Risk Modeling

Risk Modeling

In risk modeling a project is treated as model and such model is constructed based on the expected outcomes. This model then checks by changing the outcomes (i.e. inflow and outflows).

1.    Model Construction

First step in risk modeling is construction of well planned model. Such model is based on future expected outcome is created. a lot of working and detail analyses is performed to create a suitable model for project.

2.    Analyses with Variation

Second step is risk Modeling is analyses with variation in outcome. It means that how the result (NPV) will change by changing the different outcome (variable) of model. For investment appraisal mainly there are two main variable revenue, cost, and investments.

NPV Sensitivity Analyses

NPV Sensitivity Analyses

In NPV sensitivity analyses, we recognize the impact of future uncertainty of cash flow on the NPV. We calculate margin of safety for different cash flow items i.e. revenue, cost, and contribution. Such analyses also give us an idea of contribution (importance) of each item in the NPV.

1.    NPV Sensitivity analyses for Cost

NPV Sensitivity analyses for cost are performed by calculating the margin of safety for cost. This margin of safety shows that what % of cost increase would make the NPV zero.

2.    NPV Sensitivity analyses for Revenue

NPV Sensitivity analyses for revenue is performed by calculating the margin of safety for revenue, that shows that how much decrease in revenue will bring the NPV at zero level.

3.    NPV Sensitivity analyses for Contribution

NPV Sensitivity analyses for contribution is performed by calculating the margin of safety for contribution, which shows that how much decrease in contribution in terms of percentage will bring NPV to zero.

Sensitivity Analyses for Cost Example

Sensitivity Analyses for Cost Example

In sensitivity analyses for cost, we see sensitivity (reaction) of NPV to cost. We calculate a margin of safety for cost. There are three steps for these analyses. In first place we calculate NPV, then we calculated Present value of cost and in last we calculate margin of safety for cost. (How much cost can be increase to get zero NPV?

Example of Sensitivity & Variable

Initial Investment	200,000
Volume of Sales	20,000 Units
Selling Price	12
Variable Price	8
Project term 4 years	4 years

Cost of Capital is 10%

Solution

1.     Calculate NPV

Cash outflow	$ 200,000
Cash inflow ( $ 20,000 x 4 x 3.170)	$ 253,600
NPV (253,600-200,000)	$ 53,600

2.     Calculate present Value of Variable Cost

Variable Cost ( 20,000 @ 8 )	160,000
Annuity Factor 4 years	3.170
Present Value of Variable Cost	$ 507,200

3.    Margin of safety for contribution

= $ 53,600/$ 507,200 x 100

=10.56%

Cost is to be raised by 10.56% to bring the NPV to the level of Zero. Therefore variable cost is more sensitive to the NPV.

Disadvantages of Expected Value

Disadvantages of Expected Value

Disadvantages of expected value can be explained in term subjective calculation, average results, limited use.

1.    Subjective Calculation

Expected value highly depends on the probability, which is a subjective thing. It means no accurate probabilities can be calculated, different people would give you different expectation (probabilities of outcome).

2.    Average Value

Expected value gives you an average result and not actual outcome. It means that results of expected can only be tele with actual result by chance.

3.    Only useful for repetitive outcome

Expected value concept has more usefulness, where outcome repeated. In case of one time activity (project analyses), it has little usefulness.

NPV (x)	Probability (p)	Expected Value (P*x)
5000	.2	1000
10,000	.8	8000
Expected Value		9,000

Calculate Money Price Level

Calculate Money Price Level

Money price level can be calculated from today price level (real price level).

 Money price level Example

Sales recorded for year 2001 at today price level in 3 years would be 600,000. What would be money price level, if inflation is 12%.

Solution

Today price level = 600,000

Inflated price level = 600,000 (1+.12)³

842,957 (money price level)

Today Price Level

Today Price Level

Today price level means there is no inflation accounted for or allowed (prices without inflation). Today price level is also known as real price level.

Today price level Example

Revenue at today price level in 5 years would be 400,000. What would be inflated price level, if inflation is 9%.

Solution

Today price level = 400,000

Inflated price level = 400,000 (1+.09)⁵

615,450 (Inflated price level)

Tax and cash Flows

Tax and cash Flows

Tax on profit or income will reduce your cash flows, because you need to pay tax which is an outflow of cash, while tax on expense will reduce improve your cash flow due to tax saved on expenses.

Expenses = save tax = tax payment reduces= cash outflow reduces

Income = Tax imposed= Tax payment = cash outflow increases

Tax and cash flows Example

ABC Co cash profit for the year ended 2001 is 70,000. Tax rate applicable on company is 30%, depreciation expense during the year 2001 was 20,000. Calculate the net cash flow.

Solution

Cash profit = 70,000

Less tax Expenses i.e. 30% of 70,000 (Cash profit) = (21,000)

Add tax saving i.e. 30% of 20,000 (Depreciation) = 6,000

Net Cash Flow = 55,000

It is important to remember that income increase tax expense, while expense reduces tax expense.