# 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

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

• 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

### 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

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

●既存の資本構成とWACC

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

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

Section B 企業財務
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