Unit 10 answers the question every business owner and investor must ask: what does it cost to raise money? Every dollar of capital — whether borrowed (debt) or raised from owners (equity) — has a cost. The Weighted Average Cost of Capital (WACC) blends these costs into a single hurdle rate that any investment must clear to create value. WACC connects all prior units: interest rates (Unit 6), bond valuation (Unit 7), CAPM and beta (Unit 8), and stock valuation (Unit 9). For BBYM entrepreneurs evaluating community enterprise investments, WACC is the foundational tool for determining whether a project is worth pursuing.
Part 1 — Core Topics Explained
Every major concept tested on the Unit 10 assessment
📋 Learning Objectives
- Explain what WACC is and why it is the appropriate discount rate for evaluating investments
- Calculate the after-tax cost of debt and explain why the tax shield matters
- Calculate the cost of preferred stock as a perpetuity
- Estimate the cost of common equity using CAPM
- Calculate WACC from component costs and capital structure weights
- Use WACC as a hurdle rate to evaluate investment projects
- Explain the concept of optimal capital structure and the debt tax shield trade-off
- Apply WACC concepts to BBYM community enterprise financing decisions
1. What Is WACC and Why Does It Matter?
A company or enterprise raises capital from three main sources: debt (loans, bonds), preferred stock, and common equity (owner investment, retained earnings). Each source has a different cost. WACC is the blended, weighted average cost of all capital sources — the overall rate of return the firm must earn on its assets to satisfy all of its investors.
WACC as the Hurdle Rate:
If a BBYM community enterprise has a WACC of 9%, every new project must earn at least 9% to create value for investors. A project returning 12% clears the hurdle and adds value. A project returning 7% destroys value — the firm is earning less than what its capital costs. WACC is the minimum acceptable return — the benchmark against which all investment decisions are measured.
If a BBYM community enterprise has a WACC of 9%, every new project must earn at least 9% to create value for investors. A project returning 12% clears the hurdle and adds value. A project returning 7% destroys value — the firm is earning less than what its capital costs. WACC is the minimum acceptable return — the benchmark against which all investment decisions are measured.
Debt (cheapest — tax-deductible)
Preferred Stock (mid-cost — fixed, not deductible)
Common Equity (most expensive — residual risk)
Illustrative capital structure. WACC = weighted average of each component's after-tax cost.
2. The Three Capital Sources and Their Costs
| Capital Source | Cost Measure | Tax Deductible? | Typical Cost Range | Why It Costs This |
|---|---|---|---|---|
| Debt (loans, bonds) | After-tax cost = YTM × (1−T) | Yes — interest payments are a tax deduction | 3–7% after-tax | Lowest cost because lenders have priority claim and interest is tax-deductible; cheapest capital source |
| Preferred Stock | rᵔₛ = Dividend ÷ Price | No — dividends are paid from after-tax earnings | 6–10% | Higher than debt (no tax shield, junior to debt in bankruptcy) but lower than common equity (fixed dividend, priority over common) |
| Common Equity | rₛ = rᵣᵓ + RPᵖ × β (CAPM) | No — dividends/returns paid from after-tax earnings | 9–15% | Most expensive: equity holders bear the most risk (last in bankruptcy, variable returns) and demand the highest return |
Why Debt Is Always the Cheapest Capital Source:
Debt is cheap for two compounding reasons. First, lenders bear less risk than equity holders — they have a senior legal claim and are repaid before anyone else. Less risk means they accept a lower return. Second, the government subsidizes debt through the tax code: interest payments reduce taxable income, creating a tax shield. A company paying 6% interest in a 21% tax bracket effectively pays only 6% × (1−0.21) = 4.74% after the tax savings. Common equity has no such subsidy.
Debt is cheap for two compounding reasons. First, lenders bear less risk than equity holders — they have a senior legal claim and are repaid before anyone else. Less risk means they accept a lower return. Second, the government subsidizes debt through the tax code: interest payments reduce taxable income, creating a tax shield. A company paying 6% interest in a 21% tax bracket effectively pays only 6% × (1−0.21) = 4.74% after the tax savings. Common equity has no such subsidy.
3. The Three Cost Formulas
After-Tax Cost of Debt
rₛ(1−T) = YTM × (1 − Marginal Tax Rate)
YTM = yield to maturity on the firm's debt (pre-tax cost) | T = marginal corporate tax rate
Example: 6% YTM, 21% tax rate → After-tax cost = 6% × (1−0.21) = 6% × 0.79 = 4.74%
Example: 6% YTM, 21% tax rate → After-tax cost = 6% × (1−0.21) = 6% × 0.79 = 4.74%
Cost of Preferred Stock
rᵔₛ = Dᵔₛ ÷ Pᵔₛ
Dᵔₛ = annual preferred dividend | Pᵔₛ = current preferred stock price (or net proceeds if newly issued)
Example: $6 annual dividend, $85 price → rᵔₛ = $6 ÷ $85 = 7.06%
Example: $6 annual dividend, $85 price → rᵔₛ = $6 ÷ $85 = 7.06%
Cost of Common Equity (CAPM)
rₛ = rᵣᵓ + RPᵖ × β
Same CAPM formula from Unit 8 — the required return on equity IS the cost of equity
Example: rᵣᵓ = 4%, RPᵖ = 6%, β = 1.3 → rₛ = 4% + 6% × 1.3 = 11.8%
Example: rᵣᵓ = 4%, RPᵖ = 6%, β = 1.3 → rₛ = 4% + 6% × 1.3 = 11.8%
Weighted Average Cost of Capital (WACC)
WACC = wₛ × rₛ(1−T) + wᵔₛ × rᵔₛ + wᶜᵉ × rₛ
w = weight (proportion) of each capital source in the total capital structure
Weights are based on market values (not book values) and must sum to 1.0
Assessment Q10: wₛ=0.40, rₛ=6%, T=21%, wᶜᵉ=0.60, rₛ=12% → WACC = 0.40×4.74% + 0.60×12% = 1.90% + 7.20% = 9.1%
Weights are based on market values (not book values) and must sum to 1.0
Assessment Q10: wₛ=0.40, rₛ=6%, T=21%, wᶜᵉ=0.60, rₛ=12% → WACC = 0.40×4.74% + 0.60×12% = 1.90% + 7.20% = 9.1%
4. WACC as Hurdle Rate — Accept/Reject Logic
| Project Return vs. WACC | Decision | Reason | Effect on Firm Value |
|---|---|---|---|
| Project Return > WACC | ✓ Accept | Project earns more than it costs to finance — generates surplus value | Increases firm value (NPV > 0) |
| Project Return = WACC | ≈ Break-even | Project earns exactly its financing cost — no value creation or destruction | No change in firm value (NPV = 0) |
| Project Return < WACC | ✗ Reject | Project earns less than it costs to finance — destroys value | Decreases firm value (NPV < 0) |
BBYM Community Enterprise Application — Evaluating a Youth Workforce Training Center:
BBYM's WACC = 9.5% (blending CDFI loan cost and community equity investment).
Option A — Workforce Training Center: Projected annual return = 13.2% → EXCEEDS WACC → Accept ✓
Option B — Community Kitchen Expansion: Projected annual return = 7.8% → BELOW WACC → Reject ✗ (at least at current cost structure — could revisit if CDFI grants reduce the cost of capital)
Option A creates value for the community; Option B destroys it. WACC forces discipline — it prevents investing in feel-good projects that don't generate sufficient returns to sustain the enterprise long-term.
BBYM's WACC = 9.5% (blending CDFI loan cost and community equity investment).
Option A — Workforce Training Center: Projected annual return = 13.2% → EXCEEDS WACC → Accept ✓
Option B — Community Kitchen Expansion: Projected annual return = 7.8% → BELOW WACC → Reject ✗ (at least at current cost structure — could revisit if CDFI grants reduce the cost of capital)
Option A creates value for the community; Option B destroys it. WACC forces discipline — it prevents investing in feel-good projects that don't generate sufficient returns to sustain the enterprise long-term.
5. The Debt Tax Shield — Why Governments Subsidize Borrowing
The most powerful and often under-appreciated feature of debt financing is the interest tax shield: because interest is tax-deductible, the government effectively subsidizes a portion of every interest payment.
Tax Shield Calculation — $500,000 CDFI Loan at 7%:
Annual interest payment: $500,000 × 7% = $35,000
Tax shield (at 21% tax rate): $35,000 × 0.21 = $7,350/year
After-tax cost of interest: $35,000 − $7,350 = $27,650/year
After-tax interest rate: $27,650 ÷ $500,000 = 5.53% (vs. 7% pre-tax)
The IRS effectively pays $7,350/year of BBYM's interest bill. Over a 10-year loan term, the tax shield saves $73,500 that can be reinvested in community programs. This is why the after-tax cost of debt always appears in the WACC formula — and why profitable businesses use debt strategically.
Annual interest payment: $500,000 × 7% = $35,000
Tax shield (at 21% tax rate): $35,000 × 0.21 = $7,350/year
After-tax cost of interest: $35,000 − $7,350 = $27,650/year
After-tax interest rate: $27,650 ÷ $500,000 = 5.53% (vs. 7% pre-tax)
The IRS effectively pays $7,350/year of BBYM's interest bill. Over a 10-year loan term, the tax shield saves $73,500 that can be reinvested in community programs. This is why the after-tax cost of debt always appears in the WACC formula — and why profitable businesses use debt strategically.
Part 2 — WACC Calculations: Step-by-Step Worked Examples
Five complete WACC problems from simple to complex, including the Assessment Q10
Example 1 — Assessment Q10 (Exact)
Setup: 40% debt at 6% cost, 60% equity at 12% cost. Tax rate = 21%.
Step 1 — After-tax cost of debt:
rₛ(1−T) = 6% × (1−0.21) = 6% × 0.79 = 4.74%
Step 2 — WACC:
WACC = 0.40 × 4.74% + 0.60 × 12.0%
= 1.896% + 7.200%
= 9.096% ≈ 9.1%
The answer is 9.1%. Common error: forgetting to apply the (1−T) tax adjustment to debt — without it, WACC = 0.40×6% + 0.60×12% = 9.6%, which is wrong.
Step 1 — After-tax cost of debt:
rₛ(1−T) = 6% × (1−0.21) = 6% × 0.79 = 4.74%
Step 2 — WACC:
WACC = 0.40 × 4.74% + 0.60 × 12.0%
= 1.896% + 7.200%
= 9.096% ≈ 9.1%
The answer is 9.1%. Common error: forgetting to apply the (1−T) tax adjustment to debt — without it, WACC = 0.40×6% + 0.60×12% = 9.6%, which is wrong.
Example 2 — Three-Component WACC (Debt + Preferred + Equity)
Setup: Capital structure: 35% debt (YTM 7%), 10% preferred stock ($5 dividend, $80 price), 55% common equity (CAPM: rᵣᵓ=4%, RPᵖ=6%, β=1.2). Tax rate = 25%.
Step 1 — Cost of each component:
After-tax debt: 7% × (1−0.25) = 7% × 0.75 = 5.25%
Preferred stock: $5.00 ÷ $80.00 = 6.25%
Common equity (CAPM): 4% + 6% × 1.2 = 4% + 7.2% = 11.2%
Step 2 — WACC:
WACC = 0.35 × 5.25% + 0.10 × 6.25% + 0.55 × 11.2%
= 1.838% + 0.625% + 6.160%
= 8.62%
Step 1 — Cost of each component:
After-tax debt: 7% × (1−0.25) = 7% × 0.75 = 5.25%
Preferred stock: $5.00 ÷ $80.00 = 6.25%
Common equity (CAPM): 4% + 6% × 1.2 = 4% + 7.2% = 11.2%
Step 2 — WACC:
WACC = 0.35 × 5.25% + 0.10 × 6.25% + 0.55 × 11.2%
= 1.838% + 0.625% + 6.160%
= 8.62%
Example 3 — BBYM Social Enterprise (CDFI Financing)
Setup: A BBYM youth workforce enterprise raises $200,000: $80,000 CDFI loan (8% interest), $20,000 from preferred community investors ($1,600 annual dividend, $20,000 price), $100,000 community equity (rᵣᵓ=4%, RPᵖ=6%, β=0.9). Tax rate = 21%.
Step 1 — Weights:
wₛ = $80,000/$200,000 = 40% | wᵔₛ = $20,000/$200,000 = 10% | wᶜᵉ = $100,000/$200,000 = 50%
Step 2 — Component costs:
Debt: 8% × (1−0.21) = 8% × 0.79 = 6.32%
Preferred: $1,600 ÷ $20,000 = 8.00%
Equity (CAPM): 4% + 6% × 0.9 = 4% + 5.4% = 9.40%
Step 3 — WACC:
WACC = 0.40 × 6.32% + 0.10 × 8.00% + 0.50 × 9.40%
= 2.528% + 0.800% + 4.700%
= 8.03%
Any BBYM enterprise project must earn at least 8.03% to create value. A job-training program generating a social + financial return of 11% clears this bar; a food pantry generating 5% financial return would not (though it might be supported by grants that effectively lower WACC).
Step 1 — Weights:
wₛ = $80,000/$200,000 = 40% | wᵔₛ = $20,000/$200,000 = 10% | wᶜᵉ = $100,000/$200,000 = 50%
Step 2 — Component costs:
Debt: 8% × (1−0.21) = 8% × 0.79 = 6.32%
Preferred: $1,600 ÷ $20,000 = 8.00%
Equity (CAPM): 4% + 6% × 0.9 = 4% + 5.4% = 9.40%
Step 3 — WACC:
WACC = 0.40 × 6.32% + 0.10 × 8.00% + 0.50 × 9.40%
= 2.528% + 0.800% + 4.700%
= 8.03%
Any BBYM enterprise project must earn at least 8.03% to create value. A job-training program generating a social + financial return of 11% clears this bar; a food pantry generating 5% financial return would not (though it might be supported by grants that effectively lower WACC).
Example 4 — Finding WACC When Dollar Amounts Are Given
Setup: A firm has: $3M in bonds (6% coupon, tax rate 21%), $1M preferred stock (8% yield), $6M common equity (CAPM: r=13%). Find WACC.
Step 1 — Calculate weights from dollar amounts:
Total capital = $3M + $1M + $6M = $10M
wₛ = $3M/$10M = 30% | wᵔₛ = $1M/$10M = 10% | wᶜᵉ = $6M/$10M = 60%
Step 2 — Component costs:
Debt: 6% × (1−0.21) = 4.74% | Preferred: 8.00% | Equity: 13.00%
Step 3 — WACC:
WACC = 0.30 × 4.74% + 0.10 × 8.00% + 0.60 × 13.00%
= 1.422% + 0.800% + 7.800%
= 10.02%
Step 1 — Calculate weights from dollar amounts:
Total capital = $3M + $1M + $6M = $10M
wₛ = $3M/$10M = 30% | wᵔₛ = $1M/$10M = 10% | wᶜᵉ = $6M/$10M = 60%
Step 2 — Component costs:
Debt: 6% × (1−0.21) = 4.74% | Preferred: 8.00% | Equity: 13.00%
Step 3 — WACC:
WACC = 0.30 × 4.74% + 0.10 × 8.00% + 0.60 × 13.00%
= 1.422% + 0.800% + 7.800%
= 10.02%
WACC Sensitivity — How Capital Structure Affects the Rate
| Debt Weight | Equity Weight | After-Tax Debt Cost | Equity Cost | WACC | Assessment |
|---|---|---|---|---|---|
| 0% (all equity) | 100% | — | 12% | 12.00% | Highest WACC — no tax shield |
| 20% | 80% | 4.74% | 12% | 10.55% | Some benefit from cheap debt |
| 40% | 60% | 4.74% | 12% | 9.10% | Assessment Q10 answer |
| 60% | 40% | 4.74% | 12% | 7.64% | Lower WACC but rising financial risk |
| 80% | 20% | 4.74% | 12% | 6.19% | Very low WACC but very high financial risk |
Adding more cheap debt reduces WACC — but only to a point. As debt rises, the firm becomes riskier, lenders charge higher interest (raising rₛ), and equity holders demand more return (raising rₛ). The optimal capital structure minimizes WACC at a moderate debt level.
Part 3 — Capital Structure & BBYM Enterprise Finance
How firms choose the right mix of debt and equity — and what it means for community enterprises
Optimal Capital Structure — Balancing Debt Benefits vs. Financial Risk
The optimal capital structure is the debt-equity mix that minimizes WACC and therefore maximizes firm value. It balances two forces pulling in opposite directions:
| Factor | Effect of Adding More Debt | Effect of Having Too Much Debt |
|---|---|---|
| Tax Shield Benefit | Increases — more interest deductions, lower after-tax cost | Diminishing returns — tax savings plateau as equity becomes scarce |
| Interest Cost (rₛ) | Stable initially — moderate debt is expected and priced efficiently | Rises sharply — lenders charge higher rates as default risk increases |
| Equity Cost (rₛ) | Stable initially — small additional debt barely affects equity risk | Rises — equity holders demand more return as financial distress risk grows |
| Financial Distress Risk | Low — modest debt is manageable for healthy businesses | High — high debt loads can trap companies in bankruptcy during downturns |
| WACC | Falls — cheap debt displaces expensive equity | Rises — higher rₛ and rₛ more than offset cheap debt benefit |
The Optimal Capital Structure Concept — Illustrated:
At zero debt: WACC = cost of equity (12%) — no tax shield benefit whatsoever.
At moderate debt (30–50%): WACC reaches its minimum (~9–10%) — debt's tax advantage is captured without materially raising financial distress risk.
At excessive debt (70%+): WACC rises as both lenders and equity holders demand higher returns to compensate for elevated bankruptcy risk. The firm is fragile — one bad year can trigger a debt crisis.
Most large US corporations target a debt ratio of 25–50% of total capital. Community enterprises and nonprofits often target lower (10–30%) for stability and mission alignment.
At zero debt: WACC = cost of equity (12%) — no tax shield benefit whatsoever.
At moderate debt (30–50%): WACC reaches its minimum (~9–10%) — debt's tax advantage is captured without materially raising financial distress risk.
At excessive debt (70%+): WACC rises as both lenders and equity holders demand higher returns to compensate for elevated bankruptcy risk. The firm is fragile — one bad year can trigger a debt crisis.
Most large US corporations target a debt ratio of 25–50% of total capital. Community enterprises and nonprofits often target lower (10–30%) for stability and mission alignment.
BBYM Capital Sources and Their Costs
| Capital Source | Typical BBYM Access | Approximate Cost | Tax Deductible? | Advantages for BBYM |
|---|---|---|---|---|
| CDFI Loans | Community Development Financial Institutions serving underserved markets | 4–8% (below market) | Yes | Mission-aligned lenders; flexible terms; technical assistance often bundled; builds credit history |
| SBA Loans (7a/504) | Small Business Administration guaranteed loans through banks | 6–10% | Yes | Government guarantee enables access; long terms (10–25 years); lower down payment requirements |
| Community Grants | Federal, state, foundation, and corporate grants for nonprofits/social enterprises | 0% (free capital) | N/A | Zero cost capital that dramatically lowers WACC; best for capital costs, not operating expenses |
| Program-Related Investments (PRIs) | Below-market loans/equity from foundations aligned with BBYM mission | 1–4% | Depends on structure | Very low cost; patient capital; aligned with social mission; flexible terms |
| Community Equity | Ownership stakes from community investors, cooperative members | 8–14% (CAPM-based) | No | Permanent capital; aligns investors with community mission; no repayment obligation |
| Retained Earnings | Reinvested surplus from BBYM operations | Same as equity cost | No | No transaction costs or dilution; the cheapest form of equity because no new shares are issued |
Why Grants Dramatically Lower WACC for Nonprofits:
If BBYM receives a $100,000 grant for a $300,000 project and finances the remaining $200,000 with a 7% CDFI loan (21% tax rate):
w_grant = $100,000/$300,000 = 33.3% at 0% cost
w_debt = $200,000/$300,000 = 66.7% at 5.53% (after-tax)
WACC = 0.333 × 0% + 0.667 × 5.53% = 3.69%
The grant subsidizes the entire project's cost of capital from 5.53% down to 3.69%. A project returning just 5% clears this blended WACC even though the loan alone costs 5.53%. Grant funding is the most powerful WACC-reduction tool available to mission-driven organizations — it's why grant-writing capacity is financially strategic, not just administratively burdensome.
If BBYM receives a $100,000 grant for a $300,000 project and finances the remaining $200,000 with a 7% CDFI loan (21% tax rate):
w_grant = $100,000/$300,000 = 33.3% at 0% cost
w_debt = $200,000/$300,000 = 66.7% at 5.53% (after-tax)
WACC = 0.333 × 0% + 0.667 × 5.53% = 3.69%
The grant subsidizes the entire project's cost of capital from 5.53% down to 3.69%. A project returning just 5% clears this blended WACC even though the loan alone costs 5.53%. Grant funding is the most powerful WACC-reduction tool available to mission-driven organizations — it's why grant-writing capacity is financially strategic, not just administratively burdensome.
Connecting Units 5–10: The WACC Integration
How Every Prior Unit Feeds Into WACC:
Unit 5 (TVM): WACC is the discount rate used in Net Present Value calculations — the most direct application of TVM to corporate finance.
Unit 6 (Interest Rates): The cost of debt starts with rₛ = r* + IP + DRP + LP + MRP. A firm's creditworthiness determines its DRP and therefore its pre-tax cost of debt.
Unit 7 (Bonds): The YTM on a firm's existing bonds is the market's estimate of the pre-tax cost of debt. Bond pricing reveals what investors require to hold the firm's debt.
Unit 8 (CAPM): CAPM provides the cost of equity: rₛ = rᵣᵓ + RPᵖ × β. Beta measures the systematic risk of the equity claim, determining the equity risk premium.
Unit 9 (Stock Valuation): The Gordon Growth Model provides an alternative cost-of-equity estimate: rₛ = D₁/P₀ + g — what the market implies investors require based on the current stock price and growth expectations.
WACC synthesizes all of these into one number that drives all capital budgeting decisions in Units 11–12.
Unit 5 (TVM): WACC is the discount rate used in Net Present Value calculations — the most direct application of TVM to corporate finance.
Unit 6 (Interest Rates): The cost of debt starts with rₛ = r* + IP + DRP + LP + MRP. A firm's creditworthiness determines its DRP and therefore its pre-tax cost of debt.
Unit 7 (Bonds): The YTM on a firm's existing bonds is the market's estimate of the pre-tax cost of debt. Bond pricing reveals what investors require to hold the firm's debt.
Unit 8 (CAPM): CAPM provides the cost of equity: rₛ = rᵣᵓ + RPᵖ × β. Beta measures the systematic risk of the equity claim, determining the equity risk premium.
Unit 9 (Stock Valuation): The Gordon Growth Model provides an alternative cost-of-equity estimate: rₛ = D₁/P₀ + g — what the market implies investors require based on the current stock price and growth expectations.
WACC synthesizes all of these into one number that drives all capital budgeting decisions in Units 11–12.
Part 4 — Key Terms Defined
Master these 14 terms for the Unit 10 assessment
Weighted Average Cost of Capital (WACC)
The blended cost of all capital sources, weighted by their proportion in the firm's capital structure. Formula: WACC = wₛ·rₛ(1−T) + wᵔₛ·rᵔₛ + wᶜᵉ·rₛ. Serves as the firm's hurdle rate — the minimum return any investment must earn to create value. The Assessment Q10 answer: 9.1%.
Cost of Debt (rₛ)
The pre-tax cost of the firm's debt financing, equal to the yield to maturity (YTM) on its outstanding bonds or the interest rate on its loans. The after-tax cost — used in WACC — is rₛ(1−T), reflecting the tax deductibility of interest payments. Always the lowest-cost component of capital because lenders bear the least risk.
After-Tax Cost of Debt
The effective cost of debt after accounting for the interest tax shield: rₛ(1−T) = YTM × (1 − marginal tax rate). Always lower than the pre-tax cost. The tax rate used is the marginal corporate rate — the rate paid on the last dollar of income, not the average rate. This is the cost figure that appears in the WACC formula.
Interest Tax Shield
The tax savings generated by the deductibility of interest payments. Equal to interest paid × tax rate. Represents a direct government subsidy of debt financing. A firm paying $1,000,000 in interest at a 21% tax rate saves $210,000 in taxes annually — the government effectively pays 21 cents of every interest dollar. A core reason why WACC decreases as moderate debt is added.
Cost of Preferred Stock (rᵔₛ)
The return required by preferred stockholders, calculated as the annual dividend divided by the preferred stock's current price: rᵔₛ = Dᵔₛ ÷ Pᵔₛ. NOT tax-deductible (preferred dividends are paid from after-tax income). Typically falls between the cost of debt (lower) and cost of common equity (higher) because preferred holders bear intermediate risk.
Cost of Common Equity (rₛ)
The return required by common stockholders — the most expensive component of capital because equity holders bear the most risk (last in bankruptcy, variable returns). Estimated using CAPM (rₛ = rᵣᵓ + RPᵖ×β) or the Gordon Growth Model (rₛ = D₁/P₀ + g). NOT tax-deductible. The dominant driver of WACC for most firms because equity is typically the largest capital component.
Capital Structure
The mix of debt, preferred stock, and common equity a firm uses to finance its assets. Described by weights (proportions) that sum to 1.0. The most important financing decision a firm makes — it directly determines WACC and therefore the firm's value and investment decisions. Weights in WACC should be based on market values, not accounting book values.
Optimal Capital Structure
The debt-equity mix that minimizes WACC and thereby maximizes firm value. Found at the point where the tax shield benefit of additional debt is just offset by rising financial distress costs. In practice, most firms target a moderate debt ratio (25–50%) rather than extremes. Too little debt forgoes the tax shield; too much debt raises all component costs and creates bankruptcy risk.
Hurdle Rate
The minimum required rate of return on a new investment — typically set equal to the firm's WACC for average-risk projects. An investment must clear the hurdle rate (earn more than WACC) to create value. Projects below the hurdle rate destroy value and should be rejected. Projects above it create value and should be accepted. The bridge between WACC (financing) and capital budgeting (investment decisions).
Financial Distress
The condition in which a firm has difficulty meeting its debt obligations, potentially leading to bankruptcy. Excessive debt amplifies financial distress risk — even small revenue declines can trigger an inability to service debt. Financial distress has direct costs (legal fees, management distraction) and indirect costs (lost customers, key employee departures, inability to raise capital). The primary reason excessive debt raises both rₛ and rₛ, ultimately increasing WACC.
Retained Earnings
Profits kept within the firm rather than paid as dividends — the most common and lowest-cost source of equity. No flotation costs, no dilution of existing shares. Cost is still the opportunity cost of equity (CAPM rate) because shareholders could have received these funds as dividends and invested them elsewhere. Often the first source of equity financing considered before issuing new common stock.
Flotation Costs
Transaction costs incurred when a firm issues new securities — underwriter fees, legal costs, registration fees. Typically 3–7% of proceeds for equity, 1–3% for bonds. Raise the effective cost of new capital above the CAPM or Gordon Growth Model estimates. This is why retained earnings (no flotation costs) are cheaper than newly issued equity, and why firms prefer internal financing first.
Book Value vs. Market Value Weights
WACC calculations should use market value weights (current market prices of debt and equity), not book value (historical accounting values). Book values reflect historical costs and can be significantly different from what investors actually value the securities at today. Market-value weights reflect the true current cost of each capital source to the firm.
CDFI (Community Development Financial Institution)
A financial institution certified by the US Treasury to provide affordable capital to underserved communities and businesses. CDFIs offer below-market loan rates, flexible underwriting, and often bundle technical assistance with financing. For BBYM enterprises, CDFIs are the primary source of debt capital — providing the "wₛ × rₛ(1−T)" component of WACC at more favorable rates than conventional banks.
Part 5 — Practice Questions
Show all work — these mirror the Unit 10 assessment format exactly
Conceptual Questions
Q1A firm has 40% debt at 6%, 60% equity at 12%, tax rate 21%. Approximate WACC is: A) 7.2% B) 9.1% C) 10.5% D) 9.6%. (Unit 10 curriculum assessment question.)▼
Answer: B — 9.1%
After-tax cost of debt = 6% × (1 − 0.21) = 6% × 0.79 = 4.74%
WACC = 0.40 × 4.74% + 0.60 × 12.0% = 1.896% + 7.200% = 9.096% ≈ 9.1%
Common errors: A (7.2%) uses only the debt portion; C (10.5%) doesn't use the tax adjustment and rounds differently; D (9.6%) forgets the tax shield entirely (0.40×6% + 0.60×12% = 9.6%). The tax shield reduces the effective debt cost from 6% to 4.74%, making B the correct answer.
After-tax cost of debt = 6% × (1 − 0.21) = 6% × 0.79 = 4.74%
WACC = 0.40 × 4.74% + 0.60 × 12.0% = 1.896% + 7.200% = 9.096% ≈ 9.1%
Common errors: A (7.2%) uses only the debt portion; C (10.5%) doesn't use the tax adjustment and rounds differently; D (9.6%) forgets the tax shield entirely (0.40×6% + 0.60×12% = 9.6%). The tax shield reduces the effective debt cost from 6% to 4.74%, making B the correct answer.
Q2Explain why the after-tax cost of debt is used in the WACC formula rather than the pre-tax interest rate. Use a numerical example to illustrate the tax shield.▼
The WACC formula uses after-tax cost of debt because interest payments are tax-deductible — the government effectively subsidizes a portion of every interest payment, reducing the true economic cost to the firm.
Numerical example — $1,000,000 loan at 8%, tax rate 25%:
Pre-tax interest: $1,000,000 × 8% = $80,000/year
Tax shield: $80,000 × 25% = $20,000/year saved in taxes
Actual net cash cost: $80,000 − $20,000 = $60,000/year
After-tax rate: $60,000 ÷ $1,000,000 = 6% (= 8% × (1−0.25))
Using 8% (pre-tax) in WACC would overstate the true cost of debt by $20,000/year — ignoring a real government subsidy that reduces the firm's financing burden. Using 6% (after-tax) accurately reflects what debt actually costs the firm in net economic terms. The tax deductibility of debt is one reason why profitable firms use debt strategically.
Numerical example — $1,000,000 loan at 8%, tax rate 25%:
Pre-tax interest: $1,000,000 × 8% = $80,000/year
Tax shield: $80,000 × 25% = $20,000/year saved in taxes
Actual net cash cost: $80,000 − $20,000 = $60,000/year
After-tax rate: $60,000 ÷ $1,000,000 = 6% (= 8% × (1−0.25))
Using 8% (pre-tax) in WACC would overstate the true cost of debt by $20,000/year — ignoring a real government subsidy that reduces the firm's financing burden. Using 6% (after-tax) accurately reflects what debt actually costs the firm in net economic terms. The tax deductibility of debt is one reason why profitable firms use debt strategically.
Q3Why is common equity typically the most expensive source of capital? Rank the three sources (debt, preferred stock, common equity) from cheapest to most expensive and explain the ranking.▼
Ranking from cheapest to most expensive: Debt < Preferred Stock < Common Equity
Debt is cheapest for two reasons: (1) lenders have the highest-priority claim in bankruptcy — they bear the least risk and therefore accept the lowest return, and (2) interest is tax-deductible, creating an after-tax subsidy that further reduces the effective cost.
Preferred stock is in the middle because: (1) preferred holders rank above common equity in bankruptcy but below debt, bearing intermediate risk, and (2) preferred dividends are NOT tax-deductible — the company loses the tax shield that makes debt so cheap. The combination of intermediate risk and no tax benefit places preferred between debt and common equity in cost.
Common equity is most expensive because: (1) common holders are last in bankruptcy — they bear all residual risk and demand the highest return to compensate, (2) dividends are not tax-deductible, and (3) the return is not fixed — stockholders face uncertainty about both dividends and capital gains. This combination of maximum risk, no tax shield, and maximum uncertainty demands the highest required return.
Debt is cheapest for two reasons: (1) lenders have the highest-priority claim in bankruptcy — they bear the least risk and therefore accept the lowest return, and (2) interest is tax-deductible, creating an after-tax subsidy that further reduces the effective cost.
Preferred stock is in the middle because: (1) preferred holders rank above common equity in bankruptcy but below debt, bearing intermediate risk, and (2) preferred dividends are NOT tax-deductible — the company loses the tax shield that makes debt so cheap. The combination of intermediate risk and no tax benefit places preferred between debt and common equity in cost.
Common equity is most expensive because: (1) common holders are last in bankruptcy — they bear all residual risk and demand the highest return to compensate, (2) dividends are not tax-deductible, and (3) the return is not fixed — stockholders face uncertainty about both dividends and capital gains. This combination of maximum risk, no tax shield, and maximum uncertainty demands the highest required return.
Q4A BBYM project is expected to return 8.5% annually. BBYM's WACC is 9.3%. Should this project be accepted? What if a grant reduces the effective WACC to 6.8%?▼
Without grant: Project return (8.5%) < WACC (9.3%) → Reject ✗
The project destroys value. Every dollar invested in it earns 8.5% but costs 9.3% to finance — a net loss of 0.8 cents per dollar. This means BBYM is earning less from the project than it is paying its investors (lenders + equity holders). Accepting it would reduce the organization's financial health and reduce its ability to fund future community programs.
With grant: Project return (8.5%) > Blended WACC (6.8%) → Accept ✓
The grant changes the financial calculus completely. By injecting free capital (0% cost), it lowers the effective financing cost to 6.8%. Now the project earns 8.5% while costing only 6.8% — a 1.7% surplus. This illustrates why grant-writing is financially strategic for BBYM: grants don't just fund programs, they enable financially marginal projects to become value-creating by lowering WACC below the project's return.
The project destroys value. Every dollar invested in it earns 8.5% but costs 9.3% to finance — a net loss of 0.8 cents per dollar. This means BBYM is earning less from the project than it is paying its investors (lenders + equity holders). Accepting it would reduce the organization's financial health and reduce its ability to fund future community programs.
With grant: Project return (8.5%) > Blended WACC (6.8%) → Accept ✓
The grant changes the financial calculus completely. By injecting free capital (0% cost), it lowers the effective financing cost to 6.8%. Now the project earns 8.5% while costing only 6.8% — a 1.7% surplus. This illustrates why grant-writing is financially strategic for BBYM: grants don't just fund programs, they enable financially marginal projects to become value-creating by lowering WACC below the project's return.
Calculation Questions
Q5Calculate WACC: 50% debt (YTM 7%), 50% equity (CAPM: rᵣᵓ=3.5%, MRP=5.5%, β=1.1). Tax rate = 25%.▼
Step 1 — Component costs:
After-tax debt: 7% × (1−0.25) = 7% × 0.75 = 5.25%
Equity (CAPM): 3.5% + 5.5% × 1.1 = 3.5% + 6.05% = 9.55%
Step 2 — WACC:
WACC = 0.50 × 5.25% + 0.50 × 9.55%
= 2.625% + 4.775%
= 7.40%
After-tax debt: 7% × (1−0.25) = 7% × 0.75 = 5.25%
Equity (CAPM): 3.5% + 5.5% × 1.1 = 3.5% + 6.05% = 9.55%
Step 2 — WACC:
WACC = 0.50 × 5.25% + 0.50 × 9.55%
= 2.625% + 4.775%
= 7.40%
Q6A firm's capital: $4M bonds (8% YTM), $1M preferred stock (7% yield), $5M common equity (r=13%). Tax rate = 21%. (a) Calculate weights. (b) Calculate WACC.▼
(a) Total capital = $4M + $1M + $5M = $10M
wₛ = 4/10 = 40% | wᵔₛ = 1/10 = 10% | wᶜᵉ = 5/10 = 50%
(b) Component costs:
After-tax debt: 8% × (1−0.21) = 8% × 0.79 = 6.32%
Preferred: 7.00%
Equity: 13.00%
WACC = 0.40 × 6.32% + 0.10 × 7.00% + 0.50 × 13.00%
= 2.528% + 0.700% + 6.500%
= 9.73%
wₛ = 4/10 = 40% | wᵔₛ = 1/10 = 10% | wᶜᵉ = 5/10 = 50%
(b) Component costs:
After-tax debt: 8% × (1−0.21) = 8% × 0.79 = 6.32%
Preferred: 7.00%
Equity: 13.00%
WACC = 0.40 × 6.32% + 0.10 × 7.00% + 0.50 × 13.00%
= 2.528% + 0.700% + 6.500%
= 9.73%
Q7BBYM secures a $150,000 CDFI loan at 6.5% interest and $100,000 in community equity (CAPM: rᵣᵓ=4%, MRP=6%, β=0.7). Tax rate = 21%. (a) Calculate weights. (b) Find each component cost. (c) Calculate WACC. (d) If a proposed program generates 9% return, should it proceed?▼
(a) Total = $150,000 + $100,000 = $250,000
wₛ = 150/250 = 60% | wᶜᵉ = 100/250 = 40%
(b) Component costs:
After-tax debt: 6.5% × (1−0.21) = 6.5% × 0.79 = 5.135%
Equity (CAPM): 4% + 6% × 0.7 = 4% + 4.2% = 8.20%
(c) WACC = 0.60 × 5.135% + 0.40 × 8.20%
= 3.081% + 3.280%
= 6.36%
(d) Project return (9%) > WACC (6.36%) → Accept ✓
The program generates 9% while costing only 6.36% to finance, creating a 2.64% surplus. The project adds value and should proceed. The relatively low WACC (6.36%) reflects the CDFI's below-market rate and the defensive equity beta (0.7), making many community programs financially viable.
wₛ = 150/250 = 60% | wᶜᵉ = 100/250 = 40%
(b) Component costs:
After-tax debt: 6.5% × (1−0.21) = 6.5% × 0.79 = 5.135%
Equity (CAPM): 4% + 6% × 0.7 = 4% + 4.2% = 8.20%
(c) WACC = 0.60 × 5.135% + 0.40 × 8.20%
= 3.081% + 3.280%
= 6.36%
(d) Project return (9%) > WACC (6.36%) → Accept ✓
The program generates 9% while costing only 6.36% to finance, creating a 2.64% surplus. The project adds value and should proceed. The relatively low WACC (6.36%) reflects the CDFI's below-market rate and the defensive equity beta (0.7), making many community programs financially viable.
Q8A company currently has WACC = 10% with 30% debt. A CFO proposes increasing debt to 50% by issuing bonds at 7% YTM (tax rate 25%). The equity cost remains at 13%. (a) Calculate old WACC. (b) Calculate new WACC. (c) Did the restructuring help?▼
(a) Old WACC (30% debt, 70% equity, 7% debt, 13% equity, 25% tax):
After-tax debt: 7% × 0.75 = 5.25%
WACC = 0.30 × 5.25% + 0.70 × 13% = 1.575% + 9.100% = 10.68%
(Note: The problem states old WACC = 10% — this assumes slightly different inputs for the old structure. Working with the new inputs as stated.)
(b) New WACC (50% debt, 50% equity):
After-tax debt: 7% × 0.75 = 5.25%
WACC = 0.50 × 5.25% + 0.50 × 13% = 2.625% + 6.500% = 9.125%
(c) Yes, the restructuring helps — WACC falls by approximately 1.6 percentage points. By replacing expensive equity (13%) with cheaper after-tax debt (5.25%), the firm lowers its overall financing cost. Caveat: This analysis assumes equity holders don't demand higher returns due to the increased financial leverage. In reality, adding more debt increases equity risk (beta rises), which would increase rₛ and partially offset the WACC reduction.
After-tax debt: 7% × 0.75 = 5.25%
WACC = 0.30 × 5.25% + 0.70 × 13% = 1.575% + 9.100% = 10.68%
(Note: The problem states old WACC = 10% — this assumes slightly different inputs for the old structure. Working with the new inputs as stated.)
(b) New WACC (50% debt, 50% equity):
After-tax debt: 7% × 0.75 = 5.25%
WACC = 0.50 × 5.25% + 0.50 × 13% = 2.625% + 6.500% = 9.125%
(c) Yes, the restructuring helps — WACC falls by approximately 1.6 percentage points. By replacing expensive equity (13%) with cheaper after-tax debt (5.25%), the firm lowers its overall financing cost. Caveat: This analysis assumes equity holders don't demand higher returns due to the increased financial leverage. In reality, adding more debt increases equity risk (beta rises), which would increase rₛ and partially offset the WACC reduction.
Q9A preferred stock pays a $3.60 annual dividend and was originally priced at $60. (a) What is its cost of preferred stock? (b) If interest rates rise and the market price falls to $45, what happens to the cost of preferred stock? (c) How does this affect WACC?▼
(a) Original cost: rᵔₛ = $3.60 ÷ $60 = 6.00%
(b) After rate rise: rᵔₛ = $3.60 ÷ $45 = 8.00%
The cost of preferred stock increases from 6% to 8% because the price fell while the fixed dividend remained unchanged. Investors now demand 8% to hold the preferred stock at its new market price.
(c) Effect on WACC: If preferred stock represents 10% of the capital structure, the WACC increases by:
0.10 × (8.00% − 6.00%) = 0.10 × 2% = +0.20 percentage points
This illustrates a key point: WACC is not static. Rising interest rates increase the cost of all components — debt (YTM rises), preferred stock (price falls, yield rises), and equity (rᵣᵓ rises in CAPM). When the Fed raises rates, every firm's WACC increases, raising the hurdle rate and making some previously viable projects uneconomical.
(b) After rate rise: rᵔₛ = $3.60 ÷ $45 = 8.00%
The cost of preferred stock increases from 6% to 8% because the price fell while the fixed dividend remained unchanged. Investors now demand 8% to hold the preferred stock at its new market price.
(c) Effect on WACC: If preferred stock represents 10% of the capital structure, the WACC increases by:
0.10 × (8.00% − 6.00%) = 0.10 × 2% = +0.20 percentage points
This illustrates a key point: WACC is not static. Rising interest rates increase the cost of all components — debt (YTM rises), preferred stock (price falls, yield rises), and equity (rᵣᵓ rises in CAPM). When the Fed raises rates, every firm's WACC increases, raising the hurdle rate and making some previously viable projects uneconomical.
Q10The Swanson Initiative is evaluating two programs: Program A costs $200,000 and returns $18,000/year in combined financial + social value. Program B costs $200,000 and returns $15,000/year. BBYM WACC = 8.5%. A foundation offers a $60,000 grant toward either program. Which program benefits more from the grant, and should both be accepted?▼
First, calculate return rates:
Program A: $18,000 ÷ $200,000 = 9.0%
Program B: $15,000 ÷ $200,000 = 7.5%
Without grant:
Program A: 9.0% > WACC 8.5% → Accept ✓ (marginal but positive)
Program B: 7.5% < WACC 8.5% → Reject ✗
With $60,000 grant applied to Program B:
Funded cost = $200,000 − $60,000 = $140,000 (remaining financed at WACC 8.5%)
Blended WACC with grant = (60,000/200,000)×0% + (140,000/200,000)×8.5% = 0% + 5.95% = 5.95%
Program B return (7.5%) > Blended WACC (5.95%) → Now Accept ✓
Recommendation: Apply the grant to Program B — it benefits more (transforms a rejection into an acceptance) while Program A already clears the hurdle without it. Both programs can be pursued if the grant goes to B. This is the optimal allocation of grant capital: direct it to the highest-impact programs that are closest to the break-even threshold.
Program A: $18,000 ÷ $200,000 = 9.0%
Program B: $15,000 ÷ $200,000 = 7.5%
Without grant:
Program A: 9.0% > WACC 8.5% → Accept ✓ (marginal but positive)
Program B: 7.5% < WACC 8.5% → Reject ✗
With $60,000 grant applied to Program B:
Funded cost = $200,000 − $60,000 = $140,000 (remaining financed at WACC 8.5%)
Blended WACC with grant = (60,000/200,000)×0% + (140,000/200,000)×8.5% = 0% + 5.95% = 5.95%
Program B return (7.5%) > Blended WACC (5.95%) → Now Accept ✓
Recommendation: Apply the grant to Program B — it benefits more (transforms a rejection into an acceptance) while Program A already clears the hurdle without it. Both programs can be pursued if the grant goes to B. This is the optimal allocation of grant capital: direct it to the highest-impact programs that are closest to the break-even threshold.
Q11Explain in your own words why WACC links together everything learned in Units 5 through 9. What would a student be missing if they tried to calculate WACC without understanding each prior unit?▼
WACC is the convergence point of the entire first semester of this curriculum:
Without Unit 5 (TVM): You wouldn't understand why WACC is used as a discount rate — or what "present value" of future cash flows even means. WACC is the denominator in NPV calculations that determine whether investments create value.
Without Unit 6 (Interest Rates): You wouldn't know how the cost of debt is determined. The YTM on a firm's bonds = r* + IP + DRP + LP + MRP — and the firm's creditworthiness (DRP) is the biggest variable the firm can control through financial management.
Without Unit 7 (Bonds): You couldn't extract the after-tax cost of debt from bond market prices. The YTM formula from Unit 7 is precisely the pre-tax debt cost used in WACC. Bond pricing also shows how market rates affect the cost of raising new debt.
Without Unit 8 (CAPM): You couldn't calculate the cost of equity — the largest component of WACC. rₛ = rᵣᵓ + RPᵖ×β IS the cost of equity in WACC. Without beta and CAPM, the equity term has no foundation.
Without Unit 9 (Stock Valuation): You'd miss the alternative cost-of-equity estimate (Gordon Growth: rₛ = D₁/P₀ + g) and the understanding that the cost of equity is what the market currently requires — derived from actual stock prices and growth expectations.
WACC without these foundations is just arithmetic. With them, it is a complete theory of how capital markets price risk and reward — made actionable for BBYM community enterprise decisions.
Without Unit 5 (TVM): You wouldn't understand why WACC is used as a discount rate — or what "present value" of future cash flows even means. WACC is the denominator in NPV calculations that determine whether investments create value.
Without Unit 6 (Interest Rates): You wouldn't know how the cost of debt is determined. The YTM on a firm's bonds = r* + IP + DRP + LP + MRP — and the firm's creditworthiness (DRP) is the biggest variable the firm can control through financial management.
Without Unit 7 (Bonds): You couldn't extract the after-tax cost of debt from bond market prices. The YTM formula from Unit 7 is precisely the pre-tax debt cost used in WACC. Bond pricing also shows how market rates affect the cost of raising new debt.
Without Unit 8 (CAPM): You couldn't calculate the cost of equity — the largest component of WACC. rₛ = rᵣᵓ + RPᵖ×β IS the cost of equity in WACC. Without beta and CAPM, the equity term has no foundation.
Without Unit 9 (Stock Valuation): You'd miss the alternative cost-of-equity estimate (Gordon Growth: rₛ = D₁/P₀ + g) and the understanding that the cost of equity is what the market currently requires — derived from actual stock prices and growth expectations.
WACC without these foundations is just arithmetic. With them, it is a complete theory of how capital markets price risk and reward — made actionable for BBYM community enterprise decisions.
Part 6 — Quick Reference Summary
Read this the night before the assessment
Unit 10 in 5 Essential Sentences
Sentence 1
WACC = wₛ·rₛ(1−T) + wᵔₛ·rᵔₛ + wᶜᵉ·rₛ — the weighted average of after-tax debt cost, preferred stock cost, and equity cost; Assessment Q10: 0.40×6%×0.79 + 0.60×12% = 1.90% + 7.20% = 9.1%.
Sentence 2
Debt is the cheapest capital source because interest is tax-deductible (after-tax cost = YTM × (1−T)); preferred stock is mid-cost (Dividend ÷ Price, no tax shield); common equity is most expensive (CAPM, no tax shield, maximum risk).
Sentence 3
WACC is the hurdle rate: accept projects with return > WACC (adds value), reject those with return < WACC (destroys value); grants lower WACC by injecting 0%-cost capital, enabling borderline projects to clear the hurdle.
Sentence 4
The optimal capital structure minimizes WACC by balancing the tax shield benefit of debt against rising financial distress costs at high leverage; most firms target 25–50% debt.
Sentence 5
WACC synthesizes every prior unit: TVM (discount rate concept), interest rates (debt cost components), bonds (YTM = pre-tax debt cost), CAPM (cost of equity), and stock valuation (Gordon Growth as alternative equity cost estimate).
Must-Know Facts for the Assessment
| Concept / Formula | Answer |
|---|---|
| WACC formula | wₛ·rₛ(1−T) + wᵔₛ·rᵔₛ + wᶜᵉ·rₛ |
| After-tax cost of debt | YTM × (1 − Tax Rate) |
| Cost of preferred stock | Annual Dividend ÷ Current Price |
| Cost of common equity | CAPM: rᵣᵓ + RPᵖ × β |
| Assessment Q10 answer | 0.40×6%×0.79 + 0.60×12% = 1.90% + 7.20% = 9.1% |
| Why debt is cheapest | Senior priority (less risk) + interest is tax-deductible (government subsidy) |
| Interest tax shield value | Interest Paid × Tax Rate = annual tax savings |
| Hurdle rate rule | Accept if project return > WACC; Reject if project return < WACC |
| Weights should be based on | Market values (not book/accounting values) |
| Optimal capital structure | Debt-equity mix that minimizes WACC; typically 25–50% debt for most firms |
| Grants reduce WACC because | Grant cost = 0%; blending 0%-cost capital with positive-cost capital lowers the weighted average |
| Cost of retained earnings | Same as cost of equity (opportunity cost) but no flotation costs — cheapest equity source |
| Gordon Growth equity cost | rₛ = D₁/P₀ + g — alternative to CAPM for estimating cost of equity |
| WACC increases when | Interest rates rise (all component costs rise), debt ratio exceeds optimal level, or firm's risk profile worsens |