22 Chapter 11 – Capital Budgeting

Conceptual Questions

1. What is capital budgeting, and why is it important for making long-term investment decisions?

•Capital budgeting is the process of evaluating and selecting long-term investment projects to allocate resources effectively. It helps firms assess the profitability, risk, and strategic alignment of potential investments, ensuring that scarce resources are used to maximize shareholder value.

2. Differentiate between incremental cash flows and sunk costs. Provide an example of each.

•Incremental cash flows: Additional cash inflows or outflows directly resulting from a project.

Example: Revenue generated from a new product line.

•Sunk costs: Costs that have already been incurred and cannot be recovered.

Example: Market research costs incurred before deciding on a project.

3. Why are opportunity costs considered in capital budgeting? Explain with an example.

•Opportunity costs represent the value of the next best alternative forgone.

Example: If a firm uses its existing facility for a new project instead of renting it out for $500,000 annually, the opportunity cost is the forgone rental income.

4. What is NPV, and how does it differ from other evaluation metrics like IRR and Payback Period?

•NPV: Measures the present value of future cash flows minus the initial investment. It provides the absolute value added by a project.

•IRR: Identifies the discount rate that makes NPV zero but may not provide consistent rankings for mutually exclusive projects.

•Payback Period: Measures how quickly the investment is recovered, ignoring the time value of money and cash flows beyond the payback period.

5. How do real options such as the option to delay, expand, or abandon a project enhance decision-making in capital budgeting?

•Real options provide flexibility in managing projects under uncertainty.

•Delay: Reduces risk by waiting for more information.

•Expand: Captures additional value if conditions improve.

•Abandon: Limits losses if the project becomes unviable.

Short Calculations

1. 1. Depreciation Calculation

      • Formula:
        Depreciation Expense = Cost of Asset / Useful Life
      • Calculation:
        600,000 / 8 = 75,000 per year

   2. Free Cash Flow Calculation

      • Formula:
        FCF = Incremental Earnings + Depreciation − Capital Expenditures − Δ NWC
      • Calculation:
        FCF = 300,000 + 80,000 − 100,000 − 40,000 = 240,000

   3. Net Present Value Calculation

      • Formula:
        NPV = ∑ (FCF_t / (1 + r)^t) − Initial Investment
        Where:
        FCF = 400,000
        r = 0.10
        n = 4
        Initial Investment = 1,200,000
      • Calculation:
        Present Value of Cash Flows:
        PV = 400,000 / 1.10 + 400,000 / (1.10)^2 + 400,000 / (1.10)^3 + 400,000 / (1.10)^4 ≈ 1,268,200
        NPV = 1,268,200 − 1,200,000 = 68,200
      • Conclusion: The project is viable with an NPV of $68,200.

Scenario-Based Problems

1. Break-Even Analysis

•Formula:

[latex]\text{Break-Even Sales Volume} = \frac{\text{Fixed Costs}}{\text{Price per Unit} - \text{Variable Cost per Unit}}[/latex]

Calculation:

[latex]\text{Break-Even Sales Volume} = \frac{500,000}{60 - 35} = \frac{500,000}{25} = 20,000 , \text{units}[/latex]

2. Sensitivity Analysis

•Base Case: Revenue growth = 12%, NPV = $400,000

•Scenario 1: Revenue growth = 8%

NPV reduction = 4% drop in growth × project’s revenue sensitivity. Assume this reduces NPV by $120,000.

New NPV = $400,000 – $120,000 = $280,000

•Scenario 2: Revenue growth = 15%

NPV increase = 3% rise in growth × revenue sensitivity. Assume this increases NPV by $90,000.

New NPV = $400,000 + $90,000 = $490,000

Conclusion: The project is still viable under all scenarios but is more attractive in the high-growth scenario.

3. Real Options Challenge

•Circumstances Favoring Delay:

•High uncertainty in market demand or pricing.

•Significant changes in input costs or regulatory conditions anticipated.

•Factors Influencing the Decision:

•Costs of delaying, such as holding costs or opportunity losses.

•Improved information or reduction in uncertainty over the year.

•Potential value added by waiting (e.g., better pricing, reduced risk).

Conclusion: Delaying the project adds value if the market information gained outweighs holding costs and opportunity losses.

Interactive Challenge Answer Key

1. 1. Assessing Project Viability

      NPV Calculation:

      • Formula:
        NPV = ∑ (FCF_t / (1 + r)^t) − Initial Investment

      • Given:
        FCF = 600,000
        r = 0.08
        n = 5
        Initial Investment = 2,000,000

      • Using a financial calculator or Excel:
        PV of Cash Flows = 600,000 / 1.08 + 600,000 / (1.08)^2 + … + 600,000 / (1.08)^5 ≈ 2,397,000
        NPV = 2,397,000 − 2,000,000 = 397,000

      • Conclusion: The project is viable with an NPV of $397,000.

   2. Real Options: Delay vs. Immediate Investment

      • Immediate Investment: Assume baseline FCF projections yield an NPV of $700,000.

      • Delayed Investment:
        If the market improves, FCF increases by 20%. Assume baseline FCF of $700,000, adjusted for the 20% increase:
        New NPV = 700,000 × 1.2 = 840,000

        Subtract the holding cost of $100,000:
        Adjusted NPV (Delayed) = 840,000 − 100,000 = 740,000

      • Conclusion: Delaying the project offers a slightly higher NPV of $740,000 compared to $700,000, making it the better option if the market data supports improved returns.

   3. Scenario Analysis for a Manufacturing Facility

      • Best-Case Scenario:
        Revenue grows to $2 million:
        Incremental NPV increase = ($2,000,000 – $1,500,000) × 5 years = $2,500,000
        Total NPV = $250,000 (base case) + $2,500,000 = $2,750,000

      • Worst-Case Scenario:
        Revenue falls to $1 million:
        Incremental NPV decrease = ($1,000,000 – $1,500,000) × 5 years = -$2,500,000
        Total NPV = $250,000 (base case) – $2,500,000 = -$2,250,000

      • Conclusion: The project remains viable under the best-case scenario but becomes unfeasible under the worst case.

   4. Identify Key Variables in Sensitivity Analysis

      • Sales Volume Change (10% Increase or Decrease):

        If sales volume increases by 10%, incremental revenue increases by $100,000 annually:
        New NPV = Base NPV + (Revenue Increase × 5 years)

        If sales volume decreases by 10%, incremental revenue decreases by $100,000 annually:
        New NPV = Base NPV − (Revenue Decrease × 5 years)

      • Rent Costs Change (15% Increase):
        A 15% increase in rent costs increases fixed expenses. If annual rent is $200,000, an increase of $30,000 annually reduces the NPV:
        New NPV = Base NPV − (30,000 × 5 years) = Base NPV − 150,000

      • Recommendation:

        • Negotiate rent discounts or fixed-term leases to control costs.
        • Build contingencies into the project for potential sales shortfalls or cost overruns.
        • Conduct additional market research to ensure demand aligns with sales projections.