<p>There is actually no single agreed upon way how to do this. As discussed by Carnot et al in Economic forecasting and Policy pp 215:</p>
<blockquote>
<p>The other conceptual problem [in the cost-benefit analysis] concerns the discount rate. First, using discounting mechanically leads to putting less weight on more distant costs and benefits-much less, in fact, when the project has an impact far into the future. This may not be sensible, notably when the project has significant long-run environmental repercussions. Second, there is the issue of the choice of an appropriate discount rate. Opting for a market rate is not a simple solution, given the dispersion of market rates from which to choose. In fact, the discount rate used by private firms is often far above any bond rate, because it reflects high opportunity costs. In the public sector, it is usually lower, albeit still above bond rates, because of budget constraints. That said, the uncertainity about the right discount rate is more of an problem when analyzing the intrinsic costs and benefit of a given project than when comparing those of competing projects pursuing the same objective.</p>
</blockquote>
<p>However, typically discount rate is set to be equal to the interest rate on government debt.  For example, Congressional Budget Office (CBO) does this as it explains in its <a href="https://www.cbo.gov/system/files/2018-07/53886-FairValuePrimer.pdf" rel="nofollow noreferrer">primer</a> on how it provides fair value estimates. Nonetheless, as <a href="https://crsreports.congress.gov/product/pdf/R/R44594/4" rel="nofollow noreferrer">this</a> report shows it will sometimes use different rates depending on the setting (e.g. different rates for military spending, or different rates if some are required to be used by regulation).</p>
<p>Some government bodies make an adjustment to this rate for a long term projects reflecting the issue discussed in the first part of the quote from Carnot et al (e.g. see this <a href="https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/620855/FRAB_130__03__Discount_rates.pdf" rel="nofollow noreferrer">HM treasury</a> report).</p>
<p>This is arguably not ideal, but as the quote above says, even though this can create inaccuracies in finding the true value of the project when you just compare two projects to each other, it is not a huge issue since you will use the same discount rate for both projects.</p>

CC BY-SA 4.0
2021-07-23T15:51:50.447Z
Thanks for your input! I will accept it as a definite answer unless something else pops up soon. But as you say: there is no agreed way upon how to tackle this issue.
babipsylon
CC BY-SA 4.0
2021-07-23T15:54:54.333Z
@babipsylon yes, although one caveat, you should not think that means anything goes, and using interest rate on government bonds of the same maturity as you believe the project will take is de facto widely used standard, but from purely scientific perspective there is no full or even just overwhelming consensus
1muflon1
CC BY-SA 4.0
2021-10-01T13:44:46.973Z
hi @1muflon1: I should probably also determine the mix of tax payer money versus borrowed money for government spending/investment in a giving year to determine the discount factor. For the tax payer's money the simplifying approximation for the discount factor could be the (expected) inflation rate, while for the borrowed money it could be the inflation rate + the interest rate for borrowing
babipsylon
CC BY-SA 4.0
2021-10-01T13:52:21.403Z
Or, wouldn't it make more sense to look at predicted growth rates of the economy?

On investopedia, they define the discount rate as:

In this context of DCF analysis, the discount rate refers to the interest rate used to determine the present value. For example, 100 invested today in a savings scheme that offers a 10% interest rate will grow to 110. In other words, 110 (future value) when discounted by the rate of 10% is worth$100 as of today.

Of course, governments only borrow and don't invest in the market. But maybe economic growth reflects the average market gains?
babipsylon
CC BY-SA 4.0
2021-10-01T13:57:44.110Z
I guess for a government you shouldn't compare to what a company with 1 billion could make in one year, but rather what the national economy has gained in that year, of will gain each year in the coming ... 20 years e.g.
babipsylon
CC BY-SA 4.0
2021-10-01T14:16:01.840Z
@babipsylon i don’t think it’s good idea to use different discount factor for taxpayer money and borrowed money. Government could take that taxpayer money and just invest them into some bonds at prevailing interest rate then earn that interest and lower taxes in the future. Typically, discount rate will include interest rate whether money is borrowed or not. Although of course you can do you and do it your way but in serious public policy research just using inflation for funds collected via taxes would not be considered sufficient. Next *nominal* interest rate, and that is the interest rate
1muflon1
CC BY-SA 4.0
2021-10-01T14:19:02.927Z
You will get when you just google interest rate already includes inflation since by Fisher equation nominal interest rate $\approx$ real interest rate (not directly observable) + inflation. If you just add nominal interest rate and inflation together you are double counting. So in both cases you should be using some interest rate. Typically prevailing nominal interest implied by bond yields is used no matter where the money came from. Using growth rate of the economy as discount factor is also reasonable and sometimes used so that would be fine as well.
1muflon1
CC BY-SA 4.0
2021-10-01T14:24:43.727Z
If you want something super fancy but very difficult you can estimate discount factors based on country residents’ utilities - this is actually the most appropriate option but that is difficult as hell so actually even in public policy think thanks or government research units in practice discount factors are not often estimated with such rigor, but if you don’t care about extra work then that’s something you can look into
1muflon1
CC BY-SA 4.0
2021-10-04T12:57:59.527Z
Thx for the comment. Probably not going into that, but what do you mean exactly with country resident's utilities?
babipsylon
CC BY-SA 4.0
2021-10-04T13:14:54.387Z
@babipsylon well every person has preferences and desires, like for example you might want to get food, shelter, go to vacation, play some board game etc. utility is a measure of satisfaction of needs people have. From relationship between needs and satisfying the needs you can construct utility function. There are two main types of utility functions ordinal (more realistic but sometimes less useful) which tells you order of preferences for a person. For example, I prefer chocolate cereal to cornflakes so that is part of my ordinal utility. Second type of utility is cardinal utility
1muflon1
CC BY-SA 4.0
2021-10-04T13:18:24.347Z
Which allows you to assign some given number to satisfaction of needs (less realistic to be actually able to calculate but often more useful), for example cardinal utility would allow me to measure that let’s say eating chocolate cereal gives me 20 utils and cornflakes gives me 10 utils so I not only prefer chocolate cereal to cornflakes but also I value choc cereal at 2x the rate that I value cornflakes. Using various statistical measures you can estimate either ordinal or cardinal utilities for various options including how much people value resources now vs future
1muflon1
CC BY-SA 4.0
2021-10-04T13:20:57.807Z
As a consequence, people’s utilities always imply that there some sort of discount factor (i.e. interest rate that gives you the degree of preference for present vs future). Theoretically, this is often the best interest rate to use for public policy as government should not simply maximize the value of public funds or just recoup loss of value of money due inflation but maximize welfare of society. However, it’s not always used as it is very difficult to precisely measure it and to estimate its value, so people might go for a bit more objective measure like rate on gov bonds
1muflon1
CC BY-SA 4.0
2021-10-04T14:19:00.040Z
Oh I see. Ow that's far stretch. Also then how would one convert utils in a discount rate. Same problem of subjectivity I guess. Within one good you have the utils discount rate maybe, but between different goods... . Same question of what the opportunity util cost of real estate housing of government services remains I guess.
babipsylon
CC BY-SA 4.0
2021-10-04T14:31:03.823Z
@babipsylon yes it also depends on different problems but Utils are just some unit of measurement like a meter so utils are simply utils but as mentioned above it’s difficult to measure utils directly so people typically work with ordinal utility but you still can get a discount rate but exactly as you said discount rate can be different for different activities
1muflon1
CC BY-SA 4.0
2021-07-20T00:56:58.187Z
2021-07-20T00:56:58.187Z
1muflon1
<p>When discounting in order to obtain the present value, one has to determine the opportunity cost of capital.</p>
<p>In this case, I don't want to do it for a project (or a comparison of two similar projects), but try to determine it for a government spending/consumption/investing. E.g. buying or renting a federal building, where governmental services take place.</p>
<p>What indicators provided by gouvernemental bodies/financial services, or which calculation can best be considered when determining the discount rate for a country/opportunity cost of capital for a given country?</p>

CC BY-SA 4.0
2021-07-19T10:15:17.503Z
Just to clarify, you want to look at the decision [invest in capital/not invest/invest in something else] now, based on future returns from that investment for an economy as a whole? If there is an alternative investment/spending what is that? For example buying government bonds, or just "consuming"?
BrsG
CC BY-SA 4.0
2021-07-19T12:53:01.943Z
Well, I'm talking about federal funds here, that could be spent, I think, at will, for example by buying any financial product available to the government. The other option is paying for a specific project (this is also non-profit, just a cost/service provided to the government itself or its citizens). So it's not a comparison between two similar projects, but rather the choice is between initiating one project, of just get maximum return on investment on the capital by any means available to the government. If that makes sense.
babipsylon
CC BY-SA 4.0
2021-07-19T12:54:00.390Z
Although "any means" is maybe limited by law as it concerns government spending. Maybe the more sensible alternative here is just not to obtain the funds at all as a government... . Hardly impossible to calculate the returns on that for the economy for one project... .
babipsylon
CC BY-SA 4.0
2021-07-19T13:07:23.630Z
Makes sense. If you are looking just at the fiscal side, I suggest to look at fiscal multipliers. They can differ considerably by "project", think about investing into public transport vs investing in schools. Not sure there are official estimates around, but especially for the US there should be some literature. Note that for governments the alternative investment is actually paying off debt. So, treasury yields would be the alternative cost to compare it with. If the focus is on the government, not private investment, I would change the title correspondingly.
BrsG
CC BY-SA 4.0
2021-07-19T13:44:44.943Z
Yes you are right, paying off governmental debt is probably a sensible way to look at the alternative. I guess I don't really have to determine the return on investment for the specific projects, which is near impossible. Although looking at fiscal multipliers is indeed a nice try at approximating this return on investment. Because if the discount rate is seen as the opportunity cost of capital, knowing the interest payed on the debt of the country each year is probably a nice vector of discount rates to apply.And that's all that is needed or what would you use the fiscal multiplier value for?
babipsylon
CC BY-SA 4.0
2021-10-01T13:54:51.767Z
Yes and no. Conceptually, yes. Practically: there are no expected incoming cash flows for your investment. The federal government pays for the building, and that's the end of the story. The only gain is non-financial: housing services for government bodies.
babipsylon
<discount-rate>
Goverment spending: how to calculate the discount rate for it? What is the opportunity cost of federal funds?
babipsylon
# Goverment spending: how to calculate the discount rate for it? What is the opportunity cost of federal funds?

(Asked by: username_0 on 2021-07-19)

When discounting in order to obtain the present value, one has to determine the opportunity cost of capital.

In this case, I don't want to do it for a project (or a comparison of two similar projects), but try to determine it for a government spending/consumption/investing. E.g. buying or renting a federal building, where governmental services take place.

What indicators provided by gouvernemental bodies/financial services, or which calculation can best be considered when determining the discount rate for a country/opportunity cost of capital for a given country?

**Tags:** discount-rate

> **Comments:**
> **username_1**: Just to clarify, you want to look at the decision [invest in capital/not invest/invest in something else] now, based on future returns from that investment for an economy as a whole? If there is an alternative investment/spending what is that? For example buying government bonds, or just "consuming"?  
> **username_0**: Well, I'm talking about federal funds here, that could be spent, I think, at will, for example by buying any financial product available to the government. The other option is paying for a specific project (this is also non-profit, just a cost/service provided to the government itself or its citizens). So it's not a comparison between two similar projects, but rather the choice is between initiating one project, of just get maximum return on investment on the capital by any means available to the government. If that makes sense.  
> **username_0**: Although "any means" is maybe limited by law as it concerns government spending. Maybe the more sensible alternative here is just not to obtain the funds at all as a government... . Hardly impossible to calculate the returns on that for the economy for one project... .  
> **username_1**: Makes sense. If you are looking just at the fiscal side, I suggest to look at fiscal multipliers. They can differ considerably by "project", think about investing into public transport vs investing in schools. Not sure there are official estimates around, but especially for the US there should be some literature. Note that for governments the alternative investment is actually paying off debt. So, treasury yields would be the alternative cost to compare it with. If the focus is on the government, not private investment, I would change the title correspondingly.  
> **username_0**: Yes you are right, paying off governmental debt is probably a sensible way to look at the alternative. I guess I don't really have to determine the return on investment for the specific projects, which is near impossible. Although looking at fiscal multipliers is indeed a nice try at approximating this return on investment. Because if the discount rate is seen as the opportunity cost of capital, knowing the interest payed on the debt of the country each year is probably a nice vector of discount rates to apply.And that's all that is needed or what would you use the fiscal multiplier value for?  
> **username_0**: Yes and no. Conceptually, yes. Practically: there are no expected incoming cash flows for your investment. The federal government pays for the building, and that's the end of the story. The only gain is non-financial: housing services for government bodies.  

---

## 1 answers

### Answer by username_2 on 2021-07-20. Score: 1 | Accepted answer

There is actually no single agreed upon way how to do this. As discussed by Carnot et al in Economic forecasting and Policy pp 215:

> The other conceptual problem [in the cost-benefit analysis] concerns the discount rate. First, using discounting mechanically leads to putting less weight on more distant costs and benefits-much less, in fact, when the project has an impact far into the future. This may not be sensible, notably when the project has significant long-run environmental repercussions. Second, there is the issue of the choice of an appropriate discount rate. Opting for a market rate is not a simple solution, given the dispersion of market rates from which to choose. In fact, the discount rate used by private firms is often far above any bond rate, because it reflects high opportunity costs. In the public sector, it is usually lower, albeit still above bond rates, because of budget constraints. That said, the uncertainity about the right discount rate is more of an problem when analyzing the intrinsic costs and benefit of a given project than when comparing those of competing projects pursuing the same objective.

However, typically discount rate is set to be equal to the interest rate on government debt. For example, Congressional Budget Office (CBO) does this as it explains in its [primer](https://www.cbo.gov/system/files/2018-07/53886-FairValuePrimer.pdf) on how it provides fair value estimates. Nonetheless, as [this](https://crsreports.congress.gov/product/pdf/R/R44594/4) report shows it will sometimes use different rates depending on the setting (e.g. different rates for military spending, or different rates if some are required to be used by regulation).

Some government bodies make an adjustment to this rate for a long term projects reflecting the issue discussed in the first part of the quote from Carnot et al (e.g. see this [HM treasury](https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/620855/FRAB_130__03__Discount_rates.pdf) report).

This is arguably not ideal, but as the quote above says, even though this can create inaccuracies in finding the true value of the project when you just compare two projects to each other, it is not a huge issue since you will use the same discount rate for both projects.

> **Comments:**
> **username_0**: Thanks for your input! I will accept it as a definite answer unless something else pops up soon. But as you say: there is no agreed way upon how to tackle this issue.  
> **username_2**: @username_0 yes, although one caveat, you should not think that means anything goes, and using interest rate on government bonds of the same maturity as you believe the project will take is de facto widely used standard, but from purely scientific perspective there is no full or even just overwhelming consensus  
> **username_0**: hi @username_2: I should probably also determine the mix of tax payer money versus borrowed money for government spending/investment in a giving year to determine the discount factor. For the tax payer's money the simplifying approximation for the discount factor could be the (expected) inflation rate, while for the borrowed money it could be the inflation rate + the interest rate for borrowing  
> **username_0**: Or, wouldn't it make more sense to look at predicted growth rates of the economy?  On investopedia, they define the discount rate as:  In this context of DCF analysis, the discount rate refers to the interest rate used to determine the present value. For example, 100 invested today in a savings scheme that offers a 10% interest rate will grow to 110. In other words, 110 (future value) when discounted by the rate of 10% is worth$100 as of today.  Of course, governments only borrow and don't invest in the market. But maybe economic growth reflects the average market gains?  
> **username_0**: I guess for a government you shouldn't compare to what a company with 1 billion could make in one year, but rather what the national economy has gained in that year, of will gain each year in the coming ... 20 years e.g.  
> **username_2**: @username_0 i don’t think it’s good idea to use different discount factor for taxpayer money and borrowed money. Government could take that taxpayer money and just invest them into some bonds at prevailing interest rate then earn that interest and lower taxes in the future. Typically, discount rate will include interest rate whether money is borrowed or not. Although of course you can do you and do it your way but in serious public policy research just using inflation for funds collected via taxes would not be considered sufficient. Next *nominal* interest rate, and that is the interest rate  
> **username_2**: You will get when you just google interest rate already includes inflation since by Fisher equation nominal interest rate $\approx$ real interest rate (not directly observable) + inflation. If you just add nominal interest rate and inflation together you are double counting. So in both cases you should be using some interest rate. Typically prevailing nominal interest implied by bond yields is used no matter where the money came from. Using growth rate of the economy as discount factor is also reasonable and sometimes used so that would be fine as well.  
> **username_2**: If you want something super fancy but very difficult you can estimate discount factors based on country residents’ utilities - this is actually the most appropriate option but that is difficult as hell so actually even in public policy think thanks or government research units in practice discount factors are not often estimated with such rigor, but if you don’t care about extra work then that’s something you can look into  
> **username_0**: Thx for the comment. Probably not going into that, but what do you mean exactly with country resident's utilities?  
> **username_2**: @username_0 well every person has preferences and desires, like for example you might want to get food, shelter, go to vacation, play some board game etc. utility is a measure of satisfaction of needs people have. From relationship between needs and satisfying the needs you can construct utility function. There are two main types of utility functions ordinal (more realistic but sometimes less useful) which tells you order of preferences for a person. For example, I prefer chocolate cereal to cornflakes so that is part of my ordinal utility. Second type of utility is cardinal utility  
> **username_2**: Which allows you to assign some given number to satisfaction of needs (less realistic to be actually able to calculate but often more useful), for example cardinal utility would allow me to measure that let’s say eating chocolate cereal gives me 20 utils and cornflakes gives me 10 utils so I not only prefer chocolate cereal to cornflakes but also I value choc cereal at 2x the rate that I value cornflakes. Using various statistical measures you can estimate either ordinal or cardinal utilities for various options including how much people value resources now vs future  
> **username_2**: As a consequence, people’s utilities always imply that there some sort of discount factor (i.e. interest rate that gives you the degree of preference for present vs future). Theoretically, this is often the best interest rate to use for public policy as government should not simply maximize the value of public funds or just recoup loss of value of money due inflation but maximize welfare of society. However, it’s not always used as it is very difficult to precisely measure it and to estimate its value, so people might go for a bit more objective measure like rate on gov bonds  
> **username_0**: Oh I see. Ow that's far stretch. Also then how would one convert utils in a discount rate. Same problem of subjectivity I guess. Within one good you have the utils discount rate maybe, but between different goods... . Same question of what the opportunity util cost of real estate housing of government services remains I guess.  
> **username_2**: @username_0 yes it also depends on different problems but Utils are just some unit of measurement like a meter so utils are simply utils but as mentioned above it’s difficult to measure utils directly so people typically work with ordinal utility but you still can get a discount rate but exactly as you said discount rate can be different for different activities  

---

