Weighted Average Cost of Capital – Chapter 13

Objectives and Big-Picture Purpose

• Understand what drives a firm’s overall cost of money, i.e., its Weighted Average Cost of Capital (WACC).
• Measure/estimate the annual cost of each financing source (debt, preferred stock, common equity).
• Combine those costs using market-value weights to get one blended rate.
• Primary uses:
  • Discount rate for Net Present Value (NPV) analysis.
  • Hurdle rate to compare against Internal Rate of Return (IRR).
  • Overall valuation of a firm or of individual projects.
• Value-creation rule:
  • If project IRR > WACC ⇒ expected to create shareholder value (e.g., IRR 18\% vs. WACC 14\%).

Financing Sources & Terminology

• Debt (bonds, notes) → interest is tax-deductible.
• Preferred stock → fixed dividend, no maturity, ranks above common but below debt.
• Common equity → residual ownership; highest risk, highest required return.
• Key distinction: Market value (current economic worth) vs. Book value (historical accounting amounts).

Step 1 – Determine Market-Value Weights

• Collect market value for EACH capital component.
  • Debt market value = Book/face value × current bond price (% of par).
  • Preferred & common equity market value = Shares outstanding × market price per share.
• Total capital V = D + PS + CE.
• Compute weights: wD = \dfrac{D}{V},\; w{PS} = \dfrac{PS}{V},\; w_{CE} = \dfrac{CE}{V}.

Example (Cannae):

• Book debt =10M, trades at 95\% of face ⇒ D=9.5M.
• Book equity =10M, but 1 000 000 shares × \$30 ⇒ CE = 30M.
• V = 39.5M.
• wD \approx 24.1\%,\; w{CE} \approx 75.9\% (book-value split would have been 50/50 ‑- illustrates why market values matter).

Real-firm capital structures (market values):

• Southern Co: CE \approx 70B, D \approx 57B (mainly equity but sizable debt).
• Amazon: CE \approx 1{,}030B, D \approx 164B (≈ 16\% debt, 84\% equity).

Step 2 – Estimate Component (Marginal) Costs

2A – Cost of Debt r_D

• Use yield to maturity (YTM) on outstanding bonds (solve for I/Y on calculator).
• Example (AT&T):
  • Pretax YTM =3.18\%.
  • After-tax cost r_D(1-T) = 3.18\% \times (1-0.25) = 2.385\%.
  • Reason: Interest expense shelters taxes; multiply by (1-T).

2B – Cost of Preferred Stock r_{PS}

• Constant-dividend security (no growth).
• Rearranged Gordon formula (zero-growth): r{PS} = \dfrac{D{PS}}{P_{PS}}.
• Example (AT&T preferred):
  • Price P = \$25.43, dividend D = \$1.37 ⇒ r_{PS}=5.39\%.
• Example (Arlington 7% Series B cum.):
  • Face =\$25, coupon rate 7\% ⇒ dividend 1.75.
  • Market price 21.22 ⇒ r_{PS} = \dfrac{1.75}{21.22}=8.25\%.

2C – Cost of Common Equity r_{CE}

Two mainstream methods:

1. CAPM / Security Market Line r{CE}= RF + \beta (RM - RF).
   • Example (AT&T): R_F=3\%, \beta=0.6, market risk premium =6\%.
   • r_{CE}=3\%+0.6\times6\%=6.6\%.
2. Dividend Growth (Gordon) Model (constant-growth firms only) r{CE}= \frac{D1}{P_0}+g.
   • Gives an alternative figure; analysts may average the two if both are credible.

Hierarchy of risk & cost: rD(1-T) < r{PS} < r_{CE}.

Step 3 – Compute WACC

General formula (after-tax for debt only):
\text{WACC}=wD\;rD(1-T)+w{PS}\;r{PS}+w{CE}\;r{CE}.

AT&T Illustration:

• Market values: CE=234B,\; PS=2B,\; D=176B, V=413B.
• Weights: w{CE}=234/413=56.6\%, w{PS}=2/413=0.5\%, w_{D}=176/413=42.6\%.
• Component costs: rD(1-T)=2.385\%, r{PS}=5.39\%, r_{CE}=6.6\%.
• WACC: 0.426\times2.385\% + 0.005\times5.39\% + 0.566\times6.6\% \approx 4.8\%.

Target Drill Practice (data provided):

• Pretax rD=6\%, tax rate 25\%, weights wD=18\%,\; w_{CE}=82\%.
• Compute: \text{WACC}=0.18\times6\%(1-0.25)+0.82\times r{CE}=10.2\% (implied r{CE} \approx 11.8\% given solution).

Applications & Managerial Interpretation

• Use WACC as discount rate in capital budgeting:
  • NPV: discount project cash flows at WACC.
  • IRR rule: accept if \text{IRR} > \text{WACC}.
• Higher risk (β, leverage, sector) ⇒ higher WACC ⇒ tougher hurdle.
• Firm-wide vs. Project-specific: Ideally match project risk; otherwise WACC is default.

Snapshot of Actual Firms (illustrative table in lecture)

• Low-risk example: Hershey
  • \beta=0.14, r{CE}=3.8\%, rD=2.9\%,\; w_D\small\text{ low}.
  • WACC \approx 3.6\%.
• High-risk example: AMD
  • \beta=2.52, much larger equity cost.
  • WACC \approx 17.6\%.
• Pattern: Tech/manufacturing & highly levered firms sit at lower list positions (high WACC); stable consumer staples/utilities at upper positions (low WACC).
• Always verify: r{CE} > rD because equity holders are residual claimants.

Ethical, Philosophical & Practical Notes

• Choosing book values understates (or misstates) current economics; ethical duty to use market data to inform shareholders accurately.
• Under-estimating WACC may lead to over-investment; over-estimating may cause firms to reject value-adding projects.
• Tax deductibility of interest creates incentives for leverage; however, excessive debt raises bankruptcy risk – a trade-off tied back to WACC.

Comprehensive Procedure Checklist

1. Gather current market values for debt, preferred, and equity.
2. Compute weights w_i by dividing each component by total V.
3. Estimate costs:
   • Debt: solve for YTM, then apply (1-T).
   • Preferred: r{PS}=D{PS}/P_{PS}.
   • Equity: use CAPM, and/or r{CE}=D1/P_0+g.
4. Plug into WACC formula; present percentage to at least one decimal place.
5. Apply WACC as discount/hurdle in all valuation exercises.

Connections to Earlier Material

• Bond valuation chapter taught solving for YTM (link to Step 2A).
• Dividend Discount Model covered formula P0 = D1/(r-g) (link to 2B & 2C).
• CAPM & β estimation came from risk-return lectures (foundation for equity cost).

End-of-Chapter Summary Bullets

• WACC captures blended, opportunity cost of capital using market values.
• Only debt enjoys a tax shield ⇒ adjust it after tax.
• Equity is always costlier than debt; firm risk profile drives both.
• Correct WACC is central to sound capital budgeting and firm valuation.
• Methodological discipline: use up-to-date market inputs, verify assumptions (constant growth, β stability, tax rate).