Capital Investment Rule - Chapter 8 Examples

Chapter 8: Capital Investment Rules Net Present Value (NPV): The difference between the market value of a project and its cost. A positive NPV indicates that the project is expected to add value to the firm and increase wealth. Calculation Steps: Estimate expected cash flows. Estimate the required return (consider similar projects with the same risk level). Find the present value of cash flows and subtract the initial investment. Example 1: Costs: $50,000 Cost of capital: 20% Cash flows: Year 1: $70,000, Year 2: $22,000, Year 3: $22,500, Year 4: $21,000 NPV Calculation: $20,000 / (1+0.20)^1 + $22,000 / (1+0.20)^2 + $22,500 / (1+0.20)^3 + $21,000 / (1+0.20)^4 - $50,000 = $5,092.59 Conclusion: Since NPV is positive, the firm should introduce the project. Example 2: Costs: $1,000,000 Cash flows: $125,000 per year for 8 years Salvage value: $100,000 after 8 years Required rate of return: 6% NPV Calculation: (Not provided in the image) Conclusion: The conclusion is not explicitly stated in the image, but based on the NPV calculation, it's likely that the NPV would be negative, suggesting that the firm should not buy the machinery. Profitability Index (PI): Measures the benefit per unit cost. A PI of 1.1 indicates that for every $1 of investment, an additional $0.10 in value is created. Payback Rule: The length of time until accumulated cash flows equal or exceed the costs. A project should be accepted if the payback period is less than a predetermined cutoff period. Example 3: Two projects with initial costs of $25,000 Cash flows: (see table in the image) Payback Period Calculation: (Not provided in the image) Payback Period Calculation: Initial investment: $25,000 Cash flows: Year 1: $5,000, Year 2: $11,000, Year 3: $18,000, Year 4: $26,000 Payback period: 3 years and a fraction Fraction needed on final year: (25,000 - 18,000) / 26,000 = 0.875 Internal Rate of Return (IRR): Definition: The discount rate that makes NPV equal to zero. Investment decision: Make the investment if IRR is greater than the cost of capital. Easy Example: Project requires $10 investment today and generates $12 in one year. NPV equation: $12 / (1+r) - $10 = 0 Solving for r: r = 20% Manual Calculation Example: Project costs: $50,000 Cost of capital: 20% Cash flows: Year 1: $20,000, Year 2: $22,000, Year 3: $22,500, Year 4: $21,000 NPV calculation: (see table in the image) Conclusion: NPV is superior to IRR. When Rules Differ: Delayed investments: Both NPV and IRR will work if all negative cash flows precede all positive cash flows. Multiple IRRs: Abs. sum of positive cash flows is less than the abs. sum of negative cash flows. Nonexistent IRR: At least one negative cash flow and one positive cash flow. Multiple IRRs: Non-linearity and sign changes can lead to multiple points of inflection. IRR is still important because it provides a sense of average return on investment. Types of Projects: Independent: Do not affect other project decisions. NPV: Choose all projects with positive NPV. IRR: Choose all projects with IRR greater than the cost of capital. Mutually Exclusive: Can choose only one. NPV: Choose the project with the highest NPV (as long as NPV is positive). IRR: Choose the project with the highest IRR (as long as IRR is greater than the cost of capital). Example: Two Mutually Exclusive Projects: Project A: Initial investment: $100 Cash flows: Year 1: $50, Year 2: $70, Year 3: $40 Cost of capital: 15% Project B: Initial investment: $100 Cash flows: Year 1: $70, Year 2: $10, Year 3: $75 Cost of capital: 15% NPV and IRR Analysis: Project NPV IRR Accept if Independent Accept if Mutually Exclusive A 22.71 28.61% Yes Project A B 17.74 25.55% Yes Project A Project Analysis: Project A: NPV: 4.12 IRR: 223.61% Choose according to IRR Project B: NPV: 20.17 IRR: 155.08% Choose according to NPV Contingent Projects: Choose all or nothing if the sum of NPVs is greater than zero. Use joint IRR if the sum of NPVs is less than zero. Example: Two Contingent Projects: Project A: Initial investment: $130 Cash flows: Year 1: $60, Year 2: $50, Year 3: $40 Cost of capital: 13% Project B: Initial investment: $120 Cash flows: Year 1: $60, Year 2: $30, Year 3: $95 Cost of capital: 13% NPV and IRR Analysis: Project CF1 CF2 CF3 NPV IRR A 200 120 0 3.60 15.85% B 135 0 0 15.60 - Weighted Average: Should accept both according to NPV and IRR. Chapter 9: Capital Budgeting: FCF: Free Cash Flow, directly created by the project. FCF Calculation: EBIT(1-t) - Depreciation - ANNG - CAPEX ANNG: Additional Net Working Capital CAPEX: Capital Expenditures Rules for FCF: Measure FCF on an incremental basis. Exclude any cash flows paid to investors. Incorporate taxes. Ignore sunk cost but include opportunity cost. Include side effects. Net operating profit after taxes (NOPAT): EBIT(1-t) - depreciation. Cash Flow from Operations: EBIT(1-t) + depreciation. Net Working Capital (NWC): Current Assets - Current Liabilities