MPV_APPE 2019, session 5
Cost–benefit analysis
(model example)
Municipality is deciding between 2 projects of a CA site. Variant A is a larger CA site (10x20m, more
containers, expected 240 ton of incoming recyclables per year), variant B is a smaller CA site (10x16m,
expected 170 ton of incoming recyclables per year). Property will be donated by the municipality.
Paved surface costs 1700 CZK/m2
, gate 10 thousand CZK, 1 m fence 150 CZK (for the gate as well), lights
30k CZK (smaller CA site 1x, larger 2x), containers for plastics 30k CZK and paper 25k CZK (larger CA site
3x, smaller 2x), WEEE box 9k CZK (1x both), shelter for the employer 80k CZK, and mobile WC 25k CZK.
Ministry will provide subvention for the construction of 250k CZK during the investment period.
Running costs consist of energies (fix) 5k CZK/year + 3k CZK/year for each light, maintenance costs 180
CZK/m2
of area per year, and personal costs of 20k CZK/month gross for a full-time employee (+34%
social security payments). In a larger CA site the employee will be available 3x per week, in smaller 2x
week (usual working hours). As social benefits consider tax corrections from the wage (difference
between total personal costs and a net income – the difference that is paid to the state), another social
benefit is 200 CZK for each collected ton of recyclables (an expert estimation of the value), and on
contrary social cost for local people is the visual aspect of the CA site and related noise estimated as
10k CZK/year for each single day of operation per week. Recyclables consists of 40% paper (selling
price 1 200 CZK/ton), 50% plastics (1 900 CZK/ton) and 10% WEEE (700 CZK/ton). Which project would
you prefer based on the CBA (financial and economic analysis) according to Ri if project lifetime is 4
years, rfa = 4 % a rea = 5 %?
We use CBA in cases where we can estimate monetary values of all considered costs and benefits,
whether directly from their market price or indirectly based on some alternative appraisal methods.
The steps of CBA consist of 2 main parts, the financial analysis, where we use direct costs and revenues
related to the project (investor’s perspective), followed by the economic analysis, that takes the result
of the financial analysis and adds social costs and benefits expressed in monetary forms. The result of
economic analysis can, depending on the situation and scope of impact, significantly affect the final
results of CBA, both positively and negatively. Moreover, in the CBA the key role is the initial part of
the complex identification of costs and revenues/benefits of the project. The more important is the
item that is not included in the CBA, the more biased results we will get.
To put it simple, the financial analysis consists of summing up investments costs together with the
cashflow of the project during its lifetime, and the economic analysis further adds to that, for instance,
the impacts on the environment, employment, life quality, etc. (the society in general).
The procedure of financial analysis is basically an NPV calculation, or the identification of costs and
revenues of the project in individual periods of its lifetime and their cumulative discounted sum,
eventually with the calculation of Ri. In the subsequent economic analysis we take the non-discounted
cashflow from individual periods (because in economic analysis we usually discount with a different
discount rate) and add social costs and benefits, and calculate NPV (or Ri) of these “economic”
cashflows. Financial and economic analyses are usually calculated separately due to the different
discount rate used. In the financial analysis of the projects co-financed by the EU we use 4% discount
rate, in the economic analysis we use 5%. Considering the result, an acceptable project is again the
one with non-negative values of NPV, at least in the economic analysis.
MPV_APPE 2019, session 5
Solution steps: For both projects we determine investment and running costs.
Type of cots A investment B investment A running B running
Paved surface 340 000 272 000
Gate 10 000 10 000
Fence 9 000 7 800
Light 60 000 30 000
Container (plastics) 90 000 60 000
Container (paper) 75 000 50 000
Container (WEEE) 9 000 9 000
Shelter 80 000 80 000
Mobile WC 25 000 25 000
Subvention from ministry -250 000 -250 000
Energies (fix costs) 5 000 5 000
Energies (lights 6 000 3 000
Maintenance 36 000 28 800
Personal costs 192 960 128 640
Sum 448 000 293 800 239 960 165 440
*personal costs (in CZ) = (gross wage)*(work range)*(12 months)*(1.34 social security contributions)
**!!we do not consider decision analysis costs when calculating CBA, if there are some!!
These are in fact sunk costs that occur independently from whether we realize the project or not.
Then we determine running revenues of the projects (per year)
Buyout price/ton Revenues A (240 ton/year) Revenues B (170 ton/year)
Plastics 1 900 228 000 161 500
Paper 1 200 115 200 81 600
WEEE 700 16 800 11 900
Sum 360 000 255 000
We calculate financial analysis (rfa = 4%), according to which we accept project B
0 1 2 3 4 NPV (FA)
A cashflow (FA) -448 000 120 040 120 040 120 040 120 040
A discounted CF -448 000 115 423 110 984 106 715 102 611 -12 267
B cashflow (FA) -293 800 89 560 89 560 89 560 89 560
B discounted CF -293 800 86 115 82 803 79 619 76 556 31 293
According to the financial analysis (FA) we accept only project B with NPV 31 293 CZK, project A is not
acceptable with NPV -12 267 CZK. According to the Ri we automatically choose project B.
Then follows the economic analysis, which continues on the result of financial analysis and includes
Social impacts A Social impacts B
Tax corrections 71 124 51 864
Benefits from waste 48 000 34 000
CA site negatives -30 000 -20 000
Sum 89 124 65 864
MPV_APPE 2019, session 5
Tax corrections from wages were calculated as the total personal (employment) costs – gross
wage*1.34 minus net wage. Do not forget that we consider part-time jobs and 12 months per year (net
wage is 10 153 for the larger CA site and 6 398 for the smaller CA site).
Finally we calculate the economic analysis (EA). We take non-discounted cashflow from the FA, add
social costs and benefits and then calculate NPV again (rea = 5%).
0 1 2 3 4 NPV (EA)
A cashflow (EA) -448 000 209 164 209 164 209 164 209 164
A discounted CF -448 000 199 204 189 718 180 684 172 080 293 685
B cashflow (EA) -293 800 155 424 155 424 155 424 155 424
B discounted CF -293 800 148 023 140 974 134 261 127 868 257 326
According to the economic analysis both projects are now acceptable, finally we calculate Ri.
Solution: From the available projects we prefer, according to the CBA, project B with Ri 0.88 over
project A with Ri 0.66. Both projects are acceptable.
MPV_APPE 2019, session 5
Shadow pricing – deriving prices from the demand curves
(model example)
Region plans to build a new bridge that would lower the travelling costs between two cities by 100
CZK/trip. This costs reduction includes shorter travelling time, lower vehicle depreciation and lower
fuel consumption of 120 CZK/trip in total minus 20 CZK toll per bridge crossing – a Region’s income.
Before the bridge there were total of 1 million trips per year, an estimate after the bridge is built is 1.5
million trips per year. Calculate annual benefits of the new bridge for drivers and for the Region.
Shadow pricing represents a way how to estimate the value of goods and services using a marketbased
approach. In an optimal situation it is possible to find an alternative to the evaluated
goods/service and use this price. If not, we can try to use shadow prices.
We use shadow pricing in situations where the actual price of goods/services does not exist or does
not reflect the true value (often due to the regulations, temporary fluctuations, or some other market
failures). A shadow price then can be perceived as a price that would be achieved in a perfect
competition market. Shadow price represents a proxy value, usually considered as a value of what one
has to sacrifice in order to get an additional unit. An estimation of a shadow price is usually done by
observing subjects’ behavior. The two main approaches to estimated shadow prices are based on
benefits or on costs.
Benefits approach includes estimation methods like change in productivity, or forgone earnings. We
can calculate these prices using a CBA for the specific goods/service. Costs approach includes methods
like replacements/restoration costs, preventive expenditure, damage avoidance costs, etc.
In praxis these methods can be used in a form of a natural experiment or pilot projects (small scale
experiments). Impacts of such projects are classified, quantified and monetized. Using an
extrapolation, shadow prices can be estimated for the whole project.
Alternative way of estimating shadow prices is by using pseudo- or quasi-demand curves. We use the
initial state and the expected state after the project’s realization and based on that estimate the
demand curve. We then calculate consumer’s benefit resulting from the change of the state.
Solution steps: In our case we have data about demand before and after the project realization, thus
we derive shadow prices from the relevant demand curve. We can start with benefits to the Region,
which are basically number of trips multiplied by the bridge crossing toll (de facto revenues).
In case of drivers we need to separate the group that would travel regardless of the new bridge – they
would enjoy benefits of the full cost saving, and the remaining group with decreasing benefits due to
the slope of the demand curve. In other words, benefit for the driver no. 1,000,001 is almost the full
costs savings, while the benefit for the driver no. 1,500,000 is basically zero – this is the very last driver
that decided to do the trip, as it was practically on par with the alternative of, for instance, staying at
home or taking an alternative route.
Solution: Benefit for the drivers is 125 mil. CZK/year, benefit for the Region is 30 mil. CZK/year.
MPV_APPE 2019, session 5
WTP – Willingness to Pay
(model example)
Municipality is considering introducing a new waste collection system – instead of central container
(fully paid by the municipality) use bins for the individual households. Estimate the social benefits of
such new system using WTP. This could tell the municipality at what level should it set the fee for the
new system in order to cover the additional expenditures.
Population (200 total) has been sorted based on their willingness to pay for the new system from the
lowest fee to the highest and divided into the quartiles. Assume that the willingness to pay grows
linearly within each quartile. First person is not willing to pay anything, person at the first quartile can
pay 300 CZK, at the second quartile 380 CZK, at the third quartile 440 CZK, and last one 560 CZK.
WTP method represents the second approach how to estimate shadow prices and is based on stated
(declared) preferences. It is a kind of a Contingent Valuation Method (CVM) that uses
questionnaires/surveys. In contrast with the market-approach based on observation of the subjects,
this approach estimates the values based on subjective opinions (theoretical preference), not from
actual behavior, that has been confirmed at the market.
The method itself consists of collecting data from a survey, in which a relevant sample of subjects state
the maximum price they are willing to pay for some goods or service. Survey can start with lower
amounts and continue higher until maximum price is stated. An alternatively is a directly question
about the highest price. Based on collected data we derive a pseudo-demand curve.
The benefits estimated by WTP method is, as with other methods based on preferences, calculated as
the consumer surplus – the area under the derived pseudo-demand curve.
Analogical method is WTA – Willingness to Accept, where you estimate the price, resp. equivalent that
would make subject accept the presence of some negative factor.
Main problem of WTP and WTA methods is in often observed difference between stated and revealed
(real, market) preferences, and the correct use of this method requires taking this into the
consideration. Respondents in case of WTP and WTA often overstate their willingness to pay, resp.
their minimal accepted equivalent for sustaining some negative effect. Another problem of these
methods is acquiring the data from a representative sample during the survey.
Solution steps: Based on the collected data we derive a pseudo-demand curve of the willingness to pay
and calculate the area under it. Total willingness to pay in 4th
quartile is (50*440+(560-440)*50/2) =
25 000 CZK, in 3rd
quartile is (380*50+(440-380)*50/2) = 20 500 CZK, in 2nd
quartile is (50*300+(380-
300)*50/2) = 17 000 CZK, and in the first quartile is (300*50/2) = 7 500 CZK.
Solution: Social benefit from new waste collection system using bins would be 70 000 CZK.
MPV_APPE 2019, session 5
Hedonic pricing method
(model example)
You are asked to evaluate benefits of an anti-flood dam that would reduce the probability of a flood in
a residential area of 80 houses. Use hedonic method for the evaluation if you know that the price of
houses in given area can be estimated using linear regression model:
𝑝𝑖 = 𝛼 + 𝛽(𝑝𝑟𝑜𝑏) + 𝛾(𝑥𝑖) + 𝜀𝑖
where 𝑝𝑖 means estimated price of the house, 𝑝𝑟𝑜𝑏 probability of a flood occurrence in some time
horizon, and 𝑥𝑖 some other parameters of house that we do not need to consider in this case.
Based on the survey of house prices the coefficients have values 𝛼 = 75, 𝛽 = −200 and 𝛾 = 1. Dam
construction is estimated to reduce the risk of flood in some time horizon from 0.4 to 0.05.
Hedonic method represents an approach used for estimating the values of certain measures, good or
services that directly affect the market prices of some other goods. Usual application area is the
realities market, which reflects the impacts of changes of local environmental attributes.
Hedonic method assumes that the price of a certain market good is directly influenced by its
characteristics and our considered measure (resp. good, service). Steps of this method consist of
collecting sufficient data regarding prices and characteristics of considered market goods and their
subsequent statistical analysis. The result is then a price function of a market good consisting of effects
of individual characteristics. Based on the impact of changing individual parameters we estimate the
social benefits of introducing evaluated measure (good, service). In contrast with the stated
preferences, here we use the real data, revealed preferences.
When applying this method in a project evaluation we examine the impact on the welfare (e.g. change
in the prices of realities) when changing selected variables that we can influence (deciding whether to
undergo the project). Final monetized value of the project realization (resp. measure introduction) is
then calculated as a difference between the original state and the new state after the project
realization.
Solution steps: In our case we calculate the difference the value of houses before and after the
construction of the anti-flood dam. Specifically we compare the total value of houses using regression
model using the original and new parameters. Numerically this is a difference between 𝑝𝑖 = 75 −
200 ∗ (0.4) = −5, and 𝑝𝑖 = 75 − 200 ∗ (0.05) = 65, resp. simplified into ∆𝑝𝑖 = −200 ∗ (0.05 −
0.4) = 70 for a single house. Other parameters than flood occurrence probability in this case do not
change, therefore we do not need to consider them in the calculation.
Change in the value of a single house in this case is a value increase by 70.
Solution: Total benefit of building an anti-flood dam for the residential area has a value of 5600.
MPV_APPE 2019, session 5
TCM – Travel Cost Method
(model example)
A municipality owns a lookout tower. Annual maintenance costs including personnel are 300,000 CZK
(material, repairs, etc.). Municipality wants to know the value of the social benefits of the tower.
Calculate them using TCM. Consider travel costs of 2 CZK/km, travel pace of 30 km/hour, average
hourly wage 120 CZK, and an entrance fee of 10 CZK/person. Further parameters are in the table.
Assume discontinuous changes in demand for visits (each zone has same demand level), and irrelevant
visits from additional zones. Also consider that visits are not cumulative (only the tower).
Zone Distance Population
Probability of visit
per year
0 1 200 50%
1 10 10,000 5%
2 30 100,000 2%
TCM represents a method of evaluating nonmarket goods based on observing the market behavior of
subject (revealed preferences). It is used mostly when appraising attractive locations (points of
interest, POI) or ecosystems, where it is naturally difficult to set a direct market monetary value.
This method assumes that the value of evaluated goods is equal to the loss (costs), that subjects are
willing to accept by travelling to the destination with the POI, specifically the costs for travelling (fuel,
public transportation), value of the lost time due to the travelling, and the entrance fees, if there are
any. These costs are different for each of the considered zones based on the distance.
Initially we identify the demand zones in the form of amounts of visits and related total costs per visit
for each considered zone. From these zones we derive a pseudo-demand curve for visiting considered
POIs. The value of POI is then represented by the area under the pseudo-demand curve.
Disadvantage of this method is, for instance, the necessity of sufficient data, as well as inaccuracies
due to the combined visits to the multiple POIs (costs are then shared between the visits), or the
perceived benefits from the travelling itself.
Solution steps: We have data about three zones, we do not consider more. We also do not consider
standard demand curve shape, but only three homogenous groups of visitors based on the zones. We
calculate costs per visit for each zone: 0) 100*(2CZK*2*1km+120CZK*2*1km/30+10CZK);
1) 500*(2CZK*2*10km+120CZK*2*10km/30+10CZK); 2) 2000*(2CZK*2*30km+120CZK*2*30km/30
+10CZK).
Solution: Benefits of the lookout tower are 2200 CZK + 65000 CZK + 740000 CZK = 807 200 CZK/year.