Understanding Equity, WACC, and Discount Rates in Finance

Equity and Financial Concepts

Free Cash Flow (FCF)

FCF_t = EBIT + DEP - CAPEX - ΔWC - TAX

ΔWC = Δreceivables + Δinventories - Δpayables + Δother items

TAX = (EBIT-Y_t)*T = EBIT*T - Y_tT

FCFE = FCF_t - Y_t - PRINC_t

FCF_t^u = FCF_t - Y_tT

Y = k_dD₀ (interest paid is cost of debt*value of debt)

Standard WACC

k_s=(1-L)k_e + Lk_d(1-T) | Use Standard WACC with FCF_u | ITS is not included in both FCF_u & k_s | Need Constant Target Leverage Ratio (L)

k_e = reflects operating and financial risk faced by investors | k_u = unlevered cost of equity (if firm had no debt), reflects operating risk

V₀ = U₀ + I₀ (Enterprise Value = value of operations + value of ITS) | Leave space for Standard WACC equation if k_its = k_d OR k_its = k_u

Standard WACC model implicitly assumes k_its = k_u | V₀ = U₀ + I₀

Vanilla WACC

k_v = (1-L)k_e + Lk_d | Use Vanilla WACC with FCF_t | ITS is included in both FCF_t & k_v | Need to know value of debt at start of each period - use Vanilla WACC with target debt schedule | STANDARD WACC AND VANILLA WACC: k_s = k_v - k_dTL

If k_its = k_d: if k_its = k_u:

Approximation error: ITS is dependent on future debt levels, just ask risky as firms debt so should be valued discount rate k_its = k_d BUT Vanilla WACC assumes k_its = k_u so k_v = k_u since approximation error is small

Recursive Standard WACC

Discount Rates

Fama French 3 Factor: E(MRP): Market Risk Premium | E(SMB) Size Premium | E(HML) Value Premium

Investors expect higher returns on: small stocks (relatively small market value of equity) & value stocks (high Book Equity/Market Equity, B/M, ratios, low P/E ratios, low growth rates) - compared to big stocks and growth stocks (low B/M ratios, high P/E, high growth rates)

Total risk to determine expected cash flows, only systematic risk for determining discount rates

Cost of Debt:

y = r_f + Credit Spread

If debt is risk free or not "too risky": k_d = y = r_f + Credit Spread | Appropriate assumption for investment grade debt rated BBB or better

Miscellaneous Issues

Surplus Assets:

cash, unused land or properties, investments in financial securities such as shares in unrelated companies, joint ventures, other non consolidated investments

Non-Consolidated Entities:

joint ventures, equity investments etc. : Firms investment in other entities which it does not control

Non-Controlling Interests:

subsidiary (or other entity in group) is controlled by the firm, consolidated financial statements, but less than 100% owned by firm. Represents external claim on FCFE generated by subsidiary. V₀ and E₀ will include value of non-controlling interest

V₀ = V^ex₀ + S₀ = D₀ + E₀ + N₀ where S = value of surplus assets, N = value of non-controlling interests

V^ex₀ = D₀ + E^ex₀ where E^ex₀ = E₀ - S₀ equity value excl. surplus assets

One-Off Items:

Income or expenditure item included in FCF which is not expected to arise again in future period

Corporate Taxes:

Estimate FCF assuming whole of EBIT is subject to tax at statutory corporate tax rate T

Leases:

If you treat lease as equivalent to debt, use FCF before lease payments & add lease liability to debt in calculating cost of capital

If you do not treat the lease as equivalent to debt: use FCF after lease payments & do not add lease liability to debt in calculating cost of capital