AF3313 Corporate Finance Review Notes

Made by Ziyang CHEN, Rocky, 陈子阳

Chapter 02

$$
\bf CF(A) = OCF - CS - ΔNWC
$$

CF(A) = CF(B) + CF(S)
- Debt (Cash Flow to Creditors, CF(B) ) = Interest - change of debt = Interest - (New debt - Retirement/payback/redeemed of debt)
- Equity (Cash Flow to Stockholders, CF(S) ) = Dividends + Repurchase of stock - new stock issue
Operating cash flow(OCF) = EBIT + Depreciation – Taxes = Net income + Depreciation = Sales - Costs - Taxex = (Sales - Costs)(1-T) + Depreciation*T
Capital spending = 购买/维修 PPE = Purchase(Acquisitions) of fixed assets - Sales of fixed assets
Additions to net working capital = ΔNWC = change of NWC -> sum = 0
- Net Working Capital (NWC) = current asset - current liability

Income Statement

Sales
- Cost of goods sold
- Selling costs/expenses
- Depreciation
EBIT
- Interest
Taxable income
- Taxes (Current + Deffered)
= Net income (Addition to retained earnings + Dividends)

OCF
- Capital spending (购买/维修 PPE)
- NWC (sum=0)
= incremental Cash Flow, CF(A)

Chapter 04. Discounted Cash Flow Valuation

The One-Period Case
$$
\bf FV=C_0(1+r)\ \ \ \ \ \ \ \ \ \ PV=\frac{C_1}{1+r}
$$
The Multiperiod Case
- Compounding 复利和Compounding Periods 多年期复利, 拿现在的钱去算将来的钱
- r代表一个单位，T代表一共多少个单位
  $$
  \bf FV=C_0(1+r)^T\ \ ➡️\ \ FV=C_0(1+\frac{r}{m})^{mT}
  $$
- Present Value and Discounting 现金与折现, 拿将来的钱去算现在的钱
  $$
  \bf PV=\frac{C_T}{(1+r)^T}
  $$
Simplifications 简化

PV 算的是 one period before the first payment
- Perpetuity 永续年金: 源源不断的现金流 (生命周期无限)
  $$
  \bf PV=\frac{C}{r}
  $$
- Growing perpetuity 增长性永续年金: 能始终以某固定的增长率保持增长的一系列现金流 (生命周期无限 + 有增长率g)
  $$
  \bf PV=\frac{C}{r-g}
  $$
- Annuity 年金: 一系列稳定有规律的、**持续一段固定时期(T)**的现金收付活动 (生命周期有限T)
  $$
  \bf PV=\frac{C}{r}[1-\frac{1}{(1+r)^T}]
  \\bf FV = PV(1+r)^T
  $$
- Growing annuity 增长型年金: **在一定时期内(T)**，保持以固定比率增长的一系列现金流 (生命周期有限T + 有增长率g)
  $$
  \bf PV=\frac{C}{r-g}[1-(\frac{1+g}{(1+r)})^T]
  $$

Chapter 05. NPV & Other Investment Rules

Independent Projects(独立项目)，可以都选。

Mutually Exclusive Projects(互斥项目)，只能二选一。

Net Present Value (NPV): 越高越好
- NPV is the sum of the present value of the cash flows from the project
- 最低可接受法则为：如果 NPV ＞0，则接受项目
- 排序法则：选择NPV最高的项目

$$
\bf NPV=C_0+\frac{C_1}{1+r}+\frac{C_2}{(1+r)^2}+…+\frac{C_t}{(1+r)^t}=C_0+\sum_{t=1}^T \frac{C_t}{(1+r)^t}\\bf C_0=positive\ cash\ flows,\ represents\ cash\ receipts\
\bf C_0=negative\ cash\ flow,\ represents\ cash\ payment
$$

Profitability Index (PI): 选>0

$$
\bf PI_2=\frac{PV}{-C_0}=\frac{\frac{C_1}{(1+r)}+\frac{C_2}{(1+r)^2}+…+\frac{C_T}{(1+r)^T}}{-C_0}\ (accept,\ if\ PI_2>1)\\ PI_1 和 PI_2 在项目选择方面应该有相同的答案，因为它们等同于数字相差1
$$

Discount Payback Period (DPB): 越小越好
- how long it takes to payback on a discounted basis 在折扣的基础上需要多长时间才能收回
- $$
  \bf Cash\ Flow\ of\ Present\ Value(PV) = \frac{C_T}{(1+r)^T}
  $$

Chapter 06. Making Capital Investment Decisions

Incremental Cash Flows = Cash Flow From Assets (CFFA)

$$
\bf Earnings ≠ Cash
$$

if the value is positive then it is a cash inflow. If the value is negative, then it is a cash outflow

$$
\bf CFFA = OCF - CS - ΔNWC

\\bf CS = capital\ spending\ (购买/维修\ PPE)

\\bf ΔNWC=change\ in\ net\ working\ capital\ (current\ assets-current\ liabilities)
$$

Operating Cash Flows (OCFs)
- 公司运营产生的现金流量
  $$
  \bf Bottom\ Up:\ OCF = Net Income + depreciation
  \\bf Top\ Down: OCF = Sales – Costs – Taxes
  \\bf Tax\ Shield: OCF = (Sales – Costs)(1 – T) + Depreciation*T\ (T是税率)
  \\bf Net\ Income(NI)=(sales-costs)-Depreciation
  $$
Change in Net working Capital (ΔNWC)
After-tax Salvage, salvage = Market value
$$
\bf After\ tax\ salvage = Salvage – T(Salvage\ –\ Book\ value)=MV-T(MV-BV)
$$

Lecture 06 Chapter 26-28

$$
\bf Inventory\ turnover=\frac{Cost\ of\ Good\ Sold}{Average\ inventory}
\\bf Inventory\ period=\frac{365}{Inventory\ turnover}
\——————————————
\\bf Accounts\ Receivable\ turnover=\frac{Sales}{Average\ Accounts\ receivable}
\\bf Accounts\ Receivable\ period=\frac{365}{Accounts\ receivable\ turnover}
\——————————————
\\bf Accounts\ Payable\ turnover=\frac{Cost\ of\ Good\ Sold}{Average\ Accounts\ Payable}
\\bf Accounts\ Payable\ period=\frac{365}{Accounts\ Payable\ turnover}
$$

Credit Management

$$
\bf One\ Time\ Sale:\ NPV = -v + \frac{(1 - \pi)P}{(1 + r)}
\\bf Repeat\ Customers:\ NPV = -v + \frac{(1-\pi)(P – v)}{r},\ \ \ defaults\ once,\ NO\ grant\ credit\ again
\\bf \ \ v=variable\ cost;\ \pi =default\ probability\ 违约率;\ P=current\ price;\ r=required\ return\ rate
$$

Chapter 08-09 Valuation of Bonds & Stocks

Bond (债券)
$$
\bf Bond\ value = \frac{C}{r} × [{1-\frac{1}{(1+r)^T}}]+\frac{FV}{(1+r)^T}
\\bf C: Coupon\ paid\ each\ period=Coupon\ rate*FV
\\bf interest\ rates ⬆️\ present\ values ⬇️,\ interest\ rates ⬆️\ bond\ prices ⬇️
$$
Stocks (股票)
- Zero Growth (Dividends will remain at the sa‘；me level forever) 生命周期无限，未来现金流是恒定的
  $$
  \bf P_0=\frac{Div_1}{R}
  $$
- Constant Growth (Dividends will grow at a constant rate “g“, forever) 生命周期无限，未来现金流永远以 g 增长
  $$
  \bf P_0=\frac{Div_1}{R-g}\\bf R(cost\ of\ equity)=Dividend\ yield+Capital\ gains\ yeild=\frac{Div_1}{P_0}+g
  $$
- Differential Growth (Dividends will *grow at rate g1 for N years* and *grow at rate g2 thereafter*.
  $$
  \bf P_0=\frac{C_0×(1+g_1)}{r-g_1}[1-\frac{(1+g_1)^T}{(1+r)^T}]+\frac{\frac{C_0×(1+g_1)^T(1+g_2)}{R-g_2}}{(1+r)^T}
  \——————————————-
  \\bf P_n=\frac{last\ divident\ forever}{r}
  \\bf P_0=\frac{C_1}{(1+r)}+\frac{C_2}{(1+r)^2}+…+\frac{C_n+P_n}{(1+r)^n}
  $$

Chapter 11 The Capital Asset Pricing Model

Portfolios (证券投资组合)
Capital Asset Pricing Model (CAPM)
Capital market line (CML)

Final

Debt(Creditors) versus Equity(Shareholder)

Creditors generally receive the first claim on the firm’s cash flow, and they receive a fixed interest rate regardless of the performance of the business.
Shareholder’s equity is the residual difference between assets and liabilities, and they receive dividends or capital gains only if the business makes enough profit.
Shareholder’s equity take on more risk but also have a greater return than debt holders (Creditors).

The dividend growth model calculates total return, the total return of stock:

The required return (R) has two components.
Dividend yield (Div/P): This is calculated as the expected cash dividend (D) divided by the current price (P).
Capital gains yield / Dividend growth rate (g): The rate at which the value of the investment grows.

The CAPM suggests that the expected return is a function of

**Risk-free rate of return: **is the pure time value of money.
**Beta: **is the amount of systematic risk present in a particular asset. 特定资产中存在的系统性风险
Market risk premium: is the reward for bearing systematic risk. 承担系统性风险的回报
A flexible short-term finance policy would maintain a high ratio of current assets to sales.
- Keeping large cash balances and investments in marketable securities
- Large investments in inventory
- Liberal credit terms
A restrictive short-term finance policy would maintain a low ratio of current assets to sales.
- Keeping low cash balances, no investment in marketable securities
- Making small investments in inventory
- Allowing no credit sales (thus no accounts receivable)

Corporate Finance Notes

#Corporate Finance #Notes

AF3313 Corporate Finance Review Notes

http://example.com/2023/02/22/notes1/

Author

Rocky CHEN

Posted on

February 22, 2023

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