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Sensitivity Analysis

Discuss About The Demand Scenario Planned Capacity Expansion?

Capital Budgeting is the most important constitute of financial management as it involves decisions making about the capital expenditures to be made under any project. As these projects requires the deployment of huge funds for a long term, project managers must study each and every element of project in details. Capital budgeting covers the critical analysis of project and all the alternative project plans considering various factors such as risk and return factor, the discounting rate, the technological and environmental factors, the initial investment requirements etc. While selecting a project, the project manager has to analyse and access the key variations that may occur in future while undertaking the project and comprehensively examine the project’s behaviour in terms of profitability. For all the project planning decisions there are various techniques and analyses available in today’s world which are advanced enough to understand the changes in the output that may be occurred due to input variations. These techniques are sensitivity analysis, simulation analysis, scenario analysis, breakeven analysis etc. The detailed discussion on such capital budgeting technique is given below:

This technique is the most commonly used capital budgeting technique while making project planning decisions. The sensitivity analysis helps the managers to analyse the change in the project output with the changes in the key input variables (Saltelli, 2007). The basic purpose of using this approach is to examine the sensitivity of any project in terms of Net Present Value (Cao & Wan, 2017). There is no inclusive list of variable input parameters but there can be factors like interest rates, useful life of asset, the fixed cost, variable cost per unit, selling price or the number of units to be sold, residual value estimations etc. that may get changed frequently over the life of project (Edmans, Jayaraman, Schneemeier, 2017). Before investing the huge amount of funds in any project plan the firm must identify the significant parameters that may undergo changes if the assumptions goes wrong. Once the key variable factors are identified the project manager must determine the percentage change in the NPV of the project if the input factors changes with a certain percentage.

Sensitivity analysis is also known as ‘what-if’ analysis (Baker & English, 2011). This analysis has its own advantages and at the same time it has some limits which makes it unreasonable in certain situations. Following are some of the advantages and disadvantages of sensitivity analysis:

  • It enables the project managers to identify the key parameters which may impact the future cash flows of the project.
  • It helps in analysing the cause and effect of variations in the input parameters thereby enabling the managers to take appropriate actions to control them and to plan the future course of actions for the uncertainties.
  • The risk involved in the capital budgeting decisions can be analysed to a certain extent using this approach.
  • This technique does not provide managers with the firm decision rather it provides the relevant information that can be used in decision making.
  • The assumptions that the variables are not dependent on each other is not reasonable in maximum situations.
  • The probability consideration of occurrence of variations is lacking in the sensitivity analysis.
  • The project managers while undertaking the sensitivity analysis bases his assumptions for the budgeting and forecasting purpose on three approaches that are optimistic pessimistic and expected.

Advantages and Disadvantages of Sensitivity Analysis

One of the most common way of analysing the risk involved in the investment to be made by the firm is the scenario analysis (Kalyebara & Islam, 2014). Under this methodology the firm calculates the NPV of a project considering several scenarios. The scenarios that are considered under the scenario analysis are based on optimistic pessimistic and expected mind-sets. The analysis initiates with the consideration of base case scenario. The project NPVs are calculated using the base case scenario firstly and then the other possible scenarios are selected. There is no limit of numbers of scenarios a firm must consider while evaluating the project’s effectiveness in changing situations (Erdmann & Hilty, 2010). However, the three basic scenarios that are majorly considered while assessing the risk involved in any project plan (Ross, 2010). These are the worst case, best case and the normal case scenarios as the worst and the best case scenarios will give the decision makers a tentative range in which the NPV of the project will fluctuate subject to the variations. The main purpose of conducting scenario analysis is to understand the combined impact on project’s NPV of numerous factors that changes at the same time.  Scenario analysis mainly involves following essential components (Suryani, 2010). First one is the selection of the important factors based on which scenarios will be established. Then to determine the number of scenario cases so as to analyse each factor that was previously selected. After determination of scenarios the firm will have to place necessary emphasis on each critical factor (Xuan & Yue, 2017). Finally, the managers will have to allocate the probabilities to all the scenarios based on their significance. Even scenario analysis has its pros and cons which are discussed below:

This analysis helps the managers to identify the possible situation a project may have to face in future and the potential implications and advantages of each situation. As all the possible outcomes under differing situations are analysed under this technique it gets easy for the firm to take appropriate decisions.

  • Interpretation of the results provided by this analysis is difficult for the firm as it involves probability distribution. Moreover, it is difficult to decide as to which scenario must be given the preference.
  • The parameters i.e. the uncertainty and impact of each scenario is extremely subjective and hence complicated enough to be measured.

Scenario analysis is the extended application of sensitivity analysis. As sensitivity analysis uses variation in single input variable to determine the projects sensitivity, it gives less clear picture of risk analysis of a project. Whereas, scenario analysis takes into consideration more than one input variables to understand the implications of changes on the projects performance in profitability terms. Scenario analysis also considers the probability distributions of the key input parameters which is ignored in the sensitivity analysis (Gotze, Northcott & Schuster, 2016).

Scenario Analysis

This analysis is used to decide how much output the company must sell to cover the overall costs of conducting the business. Breakeven analysis is commonly known as the cost volume profit analysis as it analyses the relationship between the most important elements of any business i.e. the cost, profit and the sales elements. Breakeven technique calculates the level of sales in both monetary terms as well as in units, a firm must achieve in order to cover the total costs of business so that it does not suffer any loss (Gutierrez & Dalsted, n.d). Break-even point is the point where firm neither incurs any loss nor earn any income. The main tool to conduct breakeven analysis is the breakeven charts which indicates the overall relationship between the total cost total fixed cost and total variable cost and the total revenues of the business of the company. Breakeven analysis is conducted on certain assumptions which are as follows:

  • All the business costs can be divided into categories i.e. fixed cost and variable cost. This analysis does not take into account the semi variable costs.
  • Behaviour of costs and the revenues of the business functions in linear fashion.
  • Methods of production, technological factors and efficiency of business remains same.
  • Breakeven analysis expects that there does not arise any change in the level of inventory.
  • Total fixed costs of a business are also assumed to be constant for all the levels of output in this analysis.
  • Selling price per unit also remains same.

Due to the above assumptions breakeven analysis is not relied upon by the decision makers in every business. The assumptions puts limitations on the analysis as it totally ignores the concept of semi variable costs (Tsorakidis et al., 2011). Also, it ignores factors like technologies that keeps on changing in today’s era. Because of the unrealistic assumptions this technique losses it practical implementation in business.

Despite of various loopholes in the methodology of breakeven analysis there are certain reasons which compels the business managers to implement this approach in their businesses to determine the appropriate level of sales it must make to cover its total costs. It is considered as a suitable approach in following circumstances:

  • Before starting a new business, a firm may use break even analysis for the feasibility test of the business plan.
  • For the price fixation of the products mix manufactured by the company as it will determine the desired level of revenue from sales.
  • In the evaluation of alternatives options available with the company and the special orders that it may take besides its regular market demands.
  • To determine the minimum level activity of business without putting it jeopardy.
  • Breakeven analysis is also ideal for measuring the profit and the losses at different levels of output in the business.

Simulation is the quantitative approach of dealing with the managerial business problems using few models like mathematical or the physical models on which process of simulation is run. This technique uses few experiments by adopting trial and error approach where a series of trials are run on the simulation model to judge the projects behaviour in terms of output. Simulation analysis does not offer an optimum solution to any business problem but it aims to provide the possible set of out for the given inputs (Choe, 2016). In finance world simulation often provides assistance in the determination of risk adjusted NPV of a project. Also, it offers distribution and allocation of project’s NPV over certain factors like discounting rates (Lima et al., 2017).

Monte-Carlo simulation is the most common type of simulation used in the business and is mostly used by the project managers. The distinguishing feature of this analysis is that it offers the managers with the NPVs with their probability distribution and not with the single point estimation of NPVs. This technique initiates with the mathematical modelling of the project or any managerial business process requiring solution (Tavare, 2013). This process of project modelling involves identification of the key factors that may influence the project and the interrelationships between them (Chiarella & Iori, 2002). After process modelling the plotting of probability distribution of project NPVs based on the expected cash flows of project is undertaken. Once the probability is distributed to all the key variables the standard deviation is calculated to analyse the risk involved in the business. Simulation technique has some advantages and some disadvantages with it which are discussed below:

  • It insists the business managers to consider the uncertainties involved in the project and the inter-dependencies of various factors impacting the project growth.
  • Gives the opportunity to the decision makers to represent the complex business problems through a mathematical model as these are complicated enough to be solved with simple set of skills.
  • Difficult project modelling process and probability distribution of external variables.
  • Probability distribution of NPV is not accurate and hence it may be misleading the decision makers.
  • Risk free rate is used as discounting rate in calculation of NPV of a project in simulation analysis and therefore it is difficult to interpret the results of this technique.

Pros and Cons of Scenario Analysis

Practical analysis of capital budgeting techniques

Sales price

10

Discounting rate

10%

Units

10000

Useful life

5

VC

5

Initial investment

-20000

Fixed cost

500

YEARS 

 Cash Flows

 PVF@10%

 P.V. of Cash Flows

0

 $   -20,000

1.000

 $              - 20,000

1

 $   49,500.00

0.909

 $               45,000.00

2

 $   49,500.00

0.826

 $               40,909.09

3

 $   49,500.00

0.751

 $               37,190.08

 NPV 

   

 $           1,03,099.17

Variables

     

Sales price

8

Discounting rate

10%

Units

10000

Useful life

5

VC

5

Initial investment

-20000

Fixed cost

500

YEARS 

 Cash Flows

 PVF@10%

 P.V. of Cash Flows

0

 $     -20,000

1.000

 $                    -20,000

1

 $   29,500.00

0.909

 $                 26,818.18

2

 $   29,500.00

0.826

 $                 24,380.17

3

 $   29,500.00

0.751

 $                 22,163.79

 NPV 

   

 $                 53,362.13

Sales price

10

Discounting rate

10%

Units

10000

Useful life

5

VC

4

Initial investment

-20000

Fixed cost

500

YEARS 

 Cash Flows

 PVF@10%

 P.V. of Cash Flows

0

 $   -20,000

1.000

 $                    -20,000

1

 $   59,500.00

0.909

 $                 54,090.91

2

 $   59,500.00

0.826

 $                 49,173.55

3

 $   59,500.00

0.751

 $                 44,703.23

 NPV 

 $              1,27,967.69

From the above illustration it can be demonstrated that change in the selling price per unit has resulted in the changed NPV. Therefore, NPV is sensitive to the selling price variable. As the selling price per unit has decreased the NPV of the overall project has also decreased.

And when variable cost is decreased the NPV has increased which shows that NPV is also sensitive to it.

Initial Investment

$(100000)

Life of Project

4 years

Discounting Rate

10%

Annual Cash Flows

$20000

$30000

$40000

Probability

0.1

0.6

0.3

Years

Cash Flows (.10)

Cash Flows

(.60)

Cash Flows (.30)

Total Cash Flows

DCF @ 10%

PV of Cash Flows

0

-10000

-60000

-30000

-100000

1

-100000

1

2000

18000

12000

32000

0.909

29088

2

2000

18000

12000

32000

0.826

26432

3

2000

18000

12000

32000

0.752

24064

4

2000

18000

12000

32000

0.683

21856

4

0

6000

6000

12000

0.683

8196

   

NPV

     

9636

The overall NPV of the project will be influenced by all the scenarios that is the worst case best case and the average case

Break-even Analysis:

   

Fixed costs

     
 

Depreciation

 $   50,000.00

 
 

Insurance

 $   15,000.00

 
 

Rent

 $   10,000.00

 
 

Utilities

 $     8,000.00

 
 

Taxes

 $     6,000.00

 
     

 $   89,000.00

Variable Costs

   
 

Direct Labour

 $     8,000.00

 
 

Direct Material

 $   10,000.00

 
 

Overheads

 $   12,000.00

 
     

 $   30,000.00

TOTAL  COSTS

 

 $1,19,000.00

Number of units

10000

Selling Price per unit

 $           15.00

 

Sales

 $ 1,50,000.00

Less:

Variable Costs

 $     30,000.00

 

Contribution

 $ 1,20,000.00

 

Contribution per unit

 =120000/10000

   

 $             12.00

 

Contribution Margin

= 120000/150000*100

   

0.80

Breakeven sales

 

in $

= Total Fixed Cost

 

Contribution Ratio

 

 =$      89,000.00

 

         0.80

Breakeven Sales

 =$  1,11,250.00

in units

= Total Fixed Cost

 

   Contribution/unit

Breakeven Units

=7417 units

This indicates that the firm should at least sell 7417 in order to recover the total cost involved in the business.

Demands

Probability

cumulative probability

Range

10

0.1

0.1

00-09

15

0.25

0.35

10-24

25

0.2

0.55

25-54

40

0.35

0.9

55-89

50

0.1

1

90-99

random no:

48

78

9

51

77

Random No.

Demand (Units)

48

25

78

40

9

10

51

25

77

40

Total Demand      140 units

Conclusion

It is therefore well established from the above study that the capital budgeting techniques plays vital role in long term investment decision making which involves deployment of huge funds in capital expenditures. Before undertaking a project the firm must critically analyse all the risks involved with the project. The project managers must carefully examine the probability of variations that may be occurred in future and the implications of such variations on the overall profitability of company. After studying the possible techniques of risk analysis in capital budgeting it is implied that there is no unique technique suitable for all the circumstances rather the variety of techniques are appropriate in variety of cases. As each analysis has its own benefits and limitations, the project manager has to keep in mind the project’s characteristics and very nature whenever the risk is analysed using the above explained approaches.

References

Baker, H. and English, P., 2011. Capital Budgeting Valuation. Somerset: Wiley.

Cao, X.R. and Wan, X., 2017. Sensitivity analysis of nonlinear behavior with distorted probability. Mathematical Finance, 27(1), pp.115-150.

Chiarella, C. and Iori, G., 2002. A simulation analysis of the microstructure of double auction markets*. Quantitative finance, 2(5), pp.346-353.

Choe, G. H., 2016, Stochastic Analysis for Finance with Simulations, Springer International Publishing, Switzerland.

De Lima, J.D., Trentin, M.G., Oliveira, G.A., Batistus, D.R. and Setti, D., 2017. Systematic Analysis of Economic Viability with Stochastic Approach: A Proposal for Investment. In Engineering Systems and Networks (pp. 317-325). Springer, Cham.

Edmans, A., Jayaraman, S. and Schneemeier, J., 2017. The source of information in prices and investment-price sensitivity. Journal of Financial Economics.

Erdmann, L. and Hilty, L.M., 2010. Scenario analysis. Journal of Industrial Ecology, 14(5), pp.826-843.

Gotze, U., Northcott, D. and Schuster, P., 2016. INVESTMENT APPRAISAL. Springer International Publishing, Berlin.

Gutierrez. P. & Dalsted, N., n.d, Break-Even Method of Investment Analysis, Colorado State University, available at < https://extension.colostate.edu/docs/pubs/farmmgt/03759.pdf > (viewed on 15-09-2017).

Kalyebara, B. and Islam, S., 2014. Corporate Governance, capital markets, and capital budgeting. Dordrecht: Physica-Verlag.

 Ross, S., Traylor, R., Bird, R., Westerfield, R. & Jordan, B., 2010. Essentials of corporate finance, edn 2nd, McGraw-Hill Education.

Saltelli, A. 2007, Sensitivity analysis in practice. Chichester: John Wwiley and Sons.

Suryani, E., Chou, S.Y., Hartono, R. and Chen, C.H., 2010. Demand scenario analysis and planned capacity expansion: A system dynamics framework. Simulation Modelling Practice and Theory, 18(6), pp.732-751.

Tavare, N.S., 2013. Industrial crystallization: process simulation analysis and design. Springer Science & Business Media.

Tsorakidis, N., Papadoulos, S., Zerres, M. and Zerres, C., 2011. Break-Even Analysis. Bookboon.

Xuan, Y. and Yue, Q., 2017. Scenario analysis on resource and environmental benefits of imported steel scrap for China’s steel industry. Resources, Conservation and Recycling, 120, pp.186-198

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