Time value of money: Difference between revisions
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[[File:Wimpy.jpg|framed | [[File:Wimpy.jpg|framed|right|Figure 1. J. Wellington Wimpy,<ref>Image found: https://www.flickr.com/photos/abeckstrom/5504735515 (Accessed September 3rd, 2016).</ref> a cartoon character (and a friend of Popeye the sailor) from the 1930s famously said "I would gladly pay you Tuesday for a hamburger today!"<ref>Yale book of quotations by Fred Shapiro, pg 677 (accessed online on September 3rd, 2016): https://books.google.ca/books?id=w5-GR-qtgXsC&pg=PA677&redir_esc=y&hl=en#v=onepage&q&f=false</ref>]] | ||
<onlyinclude>Money that is held now is worth more than the same amount of money later.</onlyinclude><ref>The Economist. “Time Value of Money.” [Online], Available: http://www.economist.com/economics-a-to-z/t#node-21529371[May. 29, 2016].</ref>. This was stated rather famously by J. Wellington Wimpy (from the Popeye comic strip, see Figure 1): "I would gladly pay you Tuesday for a hamburger today!" Money that one currently holds can begin to earn interest immediately; $1000 today can grow in an account with an interest rate of 5% per year to $1050. The same $1000 received one year in the future is only worth $952.38 because it cannot earn interest over the year. In short, ''money in the present is worth more than in the future because that money can grow.'' | |||
<onlyinclude>Money that is held now is worth more than the same amount of money later.</onlyinclude><ref>The Economist. “Time Value of Money.” [Online], Available: http://www.economist.com/economics-a-to-z/t#node-21529371[May. 29, 2016].</ref>. This was stated rather famously by J. Wellington Wimpy (from the Popeye comic strip, see | |||
===Present Discounted Value (PDV)=== | ===Present Discounted Value (PDV)=== | ||
Economists have worked out a mathematical way to say how much future money or a stream of money is worth today. This is determined by the '''[[discount rate]]''', how much the value of money in the future is reduced to get the present value.<ref>R.S. Pindyck and D.L. Rubinfeld. ''Microeconomics.'' New Jersey: Pearson, 2013, pp. 255-256.</ref> If a firm is going to be paid $1000 in one year with an annual interest rate of 5% then it can calculate how much that money is worth today: | Economists have worked out a mathematical way to say how much future money or a stream of money is worth today. This is determined by the '''[[discount rate]]''', how much the value of money in the future is reduced to get the present value.<ref>R.S. Pindyck and D.L. Rubinfeld. ''Microeconomics.'' New Jersey: Pearson, 2013, pp. 255-256.</ref> If a firm is going to be paid $1000 in one year with an annual interest rate of 5% then it can calculate how much that money is worth today: | ||
::::::::PDV=<math>\frac{1000}{(1+R)}</math> → PDV= $952.38 | |||
::::::::::<big>PDV=<math>\frac{a}{(1+R)ⁿ}</math></big> | |||
:::<br /> | |||
{| class="wikitable" | |||
|+ | |||
| '''<big>a</big>''' | |||
| colspan="2" |the future amount | |||
|- | |||
| rowspan="3" | '''<big>(1+R)<sup>n</sup></big>''' | |||
|'''R''' | |||
|the interest rate | |||
|- | |||
|'''1+R''' | |||
|the amount of interest accrued over one year | |||
|- | |||
|'''n''' | |||
|the number of years over which the payment is due | |||
|} | |||
::::::::::PDV=<math>\frac{1000}{(1+R)ⁿ}</math> → PDV= $952.38 | |||
==Time is Money== | ==Time is Money== | ||
A firm that decides to build a [[nuclear power plant]] | A firm that decides to build a [[nuclear power plant]] has to accept a lower PDV of the money allocated for such a project. Due to capital intensive nature of nuclear plant construction and the significant amount of time it take to complete, the PDV is much lower than it would be if the money was allocated for another project such as a combined cycle gas turbine plant.<blockquote>In 2024, the cost of building a small modular reactor [[nuclear power plant]] (with six 80 MW small modular reactors) would be $8,936 /kW, which is ''$4,289,280'' at a net nominal capacity of 480 kW. Whereas, the cost for a simple cycle [[Hydrocarbon combustion|combustion]] turbine plant would be $836 /kW, which is ''$350,284'' at a net nominal capacity of 419 kW.<ref name=":0">EIA (2024). (Accessed July 15, 2026). ''Capital Cost and Performance Characteristic Estimates for Utility Scale Electric Power Generating Technologies'' [Online]. Available: https://www.eia.gov/analysis/studies/powerplants/capitalcost/pdf/capital_cost_AEO2025.pdf</ref></blockquote>The nuclear plant has a much higher [[capital cost|''capital cost'']] (initial cost to build). A major limiting factor of a nuclear reactor is the construction time. A nuclear plant takes approximately 42 months to construct, this is often after a long an rigorous approval process.<ref name=":0" /> A simple cycle combustion turbine plant takes approximately 22 months to construct.<ref name=":0" /> The long time horizon for a nuclear project means that the PDV of a firms capital is less than for a CT plant project. Needless to say, a firm needs to make a profit to survive and a 3.5 year period (long construction for a nuclear power plant) is a very long time to have an investment not yielding [[revenue]]. | ||
== | ==For Further Reading== | ||
*[[Discount rate]] | *[[Discount rate]] | ||
*[[Discounting]] | *[[Discounting]] | ||
*[[Profit]] | |||
*Or explore a [[Special:Random|random page]] | |||
==References== | ==References== | ||
{{reflist}} | {{reflist}} | ||
[[Category: Uploaded]] | |||
Latest revision as of 20:43, 4 August 2026
Money that is held now is worth more than the same amount of money later.[3]. This was stated rather famously by J. Wellington Wimpy (from the Popeye comic strip, see Figure 1): "I would gladly pay you Tuesday for a hamburger today!" Money that one currently holds can begin to earn interest immediately; $1000 today can grow in an account with an interest rate of 5% per year to $1050. The same $1000 received one year in the future is only worth $952.38 because it cannot earn interest over the year. In short, money in the present is worth more than in the future because that money can grow.
Present Discounted Value (PDV)
Economists have worked out a mathematical way to say how much future money or a stream of money is worth today. This is determined by the discount rate, how much the value of money in the future is reduced to get the present value.[4] If a firm is going to be paid $1000 in one year with an annual interest rate of 5% then it can calculate how much that money is worth today:
- PDV=Failed to parse (syntax error): {\displaystyle \frac{a}{(1+R)ⁿ}}
| a | the future amount | |
| (1+R)n | R | the interest rate |
| 1+R | the amount of interest accrued over one year | |
| n | the number of years over which the payment is due | |
- PDV=Failed to parse (syntax error): {\displaystyle \frac{1000}{(1+R)ⁿ}} → PDV= $952.38
Time is Money
A firm that decides to build a nuclear power plant has to accept a lower PDV of the money allocated for such a project. Due to capital intensive nature of nuclear plant construction and the significant amount of time it take to complete, the PDV is much lower than it would be if the money was allocated for another project such as a combined cycle gas turbine plant.
In 2024, the cost of building a small modular reactor nuclear power plant (with six 80 MW small modular reactors) would be $8,936 /kW, which is $4,289,280 at a net nominal capacity of 480 kW. Whereas, the cost for a simple cycle combustion turbine plant would be $836 /kW, which is $350,284 at a net nominal capacity of 419 kW.[5]
The nuclear plant has a much higher capital cost (initial cost to build). A major limiting factor of a nuclear reactor is the construction time. A nuclear plant takes approximately 42 months to construct, this is often after a long an rigorous approval process.[5] A simple cycle combustion turbine plant takes approximately 22 months to construct.[5] The long time horizon for a nuclear project means that the PDV of a firms capital is less than for a CT plant project. Needless to say, a firm needs to make a profit to survive and a 3.5 year period (long construction for a nuclear power plant) is a very long time to have an investment not yielding revenue.
For Further Reading
- Discount rate
- Discounting
- Profit
- Or explore a random page
References
- ↑ Image found: https://www.flickr.com/photos/abeckstrom/5504735515 (Accessed September 3rd, 2016).
- ↑ Yale book of quotations by Fred Shapiro, pg 677 (accessed online on September 3rd, 2016): https://books.google.ca/books?id=w5-GR-qtgXsC&pg=PA677&redir_esc=y&hl=en#v=onepage&q&f=false
- ↑ The Economist. “Time Value of Money.” [Online], Available: http://www.economist.com/economics-a-to-z/t#node-21529371[May. 29, 2016].
- ↑ R.S. Pindyck and D.L. Rubinfeld. Microeconomics. New Jersey: Pearson, 2013, pp. 255-256.
- ↑ 5.0 5.1 5.2 EIA (2024). (Accessed July 15, 2026). Capital Cost and Performance Characteristic Estimates for Utility Scale Electric Power Generating Technologies [Online]. Available: https://www.eia.gov/analysis/studies/powerplants/capitalcost/pdf/capital_cost_AEO2025.pdf