# Time value of money

Figure 1: J. Wellington Wimpy,[1] 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!"[2] This illustrates the time value of money. Money a few days from now isn't as valuable as money now.

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 that in the future because that money can grow.

## Contents

### 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=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= → PDV=$952.38

## Time is Money

A firm that decides to build a nuclear power plant had 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 CCGT plant. In 2013 the cost of building a (dual unit)nuclear reactor was $5,530 /kW ($12.35b) whereas the cost for a natural gas power plant (averaged over 5 different configurations) was $1,136.80 /kW ($376.25m).[5]

While the nuclear plant has a much higher capital cost, its ongoing costs are much lower than a natural gas plant. A major limiting factor of nuclear reactor is the construction time. A nuclear plant takes, between 36 and 72 months to complete, this is often after a long an rigorous approval process. A combined cycle gas plant plant takes between 24 and 30 months to complete with an average of 27 months. The long time horizon for a nuclear project means that the PDV of a firms capital is less than for a gas plant project. Needless to say, a firm needs to make a profit to survive and a six year period (long construction for a nuclear power station) is a very long time to have an investment not yielding revenue.

## References

1. Image found: https://www.flickr.com/photos/abeckstrom/5504735515 (Accessed September 3rd, 2016).
2. 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
3. The Economist. “Time Value of Money.” [Online], Available: http://www.economist.com/economics-a-to-z/t#node-21529371[May. 29, 2016].
4. R.S. Pindyck and D.L. Rubinfeld. Microeconomics. New Jersey: Pearson, 2013, pp. 255-256.
5. U.S Energy Information Agency (EIA). Updated Capital Cost Estimates for Utility Scale Electricity Generating Plants [Online], Available: www.eia.gov/forecasts/capitalcost/pdf/updated_capcost.pdf, 2013 [June 26, 2016].

## Authors and Editors

Lyndon G., Jordan Hanania, Jason Donev
Last updated: August 29, 2017
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