MPV_APPE 2016
Cost-minimization analysis
(model example)
Municipality has decided to build a civic amenity site. Two projects applied. Costs (investment and
running) and revenues (for selling collected separated waste) throughout the predicted lifetime are
in the following table. Which project would you choose according to the CMA if r = 0,05?
Period 0 1 2 3 4 5 6
Variant A Costs 1 500 100 100 100 100 100 100
Revenues 300 300 300 300 300 300
Variant B Costs 1 100 250 250 250 250 250 250
Revenues 500 500 500 500 500 500
CMA is a basic cost-output method, in which the primary goal is to minimize the costs. It is an
appropriate method if there is possible to sufficiently define the desired output, resp. the minimal
desired parameters. In practical application of the CMA you then choose (from the available options)
firstly those that meet the minimal desired requirements and from this subgroup choose the one
with the lowest costs.
∑
CMA method is relatively popular due to its simplicity, butt the appropriate usage requires sufficient
preparation and appropriately exact specification of minimal desired requirements.
On the other hand, CMA cannot guarantee that the most efficient option will be chosen – in such
cases a different method should be used that compares costs with the provided level of outputs, and
do not consider outputs from the yes/no perspective. CMA does take into account only the
fulfillment of the minimal required parameters, anything beyond that is irrelevant.
What can happen is that the most efficient variant would contain a significantly higher that required
level of output. With CMA it, however, does not matter, how much the minimal requirements have
been exceeded – if they have been met, all such variants are seen as equal in terms of outputs. In
such cases, on the other hand, variants with less output are in advantage, as they did not have to
spend extra sources for producing exceeding parameters.
Solution steps: For both variants we sum up discounted values of costs for the whole lifetime.
0 1 2 3 4 5 6 Σ costs
A 1 500 95.238 90.703 86.384 82.270 78.353 74.622 2 007.569
B 1 100 238.095 226.757 215.959 205.676 195.882 186.554 2 368.923
Solution: From given projects we choose, according to the CMA, project A with costs 2 007.569 over
the project B with costs 2 368.923.
MPV_APPE 2016
Cost-effectiveness analysis
(model example)
Let us use the previous example. For both variants of CA site we would consider expected amounts of
collected separated waste. Which project would you choose according to the criterion costs per
collected ton of recyclable waste?
Period 0 1 2 3 4 5 6
Variant A Costs 1 500 100 100 100 100 100 100
Recyclables 240 240 240 240 240 240
Variant B Costs 1 100 250 250 250 250 250 250
Recyclables 280 280 280 280 280 280
CEA je cost-output method that is used in cases when it is possible to measure outputs in relatively
homogenous units (whether tangible or not), and the appraisal of such units in the monetary terms is
(from whatever reasons) problematic. Typical situation is when there is no sufficient market for given
type of output and the price is not available, the estimation of price is highly inaccurate and
uncertain, or the appraisal in terms of money is unethical/politically inappropriate (e.g. healthcare).
∑
∑
⁄
We can report the results of in form of costs per unit out output (lower value is better) – see the
formulae above, or alternatively in the inverted form of output per unit of costs (higher value is
better). The choice depends on the situation, resp. which option is more clear and easier to interpret.
CEA method is popular in the area of environment or healthcare, where using units of output instead
of their transformation into the monetary form reduces the problems related to the defense of
whether they economically pay off.
With CEA we generally expect that it pays off to spend resources in order to acquire certain output,
and we are concerned with the choice of variant with the best input to output ratio (in other terms
the efficiency). The question whether it makes sense to spend resource in order to get such output is
in with CEA not considered.
Solutions steps: We sum up discounted costs for the whole lifetime as in CMA, divide it with the sum
of collected recyclables (outputs), and choose variant with the lowest costs per unit of output.
Solution: From given projects we choose, according to the CEA with output of ton of collected
recyclables, project A with costs 1 394.15 per ton of waste (resp. 0.717 ton per 1 000 units of costs)
over the project B with costs of 1 410.07 per ton of waste (resp. 0.709 ton per 1 000 units of costs).
MPV_APPE 2016
Cost–utility analysis
(model example)
Let us use the previous example with the addition of the CA site opening hours – variant A is open 2x
per week, variant B 3x per week, CA site operates 50 weeks/year. We presume that correct sorting of
2 tons of collected recyclables takes 1 full working day. Whatever beyond this the worker will not
manage to sort and will be considered as mixed waste, that the collection company will take away
with the rest of the regular mixed waste. Which project would you choose according to the criterion
od costs per ton of collected and sorted recyclables?
CUA is almost identical with the CEA, however, the output is in case of CUA usually more complex –
typically it is some kind of utility that is represented by some combination of outputs. Typical
example from healthcare is conversion of cost to the (output) unit QALY – Quality adjusted life-year.
The unit of QALY represents the combination of expected additional life year gained by undergoin
certain type of treatment and estimated level of life quality after this treatment. In case of QALY less
additional years with higher life quality can be considered as more valuable than more years with
lower life quality.
∑
∑
⁄
The use of this method is then practically identical with the CEA. After calculating the total amount of
utility for each considered variants we calculate costs per unit of utility and choose variant with costs
per utility ratio – the goal is again the efficiency. The question whether it makes sense to spend
resource in order to get such utility again irrelevant.
Solution steps: We sum up the costs for the whole lifetime as in case of CMA, divide them with the
sum collected and also sorted recyclables (utility), and choose variant with lower costs per unit of
utility. When determining the total level of utility we need to find out how many tons of waste will
get both collected and sorted. With sufficient amount of working days is the utility limited by the
amount of collected waste, on contrary with large amount of collected waste is the utility limited by
the amount of working days.
Solution: From given projects we prefer, according to the CUA method with unit of utility collected
and sorted ton of recyclables, project B with costs 1 410.07 per ton of sorted recyclables (resp. 0.709
ton of sorted recyclables per 1 000 units of costs) over the project A with costs 1 672.97 per ton of
sorted recyclables (resp. 0.598 ton of sorted recyclables per 1 000 units of costs).
MPV_APPE 2016
Cost–benefit analysis
(model example)
Municipality is deciding between 2 projects of 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, 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 employer 80k CZK, and mobile WC 25k CZK.
City will provide subvention for the construction of 250k CZK during investment period. Running
costs consists 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 for full-time employee (+34% social
security contributions). In larger CA site the employee will be available 3x per week, smaller 2x week,
usual working hours. As social benefits consider tax corrections from wage (difference between total
personal costs and net income – the difference that is paid to the state), another social benefit is 200
CZK for each collected ton of recyclables (expert estimation), and on contrary social cost for local
people is the visual side of 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 CBA
(financial and economic analysis) according to Ri if project lifetime is 4 years, r = 5% and re = 5.5%?
We use CBA in cases where we can estimate monetary values of all costs and benefits, whether
directly from their market price or indirectly based on 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 economic analysis, that takes the result of 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 CBA the key role is the initial part of 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 procedure of financial analysis is basically the 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 economic analysis we take non-discounted cashflow from
individual periods (because in economic analysis we usually discount with different rate) and add
social costs and benefits, and calculate NPV (or Ri) of these “economic” cashflows. Financial and
economic analysis are usually calculated separately due to the different discount rate used. In
financial analysis of the projects co-financed by EU we use 5% discount rate, in economic analysis we
use 5.5%. Considering the result, acceptable project is again the one with non-negative values of
NPV, at least in economic analysis.
MPV_APPE 2016
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 city -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 contribution)
**!!we do not consider decision analysis costs when calculating CBA, if there are some – sunk costs!!
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 (r = 5%), 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 -448 000 114 324 108 880 103 695 98 757 -22 344
B cashflow (FA) -293 800 89 560 89 560 89 560 89 560
B discounted CF -293 800 85 295 81 234 77 365 73 681 23 775
According to the financial analysis (FA) we accept only project B with NPV 23 775 CZK, project A is not
acceptable with NPV -22 344 CZK. According to the Ri we automatically choose project B.
Then follows economic analysis, which continues on the result of financial analysis and includes
Social impacts A Social impacts B
Tax corrections 68 940 46 284
Benefits from waste 48 000 34 000
CA site negatives -30 000 -20 000
Sum 86 840 60 284
MPV_APPE 2016
Tax corrections from wages were calculated as the total personal (employment) costs – gross
wage*1.34 minus net wage (net is in this case 16 080 per month). Do not forget that we consider
part-time jobs and 12 months per year.
Finally we calculate economic analysis (EA). We take non-discounted cashflow from FA, add social
costs and benefits and then calculate NPV again (re = 5.5%).
0 1 2 3 4 NPV (EA)
A cashflow (EA) -448 000 206 980 206 980 206 980 206 980
A discounted CF -448 000 196 190 185 962 176 267 167 078 277 496
B cashflow (EA) -293 800 149 844 149 844 149 844 149 844
B discounted CF -293 800 142 032 134 628 127 609 120 957 231 426
According to the economic analysis both project are now acceptable, finally we calculate Ri.
Solution: From available projects we prefer, according to the CBA, project B with Ri 0.79 over project
A with Ri 0.62. Both projects are acceptable.