Chapter 11 - Sensitivity and Cost of Capital4

Sensitivity Analysis

  • Presenter: Dr. Mihrimah Ozmen

  • Location: Auburn University, Samuel Ginn College of Engineering

Project Risk

  • Risk: The potential for loss in a project.

  • Project Risk: Variability in a project’s net present worth (NPW), equivalent annual worth (AW), internal rate of return (IRR), payback period (PB), or benefit-cost (BC) ratio.

  • Risk Analysis: Involves the assessment of uncertain outcomes using techniques such as sensitivity analysis, probability distributions, simulations, etc.

Describing Project Risk

  • Sensitivity Analysis: Identifying project variables and their impacts on project acceptability.

  • Break-Even Analysis: Finding the value of a key variable that results in breaking even.

  • Scenario Analysis: Evaluating base case, worst case, and best case scenarios to compare likely and extreme outcomes.

Considering Risk

  • Most parameters in engineering economic studies are uncertain, some more so than others.

  • First Cost vs. Salvage Value: Initial investment costs vs potential resale value at the end of a project's life.

  • Benefits: Often are difficult to quantify.

  • Savings vs. Sales: Comparing cost savings with revenue from sales.

Key Variables in Project Analysis

  1. First Cost (Investment)

  2. Revenues / Sales / Benefits / Savings

  3. Operating and Maintenance Expenses

  4. Financing / Loan / Mortgage

  5. Salvage Value

  6. Project Lifetime / Early Termination

  7. Minimum Attractive Rate of Return (MARR):

    • Includes risk-free return + inflation + risk premium.

Sensitivity Analysis: Influential Variable (Example 11.1)

  • Case Study: Capstone Turbine Corporation’s MicroCHP Generator.

  • Initial Investment: $55 million.

  • Key Uncertainties: Market size and growth potential.

Revenue and Cost Estimates

  • Annual Revenues: Calculated as:Revenues = market size * unit price * (1 + growth rate)^n

  • Annual Costs: Calculated as:Costs = market size * variable unit cost * (1 + growth rate)^n + fixed cost (excluding depreciation).

Cash Flow Statement for MicroCHP Project

  • Critical Variables: Market size, growth rate, unit price, variable and fixed costs, and salvage value are critical for analysis.

Sensitivity Analysis Steps

  • Start with base-case estimates.

  • Adjust variables by 5% increments (up to ±20%).

  • Analyze changes in NPW due to adjustments.

Sensitivity Graphs (Capstone MicroCHP Project)

  • Understanding sensitivity graphs shows how NPW changes with key variable adjustments.

  • Key Observations:

    • High Sensitivity: Unit price and variable cost.

    • Moderate Sensitivity: Demand.

    • Low Sensitivity: Growth rate, fixed cost, and salvage value.

  • Limitation noted: No interaction effects displayed.

Break-Even Analysis Purpose

  • Determines the threshold where sales decrease or costs increase, leading to losses.

  • Utilizes Excel’s Goal Seek to set NPW to zero.

Break-Even Analysis Example (Project Economics)

  • Key questions:

    • How much can unit price decrease before losses occur?

    • How much can unit variable cost increase before losses occur?

Scenario Analysis Purpose

  • Evaluates NPW sensitivity under multiple variables and various market conditions.

    • Best-case, worst-case, and base-case scenarios identified.

Best and Worst Case Analysis Steps

  1. Estimate best and worst outcomes for all uncertain parameters.

  2. Calculate financial performance using best and worst scenarios.

  • Companies typically concentrate on maximizing downside awareness, assessing worst-case outcomes.

Example 11.1 Scenario Outcomes

  • Worst-case: Total investment lost, with a negative rate of return.

  • Best-case: $113 million surplus with an 80% rate of return.

Input Data for Scenarios

  • Unit Price:

    • Worst-case: $72.00

    • Most Likely: $80.00

    • Best-case: $86.00

  • Demand: 1000 (Worst) to 2000 (Best).

  • Growth Rate: Range from 3% (Worst) to 8% (Best).

  • Variable Cost per unit: $65.00 (Worst) to $56.00 (Best).

Investment Risk Considerations

  • Including Risk in Investment Evaluation: Evaluates potential profits versus risks involved in investment decisions.

  • Probabilistic Cash Flow Analysis:

    • Two methods to include risk:

      1. Probabilistic assessment directly incorporating risk elements.

      2. Risk-adjusted discount rates modifying rates to reflect risk.

Value at Risk (VaR)

  • Measures potential loss over time at a certain confidence level.

  • Answers the question, "What is the maximum potential loss?"

  • Calculation involves historical returns.

Cost of Capital Overview

  • Discusses financial measures affecting investment, money retention, and projected growth for businesses.

Financing Sources

  • Debt Sources:

    • Bonds, loans, and mortgages categorized based on security levels.

  • Equity Sources:

    • Common and preferred stock.

  • Explain costs involved:

    • Cost of Debt, Cost of Equity, and Weighted Average Cost of Capital (WACC) method discussed.