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Risk Assessment Examples

New Gadget Launch

Base Case Analysis:

First, calculate the base case NPV:

  • Annual Revenue = Sales Price per Unit * Units Sold = $100 * 10,000 = $1,000,000
  • Annual Variable Costs = Variable Cost per Unit * Units Sold = $60 * 10,000 = $600,000
  • Annual Profit = Revenue - Variable Costs - Fixed Costs = $1,000,000 - $600,000 - $200,000 = $200,000
  • NPV = -Initial Investment + Σ [Annual Profit / (1 + Discount Rate)^Year]
  • NPV = -$500,000 + ($200,000 / 1.12) + ($200,000 / 1.12^2) + ($200,000 / 1.12^3) + ($200,000 / 1.12^4) + ($200,000 / 1.12^5)
  • NPV = -$500,000 + $178,571.43 + $159,438.78 + $142,356.05 + $127,103.62 + $113,485.38
  • Base Case NPV = $280,955.26

1. Sensitivity Analysis

Let's assess sensitivity to Sales Price and Units Sold.

  • Sales Price Sensitivity:

    • +10% Sales Price ($110): Annual Profit = $300,000; NPV = $602,432.89
    • -10% Sales Price ($90): Annual Profit = $100,000; NPV = -$40,544.74

  • Units Sold Sensitivity:

    • +10% Units Sold (11,000): Annual Profit = $240,000; NPV = $402,432.89
    • -10% Units Sold (9,000): Annual Profit = $160,000; NPV = $159,438.78

  • Interpretation: The project's NPV is highly sensitive to both sales price and units sold. A 10% decrease in sales price turns the NPV negative, indicating significant risk.

2. Scenario Analysis

Let's create Best-Case, Worst-Case, and Most Likely Scenarios.

  • Best-Case:

    • Sales Price: $110 (+10%)
    • Units Sold: 11,000 (+10%)
    • Variable Cost: $55 (-8.33%)
    • Annual Profit = $451,000
    • NPV = $1,125,175.46

  • Most Likely (Base Case):

    • As calculated above, NPV = $280,955.26

  • Worst-Case:

    • Sales Price: $90 (-10%)
    • Units Sold: 9,000 (-10%)
    • Variable Cost: $65 (+8.33%)
    • Annual Profit = $51,500
    • NPV = -$318,574.06

  • Interpretation: The scenario analysis reveals a wide range of potential outcomes, from a highly profitable best-case scenario to a significant loss in the worst-case scenario. This highlights the inherent risks associated with the project.

3. Break-Even Analysis

  • Break-Even Point (Units):

    • Fixed Costs = $200,000
    • Sales Price per Unit = $100
    • Variable Cost per Unit = $60
    • Break-Even Point (Units) = Fixed Costs / (Sales Price - Variable Cost) = $200,000 / ($100 - $60) = 5,000 units

  • Break-Even Point (Sales Revenue):

    • Break-Even Point (Sales Revenue) = Fixed Costs / ((Sales Price - Variable Cost) / Sales Price) = $200,000 / (($100-$60)/$100) = $500,000

  • Interpretation: The project needs to sell 5,000 units or generate $500,000 in revenue to break even. If the project's sales are consistently below this level, it will incur losses.

4. Simulation Analysis (Conceptual)

  • Instead of single point estimates, each input variable (Sales Price, Units Sold, Variable Cost, Fixed Costs) would be assigned a probability distribution (e.g., normal, triangular).
  • A computer program would then randomly select a value for each variable from its distribution.
  • The NPV would be calculated using those values.
  • This process would be repeated thousands of times, resulting in a distribution of NPV outcomes.
  • From this distribution, we could estimate the probability of achieving a positive NPV, or the probability of NPV falling below a certain threshold.

5. Decision Tree Analysis (Conceptual)

  • Imagine that after Year 2, there is a decision to either:
    • Expand the project (requiring additional investment but potentially increasing sales)
    • Abandon the project (salvaging some value from the remaining assets).
  • A decision tree would map out these two branches. Each branch would have probabilities associated with different sales levels and associated cash flows.
  • The Expected Monetary Value (EMV) of each branch would be calculated, and the decision would be made to maximize the EMV.
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