The randomized method of estimating the net present value of construction projects efficiency

Figures & data

Table 1. Rules of values estimating of the probability and severity of the revenues threats.

Conditions of tasks implementation	Probability of conditions ri,j	Severity of conditions ci,j	Comments
Favorable implementation conditions	[0,00 $÷$ 0,48]	[0,00 $÷$ 0,48]	Tasks $a_i\in A$ to be executed under the weaker than moderate impact of random threats ei,j;
Moderate implementation conditions	[0,49 $÷$ 0,51]	[0,49 $÷$ 0,51]	Tasks $a_i\in A$ to be executed under the impact of default average random threats ei,j
Difficult implementation conditions	[0,52 $÷$ 1,00]	[0,52 $÷$ 1,00]	Tasks $a_i\in A$ to be executed under the stronger than moderate impact of random threats ei,j

Table 2. Rules of values estimating of the probability and severity of the revenues threats.

Conditions of tasks implementation	Probability of conditions ri,j	Severity of conditions ci,j	Comments
Favorable implementation conditions	[0,00 $÷$ 0,48]	[0,00 $÷$ 0,48]	Tranches $b_i\in B$ to be paid under the weaker than moderate impact of random threats ei,j
Moderate implementation conditions	[0,49 $÷$ 0,51]	[0,49 $÷$ 0,51]	Tranches $b_i\in B$ to be paid under the impact of average default random threats ei,j
Difficult implementation conditions	[0,52 $÷$ 1,00]	[0,52 $÷$ 1,00]	Tranches $b_i\in B$ to be paid under stronger than moderate impact of random threats ei,j

Table 3. Endangerment of costs e_i,j.

Stage s	Number of endangerment ej	Specification
F1 ex ante	1	Modification of the terms of financing operational analysis
	2	System of communication – mistakenly referred to the scope of the reconstruction
	3	Technical conditions of connection to the utilities, e.g., water supply and sewerage, energy, communication technology, gas etc., significantly different from the assumptions
	4	Reconstruction of the collision of the technical infrastructure in a much expanded, unpredicted range
	5	Analysis of the absorbency of the terrain incompatible with possible to obtain of development
F2 ex ante	1	Collapse of the design office
	2	Modification of the rules of law or delivery terms
	3	Collapse of the housing sales market
F3 ex ante	1	Change in prices of goods and services.
	2	Collapse of the services market of construction.
	3	Collapse of the project’s general contractor.
F4 ex ante	1	Disclosure of hidden defects and removal them within the product warranty or warranty for physical defects
	2	Cost of maintenance of unsold homes (apartments, usable premise, parking lots etc. significantly exceeding budgetary assumptions)
	3	Cost of the construction completion – beyond the contract with the project’s general contractor

Table 4. Endangerment of revenues e_i,j.

Stage	Number of endangerment ej	Specification
D	1	Price decline of apartments
	2	Decline (slackening) in sale of apartments
	3	Tighter credit policies by banks (financial restriction of investment)

Table 5. Probability r_i,j of the impact of endangerment on costs and revenues.

Level number	Description	Level	ri,j
1	Much smaller than common (extremely small)	Level 1	0,00 − 0,24
2	Slightly lesser than common (little)	Level 2	0,25 − 0,49
3	Common probability of endangerment appearance	Level 3	0,50
4	Slightly greater than common (high)	Level 4	0,51 − 0,74
5	Much greater than common (extremely high)	Level 5	0,75 − 1,00

Table 6. Severity c_i,j/d_i,j of the impact of endangerment on costs (c_i,j) and revenues (d_i,j).

Level number	Description	Level	ci,j / di,j
1	Much lesser than ordinary	Level 1	0,00 − 0,24
2	Slightly lesser than ordinary	Level 2	0,25 − 0,49
3	An ordinary impact of endangerment on the task implementation costs/revenue	Level 3	0,50
4	Slightly grater than ordinary	Level 4	0,51 − 0,74
5	Much greater than ordinary	Level 5	0,75 − 1,00

Figure 1. Risk charts of the total cost and overall revenue of the example investment.

Table 7. Comparison the “behaviour” of the classical NPV indices under probabilistic conditions with the “classic” results.

	Conditions
	Deterministic	Probabilistic
Description	Classic data	Randomized data	As-built data
Market-based conditions of property sales	Extremely favorable	Difficult	Difficult
Market-based conditions for labor, works and construction products	Average	Average	Average
Overall revenue (PLN)	90 300 000	68 427 404	66 990 000
Total cost (PLN)	67 800 000	61 852 247	60 939 000
The net present value of the residential housing development efficiency	1,33	1,11	1,10
Standard deviation of the net present value of randomized efficiency		0,17
Gross profit (PLN)	22 500 000	6 575 157	6 051 000
Exceptionally possible project implementation conditions	Notably favorable	Extremely difficult
Overall revenue (PLN)	87 615 830	62 582 735
Total cost (PLN)	52 294 092	73 211 729
The net present value of randomized efficiency of the residential housing development ($\mathit{NPE}$)	1,68	0,85
Gross profit (PLN)	35 321 737	−10 628 994