Intro to Finance: Capital Budgeting - Profitability Index, PI PV of Future CFs Initial Investment

What This Is

The Profitability Index (PI) is a metric used to evaluate the attractiveness of an investment opportunity. It measures the present value of future cash flows (PVCF) relative to the initial investment. For example, consider a project with a PVCF of $1,500 and an initial investment of $1,200. The PI would be $1,500 / $1,200 = 1.25, indicating that the project is expected to generate a 25% return on investment.

Key Formulas & Symbols

• PI = PVCF / Initial Investment where PI = profitability index, PVCF = present value of future cash flows, Initial Investment = initial investment outlay.
• PVCF =? (CFt / (1 + r)^t) where PVCF = present value of future cash flows, CFt = cash flow at time t, r = discount rate, t = time period.
• CFt = FCFt + ?NWCt + ?WCt where CFt = cash flow at time t, FCFt = free cash flow to the firm, ?NWCt = change in net working capital, ?WCt = change in working capital.
• FCFt = EBITt + Depreciationt - (CapExt + ?NWCt) where FCFt = free cash flow to the firm, EBITt = earnings before interest and taxes, Depreciationt = depreciation, CapExt = capital expenditures, ?NWCt = change in net working capital.
• WACC = (E/V x Re) + ((D/V x Rd) x (1 - Tc)) where WACC = weighted average cost of capital, E = market value of equity, V = total market value, Re = cost of equity, D = market value of debt, Rd = cost of debt, Tc = corporate tax rate.
• Cost of Equity = rRF +-x (rM - rRF) where Cost of Equity = cost of equity, rRF = risk-free rate,-= beta coefficient, rM = market risk premium.

Step-by-Step Calculation

1. Estimate the free cash flows to the firm (FCFt) for each time period using the formula: FCFt = EBITt + Depreciationt - (CapExt + ?NWCt).
2. Calculate the present value of each FCFt using the formula: PVCFt = FCFt / (1 + r)^t.
3. Sum the present values of all FCFt to get the present value of future cash flows (PVCF).
4. Calculate the initial investment outlay (Initial Investment).
5. Compute the profitability index (PI) by dividing the PVCF by the Initial Investment.

Common Mistakes

• Mistake: Using the wrong discount rate (e.g., using the cost of debt instead of the weighted average cost of capital).
• Correction: Use the weighted average cost of capital (WACC) as the discount rate, which takes into account both the cost of equity and debt.
• Mistake: Forgetting to account for changes in working capital (WCt) and net working capital (NWCt).
• Correction: Include the changes in working capital and net working capital in the calculation of free cash flows to the firm (FCFt).
• Mistake: Using the book value of equity and debt instead of their market values.
• Correction: Use the market values of equity and debt to calculate the weighted average cost of capital (WACC).

Exam / CFA Tips

• Tip: Be careful with the signs of the cash flows and the discount rate. A negative cash flow should be discounted at a negative rate.
• Tip: Make sure to account for any non-operating items, such as interest income or expenses, when calculating the free cash flows to the firm.
• Tip: Use the correct formula for the weighted average cost of capital (WACC), which takes into account both the cost of equity and debt.

Quick Practice Problem

A company is considering a project with the following cash flows:

Year 1: $100 Year 2: $150 Year 3: $200

The initial investment is $500. The discount rate is 10%. What is the profitability index (PI)?

Answer: PI = $450 / $500 = 0.9

Explanation: The present value of the cash flows is $450, calculated using the formula: PVCF =? (CFt / (1 + r)^t).

Last-Minute Cram Sheet

• PI = PVCF / Initial Investment
• PVCF =? (CFt / (1 + r)^t)
• CFt = FCFt + ?NWCt + ?WCt
• FCFt = EBITt + Depreciationt - (CapExt + ?NWCt)
• WACC = (E/V x Re) + ((D/V x Rd) x (1 - Tc))
• Cost of Equity = rRF +-x (rM - rRF)
• Use the weighted average cost of capital (WACC) as the discount rate
• Include changes in working capital and net working capital in the calculation of free cash flows to the firm (FCFt)
• Use the market values of equity and debt to calculate the weighted average cost of capital (WACC)