Introductory Corporate Finance: Capital Budgeting - Profitability Index, PI PV of Future Cash Flows Initial Investment

What This Is

The Profitability Index (PI) is a metric used to evaluate the attractiveness of a project or investment by comparing its present value of future cash flows to its initial investment. It's a crucial concept in corporate finance, as it helps investors and managers decide whether to pursue a project or not. For instance, consider a company like Tesla, which is considering investing $100 million in a new electric vehicle production line. If the present value of future cash flows from this investment is $120 million, the PI would be 1.2, indicating that the investment is profitable.

Key Formulas & Models

• PI = PV of Future Cash Flows / Initial Investment – measures the return on investment.
• PV of Future Cash Flows: present value of future cash inflows and outflows.
• Initial Investment: the upfront cost of the project.
• WACC = wd × rd(1?T) + wps × rps + we × re – weighted average cost of capital; used as discount rate.
• wd: weight of debt.
• rd: cost of debt.
• T: tax rate.
• wps: weight of preferred stock.
• rps: cost of preferred stock.
• we: weight of equity.
• re: cost of equity.
• DCF = FCF / (WACC - g) – discounted cash flow model; estimates firm value.
• FCF: free cash flow.
• g: growth rate.
• FCF = EBIT + Depreciation - Capital Expenditures - Change in Working Capital – free cash flow; measures cash generated from operations.
• EBIT: earnings before interest and taxes.
• Depreciation: non-cash expense.
• Capital Expenditures: investments in assets.
• Change in Working Capital: changes in accounts receivable, inventory, etc.
• g = ROE × (1 - b) – sustainable growth rate; estimates firm growth.
• ROE: return on equity.
• b: retention ratio.
• DFL = EBIT / (1 - T) – debt-free leverage; measures EBIT sensitivity to sales.
• T: tax rate.

Step-by-Step Calculation

1. Estimate the free cash flow (FCF) using the formula: FCF = EBIT + Depreciation - Capital Expenditures - Change in Working Capital.
2. Calculate the weighted average cost of capital (WACC) using the formula: WACC = wd × rd(1-T) + wps × rps + we × re.
3. Estimate the growth rate (g) using the formula: g = ROE × (1 - b).
4. Apply the discounted cash flow (DCF) model to estimate firm value: DCF = FCF / (WACC - g).
5. Calculate the present value of future cash flows using the formula: PV of Future Cash Flows = FCF / (1 + WACC)^n, where n is the number of periods.
6. Compute the Profitability Index (PI) by dividing the present value of future cash flows by the initial investment.

Common Mistakes

• Mistake: Using book value instead of market value for WACC.
• Correction: Use market value for WACC, as it reflects the current market price of the firm's capital structure.
• Counterexample: If a company has a market value of $100 million and a book value of $50 million, using book value for WACC would result in an incorrect estimate of the firm's cost of capital.
• Mistake: Ignoring flotation costs when calculating WACC.
• Correction: Include flotation costs in the calculation of WACC, as they represent the costs associated with issuing new debt or equity.
• Counterexample: If a company issues new debt with a flotation cost of 5%, ignoring this cost would result in an incorrect estimate of the firm's cost of capital.
• Mistake: Confusing sunk cost with opportunity cost.
• Correction: Treat sunk costs as non-recoverable expenses and opportunity costs as the benefits forgone by choosing one option over another.
• Counterexample: If a company invests $100 million in a project and the opportunity cost is $50 million, the correct opportunity cost is $50 million, not $100 million.

Exam / CFA Tips

• Tip: Be able to distinguish between M&M Proposition I (no taxes) and M&M Proposition II (with taxes).
• Why: M&M Proposition I states that firm value is independent of capital structure, while M&M Proposition II states that firm value increases with debt due to the interest tax shield.
• Tip: Understand the difference between IRR and NPV ranking.
• Why: IRR ranking prioritizes projects with higher internal rates of return, while NPV ranking prioritizes projects with higher net present values.
• Tip: Be able to calculate the sustainable growth rate using the formula: g = ROE × (1 - b).

Quick Practice Problem

A company has EBIT of $10 million, interest of $2 million, and a tax rate of 25%. Compute the debt-free leverage (DFL).

Answer: DFL = $10 million / (1 - 0.25) = $13.33 million.

Explanation: The debt-free leverage measures the sensitivity of EBIT to sales, and in this case, it is $13.33 million.

Last-Minute Cram Sheet

• Profitability Index (PI): measures the return on investment by comparing the present value of future cash flows to the initial investment.
• Weighted Average Cost of Capital (WACC): estimates the firm's cost of capital by weighting the costs of debt, preferred stock, and equity.
• Discounted Cash Flow (DCF) Model: estimates firm value by discounting future cash flows using the WACC.
• Free Cash Flow (FCF): measures cash generated from operations by subtracting capital expenditures and change in working capital from EBIT.
• Sustainable Growth Rate (g): estimates firm growth by multiplying ROE by (1 - b).
• Debt-Free Leverage (DFL): measures EBIT sensitivity to sales by dividing EBIT by (1 - T).
• M&M Proposition I (no taxes): states that firm value is independent of capital structure.
• M&M Proposition II (with taxes): states that firm value increases with debt due to the interest tax shield.
• IRR vs NPV Ranking: IRR prioritizes projects with higher internal rates of return, while NPV prioritizes projects with higher net present values.
• 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.