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Fusion energy might be the future, almost all fusion reactors that are being built are just “proof-of-concept” reactors. When these reactor have proven that a sustained fusion is possible, a real commercial reactor is going to be built.
It sounds a bit science fiction but the reality is getting closer as we speak. Have a look at this Dutch article.
The wonderful thing is that the (slightly optimistic) planning calls for that commercial reactor to be operational in 2050. This is going to happen during your lifetime, you won’t even be retired by then! It is quite exiting to know that during a general election, you might be able to vote for a party that wants to build one of these reactors in the Netherlands.
Economically, it is a little bit too far in the future to take fusion into consideration. The only viable methods of producing energy are fossil fuels, nuclear, wind and solar. The incoming government has presented plans for four new nuclear power stations (fission) but building these will take at least ten years. To calculate whether it makes economical sense to embark on this project, we need to learn how to calculate the worth of a project.
Solar panels
As you know, the school is producing its own energy with the solar panels on the room. They’ve been connected in 2019 so we’re getting “free” electricity. Free is written in quotation marks because as any economist will tell you, there is no such thing as free.
The panels themselves aren’t free, they’ve been produced by payed workers, the materials had to be bought, they had to be installed on the school etc. They panels and the electrical components need maintenance and both of them will only last for so long.
Of course, there are quite a few companies and families that have solar panels placed to save the planet but an economist would like to know: How economical is it to have solar panels placed?
Cost-benefit analysis
A simple way of analysing the economic value of any project is to add up all the costs and all the benefits. When the benefits outweigh the costs, you’ll end up with a profit.
Assignment
Suppose: Placing the solar panels and the transformer will cost €4400 and the panels will produce €550 worth of electricity per year. The panels will last for 25 year but the transformer needs to be replaced after 12,5 year to a tune of €900. Every year you’ll need to spend €150 on inspection, maintenance and cleaning. Let’s also assume that you’ll need to call in an electrician five times for two hours per call (at €35/hour). After 25 years, the panels need to be replaced.
The materials can be recycled but that isn’t free either so we’ll assume that the residual value after 25 years is zero.
105. Calculate whether placing the panels is profitable or not.
The payback period
A slightly better method is to calculate how long it takes before you’ve earned your investment back. Placing the panels is quite an investment but if you turn a tidy profit every year, you can earn back that investment. The time it takes for you to earn back your investment is called the payback period. Let’s say that those panels and transformer still cost €4400 but you save €400 on electricity each year. The payback period would be 4400/400 = 11 years. All the years that the panels are still functioning after that, you''ll be in profit. When a payback period is longer than the expected lifetime of the object, it will never be profitable and you shouldn’t invest in it.
Incidental costs or benefits (those that don’t return every year) like costs of replacing the transformer (€900) and the costs of the electrician (€350) should be spread evenly over the years. This means that your profit is a little bit less every year.
106. Calculate the payback period of our solar panels.
Discounting
An even better way of determining whether a project is economically viable is to discount the costs and benefits. You know the word discount from sales in a store but in this case it is based on an economic principle:
Money now is worth more than money later.
If you need to invest money today to get a profit in ten years, you can’t use that investment to make money for ten years, it is tied up. You should also think about the interest, when you can invest and get a 2% interest in 10 years, you might as well put it in a savings account and get a better deal.
Finally, every project and investment carries a certain risk. You can invest in solar panels but if the house burns down after two year, you will have lost all that money. True, you don’t have to pay for maintenance anymore so the same thing applies to costs: costs now are a lot more annoying than costs later.
Let’s use a little 5 year project to explain the calculation.
This project requires an investment of €1000 in year 0. Every year requires maintenance at a cost of €50 and you need to make an additional investment of €250 in year 2. In year 4, you get paid out €3000. The project carries a risk of 5%.
First, write down the incoming, outgoing and net cash flows.
To calculate for the risk, and to make money now worth more than money later, decrease the nett cash flow by the risk every year. This means that the nett cash flow in year 1 is minus 5%, the nett cash flow in year 2 is minus 5% and then minus 5% again. In year three, do that three times, etc. This is called discounting.
How to do this quick and easy: Look for the part that remains, not the part that is lost. Removing 5% means that you keep 95% and that is the same as multiplying your amount by 0,95. When you have to remove 5% twice for year to, you keep 95% of 95% of your amount.
You know that 0,95.0,95 is the same as 0,952. Year three: 0,95.0,95.0,95 so 0,953. The general formula is:
Where t is the year your working on.
Now add up all the discounted cash flows. What you’ve got now it the net cash value of the project. It the net cash value is positive, it’s a profitable venture, if it’s negative, don’t invest.
The net cash value of this little project is +€991,67 so it’s economically sound. It’s not a 100% guarantee but then again, what is?
Assignment:
107. Calculate the net cash value of the solar panels.
The information again: Placing the solar panels and the transformer will cost €4400 and the panels will produce €550 worth of electricity per year. The panels will last for 25 year but the transformer needs to be replaced after 12,5 year to a tune of €900. Every year you’ll need to spend €150 on inspection, maintenance and cleaning. Let’s also assume that you’ll need to call in an electrician five times for two hours per call (at €35/hour). After 25 years, the panels need to be replaced. The materials can be recycled but that isn’t free either so we’ll assume that the residual value after 25 years is zero.
This project goes from year 0 to year 24. The transformed needs to be replaced in year 13 and the electrician is called in years 4, 9, 14, 19 and 24.
If you know how, you can use MS Excel or Apple Numbers
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