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: $w<em>D = \dfrac{D}{V},\; w</em>{PS} = \dfrac{PS}{V},\; w_{CE} = \dfrac{CE}{V}.$

Example (Cannae):

• Book debt $=10M$, trades at $95\%$ of face ⇒ $D=9.5M$.
• Book equity $=10M$, but 1 000 000 shares × $\$30$ ⇒ $CE = 30M$.
• $V = 39.5M$.
• $w<em>D \approx 24.1\%,\; w</em>{CE} \approx 75.9\%$ (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): $r<em>{PS} = \dfrac{D</em>{PS}}{P_{PS}}.$
• 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 $r<em>{CE}= R</em>F + \beta (R<em>M - R</em>F).$
   • 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) $r<em>{CE}= \frac{D</em>1}{P_0}+g.$
   • 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):
$\text{WACC}=w<em>D\;r</em>D(1-T)+w<em>{PS}\;r</em>{PS}+w<em>{CE}\;r</em>{CE}.$

AT&T Illustration:

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

Target Drill Practice (data provided):

• Pretax $r<em>D=6\%,$ tax rate $25\%,$ weights $w</em>D=18\%,\; w_{CE}=82\%.$
• Compute: $\text{WACC}=0.18\times6\%(1-0.25)+0.82\times r<em>{CE}=10.2\%$ (implied $r</em>{CE} \approx 11.8\%$ 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
  • $\beta=0.14,$ $r<em>{CE}=3.8\%,$ $r</em>D=2.9\%,\; w_D\small\text{ low}.$
  • 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: $r<em>{CE} > r</em>D$ 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: $r<em>{PS}=D</em>{PS}/P_{PS}.$
   • Equity: use CAPM, and/or $r<em>{CE}=D</em>1/P_0+g.$
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 $P<em>0 = D</em>1/(r-g)$ (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).