing of a single investment ===		=== 1. [[Timing]] of a single investment ===

	Ten years ago, John Walden planted Nordman fir trees. The plan is to fell them and sell them as christmas trees. For reasons of efficiency, it is best to fell the complete lot. But John can decide whether to harvest the trees early or to wait and get higher revenues for larger trees. The following table contains the expected revenues for felling the trees in the given year. Walden assumes a 10 % cost of capital.<br/>		Ten years ago, John Walden planted Nordman fir trees. The plan is to fell them and sell them as christmas trees. For reasons of efficiency, it is best to fell the complete lot. But John can decide whether to harvest the trees early or to wait and get higher revenues for larger trees. The following table contains the expected revenues for felling the trees in the given year. Walden assumes a 10 % cost of capital.<br/>



Zeile 19:		Zeile 18:
	\|1\|\|125		\|1\|\|125
	\|- align="center"		\|- align="center"
	\|2\|\|145 \|}		\|2\|\|145
	\|- align="center"		\|- align="center"
	\|3\|\|160		\|3\|\|160
Zeile 26:		Zeile 25:
	\|- align="center"		\|- align="center"
	\|0\|\|180		\|0\|\|180
	\|		\|}
	<br/>		<br>

	~~year alternative cash flows~~


	~~10 100~~
	~~11 125~~
	~~12 145~~
	~~13 160~~
	~~14 170~~
	~~15 180~~

	(a) Calculate the additional annual cash flow and the opportunity cost of capital for deferring the felling to years 11 to 15. Calculate the difference between additional cash flows and opportunity costs (the economic value added) for years 11 to 15. <br/>		(a) Calculate the additional annual cash flow and the opportunity cost of capital for deferring the felling to years 11 to 15. Calculate the difference between additional cash flows and opportunity costs (the economic value added) for years 11 to 15. <br/>
Zeile 44:		Zeile 33:
	(d) Given your calculations, what is the best year for felling the trees?<br/>		(d) Given your calculations, what is the best year for felling the trees?<br/>

	=== 2. Timing of ~~repeated projects~~ (the case of perpetual investment chains) ===
			=== 2. Timing of [[Ersatzproblem\|replacement]] (the case of perpetual investment chains) ===
	John Walden plans to reuse the area for the next generation of christmas trees of the same kind. Hence, the same expected revenues apply again after the life cycle of the trees.<br/>		John Walden plans to reuse the area for the next generation of christmas trees of the same kind. Hence, the same expected revenues apply again after the life cycle of the trees.<br/>
	(a) Calculate the annuity of the revenues over the different lifetimes (11 to 15 years).<br/>		(a) Calculate the annuity of the revenues over the different lifetimes (11 to 15 years).<br/>
	(b) At what age is it best to fell the christmas trees in this case?<br/>		(b) At what age is it best to fell the christmas trees in this case?<br/>

	=== 3. Life cycles of single investments and investment chains ===
			=== 3. Life cycles of single investments and [[Investitionskette\|investment chains]] ===
	Jim Weam produces premium wine whose extraordinary flavour depends on the old barrels he uses. The cost of grapes and processing are 150 € per barrel. Handling and preparing the barrel every other year of maturing costs 10 €. While maturing in barrels up to five years, the wine price increases. The following table lists the expected revenues per barrel if the wine is sold after x years of maturing:<br/>		Jim Weam produces premium wine whose extraordinary flavour depends on the old barrels he uses. The cost of grapes and processing are 150 € per barrel. Handling and preparing the barrel every other year of maturing costs 10 €. While maturing in barrels up to five years, the wine price increases. The following table lists the expected revenues per barrel if the wine is sold after x years of maturing:<br/>
	years of ~~matu-ring~~ cash flows if sold in year annual costs until ~~sales~~

	0 150		{\|align="center" border="1" cellpadding="3" cellspacing="0"
	1 230 10		\|- align="center"
	2 340 10		\|years of maturing\|\| cash flows if sold in year\|\| annual costs until sale
	3 470 10		\|- align="center"
	4 510 10		\|0\|\| \|\| 150
	5 600		\|- align="center"
			\|1\|\|230 \|\| 10
			\|- align="center"
			\|2\|\|340 \|\| 10
			\|- align="center"
			\|3\|\|470 \|\| 10
			\|- align="center"
			\|4\|\|510 \|\| 10
			\|- align="center"
			\|0\|\|600 \|\|
			\|}
			<br>


	(a) Forecast the cash flows for each year until the sales year.<br/>		(a) Forecast the cash flows for each year until the sales year.<br/>
	(b) Calculate the NPVs if the wine is sold after year 1, 2, …, 5. Which is the best year to put the wine into market?<br/>		(b) Calculate the NPVs if the wine is sold after year 1, 2, …, 5. Which is the best year to put the wine into market?<br/>
	(c) Since the barrels that guarantee the extraordinary flavour of Jim Wean’s wines are scarce and hard to get, they are reused. What does this mean for the best age of marketing Jim Wean’s wines? Compare the annuities.<br/>		(c) Since the barrels that guarantee the extraordinary flavour of Jim Wean’s wines are scarce and hard to get, they are reused. What does this mean for the best age of marketing Jim Wean’s wines? Compare the annuities.<br/>


	=== 4. Comparing investment proposals with different lifetimes ===		=== 4. Comparing investment proposals with different lifetimes ===
	A ski resort plans to install a new lift and is analyzing two different proposals. Proposal A requires an initial investment of 5 million Euro and annual maintenance cost of 900,00 Euro. The corresponding figures for proposal B are 3 million Euro of initial investment and 1.2 million Euro of annual maintenance cost. Proposal A has to be replaced after nine years, proposal B after six years.<br/>		A ski resort plans to install a new lift and is analyzing two different proposals. Proposal A requires an initial investment of 5 million Euro and annual maintenance cost of 900,000 Euro. The corresponding figures for proposal B are 3 million Euro of initial investment and 1.2 million Euro of annual maintenance cost. Proposal A has to be replaced after nine years, proposal B after six years.<br/>
	(a) Calculate the NPV and the annuity (equal annual cost – EAC) of the lift proposals.<br/>		(a) Calculate the NPV and the annuity (equal annual cost – EAC) of the lift proposals.<br/>
	(b) Which is the better project if you expect to quit operations after the economic lifetime of the lift?<br/>		(b) Which is the better project if you expect to quit operations after the economic lifetime of the lift?<br/>
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	---<br/>		---<br/>
	[[Financial Resources Formulary]]		References:<br>
	[[Financial Exercises]]		[[Financial Resources Formulary]]<br>
	[[Timing\|Investment Timing]]		[[Financial Exercises]]<br>
			[[Timing\|Investment Timing]]<br>

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=== 1. Timing of a single investment ===

Ten years ago, John Walden planted Nordman fir trees. The plan is to fell them and sell them as christmas trees. For reasons of efficiency, it is best to fell the complete lot. But John can decide whether to harvest the trees early or to wait and get higher revenues for larger trees. The following table contains the expected revenues for felling the trees in the given year. Walden assumes a 10 % cost of capital. 

{|align="center" border="1" cellpadding="3" cellspacing="0"
|- align="center"
|year|| alternative cash flows
|- align="center"
|0||100
|- align="center"
|1||125
|- align="center"
|2||145 |}
|- align="center"
|3||160
|- align="center"
|4||170
|- align="center"
|0||180
|
 

year alternative cash flows

10 100
11 125
12 145
13 160
14 170
15 180

(a) Calculate the additional annual cash flow and the opportunity cost of capital for deferring the felling to years 11 to 15. Calculate the difference between additional cash flows and opportunity costs (the economic value added) for years 11 to 15. 
(b) Calculate for years 11 to 15 the percentage change of revenues compared to the previous year. 
(c) Calculate the present values of felling in years 11 to 15. 
(d) Given your calculations, what is the best year for felling the trees? 

=== 2. Timing of repeated projects (the case of perpetual investment chains) ===
John Walden plans to reuse the area for the next generation of christmas trees of the same kind. Hence, the same expected revenues apply again after the life cycle of the trees. 
(a) Calculate the annuity of the revenues over the different lifetimes (11 to 15 years). 
(b) At what age is it best to fell the christmas trees in this case? 

=== 3. Life cycles of single investments and investment chains ===
Jim Weam produces premium wine whose extraordinary flavour depends on the old barrels he uses. The cost of grapes and processing are 150 € per barrel. Handling and preparing the barrel every other year of maturing costs 10 €. While maturing in barrels up to five years, the wine price increases. The following table lists the expected revenues per barrel if the wine is sold after x years of maturing: 
years of matu-ring cash flows if sold in year annual costs until sales

0 150
1 230 10
2 340 10
3 470 10
4 510 10
5 600

(a) Forecast the cash flows for each year until the sales year. 
(b) Calculate the NPVs if the wine is sold after year 1, 2, …, 5. Which is the best year to put the wine into market? 
(c) Since the barrels that guarantee the extraordinary flavour of Jim Wean’s wines are scarce and hard to get, they are reused. What does this mean for the best age of marketing Jim Wean’s wines? Compare the annuities. 

=== 4. Comparing investment proposals with different lifetimes ===
A ski resort plans to install a new lift and is analyzing two different proposals. Proposal A requires an initial investment of 5 million Euro and annual maintenance cost of 900,00 Euro. The corresponding figures for proposal B are 3 million Euro of initial investment and 1.2 million Euro of annual maintenance cost. Proposal A has to be replaced after nine years, proposal B after six years. 
(a) Calculate the NPV and the annuity (equal annual cost – EAC) of the lift proposals. 
(b) Which is the better project if you expect to quit operations after the economic lifetime of the lift? 
(c) What happens if we assume annual revenues of 2 million Euro, independent of the kind of lift? 
(d) Which lift would you buy if you plan to use similar lifts for at least 18 years? 

--- 
[[Financial Resources Formulary]]
[[Financial Exercises]]
[[Timing|Investment Timing]]