Assignment
分配

Executive Summary
摘要

Introduction
介绍

Background - industry, products/services, market share.
背景 - 行业、产品/服务、市场份额。

Description - SWOT - possible to include financial ratios by categories.
描述 - SWOT - 可以按类别包含财务比率。

Categories of financial ratios → Liquidity, Profitability, Operating / Efficiency, Debt / Leverage, Market eg. P/E.
财务比率的类别→流动性、盈利能力、运营/效率、债务/杠杆、市场，例如。市盈率

Use graphs:
使用图表：

Liquidity → Current ratio.
流动性 → 流动比率。

Profitability → Gross profit, Net profit.
盈利能力 → 毛利、净利润。

Operating → Inventory turnover.
经营→ 存货周转率。

Debt → Debt to Equity, Total debt.
债务 → 债务权益比，总债务。

Market → P/E.
市→市盈率

Main Body
主体

Valuation Methods
估价方法

Gordon's constant dividend growth model
Gordon 的恒定股息增长模型

P = D1/(r- g)
P = D1/（r- g）

Derive g → use past historical dividends
使用过去的历史被除数→派生 g

g → D1

Note: Justify period use to derive
注： 证明期间使用以派生

Derive r → required rate of return/cost of capital
→所需的回报率/资本成本得出 r

Use CAPM (capital pricing model)
使用 CAPM（资本定价模型）

Use WACC (weighted average cost of capital)
使用 WACC（加权平均资本成本）

Use existing information available - Justify
使用现有可用信息 - Justify

Free Cash Flow (FCF) - Firm Valuation
自由现金流 （FCF） - 公司估值

Step 1: Project future 5-year cash flows for the firm
第 1 步：预测公司未来 5 年的现金流

Assumptions:
假设：

Revenues grow by 10%
收入增长 10%

Expenses grow by 8% etc.
费用增长 8% 等。

Income statement:
损益表：

EBIT - Profit X
息税前利润 - 利润 X

EBITDA - Cash flow (use)
EBITDA - 现金流量（使用）

Earning before interest, tax, depreciation and amortisation.
利息、税项、折旧和摊销前的利润。

Step 2:
步骤2：

Assume constant cash flow from Year 6 to infinity
假设从 6 年级到无穷大的现金流恒定

OR
或

Assume constant growth cash flow Year 6 to infinity
假设第 6 年到无穷大的现金流持续增长

V5 = CF/r = 400/r (terminal value)
V5 = CF/r = 400/r（终端值）
PV = 200/(1+г)^1 + 230/(1+r)^2 + 270/(1+r)^3 + 300/(1+r)^4 + (350+P5)/(1+r) ^5
PV = 200/（1+г）^1 + 230/（1+r）^2 + 270/（1+r）^3 + 300/（1+r）^4 + （350+P5）/（1+r） ^5

Step 3: Present Value of all cash flows
第 3 步：所有现金流的现值

Step 4: Value of firm = PV of cash flows – Debt
第 4 步：公司价值 = 现金流 PV – 债务

Balance sheet as at 31 Dec 2023 → Total debt (excludes payables to suppliers) → Use total long-term debt
截至 2023 年 12 月 31 日的资产负债表 → 总债务（不包括应付给供应商的款项） → 使用长期债务总额

Step 5: Value of Share price = Value of firm /no. of shares issued.
第 5 步：股价价值 = 公司价值 / 已发行股票数量。

Compare with market price in the stock exchange.
与证券交易所的市场价格进行比较。

Discuss reasons for differences, whether the stock is overpriced or underpriced.
讨论差异的原因，股票是定价过高还是定价过低。

Recommendations: Buy or Don't Buy the share → Support decision with potential of the firm
建议：买入或不买入股票 → 支持具有公司潜力的决策

介绍

简单给一些背景经合介绍讲做啥的额

P/E市盈率

要解释数据的来源，并说明这个数据为什么我可以用

用Cash flow 不用profit X，两个不是一个东西，不要混用

最多估计五年的收益？maybe
最多估计五年的收益？也许

Lesson 8
第 8 课

Valuation = Determine a fair / maximum price to pay.
估值 = 确定要支付的公平/最高价格。

Valuation Price = Present Value (of all future cash flows received).
估值价格 = 现值（收到的所有未来现金流量）。

Valuation of stocks
股票估值

Cash flow receive → Dividends (D).
现金流收到 → 股息 （D）。

Single Period Valuation

Return % = = (Psell – Pbuy + Dividend ) / Pbuy x 100
回报 % = = = （卖出 – Pbuy + 股息 ） / Pbuy x 100

Multi-Period Valuation
多期间估价

Assume: Hold the shares to forever, continue to receive dividends to forever.
假设：永久持有股票，继续领取股息至永远。

Assumption on dividends:
股息假设：

Dividends grow at a constant rate of g% every year to forever.
股息每年以 g% 的恒定速度增长，直到永远增长。

D1 = D0 (1 + g)
D1 = D0 （1 + 克）

D2 = D1 (1 + g)
D2 = D1 （1 + 克）

D3 = D2 (1 + g)...
D3 = D2 （1 + g）...

P = D1/(1+r)^1 + D2/(1 + r)^2 +D3/(1 + r)^3 + …
P = D1/（1+r）^1 + D2/（1 + r）^2 +D3/（1 + r）^3 + ...

Where r = required rate of return
其中 r = 所需回报率

Gordon’s constant dividend growth model
Gordon 的恒定股息增长模型

P = D1 / (r – g)  OR   P = D0 (1+g) / (r-g)
P = D1 / （r – g）或 P = D0 （1+g） / （r-g）

If D1 is given     If D0 is given
如果给出 D1如果给出 D0

Dividends are constant / Fixed → D0 = D1 = D2 …
股息是恒定的 / 固定的 → D0 = D1 = D2 ...

P = D / r

eg: Preferred shared.
例如：首选共享。

Question：
问题：

Q1: A stock paying $5 in annual dividends sells now for $80 and has an expected return of 14%. What might investors expect to pay for the stock one year from now?
Q1：一只支付 5 美元年度股息的股票现在以 80 美元的价格出售，预期回报率为 14%。投资者一年后可能会期望为这只股票支付多少费用？

Q2:If next year’s dividend is forecast to be $5.00, the constant growth rate is 4%, and the discount rate is 16%, then the current stock price should be:
Q2：如果预测明年的股息为 5.00 美元，恒定增长率为 4%，贴现率为 16%，那么当前股价应为：

Q3:What should be the current price of a share of stock if a $5 dividend was just paid, the stock has a required return of 20%, and a constant dividend growth rate of 6%?
Q3：如果刚刚支付 5 美元的股息，股票的所需回报率为 20%，并且恒定的股息增长率为 6%，那么一股股票的当前价格应该是多少？

P = $5(1.06)/(.20 - .06)
P = 5 美元（1.06）/（0.20 - 0.06）

  P = 5.30/.14

  P = $37.86
P = 37.86 美元

内容

P = D1/ (r-g)
P = D1/ （r-g）

D0 = Company information
D0 = 公司信息

r = Rf +Beta (Rm – Rf)   (CAPM)
r = Rf +Beta （Rm – Rf） （CAPM）

Beta = Company information / calculate.
Beta = 公司信息 / 计算。

Rf = Average return of government bonds eg. past 3/5/7 years.
Rf = 政府债券的平均回报率，例如过去 3/5/7 年。

 (information sources / calculate)
（信息来源/计算）

论文所选择公司仅限于英美的市场。

Rm = Average return of stock market index eg.past 3/5/7 years → Standard & Poor (S&P) 500,
Rm = 股票市场指数的平均回报，例如过去3/5/7年→标准和普尔（S&P）500指数，

(information sources / calculate.)
（信息来源/计算。

g → Past dividends (company information )eg. past 3/5/7 years.
g → 过去的股息（公司信息），例如过去 3/5/7 年。

Example:
例：

Year   Divedend per share
年每股潜水人数

2023   0.76 → FV

2022 ⬆  0.62
2022⬆年 0.62

2021 ⬆  0.54
2021⬆年 0.54

2020 ⬆  0.46 → PV

g = (FV / PV )^(1/t) – 1
g = （FV / PV ）^（1/t） – 1

= (0.76 / 0.46) ^ (1/3) – 1 = 0.18218
= （0.76 / 0.46） ^ （1/3） – 1 = 0.18218

Question:
问题：

Cargo Point, Inc. has a beta of 1.10. The risk-free rate of interest is currently 6%, and the required return on the market portfolio is 13%. The company plans to pay a dividend of $2.91 in the coming year and anticipates that its future dividends will increase at an annual rate consistent with that of the period given:
Cargo Point， Inc. 的 beta 版为 1.10。目前的无风险利率为 6%，市场投资组合的所需回报率为 13%。该公司计划在来年支付 2.91 美元的股息，并预计其未来的股息将以与给定期间一致的年增长率增长： 

Year  Dividend
年股息

2021  $2.91

2020  $2.67

2019  2.45

2018  2.25

Estimate the value of Cargo Point, Inc. stock.
估计 Cargo Point， Inc. 股票的价值。

g = (2.91/2.25)^(1/3) - 1 = 0.0895
克 = （2.91/2.25）^（1/3） - 1 = 0.0895

r = 6 + 1.1(13 – 6 ) = 13.7%
r = 6 + 1.1（13 – 6 ） = 13.7%

P = D1/(r – g) = 2.91/(0.137 – 0.0895) = $61.26
P = D1/（r – g） = 2.91/（0.137 – 0.0895） = 61.26 美元

Multiple growth rates
倍增率

Multiple growth rates
倍增率

Step 1:
步骤1：

D1 = D0 (1 + g1)
D1 = D0 （1 + g1）

D2 = D1 (1 + g1)
D2 = D1 （1 + g1）

D3 = D2 (1 + g1)
D3 = D2 （1 + g1）

D4 = D3 (1 + g2)
D4 = D3 （1 + g2）

P0 = D1 / (r – g)
P0 = D1 / （r – 克）

P3 = D4 / (r – g2) → PV (D4, D5, D6… forever)
P3 = D4 / （r – g2） → PV （D4， D5， D6...永远）

Step 2:
步骤2：

P = D1 / (1 + r) ^ 1 +D2 / (1 + r) ^ 2 + (D3 + P3) / (1 + r) ^ 3
P = D1 / （1 + r） ^ 1 +D2 / （1 + r） ^ 2 + （D3 + P3） / （1 + r） ^ 3

Question：
问题：

Q1:Supernormal Growth Synovec Co. is growing quickly. Dividends are expected to grow at a rate of 30 percent for the next three years, with the growth rate falling off to a constant 4 percent thereafter. If the required return is 11 percent, and the company just paid a dividend of $2.45, what is the current share price?
Q1：超常增长Synovec Co. 正在迅速发展。预计未来三年股息将以 30% 的速度增长，此后增长率将降至 4% 的恒定水平。如果要求的回报率为 11%，而公司刚刚支付了 2.45 美元的股息，那么目前的股价是多少？

Step 1: Calculate dividend cash flows
第 1 步：计算股息现金流

D1 = D0(1+g1) = 3.185
D1 = D0（1+g1） = 3.185

D2 = D1(1+g1) = 4.1405
D2 = D1（1+g1） = 4.1405

D3 = D2(1+g1) = 5.38265
D3 = D2（1+g1） = 5.38265

D4 = D3(1+g2) = 5.38265(1+0.04) = 5.597956
D4 = D3（1+g2） = 5.38265（1+0.04） = 5.597956

P3 = D4/(r – g2) = 5.597956/ (0.11 – 0.04) = 79.9708
P3 = D4/（r – g2） = 5.597956/ （0.11 – 0.04） = 79.9708

Step 2: Present value all the dividend cash flows
第 2 步：对所有股息现金流进行现值

P = D1/(1+r)^1 + D2/(1+r)^2 + (D3+P3)/(1+r)^3
P = D1/（1+r）^1 + D2/（1+r）^2 + （D3+P3）/（1+r）^3

= 3.185/(1+0.11)^1 + 4.1405/(1+0.11)^2 + (5.38265+79.9708)/(1+0.11)^3
= 3.185/（1+0.11）^1 + 4.1405/（1+0.11）^2 + （5.38265+79.9708）/（1+0.11）^3

P0 = $68.64
P0 = 68.64 美元

Q2:You are considering investing in Facial Laboratories. Suppose Facial is currently undergoing expansion and is not expected to change its cash dividend while expanding for the next 4 years. This means that its current annual $3.00 dividend will remain for the next 4 years. After the expansion is completed, higher earnings are expected to result causing a 30% increase in dividends each year for 3 years. After these three years of 30% growth, the dividend growth rate is expected to be 2% per year forever. If the required return for Facial’s common stock is 11%, what is a share worth today?
Q2：您正在考虑投资 Facial Laboratories。假设 Facial 目前正在进行扩张，预计在未来 4 年内不会在扩张时改变其现金股息。这意味着其目前的年度 3.00 美元股息将在未来 4 年内保持不变。扩建完成后，预计将产生更高的收益，导致股息在 3 年内每年增加 30%。经过这三年 30% 的增长，股息增长率预计将永远保持在每年 2%。如果 Facial 普通股的要求回报率为 11%，那么今天的股票值多少钱？

D1 = 3

D2 = 3

D3 = 3

D4 = 3

D5 = 3(1+0.3) = 3.90
D5 = 3（1+0.3） = 3.90

D6 = 3.9(1+0.3) = 5.07
D6 = 3.9（1+0.3） = 5.07

D7 = 5.07(1+0.3) = 6.59
D7 = 5.07（1+0.3） = 6.59

D8 = 6.59 (1+0.02) = 6.72
D8 = 6.59 （1+0.02） = 6.72

P7 = D8/(r – g2) = 6.72/(0.11 – 0.02) = 74.70
P7 = D8/（r – g2） = 6.72/（0.11 – 0.02） = 74.70

P = 3/(1+0.11)^1 + 3/(1+0.11)^2 + 3/(1+0.11)^3 + 3/(1+0.11)^4 + 3.9/(1+0.11)^5 + 5.07/(1+0.11)^6 + (6.59+74.70)/(1+0.11)^7 = $53.49
P = 3/（1+0.11）^1 + 3/（1+0.11）^2 + 3/（1+0.11）^3 + 3/（1+0.11）^4 + 3.9/（1+0.11）^5 + 5.07/（1+0.11）^6 + （6.59+74.70）/（1+0.11）^7 = 53.49 美元

论文相关

Valuation of shares
股票估值

Method 1: Discounted cash flows(DCF) – listed firms
方法 1：贴现现金流 （DCF） – 上市公司

Method 2: Comparables Industry Average – unlisted firms.
方法 2：可比行业平均水平 – 非上市公司。

Valuation of firm
公司估值

Income Statement
损益表

Revenues
收入

Less: COGS- Cost of Goods Sold/COS – Cost of Sales
减：销货成本 - 销货成本/COS - 销售成本

Gross Profit
毛利

Less: Admin expenses  →→→  Cash Flow (EBITDA)
减：管理费用→→→ 现金流 （EBITDA）

     Depreciation
折旧

EBIT       Profits
EBIT产品

(Earnings before interest and tax)
（息税前利润）

Profits are NOT equal to Cash Flows
利润不等于现金流

Profits include non-cash flow items eg. Depreciation
利润包括非现金流项目，例如。折旧

Profits are based on accrual accounting eg. GAAP, FASB
利润基于权责发生制会计，例如。美国通用会计准则 （GAAP）、美国财务会计准则 （FASB）

Cash flow = Profits + Depreciation → EBITDA
现金流量 = 利润 + 折旧 → EBITDA

(Earnings before interest, tax, depreciation and amortization)
（未计利息、税项、折旧及摊销前利润）

Profit = Cash flow – Depreciation → EBIT
利润 = 现金流量 – 折旧 → 息税前利润

FCF = Free Cash Flow
FCF = 自由现金流

FCF = Profits (EBIT) + Depreciation – Tax
FCF = 利润 （EBIT） + 折旧 – 税

FCF → Value of firm = PV of FCF
自由现金流 → 公司价值 = 自由现金流的 PV

Value of share
股票价值

= (PV of FCF) – Debt + Cash/Marketable Securities
= （FCF 的 PV） – 债务 + 现金/有价证券

  No. of shares outstanding
不。流通股数

Methods to derive FCF
派生 FCF 的方法

Estimated cash flow = EBITDA
预计现金流量 = EBITDA

(Earnings before interest, tax, depreciation and amortization).
（息税折旧摊销前利润）。

If EBIT is given: Tc = Corporate Tax rate
如果给出 EBIT：Tc = 公司税率

FCF = EBIT x (1 – Tc) + Depreciation – Increase (change) in capital expenditure – Increase (change) in working capital.
自由现金流 = 息税前利润 x （1 – Tc） + 折旧 – 资本支出增加（变化） – 营运资金增加（变化）。

If Profit after tax is given:
如果给出了税后利润：

FCF = Profit after tax + Depreciation – Increase (change) in capital expenditure – Increase (change) in working capital.
FCF = 税后利润 + 折旧 - 资本支出的增加（变化） - 营运资金的增加（变化）。

Given are the following data for year 1:
给定的是第 1 年的数据：

Profits after taxes = $14 million; Depreciation = $6 million; Interest expense = $6 million; Investment in fixed assets = $12 million; Investment in working capital = $3 million. Calculate the free cash flow (FCF) for year 1:
税后利润 = 1400 万美元;折旧 = 600 万美元;利息支出 = 600 万美元;固定资产投资 = 1200 万美元;营运资金投资 = 300 万美元。计算第 1 年的自由现金流 （FCF）：

FCF = 14 + 6 - 12 - 3 = $5 million.
FCF = 14 + 6 - 12 - 3 = 500 万美元。

Given are the following data for year 1: Profit after taxes = $5 million; Depreciation = $2 million; Investment in fixed assets = $4 million; Investment net working capital = $1 million. Calculate the free cash flow (FCF) for year 1:
给出的是第 1 年的以下数据：税后利润 = 500 万美元;折旧 = 200 万美元;固定资产投资 = 400 万美元;投资净营运资金 = 100 万美元。计算第 1 年的自由现金流 （FCF）：

FCF = 5 + 2 - 4 - 1 = 2.
FCF = 5 + 2 - 4 - 1 = 2。

Lesson 9
第 9 课

Methods to derive FCF
派生 FCF 的方法

EEstimated cash flow = EBITDA
E 估计的现金流 = EBITDA

(Earnings before interest, tax, depreciation and amortization).
（息税折旧摊销前利润）。

If EBIT is given: Tc = Corporate Tax rate
如果给出 EBIT：Tc = 公司税率

FCF = EBIT x (1 – Tc) + Depreciation – Increase (change) in capital expenditure – Increase (change) in working capital.
自由现金流 = 息税前利润 x （1 – Tc） + 折旧 – 资本支出增加（变化） – 营运资金增加（变化）。

If Profit after tax is given:
如果给出了税后利润：

FCF = Profit after tax + Depreciation – Increase (change) in capital expenditure – Increase (change) in working capital.
FCF = 税后利润 + 折旧 - 资本支出的增加（变化） - 营运资金的增加（变化）。

Value of firm → growth rate → Plowback rate.
公司价值 →增长率 → 犁回溯率。

Assumptions: Value of the Growth rate of the free cash flows.
假设：自由现金流增长率的值。

Gordon’s model → growth rate → Dividend payout rate.
Gordon 的模型→增长率→股息支付率。

Assumptions: Value of the Growth rate of the dividends.
假设：股息增长率的值。

Valuation of firm     Horizon Period
firmHorizon Period 估值

g = use past cash flows to estimate or plowback rate to estimate.
g = 使用过去的现金流进行估计，或使用 Plowback Rate 进行估计。

Gordon’s model from Year 6
Gordon 的 6 年级模型

FCF6 = FCF5 *(1 + g)
FCF6 = FCF5 *（1 + 克）

V5 = FCF6 / (r – g)   Horizon Value
V5 = FCF6 / （r – g） 水平值

Value of firm = FCF1 / (1 + r)^1 + FCF2 / (1 + r)^2 + FCF3 / (1 + r)^3 + FCF4 / (1 + r)^4 + (FCF5 + V5) / (1 + r)^5
公司价值 = FCF1 / （1 + r）^1 + FCF2 / （1 + r）^2 + FCF3 / （1 + r）^3 + FCF4 / （1 + r）^4 + （FCF5 + V5） / （1 + r）^5

Where
哪里

r = Weighted Average Cost of Capital of firm (WACC).
r = 公司加权平均资本成本 （WACC）。

OR
或

r = Capital Asset Pricing Model (CAPM)
r = 资本资产定价模型 （CAPM）

(Assume the firm has no debt)
（假设公司没有债务）

Question:
问题：

Q1: Consider the following data:
Q1：请考虑以下数据：

FCF1 = $7 million; FCF2 = $45 million; FCF3 = $55 million. Assume that free cash flow grows at a rate of 4% for year 4 and beyond. If the weighted average cost of capital (required rate of return) is 10%, calculate the value of the firm.
FCF1 = 700 万美元;FCF2 = 4500 万美元;FCF3 = 5500 万美元。假设自由现金流在第 4 年及以后以 4% 的速度增长。如果加权平均资本成本（所需回报率）为 10%，则计算公司的价值。

Horizon value in year 3 = (55)(1.04)/(0.10 - 0.04) = $953.33 million;
第 3 年的地平价 = （55）（1.04）/（0.10 - 0.04） = 9.5333 亿美元;

PV = (7/1.10) + (45/1.10^2) + [(55 + 953.33)/(1.10^3)] = $801.12 million.
PV = （7/1.10） + （45/1.10^2） + [（55 + 953.33）/（1.10^3）] = 8.0112 亿美元。

Q2: Consider the following data:
Q2：请考虑以下数据：

FCF1 = $20 million; FCF2 = $20 million; FCF3 = $20 million. Assume that free cash flow grows at a rate of 5% for year 4 and beyond. If the weighted average cost of capital (required rate of return) is 12%, calculate the value of the firm.
FCF1 = 2000 万美元;FCF2 = 2000 万美元;FCF3 = 2000 万美元。假设自由现金流在第 4 年及以后以 5% 的速度增长。如果加权平均资本成本（所需回报率）为 12%，则计算公司的价值。

Horizon value in year 3 = (20)(1.05)/(0.12 - 0.05) = $300 million;
第 3 年的水平值 = （20）（1.05）/（0.12 - 0.05） = 3 亿美元;

PV = (20/1.12) + (20/1.12^2) + [(20 + 300)/(1.12^3)] = $261.57 million.
PV = （20/1.12） + （20/1.12^2） + [（20 + 300）/（1.12^3）] = 2.6157 亿美元。

Q3: Adjusted Cash Flow from Assets Pearl Corp. is expected to have an EBIT of $1.8 million next year. Depreciation, the increase in net working capital, and capital spending are expected to be $155,000, $75,000, and $115,000, respectively. All are expected to grow at 18 percent per year for four years. The company currently has $9.5 million in debt and 750,000 shares outstanding. After Year 5, the adjusted cash flow from assets is expected to grow at 3 percent indefinitely. The company’s Weighted Average Cost of Capital is 8.5 percent and the tax rate is 21 percent. What is the price per share of the company’s stock?
第 3 季度： Pearl Corp. 的调整后资产现金流预计明年的息税前利润为 180 万美元。折旧、净营运资金的增加和资本支出预计分别为 155,000 美元、75,000 美元和 115,000 美元。预计所有项目都将在四年内以每年 18% 的速度增长。该公司目前有 950 万美元的债务和 750,000 股流通股。第 5 年之后，调整后的资产现金流预计将无限期地增长 3%。该公司的加权平均资本成本为 8.5%，税率为 21%。公司股票的每股价格是多少？

FCF = EBIT + Depreciation - (EBIT x Tc) – Change in Capital Spending – Change in Net Working Capital (NWC).
FCF = 息税前利润 + 折旧 - （息税前利润 x Tc） - 资本支出变化 - 净营运资本 （NWC） 变化。

FCF6 = FCF5(1+g)
FCF6 = FCF5（1+克）

The value of the company today is the present value of the first five FCFs, plus the value today of the terminal value, or:
公司今天的价值是前 5 个 FCF 的现值，加上今天的终值，即：

Company value = $1,387,000/(1+0.085)^1 + $1,636,660/(1+0.085)^2 + $1,931,259/(1+0.085)^3 + $2,278,885/(1+0.085)^4 + ($2,689,085 + 50,359,223.56)/(1+0.085)^5
公司价值 = 1,387,000 美元/（1+0.085）^1 + 1,636,660 美元/（1+0.085）^2 + 1,931,259 美元/（1+0.085）^3 + 2,278,885 美元/（1+0.085）^4 + （2,689,085 美元 + 50,359,223.56）/（1+0.085）^5

Company value = $41,104,528.40
公司价值 = 41,104,528.40 美元

Price per share = (Corporate value – Debt)/no. of shares
每股价格 = （公司价值 - 债务）/否。股数

To find the value of equity, we subtract the value of the debt from the total value of the company, which is:
为了找到权益的价值，我们从公司的总价值中减去债务的价值，即：

Equity value = $41,104,528.40 – 9,500,000
净值 = 41,104,528.40 美元 – 9,500,000 美元

Equity value = $31,604,528.40
净值 = 31,604,528.40 美元

Finally, the value per share is the total equity value divided by the shares outstanding, or:
最后，每股价值是总权益价值除以已发行股票，即：

Share price = $31,604,528.40/750,000
股价 = 31,604,528.40 美元/750,000 美元

Share price = $42.14
股价 = 42.14 美元

论文相关：Industry comparables
论文相关：行业可比

Industry comparables → cross-check your values.
行业可比对象→交叉检查您的值。

Eg. Price to Earnings ratio (P/E)
例如。市盈率 （P/E）

Price of share = Earnings per share x Price to Earnings ratio
股票价格 = 每股收益 x 市盈率

Industry average。从股票网站获得
行业平均水平。从股票网站获得

price to earning rate of technology industry
技术行业的价格与收益率

price to earning ratio of automobile industry
汽车行业的市盈率

Assignment: 16.33
分配：16.33

Explain why choose these 2 methods = Advantages.
解释为什么选择这 2 种方法 = 优势。

Presentation of the calculations of the 2 valuation methods.
介绍 2 种估值方法的计算。

ALL data presented must be justified.
提供的所有数据都必须有理由。

Explain the differences in the values from the 2 methods.
解释 2 种方法的值差异。

why there is a difference.
为什么会有区别。

which you think is more accurate value / which is the more suitable method for share valuation.
您认为哪个值更准确/哪个是更适合的股票估值方法。

Limitations/disadvantages of each method.
每种方法的局限性/缺点。

If believe market is efficient → unable to beat the market eg. Stock picks will not work.
如果相信市场是有效的→就无法击败市场，例如。选股不起作用。

Due to the theory of market efficiency → more investors today believe they are unable to beat the market.
由于市场效率理论→今天有更多的投资者认为他们无法击败市场。

Evidence: Growth of Exchange Traded Funds (ETFs).
证据：交易所交易基金 （ETF） 的增长。

Success → abnormal returns → more than risk-free rate.
成功→异常回报→超过无风险率。

Meaning of market efficiency → Future prices are unpredictable.
市场效率的含义 → 未来价格是不可预测的。

If there is some element of predictability → inefficiencies exist.
如果存在一些可预测性因素→则存在效率低下。

Market Efficiency = Price efficiency
市场效率 = 价格效率

→ speed at which prices adjust to new information.
→价格根据新信息进行调整的速度。

Faster speed → Higher efficiency.
更快的速度→更高的效率。

Consequence: Prices are correct/equilibrium as at a point in time → No mis-pricing (no undervalued or overvalued).
结果：价格在某个时间点是正确的/均衡的 → 没有错误定价（没有被低估或高估）。

→ Prices are on the SML.
→ 价格在 SML 上。

Approaches to analysing securities:
分析证券的方法：

Fundamental Analysis – Economic data and Industry/Firm specific data → Forecast data into the future → Determine stock price in the future.
基本面分析 – 经济数据和行业/公司特定数据 → 预测未来的数据 → 确定未来的股票价格。

Technical Analysis – Stock Price movements of the firm in the past → Determine patterns → Forecast future stock price movement of the firm.
技术分析 – 公司过去 → 的股价走势 确定模式 → 预测公司未来的股价走势。

Determine what are “Hot” stocks.
确定什么是“热门”股票。

Evergrande, Country Garden, Greenland.
恒大，碧桂园，格陵兰岛。

要解释为什么选这个公司

Technical analysis – Charting using past data of stock price movements → determine trends/patterns → predict future price.
技术分析 – 使用股票价格变动的过去数据绘制图表→确定趋势/模式→预测未来价格。

Example: Resistance (sell) and Support (buy) lines.
示例：阻力 （卖出） 和支撑 （买入） 线。

Popular technical analysis strategies – Japanese Candlestick Theory → Based on the opening and closing prices for the day → predict next day’s price movements.
流行的技术分析策略 – 日本烛台理论 → 根据当天的开盘价和收盘价，→预测第二天的价格走势。

Limitation of Technical Analysis – Theory of Market efficiency (EMH – Efficient Market Hypothesis - Fama).
技术分析的局限性 – 市场效率理论 （EMH – 有效市场假说 - Fama）。

Forms of EMH – (1) Weak (2) Semi-Strong (3) Strong.
EMH 的形式 – （1） 弱 （2） 半强 （3） 强。

Weak Form – Stock prices demonstrate random walk – Future prices are not a function of past prices → unable to predict future prices from past data.
弱形式 – 股票价格表现出随机游走 – 未来价格不是过去价格的函数，→无法从过去的数据中预测未来价格。

→ Appropriate strategy – Fundamental Analysis.
→ 合适的策略 – 基本面分析。

Based on semi-strong form and strong form of EMH.
基于 EMH 的半强形式和强形式。

Assumption: Information of the firm which is not available to public as yet.
假设：尚未公开的公司信息。

Current themes = ESG investments (Moral investing).
当前主题 = ESG 投资（道德投资）。

ESG – Environmental, Social, Governance.
ESG – 环境、社会、治理。

Investing in ethical companies.
投资于有道德的公司。

Higher degrees of market efficiency → Prices are in equilibrium (stable) - Passive type of investment strategies.
更高程度的市场效率 → 价格处于均衡（稳定） - 被动类型的投资策略。

Eg. Growth index funds, Exchange Traded Funds (ETFs).
例如。增长指数基金、交易所交易基金 （ETF）。

Index is used to compare performance of fund manager.
指数用于比较基金经理的表现。

Why should markets be efficient? – Workings of Market (Competition)
为什么市场应该是高效的？– 市场运作（竞争）

→ Security prices are not correct all the time.
→ Security 价格并非一直正确。

→ Opportunities to exploit the price differences to make abnormal returns.
→ 利用价差获得异常回报的机会。

→ Prices return to equilibrium (correct prices).
→ 价格恢复平衡（正确的价格）。

Implication to investment management → Active Portfolio may be feasible.
对 Active Portfolio →投资管理的影响可能是可行的。

If market is efficient (no inefficiencies) → Only Passive Strategies are feasible.
如果市场是有效的（没有低效率）→只有被动策略是可行的。

A strict definition of market efficiency:
市场效率的严格定义：

Security prices reflect all available information at any point in time.
证券价格反映了任何时间点的所有可用信息。

If this is not possible all the time, market then would have varying degrees of inefficiencies.
如果这不可能一直存在，那么 market 将有不同程度的低效率。

Lesson 10
第 10 课

Challenges to EMH or market efficiency.
对 EMH 或市场效率的挑战。

Stock market Anomalies.
股票市场异常。

Evidence on stock market inefficiencies.
股票市场效率低下的证据。

Challenges to Market Efficiency.
市场效率面临的挑战。

Prices are predictable / Prices are not in equilibrium.
价格是可预测的 / 价格不平衡。

Examples of Stock Market Anomalies
股票市场异常示例

Weekend Effect
周末效果

If initial part of the week, the market is overbought, end of the week price will decline.
如果本周初期市场超买，则周末价格将下跌。

If initial part of the week, the market is oversold, end of the week price will increase.
如果本周开始时，市场超卖，则周末价格将上涨。

January effect = first few weeks of the year, prices increase.
一月效应 = 今年的前几周，价格上涨。

Noise trader effect eg. Gamestop.
Noise trader 效果，例如游戏顶部。

Momentum effect = Prices continue to more upwards or downwards over a period of time.
动量效应 = 价格在一段时间内继续上涨或下跌。

Arbitrage = Based on the theory of the Law of One Price (LOOP).
套利 = 基于单价定律 （LOOP） 理论。

→ Price of an identical product must be the same in different locations → if not the same, then buy where the price is low and sell where the price is high → riskless profit.
→ 相同产品在不同地点的价格必须相同→如果不是相同的，则在价格低的地方买入，在价格高的地方卖出→无风险的利润。

Example: MYR/SGD MYR 3/SGD
示例：MYR/SGD MYR 3/SGD

   Singapore   Malaysia
新加坡马来西亚

Shampoo  $10    MYR 30
洗发水$10MYR 30

     If MYR 20
如果 MYR 20

Small firm effect → Potential for growth – prices have a tendency to increase.
小公司效应 → 增长潜力 – 价格有上涨的趋势。

Growth stocks (based on trend) – “Hot” Industries.
成长型股票 （基于趋势） – “热门” 行业。

BigTech → Fintech → Artificial Intelligence.
BigTech →金融科技→人工智能。

Value Investing accounting information of the firm.
公司的价值投资会计信息。

Price to Earnings ratio (P/E)
市盈率 （P/E）

If the P/E ratio is low as compared to the industry, then prices increase .
如果市盈率与行业相比较低，那么价格就会上涨。

If the P/E ratio is high as compared to the industry, then prices decrease.
如果市盈率与行业相比高，那么价格就会下降。

Price to Book Value ratio.
价格与账面价值比率。

If the value is low, potential for the firm to invest more in real assets → increase production → increase profits → increase in share price.
如果价值较低，公司有可能更多地投资于实物资产→增加产量→增加利润→股价上涨。

Bonds – Debt
债券 – 债务

Bills → short-term ( < 1 year) – Money Market
短期票据 → （ x3C 1 年） – 货币市场

Bonds → Long-term ( > 1 year) – Capital Market
长期→债券 （ x3E 1 年） – 资本市场

Issuers of Bonds (Borrower) = Governments (Treasury), Governments Agencies, Corporations.
债券发行人（借款人）= 政府（财政部）、政府机构、公司。

Issuers of Bonds (Borrower) = Governments (Treasury), Government Agencies, Corporations.
债券发行人（借款人）= 政府（财政部）、政府机构、公司。

Credit Ratings → International Credit Rating Agencies.
国际信用评级机构→信用评级。

Eg. Standard & Poor (S&P), Moody’s
例如。标准和穷人（S&P），穆迪

Valuation = Present Value (of all future cash flows received).
估值 = 现值（收到的所有未来现金流量）。

Future cash flows (Bonds) = Features of bonds.
未来现金流（债券）= 债券的特点。

Example:
例：

Face value (FV) = $1,000
面值 （FV） = 1000 美元

Coupon rate = 10%
票面息率 = 10%

Coupon (C) = Coupon rate x face value = 0.1 x 1,000 = $100
票息 （C） = 票面利率 x 面值 = 0.1 x 1,000 = 100 美元

Maturity (t) = 3 years
到期日 （t） = 3 年

|----------------|----------------|----------------|

0   1   2   3

  $100   $100  $100+$1,000
100 美元 100 美元 100 美元 + 1,000 美元

  C   C   C+V
C C C + V

Price = P = C / r [ 1 – 1 / (1 + r) ^n ] + FV / (1 + r) ^n
价格 = P = C / r [ 1 – 1 / （1 + r） ^n ] + FV / （1 + r） ^n

P = 100 / r [1 – 1 / (1 + r) ^3 ] + 1000 / (1 + r) ^3 

Where r =required rate of return / discount rate / Yield to Maturity (YTM) 

Question: 

Q1: Suppose a German company issues a bond with a par value of €1,000, 23 years to maturity, and a coupon rate of 3.8 percent paid annually. If the yield to maturity is 4.7 percent, what is the current price of the bond? 

P = C/r [ 1 – 1/(1+r)^t] + FV/(1+r)^t 

C = 0.038 x 1,000 = 38 

t = 23 

FV = 1,000 

r = 0.047 

P = 38/0.047 [ 1 – 1/(1+0.047)^23 ] + 1000/(1+0.047)^23 = €875.09 

Q2: Coupons can be paid annually or semi-annually 

If semi-annual C/2, r/2, t x2 

Bond Prices Weismann Co. issued 15-year bonds a year ago at a coupon rate of 4.9 percent. The bonds make semi-annual payments and have a par value of $1,000. If the YTM on these bonds is 4.5 percent, what is the current bond price? 

P = C/r [1 – 1/(1+r)^t] + FV/(1+r)^t 

C = (0.049 x 1000)/2 

FV = 1,000 

r = 0.045/2 

t = 14 x 2 = 28 

P = $1,041.22 

Valuation 

P = C / r [ 1 – 1 / (1 + r) ^t ] + FV / (1 + r) ^t 

C / r [ 1 – 1 / (1 + r) ^t ] + FV / (1 + r) ^t – P = 0 

P → Market Price 

Solve for r → return generated by the bond investment if hold the bond till maturity = Yield to Maturity (YTM). 

Maturity (t) = 3 years 

|----------------|----------------|----------------| 

0   1   2   3 

$950  $100   $100  $100+$1,000 

C / r [ 1 – 1 / (1 + r) ^t ] + FV / (1 + r) ^t – P = 0 

100 / r [1 – 1 / (1 + r) ^3 ] + 1000 / (1 + r) ^3 – 950 = 0 

Solve for r: 

MS-Excel  

Financial Calculator. 

Approximate r: 

r = C + [ ( Par – Price ) / t ]  

[ Par + Price ] / 2 

Par = FV = 1000 

Price = 950 

=100+[(1000-950)/3]  

[1000+950]/2 

= 11.97% 

Question: 

Q1: Bond Yields [LO2] A Japanese company has a bond outstanding that sells for 105.43 percent of its ¥100,000 par value. The bond has a coupon rate of 3.4 percent paid annually and matures in 16 years. What is the yield to maturity of this bond? 

Approximate r 

= C + [ ( Par – Price ) / t ] 

[ Par + Price ] /2 

FV = 100,000 

C = 0.034 x 100,000 = 3400 

t = 16 

P = 1.0543 x 100,000 = 105,430 

R = 3400 + [ (100,000 – 105,430) / 16 ] 

  [ 100,0000 + 105,430 ] / 2 

R = YTM = 2.98% 

Q2: ​​RG Coffee House issued a $1,000 par value bond that pays a 9 percent interest annually. The bond matures in 14 years and is currently selling at $1,120. Your required rate of return is 8.5 percent. 

Compute the bond’s expected rate of return. 

r  = C + [ (Par – Price) / n ] 

  [Par + Price] / 2 

 = 90 + [ (1000 – 1120) / 14 ] 

   [1000 + 1120]/2 

= 0.077 or 7.7% 

Determine the value of the bond to you, given your required rate of return. 

P = C/r [ 1 – 1/(1+r)^n ] + FV/(1+r)^n 

= 90/0.085 [ 1 – 1/(1+0.085)^14 ] + 1000/(1+0.085)^14 

= $1,040.05 

Should you purchase the bond? 

From (a) Required rate of return > Return from bond 

   8.5%  > 7.7% 

  → Don’t buy 

From (b) Market Price > Valuation Price 

  $1,120 > $1,040.05 → over-priced 

  → Don’t buy 

Conclusion: Don’t buy