Construction Materials & Management Test 2

Concept

Indirect project Cost: Indirect project cost re those expenditures which cannot be clearly allocated to the individual activities of the project, but are assessed as a whole.

The indirect cost rises with an increase in duration. 

Direct Project Cost: These include labour cost, material cost, equipment cost etc.

Direct cost decreases with increase in duration.

Note: Here the activity duration is crashed i.e. Reducing activity duration (from 25 to 22 days)

∴ Indirect cost decreases as time is decreasing

Direct cost increases

Calculation

Given,

Normal activity duration = 25 days

Crash activity duration = 22 days

Cost slope = 1500/- , Indirect cost = 1000/- per day

Normal cost of activity = 50,000 /-

No. of days crashed = 25 - 22 = 3 days. 

The increase in direct cost for 3 days crashing

= Cost Slope × 3

= \(1500× 3\)

= 4500 rupees

The decrease in indirect cost for 3 days

= \(1000× 3\)

= 3000 rupees

Total project cost = Direct cost + Indirect cost

The total cost of the activities after crashing

=  50000 + 4500 - 3000

= 51500 rupees

∴ Total cost = 51,500 /-

 

Concept

By Straight line method 

Depreciation is given by 

\({D_m} = \frac{{{C_i} - {C_s}}}{n}\)

Where D_m is depreciation 

C_i is Initial cost of an asset

C_s is Salvage or scrap value (Estimated at the end of utility period)

Book value (B_m) at the end of 'm ' years life is given by 

\({B_m} = {C_i} - m × {D_m}\)

Calculation

Given,

C_i = 1,00,000 /-, C_s = 40,000 /- 

n = 5 years

Depreciation is 

\({D_m} = \frac{{1,00,000 - 40000}}{5} = 12,000\)

Book value at the end of 2 years of lifetime is given by

\({B_m} = {C_i} - m × {D_m}\)

= 1,00,000 - 2 × 12,000

 = 76,000 /-

 

 

Item rate contract: It is also known as unit-price contract or schedule contract. For such contracts, contractors are required to quote rates for individual items of work on the basis of schedule of quantities furnished by the department. This type of contract is followed by Central Public works and Railway departments.

Lump-Sum Contract: In this form of contract, the contractors are required to quote a fixed sum for execution of a work complete in all respect i.e. according to the drawing, designs and specifications supplied to them with the tender within the specified time.

The departmental schedule of rates for various items of work are also provided which regulates the payment to the contractor in respect of the items of works involved for any additions and alterations not covered by the original work.

Price Work Agreement: It is type of contract in which the rate is agreed upon without reference to the total quantity of work to be done or the quantity of work to be done within a given period. But the detailed specifications and the total cost of the whole work to be done are mentioned.

There is no security money and penalty clause and it is usually adopted for urgent small work and may be taken up for execution without inviting tender and a reasonable time is saved.

Target contract: It is the type of contract where the contractor is paid on a cost-plus percentage basis for work performed under this contract, and in addition he receives a percentage plus or minus on savings or excess effected against either a prior agreed estimate of total cost or a target value arrived at by measuring the work on completion and valuing prior agreed rates.

Concept:

The expected completion time (tE)

\({t_E} = \frac{{{t_0} + 4{t_L} + {t_P}}}{6}\)

Variance = \([\frac{{t_p - t_o}}{6}]^2\)

Where,

t0 = optimistic time

tL = most likely time

tP = pessimistic time

The probable range is from \((t_e - 3\sigma)\; to\;(t_e + 3\sigma)\)

Solution:

The expected completion time (tE)​

\(\begin{array}{l} \therefore {t_E} = \frac{{8\; + \;4 \;\times\; 15 \;+ \;18}}{6} \\ {t_E} = 14.33\;weeks \end{array}\)

Variance = \([\frac{{18 - 8}}{6}]^2 = 2.78\;weeks\)

Standard Deviation, \(\sigma = \sqrt{2.78} = 1.67\;weeks\)

The Probable range of completion time of the activity will be from \((t_e - 3\sigma)\; to\;(t_e + 3\sigma)\)

i.e. \((14.33 - 3\times1.67)\; to\;(14.33 + 3\times1.67)\)

\(9.32\;weeks\; to\;19.34\;weeks\)

 

Concept

Capital Recover Factor is given by 

\(\frac{{i \times {{\left( {1 + i} \right)}^n}}}{{{{\left( {1 + i} \right)}^n} - 1}}\)

Where,

i is the annual interest rate and

n is the number of annual interest periods

Calculation

Given,

 i = 6 % , n = 8 years

\(CRF = \frac{{{{\left( {1 + i} \right)}^n}i}}{{{{\left( {1 + i} \right)}^n} - 1}} = \frac{{{{\left( {1 + 0.06} \right)}^8} \times \left( {0.06} \right)}}{{{{\left( {1 + 0.06} \right)}^8} - 1}} \Rightarrow 0.16\)

 

Concept:

In Crashing 

The first step is to find the critical path 

then, the Cost slope of all activities in the critical path is calculated.

Activity with minimum cost slope is required to crash first.

\({\rm{Cost\;slope}} = \frac{{{\rm{Crash\;cost}} - {\rm{Normal\;cost}}}}{{{\rm{Normal\;time}} - {\rm{Crash\;time}}}}\)

\(∴ {\rm{CS}} = \frac{{{{\rm{C}}_{\rm{c}}} - {{\rm{C}}_{\rm{n}}}}}{{{{\rm{t}}_{\rm{n}}} - {{\rm{t}}_{\rm{c}}}}} = \frac{{{\rm{\Delta C}}}}{{{\rm{\Delta t}}}}\)

Calculation:

Activities	ΔC (₹)	Δt (weeks)	Cost slope ₹ /week
1 - 2	12000 - 4000 = 8000	4 - 2 = 2	4000
2 - 3	7500 - 3000 = 4500	5 - 2 = 3	1500
2 - 4	6000 - 3600 = 2400	7 - 5 = 2	1200
3 - 4	10000 - 5000 = 5000	4 - 2 = 2	2500

 

For network 1-2, 2- 4 duration is 11 days

∴ The critical path for the given network is 1 - 2, 2 - 3 and

3 - 4 i.e. 13 days.

∴ Although the cost slope is minimum for activity 2 - 4 (but not in a critical path ),

∴ The activity to be crashed first is 2 - 3.

Concept:

PERT approach takes account of the uncertainties. In this approach, 3 - time values are associated which each activity. So it is probabilistic.

Whereas CPM involves the critical path which is the largest path in the network from starting to end event and defines the minimum time required to complete the project. So it is deterministic.

CPM	PERT
CPM is an activity-oriented network diagram	PERT is an event-oriented network diagram
CPM is based upon a deterministic approach	It is based on Probabilistic approach
Only one time estimates are made for each activity	Three-time estimates are made for each activity
Each activity follows a normal distribution	Each activity follows β distribution