Part 2 Section B.2.2. Cost of Capital 資本コスト

Weighted-Average Cost of Capital 加重平均資本コスト

Overall

\( \displaystyle \bf WACC = \frac{Total~After~Tax~Costs~of~Financing}{Total~Market~Value~of~Financing} \)

負債コスト(支払利息)は税引後に調整する
各資本は時価評価(=市場価格、flotation cost, issue cost は控除後)

  • WACCの計算手順
    1. Calculate the annual after-tax cost of each individual component
    2. Assess the firm’s capital structure to determine the appropriate weighting
    3. Calculate the WACC by summing the products of the weights and the after-tax cost

Step 1: Calculating Costs of the Component of Capital Structure

Cost of Debt

\( \displaystyle \bf C_d = C(1 – t) \)

Where:
Cd = Cost of debt after tax
C = Cost of debt before tax (実効年利であって、クーポンレートではない)
t = Marginal tax cost

Cost of Preferred Stock

\( \displaystyle \bf C_{np} = \frac{D}{P_n} \)

Where:
Cnp = Cost of new preferred stock
D = Yearly dividend per share
Pn = Net proceeds per share of the issue (selling price から発行コストを差し引く)

Cost of Common Stock

  1. Retained earnings: 株主の opportunity cost があるのでただではない
  2. New common equity: 発行コストがかかる分だけ割高になる
Models for Calculating the Cost of Retained Earnings
  1. Dividend (Gordon) Growth model
  2. Capital Asset Pricing Model (CAPM)
  3. Before-Tax Cost of Debt Plus Risk Premium
1. Dividend (Gordon) Growth Model

\( \displaystyle \bf C_{re} = \frac{D_1}{P_0} + G \)

Where:
Cre = Cost of retained earnings (Investors’ required rate of return)
D1 = The next annual dividend (来年の配当 or 従来の配当×成長率)
P0 = Common stock price per share today
G = The annual expected % growth in dividend

2. CAPM

\( \displaystyle \bf R = R_F + \beta (R_M – R_F) \)

Where:
R = Investors’ required rate of return (cost of retained earnings)
RF = Risk-free rate of return
β = Beta coefficient
RM = Expected rate of return for the market portfolio

3. Before-Tax Cost of Debt Plus Risk Premium

Cost of Equity = Before Tax Cost of Debt + Risk Premium in Expected Return for Stock Over Debt

注)試験的には、GordonモデルとCAPMで解けない場合でのみ使用する

Step 2: Assessing the Firm’s Capital Structure

簿価ではなく、市場価値で計算する以外に重要な論点無し

Step 3: Calculating the WACC

Weighted-Average Cost of Capital と Weighted Marginal Cost of Capital の問題が2つある

The breakpoint

従来の資本構成を崩さずに利益剰余金と合計した普通株式の新規増資可能リミットを求める

\( \bf Equity~Breakpoint = \frac{Available~Retained~Earnings}{Percentage~of~Common~Equity~to~Total~Capital} \)

●既存の資本構成とWACC

Debt$200,000,00040%0.40×0.06=0.0240
Preferred equity50,000,00010%0.10×0.084=0.0084
Common equity250,000,00050%0.50×0.12=0.0600
Total/WACC$500,000,000100%0.0924

planning capital projects: $100,000,000
retained earnings: $10,000,000

Equity breakpoint = $10,000,000 ÷ 0.5 = $20,000,000 
(資本構成を崩さずに普通株式で調達できる上限)
→ この内、$10,000,000 は利益剰余金を使い、残りの $10,000,000 が新規増資分で充足することになる

●利益剰余金で充当する分(利益剰余金は $10,000,000 で、トータルの資金調達額は $20,000,000)

Preferred equity の発行コストは、0.09 とする

Debt$8,000,00040%0.40×0.06=0.0240
Preferred equity2,000,00010%0.10×0.09=0.0090
Common equity10,000,00050%0.50×0.12=0.0600
Total/WACC$20,000,000100%0.0930
※ Debt と Preferred Stock の調達分は下の分とトータルではだぶっている

●普通株式の新規発行で充当する分($100,000,000-$10,000,000(利益剰余金)=$90,000,000)

Common Stock の発行コストは、0.13 とする

Debt$36,000,00040%0.40×0.06=0.0240
Preferred equity9,000,00010%0.10×0.09=0.0090
Common equity45,000,00050%0.50×0.13=0.0650
Total/WACC$90,000,000100%0.0980

●資金調達後の全合計($500,000,000+$90,000,000=$590,000,000)

Debt$236,000,00040%0.40×0.06=0.0240
Preferred equity59,000,00010%0.10×0.085=0.0085
Common equity295,000,00050%0.50×0.122=0.0610
Total/WACC$590,000,000100%0.0935
※1 (50÷59×0.084)+(9÷59×0.09)=0.085
※2 (250÷295×0.12)+(45÷295×0.13)=0.122

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