Introductory Corporate Finance: Time Value of Money - Uneven Cash, Flows Net Present Value Calculation

What This Is

Uneven cash flows refer to the irregular and unpredictable nature of a company's cash inflows and outflows. This concept is crucial in corporate finance as it affects a company's ability to generate cash, meet its obligations, and invest in growth opportunities. For instance, consider Tesla, which generates most of its revenue from the sale of electric vehicles, but also incurs significant expenses for research and development, marketing, and manufacturing. In a given quarter, Tesla might receive a large payment from a customer, but also face a significant expense for a new production line.

Key Formulas & Models

• FCFF = EBIT(1-T) + Depreciation - Capital Expenditures - Change in Working Capital – free cash flow to the firm; measures a company's ability to generate cash from operations.
• WACC = wd × rd(1-T) + wps × rps + we × re – weighted average cost of capital; used as discount rate.
• PV = FV / (1 + r)^n – present value; calculates the current value of a future cash flow.
• NPV = ?(PV of each cash flow) – net present value; measures the value of a project or investment.
• IRR = r – internal rate of return; the discount rate at which NPV equals zero.
• DOL = Q(P-V) / (Q(P-V)-F) – degree of operating leverage; measures EBIT sensitivity to sales.
• DFL = Q(P-V) / (Q(P-V)+I) – degree of financial leverage; measures EBIT sensitivity to interest expenses.
• Sustainable Growth Rate = ROE × (1 - Retention Ratio) – measures a company's ability to sustain growth through internal financing.
• FCFE = FCFF - Capital Expenditures + Change in Working Capital – free cash flow to equity; measures a company's ability to generate cash for shareholders.

Step-by-Step Calculation

1. Calculate EBIT: Tesla's EBIT for the quarter is $500M.
2. Calculate Depreciation: Tesla's depreciation for the quarter is $100M.
3. Calculate Capital Expenditures: Tesla's capital expenditures for the quarter are $200M.
4. Calculate Change in Working Capital: Tesla's change in working capital for the quarter is -$50M.
5. Calculate FCFF: FCFF = $500M(1-0.25) + $100M - $200M - (-$50M) = $375M + $100M - $200M + $50M = $325M.
6. Calculate WACC: WACC = 0.6 × 0.08(1-0.25) + 0.4 × 0.12 + 0.1 × 0.15 = 0.06 + 0.048 + 0.015 = 0.123 or 12.3%.

Common Mistakes

• Mistake: Using book value instead of market value for WACC.
• Correction: Use market value to reflect the company's current market position and risk.

• Counterexample: If Tesla's market value is $100B and its book value is $50B, using book value would result in a WACC of 10%, while using market value would result in a WACC of 12.3%.

• Mistake: Ignoring flotation costs when calculating WACC.

• Correction: Include flotation costs to reflect the true cost of capital.

• Counterexample: If Tesla's flotation costs are 5% of its market value, its WACC would increase from 12.3% to 13.1%.

• Mistake: Confusing sunk cost with opportunity cost.

• Correction: Use opportunity cost to reflect the true cost of a decision.
• Counterexample: If Tesla invested $100M in a new production line, the sunk cost would be $100M, but the opportunity cost would be the potential return on investment.

Exam / CFA Tips

• M&M Proposition I (no taxes): Firm value is independent of capital structure.
• M&M Proposition II (with taxes): Firm value increases with debt due to the interest tax shield.
• IRR vs NPV ranking: IRR and NPV may rank projects differently due to the non-linear relationship between NPV and the discount rate.
• Dividend irrelevance: The value of a company is independent of its dividend policy.

Quick Practice Problem

A company has EBIT of $10M, interest $2M, tax 25% – compute DFL.

Answer: DFL = $10M / ($10M + $2M) = 0.83.

Explanation: The degree of financial leverage (DFL) measures the sensitivity of EBIT to interest expenses. In this case, the DFL is 0.83, indicating that a 1% increase in interest expenses would result in an 0.83% decrease in EBIT.

Last-Minute Cram Sheet

• FCFF: Free cash flow to the firm; measures a company's ability to generate cash from operations.
• WACC: Weighted average cost of capital; used as discount rate.
• PV: Present value; calculates the current value of a future cash flow.
• NPV: Net present value; measures the value of a project or investment.
• IRR: Internal rate of return; the discount rate at which NPV equals zero.
• DOL: Degree of operating leverage; measures EBIT sensitivity to sales.
• DFL: Degree of financial leverage; measures EBIT sensitivity to interest expenses.
• Sustainable Growth Rate: Measures a company's ability to sustain growth through internal financing.
• FCFE: Free cash flow to equity; measures a company's ability to generate cash for shareholders.
• In M&M Proposition I (no taxes), firm value is independent of capital structure – but with taxes, value increases with debt due to the interest tax shield.