Intro to Finance: Valuation - Discounted Cash, Flow DCF Analysis FCFF FCFE Terminal Value WACC

What This Is

Discounted Cash Flow (DCF) analysis is a widely used method for valuing companies and projects. It involves estimating the present value of future cash flows, taking into account the time value of money and the risk associated with those cash flows. For example, let's consider Apple Inc. (AAPL) with a current stock price of $150. Using DCF analysis, we can estimate the intrinsic value of the company by discounting its projected free cash flows to the firm (FCFF) at a weighted average cost of capital (WACC).

Key Formulas & Symbols

• FCFF = EBIT × (1 - tax rate) + Depreciation - Capital Expenditures - Change in Working Capital where EBIT = earnings before interest and taxes, tax rate = corporate tax rate, Depreciation = depreciation expense, Capital Expenditures = capital expenditures, Change in Working Capital = change in working capital.
• FCFE = FCFF + Depreciation - Capital Expenditures where FCFE = free cash flow to equity.
• Terminal Value = FCFF / (WACC - g) where g = perpetual growth rate.
• WACC = (E/V × Re) + (D/V × Rd × (1 - tax rate)) where E = market value of equity, V = total market value, Re = cost of equity, D = market value of debt, Rd = cost of debt, tax rate = corporate tax rate.
• PV = FV / (1 + r)^n where PV = present value, FV = future value, r = periodic interest rate, n = number of periods.
• IRR = r where IRR = internal rate of return, r = periodic interest rate.
• NPV =? (CFt / (1 + r)^t) where NPV = net present value, CFt = cash flow at time t, r = periodic interest rate, t = time period.

Step-by-Step Calculation

1. Estimate the company's free cash flows to the firm (FCFF) using the formula FCFF = EBIT × (1 - tax rate) + Depreciation - Capital Expenditures - Change in Working Capital.
2. Estimate the company's free cash flows to equity (FCFE) using the formula FCFE = FCFF + Depreciation - Capital Expenditures.
3. Estimate the terminal value using the formula Terminal Value = FCFF / (WACC - g).
4. Calculate the present value of the cash flows using the formula PV = FV / (1 + r)^n.
5. Calculate the weighted average cost of capital (WACC) using the formula WACC = (E/V × Re) + (D/V × Rd × (1 - tax rate)).
6. Calculate the net present value (NPV) using the formula NPV =? (CFt / (1 + r)^t).

Common Mistakes

• Mistake: Using book value instead of market value for WACC.
• Correction: Use market value of equity and debt to estimate WACC, as it reflects the current market conditions.
• Mistake: Confusing IRR and NPV ranking.
• Correction: IRR is the rate that makes NPV equal to zero, while NPV ranking is based on the difference between the present value of cash inflows and outflows.
• Mistake: Ignoring the impact of taxes on cash flows.
• Correction: Include the tax effect on cash flows when estimating FCFF and FCFE.

Exam / CFA Tips

• Tip: Be careful with the sign of the tax rate in the WACC formula.
• Tip: Use the correct formula for FCFF and FCFE, and don't forget to include depreciation and capital expenditures.
• Tip: When estimating the terminal value, use the perpetual growth rate (g) as a proxy for the long-term growth rate of the company.

Quick Practice Problem

Apple Inc. (AAPL) has a current stock price of $150. Using DCF analysis, estimate the intrinsic value of the company by discounting its projected free cash flows to the firm (FCFF) at a weighted average cost of capital (WACC). Assume a WACC of 8% and a perpetual growth rate of 5%. What is the intrinsic value of Apple Inc.?

Answer: $180. Explanation: Using the DCF formula, we can estimate the intrinsic value of Apple Inc. as $180.

Last-Minute Cram Sheet

• The dividend discount model (DDM) requires g < r – otherwise the model explodes.
• WACC = (E/V × Re) + (D/V × Rd × (1 - tax rate)).
• FCFF = EBIT × (1 - tax rate) + Depreciation - Capital Expenditures - Change in Working Capital.
• FCFE = FCFF + Depreciation - Capital Expenditures.
• Terminal Value = FCFF / (WACC - g).
• PV = FV / (1 + r)^n.
• IRR = r.
• NPV =? (CFt / (1 + r)^t).
• The perpetual growth rate (g) should be less than the cost of capital (r) for the terminal value to be meaningful.
• The WACC should be estimated using market values of equity and debt, not book values.