Part 2 Section B.2. Long-Term Financial Management 長期の財務管理

Capital Structure 資本構成

  • External Funds
    • Long-term debt
    • Preferred stock
    • Common stock
  • Internal Funds
    • Retained earnings

External Funds 外部資金調達 

Default Risk デフォルトリスク

Default risk is the probability of a security issuer being unable to meet its contractual obligations of interest and principal payments. A greater risk increases the yield because the investor is paid a premium for taking the default risk.

Marketability 市場性

Marketability of a security is the ability to buy and sell the security on a secondary market and relates to the owner’s ability to convert it into cash. A lower marketability increases the yield because the investor is paid a premium for the lack of marketability.

Maturity 満期

Maturity is the length of time remaining until a security is redeemed by the original issuer. A longer maturity means an investor has a greater exposure to risk. This risk increases the yield.

Financial instruments 金融商品ごとの評価

Certified of Deposit:
  • Default risk:
    • The risk of the issuing bank failing, a probability that is low in most cases.
  • Marketability:
    • Negotiable CDs issued by top money center banks are marketable in the national money markets. Other negotiable CDs may have a poor secondary market.
  • Maturity:
    • Original maturities are short-term and generally range from 30 days to one year.
U.S. Treasury Bills:
  • Default risk:
    • Default risk is negligible because the bills are guaranteed by the U.S. government.
  • Marketability:
    • The market activity is excellent and the transaction costs involved in their sale in the secondary market are small.
  • Maturity:
    • Treasury bills are auctioned weekly by the treasury with short-term maturities of 3 months, 6 months, and one year.
Preferred Stock of Domestic Corporations:
  • Default risk:
    • Preferred stock does not have default risk as such, because the preferred stock investor does not have to be repaid by the company. However, a company issuing preferred stock can declare bankruptcy and be liquidated. Preferred stockholders would have priority over common stockholders in a bankruptcy, but there is no guarantee that preferred stockholders would receive their invested funds bank.
  • Marketability:
    • Marketability of preferred stock is very good for a listed issue. The realized price dimension of marketability is not as good because of the volatility of preferred stock prices.
  • Maturity:
    • Preferred stock has no maturity.

Bonds (Debt Securities) 負債調達

Bond Interest Rate – Factors

  1. Risk-free rate
  2. Implied inflation factor
  3. Credit or default risk of issuer
  4. Liquidity of bond
  5. Tax Status of bond
  6. Term to maturity
  7. Risk of loss of principal due to a general increase in market rates
  8. Any special provisions of the bond

To convert a tax-exempt interest to a taxable equivalent rate

● \( \displaystyle \bf Taxable~Equivalent~Interest~Rate \\ ~= \frac{Tax –Exempt~Interest~Rate}{(1- Tax~Rate)} \)

\( \displaystyle \bf 0.07 = \frac{0.05}{(1- 0.3)} \)

● \( \displaystyle \bf Tax–Exempt~Interest~Rate \\ ~= Taxable~Equivalent~Interest~Rate \times (1- Tax~Rate) \)

\( \displaystyle \bf 0.05 = 0.07 \times (1- 0.3) \)

税率が30%の場合、税引前の5%の利回り(利率)は、税引後では7%に相当する。差の2%は、支払利息の節税効果(タックスシールド)に相当する。

The after-tax interest rate = the exempt interest rate

Liquidity 流動性

Importance of liquidity 流動性の重要性

Liquidity is the ability of an asset to be converted into cash without significant price concessions. Liquidity is important to the company because current obligations will continue if there is a strike. Understanding the company’s ability to meet its obligations even if normal cash receipts are not forthcoming would give management an indication of whether or not – and for how long – it could weather a strike. Lack of liquidity can limit a company’s financial flexibility, making it unable to take advantage of discounts and other profitable opportunities. Liquidity problems can also lead to financial distress or bankruptcy.

Measures of liquidity 流動性の指標
  • Current ratio: current assets ÷ current liabilities
  • Quick ratio (acid test ratio) : (cash + marketable securities + net accounts receivable) ÷ current liabilities.
    • The quick ratio excludes inventory and prepaid expenses from cash resources.
  • Cash ratio: (cash & cash equivalents + marketable securities) ÷ current liabilities
    • Only cash and securities that are easily convertible into cash are used.
  • Net working capital: current assets – current liabilities
  • Net working capital ratio: net working capital ÷ total assets
  • Accounts receivable turnover: net annual credit sales ÷ average gross receivables
  • Days sales in receivables: 365 ÷ accounts receivable turnover ratio
  • Inventory turnover: annual cost of goods sold ÷ average inventory
  • Days sales in inventory: 365 ÷ inventory turnover ratio

Equity Financing 資本による資金調達

  • Common shares
  • Preferred shares
  • Retained earnings

Calculating the Price of Share 株式の価格

公正価値 fair value の求め方(計算問題の出題パターン)は9つ

  1. Zero growth dividend model
  2. Constant growth dividend model
  3. Valuing shares at a future date
  4. Valuing shares using dividends and expected sale price
  5. Valuing shares that do not pay a dividend
  6. Using CAPM to value a share
  7. Two stage dividend discount model
  8. The P/E multiple model
  9. Market multiples approach

Zero Growth Dividend Model

\( \displaystyle \bf P_0 = \frac{Annual~Dividend}{Investors’~Required~Rate~of~Return} \)

$1.00 の配当金で、利回り 5% が期待されている株式の価格(P0)は、

\( \displaystyle \bf P_0 = \frac{$1.00}{0.05} = $20.00 \)

Dividend Growth Model / Constant Growth Model

\( \displaystyle \bf P_0 = \frac{D_1}{R – G} \)

Where:
P0 = Fair Value of common stock today
D1 = The next annual dividend to be paid
R = The investors’ required rate of return
G = The annual expected % growth rate of dividends

● 去年の配当が $1.10 で、成長率が 5% で、期待収益率が 12% の場合の株価は、

\( \displaystyle \bf P_0 = \frac{$1.10 \times 1.05}{0.12 – 0.05} = \frac{$1.155}{0.07} = $16.50 \)

Valuing Stock at Future Day

● 去年の配当が $1.50 で、成長率が 2% で、期待収益率10% の3年後 (in 3 years)の株価は、

<方式1:現在株価を先に求める方式>

①現在の株価 P0 を求める
\( \displaystyle \bf P_0 = \frac{$1.50 \times 1.02}{0.10 – 0.02} = $19.125 \)

②3年後の株価 P3 を求める
\( \displaystyle \bf P_3 = $19.125 \times 1.02^3 = $20.30 \)

<方式2:3年後の配当金額を先に求める方式>

①3年後の配当 D3 を求める→去年の配当D0 から見れば、4年後の話になるので、
\( \displaystyle \bf D_3 = $1.50 \times 1.02^4 = $1.6236 \)

②3年後の株価 P3 を求める
\( \displaystyle \bf P_3 = \frac{$1.6236}{0.10 – 0.02} = $20.30 \)

Valuing Stock Using Dividends and Expected Sale Price

● 次期の配当額が与えられて、期待収益率が分からず、1年後の株価が分かっている場合、
dividend growth model を変形して、現在株価を求める。

\( \displaystyle \bf P_0 = \frac{d_1 + P_1}{1 + r} \)

Where:
P0 = the fair value today of a share of stock
P1= the expected price of the stock at the end of one year
d1 = the next annual dividend to be paid
r = the investors’ required rate of return

Valuing Stock with No dividend

● 無配だが、EPSとその期待収益率が分かっている場合、
dividend growth model を変形して、現在株価を求める。

\( \displaystyle \bf P_0 = \frac{E_1}{R – G} \)

Where:
P0 = the fair Value today of a share of tock
E1 = The next year’s earnings per share
R = The investors’ required rate of return
G = The annual expected % growth rate of dividends

The Stock Right

Valuing the Stock Right – Rights-On

\( \displaystyle \bf V_r = \frac{P_0 – P_n}{r + 1} \)

Where:
P0 = The value of a share with the rights still attached
Pn = The subscription (sales) price of a share
r = The number of rights needed to buy a new share
Vr = The value of the right

<新株優先引受権の価値>

● 現在の発行済株式総数: 5,000,000, 追加の新株発行金額: $100,000,000, 現在株価: $50, 新株発行価格: $40, 株式の希釈化を避けるため、既存株主に優先して新株を有償で割り当てるとすると、

①追加発行株式総数は、

\( \displaystyle \bf \#of~new~shares = $100,000,000 \div $40 = 2,500,000 \)

②新株1株引受に必要な株式数 r は、

\( \displaystyle \bf r = (5,000,000 \times 1) \div 2,500,000 = 2 \)

③新株優先引受権の価値 Vr は、

\( \displaystyle \bf V_r = \frac{$50 – $40}{2 + 1} = $3.333 \)

Valuing the Stock Right – Ex-Rights

新株優先引受権付き株式の権利落ち価格は、新株優先引受権の価値式を応用することで、次のように表現できる

\( \displaystyle \bf V_r = \frac{P_{ex} – P_n}{r} \)

Where:
Pex = The value of a share without the rights attached
Pn = The subscription (sales) price of a share
r = The number of rights needed to buy a new share
Vr = The value of the right

①理論値として、権利落ち価格 Pex は、権利付き株価から、新株優先引受権の価値を差し引いた残りなので、

\( \displaystyle \bf P_{ex} = P_0 – V_r = $50 – $3.333 = $46.667 \)

②これを、Vr と Pexの式に代入すると、

\( \displaystyle \bf V_r = \frac{$46.667 – $40}{2} = $3.333 \)

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