COMM 309 — Business Finance | Chapter 20: Cost of Capital | Exam Preparation Notes
COMM 309 — Business Finance
CHAPTER 20: Cost of Capital
Comprehensive Exam Preparation Notes
20.1 FINANCING SOURCES
Capital Structure
A firm's balance sheet has two sides: the asset side (current assets + net fixed assets = total assets)
and the liability/equity side. The method used to finance total assets is called the financial structure
decision — it reflects all of the firm's liabilities including invested capital. Capital structure refers
specifically to how the firm finances its invested capital (explicit debt + shareholders' equity + minority
interest).
For WACC purposes, only invested capital matters. Accounting accruals (e.g., wages payable,
accounts payable) and non-debt items (deferred taxes, pension obligations) are excluded from capital.
The only current liabilities that represent invested capital are bank debt, short-term debt, and the
current portion of long-term debt.
📌 Financial Structure vs. Capital Structure
Financial Structure = Total Assets (all sources of financing, including accruals).
Capital Structure = Invested Capital only = Interest-bearing debt + Shareholders' Equity (+ Minority
Interest).
Example: If Total Assets = $2,000, Short-term debt = $50, Long-term debt = $650, Equity = $1,000 →
Capital Structure = $1,700; Debt-to-Equity Ratio = $700 / $1,000 = 0.70.
Canadian firms averaged a D/E ratio of ~1.2 in early 1990s, declining to ~0.9 by 2015.
Market values vs. book values: For WACC calculations, market values must be used — not book
values. The market-to-book (M/B) ratio converts book equity to market equity (M/B × Book Equity =
Market Equity). Book and market values of debt are usually close unless interest rates have changed
significantly since issuance.
Three Ways of Using the Valuation Equation
The perpetuity valuation equation for a firm's equity (assuming constant earnings with no growth) is:
Eq. 20-1 | Perpetuity Valuation (Share Value)
S = Value of the perpetuity (firm equity)
X = Forecast earnings (assumed constant forever)
S = X / Ke Ke = Investors' required rate of return on equity
Example: X = $1 per share, Ke = 10% → S = $.10 =
$10
Page 1
,COMM 309 — Business Finance | Chapter 20: Cost of Capital | Exam Preparation Notes
This single equation can be rearranged three ways, each serving a different practical purpose in
corporate finance:
• Solve for S (Valuation Problem): Given earnings X and required return Ke, what is the firm
worth? Used in securities valuation (Chapters 5–7).
Eq. 20-2 | Earnings Yield (Cost of Equity Estimation)
Rearranges Eq. 20-1 to find the investors' required return.
Called the earnings yield — forecast EPS ÷ market price.
Limitation: Rarely adequate because most firms have growth
Ke = X / S
expectations. Stock price already reflects growth
opportunities, so earnings yield understates Ke. Was useful
in 1950s when inflation and growth were minimal.
• Solve for X (Required Earnings Problem): Given the firm's value and Ke, what earnings must
the firm generate?
Eq. 20-3 | Required Earnings
Used by regulators in 'rate of return regulation' (utilities).
Regulators determine required earnings, then set prices
accordingly.
X = Ke × S Example: S = $10, Ke = 10% → X = 0.10 × $10 = $1 per
share
This is how telephone, water, gas, and electric bills are
set.
⚠️
Key Insight: Three Uses of One Equation
The same equation — S = X / Ke — answers three distinct questions:
1. What is the security worth? (Valuation) → solve for S
2. What return do investors require? (Cost of Capital) → solve for Ke
3. What must the firm earn? (Required Earnings / Regulatory Pricing) → solve for X
Understanding this flexibility is fundamental to all of corporate finance.
Deriving the Required Income Statement
Using the third approach (solving for required earnings X), we can construct the income statement 'from
the bottom up' — starting with what shareholders require and working upward to determine the
necessary sales level. This is exactly how regulators set prices for utility companies.
Using our example firm (market value of equity S = $2,500, Ke = 12%; market value of debt D = $700,
Kd = 6%; tax rate T = 25%; operating costs = $300 variable + $258 fixed):
TABLE 20-3: Required Income Statement (Bottom-Up Construction)
Sales $1,000
Page 2
, COMM 309 — Business Finance | Chapter 20: Cost of Capital | Exam Preparation Notes
Variable costs 300
Fixed costs 258
EBIT 442
Interest 42
Tax (25%) 100
Net income $300
From this we can derive several key financial ratios:
• Asset Turnover Ratio: Sales ÷ Total Assets = $1,000 ÷ $2,000 = 0.50
• Return on Assets (ROA): Net Income ÷ Total Assets = $300 ÷ $2,000 = 15%
• Return on Invested Capital (ROIC): EBIT ÷ Book IC = $442 ÷ $1,700 = 26% (pre-tax); After-tax
ROIC = 26% × 0.75 = 19.5%
• Return on Equity (ROE): Net Income ÷ Book Equity = $300 ÷ $1,000 = 30%
• Earnings Per Share (EPS): NI ÷ Shares = $300 ÷ 1,000 = $0.30/share
Eq. 20-4 | Price Per Share (Perpetuity with Growth Via ROE)
BVPS = Book Value Per Share = Equity ÷ Shares
ROE = Return on Equity (earnings rate on book value)
P = EPS / Ke = (ROE × BVPS) / Ke
Example: EPS = $0.30, Ke = 12% → P = $0..12 =
$2.50 per share
Eq. 20-5 | Market-to-Book (M/B) Ratio
If ROE > Ke → M/B > 1 (shares trade above book value;
value is being created)
If ROE < Ke → M/B < 1 (shares trade below book value;
value is being destroyed)
P / BVPS = ROE / Ke If ROE = Ke → M/B = 1 (shares trade at book value)
Example: ROE = 30%, Ke = 12% → M/B = 0..12 =
2.50
This is a basic law of finance: exceeding investor
expectations drives prices above book value.
20.2 THE COST OF CAPITAL
Determining the Weighted Average Cost of Capital (WACC)
The total enterprise value (V) of a firm is the market value of all invested capital: V = D + S (debt +
equity). We can extend the perpetuity valuation equation to the entire firm using after-tax EBIT (i.e.,
EBIT(1−T)), which represents what the firm earns if financed 100% with equity — it excludes the
interest tax shield.
Eq. 20-6 | Total Enterprise Value
Page 3
COMM 309 — Business Finance
CHAPTER 20: Cost of Capital
Comprehensive Exam Preparation Notes
20.1 FINANCING SOURCES
Capital Structure
A firm's balance sheet has two sides: the asset side (current assets + net fixed assets = total assets)
and the liability/equity side. The method used to finance total assets is called the financial structure
decision — it reflects all of the firm's liabilities including invested capital. Capital structure refers
specifically to how the firm finances its invested capital (explicit debt + shareholders' equity + minority
interest).
For WACC purposes, only invested capital matters. Accounting accruals (e.g., wages payable,
accounts payable) and non-debt items (deferred taxes, pension obligations) are excluded from capital.
The only current liabilities that represent invested capital are bank debt, short-term debt, and the
current portion of long-term debt.
📌 Financial Structure vs. Capital Structure
Financial Structure = Total Assets (all sources of financing, including accruals).
Capital Structure = Invested Capital only = Interest-bearing debt + Shareholders' Equity (+ Minority
Interest).
Example: If Total Assets = $2,000, Short-term debt = $50, Long-term debt = $650, Equity = $1,000 →
Capital Structure = $1,700; Debt-to-Equity Ratio = $700 / $1,000 = 0.70.
Canadian firms averaged a D/E ratio of ~1.2 in early 1990s, declining to ~0.9 by 2015.
Market values vs. book values: For WACC calculations, market values must be used — not book
values. The market-to-book (M/B) ratio converts book equity to market equity (M/B × Book Equity =
Market Equity). Book and market values of debt are usually close unless interest rates have changed
significantly since issuance.
Three Ways of Using the Valuation Equation
The perpetuity valuation equation for a firm's equity (assuming constant earnings with no growth) is:
Eq. 20-1 | Perpetuity Valuation (Share Value)
S = Value of the perpetuity (firm equity)
X = Forecast earnings (assumed constant forever)
S = X / Ke Ke = Investors' required rate of return on equity
Example: X = $1 per share, Ke = 10% → S = $.10 =
$10
Page 1
,COMM 309 — Business Finance | Chapter 20: Cost of Capital | Exam Preparation Notes
This single equation can be rearranged three ways, each serving a different practical purpose in
corporate finance:
• Solve for S (Valuation Problem): Given earnings X and required return Ke, what is the firm
worth? Used in securities valuation (Chapters 5–7).
Eq. 20-2 | Earnings Yield (Cost of Equity Estimation)
Rearranges Eq. 20-1 to find the investors' required return.
Called the earnings yield — forecast EPS ÷ market price.
Limitation: Rarely adequate because most firms have growth
Ke = X / S
expectations. Stock price already reflects growth
opportunities, so earnings yield understates Ke. Was useful
in 1950s when inflation and growth were minimal.
• Solve for X (Required Earnings Problem): Given the firm's value and Ke, what earnings must
the firm generate?
Eq. 20-3 | Required Earnings
Used by regulators in 'rate of return regulation' (utilities).
Regulators determine required earnings, then set prices
accordingly.
X = Ke × S Example: S = $10, Ke = 10% → X = 0.10 × $10 = $1 per
share
This is how telephone, water, gas, and electric bills are
set.
⚠️
Key Insight: Three Uses of One Equation
The same equation — S = X / Ke — answers three distinct questions:
1. What is the security worth? (Valuation) → solve for S
2. What return do investors require? (Cost of Capital) → solve for Ke
3. What must the firm earn? (Required Earnings / Regulatory Pricing) → solve for X
Understanding this flexibility is fundamental to all of corporate finance.
Deriving the Required Income Statement
Using the third approach (solving for required earnings X), we can construct the income statement 'from
the bottom up' — starting with what shareholders require and working upward to determine the
necessary sales level. This is exactly how regulators set prices for utility companies.
Using our example firm (market value of equity S = $2,500, Ke = 12%; market value of debt D = $700,
Kd = 6%; tax rate T = 25%; operating costs = $300 variable + $258 fixed):
TABLE 20-3: Required Income Statement (Bottom-Up Construction)
Sales $1,000
Page 2
, COMM 309 — Business Finance | Chapter 20: Cost of Capital | Exam Preparation Notes
Variable costs 300
Fixed costs 258
EBIT 442
Interest 42
Tax (25%) 100
Net income $300
From this we can derive several key financial ratios:
• Asset Turnover Ratio: Sales ÷ Total Assets = $1,000 ÷ $2,000 = 0.50
• Return on Assets (ROA): Net Income ÷ Total Assets = $300 ÷ $2,000 = 15%
• Return on Invested Capital (ROIC): EBIT ÷ Book IC = $442 ÷ $1,700 = 26% (pre-tax); After-tax
ROIC = 26% × 0.75 = 19.5%
• Return on Equity (ROE): Net Income ÷ Book Equity = $300 ÷ $1,000 = 30%
• Earnings Per Share (EPS): NI ÷ Shares = $300 ÷ 1,000 = $0.30/share
Eq. 20-4 | Price Per Share (Perpetuity with Growth Via ROE)
BVPS = Book Value Per Share = Equity ÷ Shares
ROE = Return on Equity (earnings rate on book value)
P = EPS / Ke = (ROE × BVPS) / Ke
Example: EPS = $0.30, Ke = 12% → P = $0..12 =
$2.50 per share
Eq. 20-5 | Market-to-Book (M/B) Ratio
If ROE > Ke → M/B > 1 (shares trade above book value;
value is being created)
If ROE < Ke → M/B < 1 (shares trade below book value;
value is being destroyed)
P / BVPS = ROE / Ke If ROE = Ke → M/B = 1 (shares trade at book value)
Example: ROE = 30%, Ke = 12% → M/B = 0..12 =
2.50
This is a basic law of finance: exceeding investor
expectations drives prices above book value.
20.2 THE COST OF CAPITAL
Determining the Weighted Average Cost of Capital (WACC)
The total enterprise value (V) of a firm is the market value of all invested capital: V = D + S (debt +
equity). We can extend the perpetuity valuation equation to the entire firm using after-tax EBIT (i.e.,
EBIT(1−T)), which represents what the firm earns if financed 100% with equity — it excludes the
interest tax shield.
Eq. 20-6 | Total Enterprise Value
Page 3
