答題框架 Exam Framework · Time Management
時間管理（總 90 分鐘）· Time Budget
| 題型 | Typical Marks | 時間 |
|---|---|---|
| 理論概念 Agency / EMH / IPO-SEO / Bond / Dividend | 10–15 | 15–20 min |
| 計算題 Rights issue / Bond / Voting / Dividend | 15–25 | 20–25 min |
| 案例應用 Case application（公司背景 + 判斷） | 15–20 | 15–20 min |
Essay / 案例題：四步答題模板 · 4-Step Template
- Direct answer：第一句明講 Yes / No / 邊種形式。第一句即直接回答。
- Definition：用標準定義把核心概念釘住。用標準定義鎖定概念。
- Application：將定義套到題目嘅具體數字／事實。將定義套用到題目數字。
- Conclusion：一句話回扣問題。一句話回扣問題。
計算題通用規則 · Calculation Rules
- Units：million / billion 先統一再計算，答案標明單位。
- Write the formula first，然後再代入。先寫公式再代數。
- 過程保留 2–4 位小數，最終答案按題目要求（通常 2 位）。
- Interpret：加一句 "This is higher/lower than par because…"
- 最易錯＝數字放錯位置。用「必背」第 F 部分嘅映射表同「自测」嘅計數題訓練。可以用右下角計數機核數。
最後 10 分鐘檢查清單 · Final Checklist
- 所有計算已先寫公式再代數？
- 所有 essay 都有 direct answer + definition + application？
- 案例題有引用題目嘅具體數字／事實？
- 冇空題？唔肯定都要寫相關概念。
- 單位正確（million / billion、股數）？
- 英文文法 / 拼寫基本正確？
必背 · Definitions & Formulas Definitions you must be able to write in English
A. Lecture 1 · Agency Problem
解決 agency problem 嘅措施 · Solutions（答題時列舉題目冇提及嘅）：
| # | English | 中文 |
|---|---|---|
| 1 | Stock options / performance-linked compensation | 管理層薪酬同股價／業績掛鉤 |
| 2 | Managerial labour market (reputation pressure) | 經理人嘅聲譽壓力 |
| 3 | Market for corporate control / threat of takeover | 被收購威脅 |
| 4 | Other stakeholders' monitoring (gov't, bondholders, institutional investors) | 其他利益相關者監察 |
| 5 | Regular external audits & transparent financial reporting | 獨立審計、透明披露 |
| 6 | Independent board of directors | 獨立董事會 |
B. Lecture 2 · Efficient Market Hypothesis
| Form | Information reflected in price | 中文 |
|---|---|---|
| Weak | Historical prices, trading volume only | 僅歷史價格、成交量 |
| Semi-strong | All public information (historical + new announcements) | 所有公開資訊（歷史＋新公告） |
| Strong | All information, public AND private/inside | 所有資訊，公開及私人／內部 |
- Price moves before announcement → strong form（inside info leaked）。
- Price moves on announcement day, then stable → semi-strong（efficient）。
- Price drifts after announcement → violates semi-strong; abnormal return possible.
- Overreaction：excessive drop, then gradual recovery → buy at the undervalued price.
- CAR diagram：應喺公告後平穩；持續下降＝違反 semi-strong。
C. Lecture 3 · IPO vs SEO & 配股 Rights Issue
配股（Rights Issue）公式
| Symbol | 意思 |
|---|---|
| P₀ | 配股前股價（rights-on price） |
| N | 認購 1 股新股所需嘅舊股權數（＝舊股數 ÷ 新股數） |
| Pₛ | 認購價（subscription price） |
| N₀ / N₁ | 舊股數 / 新股數 |
Value of a right Vr = P₀ − Pex = (P₀ − Pₛ) / (N + 1) = (Pex − Pₛ)/N
New market value MVnew = (N₀ × P₀) + (N₁ × Pₛ)
投資者獲得配股权後三個選擇：
- Subscribe（喺 Pₛ 買入）— 認為股價合理或會上升
- Sell the rights — 認為股價高估或會下跌
- Let rights expire — 股價已跌至 Pₛ 以下，rights 冇價值
為何配股公告後股價下跌 · Why price falls after a rights issue：
- Dilution from the lower subscription price
- Manager timing / signalling possible overvaluation
- Possible intent to reduce the debt-equity ratio（financial distress）
- Funding need due to unanticipated earnings shortfalls
D. Lecture 4 · 債券 Bond Pricing & 投票 Voting
三種現金發行方式 · Three cash offer methods
| Method | Definition |
|---|---|
| Firm commitment | The underwriter buys all the new shares at a price below the offering price and bears the risk of not being able to sell them. |
| Best efforts | The underwriter sells as many shares as possible for a commission; bears no risk; can withdraw if demand is low, but the issuer bears all costs already incurred. |
| Dutch auction | The underwriter accepts a series of bids (price + quantity); all shares are sold at the lowest clearing price. |
債券定價 · Bond pricing
| Symbol | 意思 |
|---|---|
| C | 年息票（coupon） |
| r₀ | 目前市場利率 |
| r↑ / r↓ | 明年利率上升／下跌後嘅水平 |
| P(↑) / P(↓) | 利率上升／下跌嘅概率 |
| Call Price | 贖回價 = Par + Call Premium |
Non-callable P₀ = [ C + C/r↑ × P(↑) + C/r↓ × P(↓) ] / (1 + r₀)
Callable（called when rates fall） P₀ = [ C + C/r↑ × P(↑) + Call Price × P(↓) ] / (1 + r₀)
投票權 · Voting
Cumulative voting（guarantee n directors） X = n × S / (D + 1) + 1
S = 總股本，D = 待選董事總數，n = 想選出嘅董事數。
E. Lecture 5 · 股利 Dividends
Dividend = Earnings × Payout ratio
Retention ratio = 1 − Payout ratio
Ex-dividend price = Current price − DPS
Current firm value（MM, not yet paid） V₀ = D + V₁ / (1 + r)
現金股利 vs 回購 · Cash dividend vs share repurchase（same amount spent）：
| Item | Cash Dividend | Repurchase |
|---|---|---|
| Share price | Falls by DPS | Unchanged |
| Wealth per share | Same | Same |
| Total equity | Unchanged | Unchanged |
| EPS | Unchanged | Rises（fewer shares） |
| P/E ratio | Same | Same |
F. 數字放對位置 · Mapping
呢個係最容易出錯嘅地方。以下三個實例示範點樣將題目數字放對位置。
例 1 · 配股（AquaGen 類）
舊股 400,000，股價 $120；發售 80,000 新股，認購價 $100。
例 2 · 投票（Logan 類，cumulative）
總股本 387,076,150 股，待選董事 7 名，想保證選出 1 名。
例 3 · 可贖回債券（Logan 類）
永續債，coupon 7.5%，par $1,000，現利率 7.5%。明年：利率升 9%（概率 30%）/ 跌 6%（概率 70%）。利率跌時公司會贖回，call premium = 一年息票。
求使債券按面值出售嘅 coupon C：令上式 = $1,000，解出 C ≈ $74.50（coupon rate ≈ 7.45%）。
長篇 Essay 英文範例 Model long-form answers in English
範例 1 · Agency problem（Lecture 1）
DirectModern corporations frequently face agency problems, which stem from the separation of ownership and control.
DefinitionIn a modern corporation, shareholders are the owners (principals) but they are rarely involved in day-to-day operations, whereas managers (agents) run the business but typically hold little or no ownership. An agency problem arises when there is a conflict of interest between the two, i.e. when managerial goals diverge from shareholder goals.
ApplicationIn the case described, the CEO pushed through an acquisition that the board considered overpriced and of limited long-term value. His stated objective — to grow the company from second to first place — reflects a focus on company size and empire-building rather than on the timing, magnitude and risk of the cash flows that drive shareholder wealth. Because profits are not cash flows and can be manipulated, "maximising profit" is not the correct goal of financial management. Paying a price well above the target's actual value would destroy, not create, shareholder value. The agency cost here is the value lost to shareholders as a result of this misaligned decision.
ConclusionThe agency problem can be mitigated by aligning managerial compensation with stock performance, by the threat of takeover in the market for corporate control, by managerial labour-market reputation pressures, and by independent boards and external auditing. The two measures not yet mentioned in the case are the managerial labour market and the market for corporate control.
範例 2 · Market efficiency（Lecture 2）
DirectThe scenario is consistent with the strong form of market efficiency.
DefinitionUnder the efficient markets hypothesis, in the strong form all information — both public and private — is fully and immediately reflected in the stock price. In the semi-strong form, all publicly available information is reflected, while the weak form requires only that historical prices and volumes are reflected.
ApplicationBecause the stock price fell sharply in the days before the acquisition was announced, some investors must have acted on leaked or inside information. Once the information became public, the price merely fluctuated slightly, indicating that no new information remained to be incorporated. This is exactly the behaviour predicted by the strong form.
ContrastIf instead the price had continued to drift after the announcement, that would have violated the semi-strong form, since investors could still earn abnormal returns by trading on the delayed adjustment.
自测 · Quiz 24 questions · with hints
深入理解 · Derivations Why the formulas work
D1. Cumulative Voting — why D+1, not D?
結論先講：D+1 係為保證「反對派無論如何分配票數都無法阻礙」你選出 n 名董事。用 D 會留下漏洞。
機制
每股持 D 票（D = 待選董事總數），股東可將全部票數集中投俾同一候選人（呢個就係 cumulative voting 對 straight voting 嘅改進）。總票數 = S × D。
點解 D+1？
假設你持有 X 股，想選 n 名董事，將 X×D 票平均分畀 n 名候選人。反對派有 (S−X)×D 票。為保證你嘅 n 名候選人喺任何票數分配下都勝出，需要：
+1 確保嚴格大於，令你在邊界情況仍然勝出。直覺：D+1 確保你嘅投票比例高到「即使反對派將票數以最有利方式集中，都冇辦法阻止你嘅 n 名候選人當選」。
D2. Callable Bond — why Call Price, not C/r↓?
結論先講：利率跌時（r↓），債券市價 = C/r↓ > Par。公司可以按 Call Price（= Par + Premium）贖回，呢個低於市價。公司會選擇贖回，因為：(i) 用較低成本再融資；(ii) 按 Call Price 贖回比按市價回購便宜。債權人知道呢一點，所以喺利率下跌嘅情景（概率 P(↓)），佢哋預期收到嘅係 Call Price（唔係更高嘅市價 C/r↓）。可贖回條款限制了持有人喺利率下跌時嘅上行收益，所以 callable bond 價格通常低於非 callable bond。
D3. Ex-rights Price 同 Value of a Right 點點相等？
配股後，舊股東持 N 股舊股 + 1 股新股，共 N+1 股。新總市值：
每股新股嘅內在價值 = Pex − Pₛ。由於 N 份 rights 先能認購 1 股新股，每份 right 嘅價值：
D4. MM — why V₀ unchanged after issuing new shares?
MM 定理：喺無稅、無交易成本、完美市場下，公司價值獨立於股利政策。證明（簡化）：
- 公司現有 1 年後價值 V₁，需派股息 D，現有現金只夠派 D₀ < D，缺口 = D − D₀。
- 賣新股集入 D−D₀，新股持有人 1 年後對公司嘅索償 = (D−D₀)×(1+r)。
- 舊股東 1 年後嘅剩餘 = V₁ − (D−D₀)(1+r)。
- V₀ = D + [V₁ − (D−D₀)(1+r)] / (1+r) = V₁/(1+r) + D₀
- 即 V₀ 同冇賣新股時完全相同。
D5. 配股後股價點解一定下跌？
配股 = 以低於市價 Pₛ < P₀ 賣新股。由於新股按折讓價賣出，平均每股價值被拉低：
所以 Pex 必然 < P₀。呢個唔代表公司價值減少（股東總財富不變），只係稀釋（dilution）效應。
D6. Strong vs Semi-strong — how to tell from the question
| 題目線索 | 形式 |
|---|---|
| 股價喺公告前已大幅變動 | Strong form（inside info leaked） |
| 股價喺公告日即時調整，之後平穩 | Semi-strong（efficient） |
| 股價喺公告後持續漂移 | Violates semi-strong |
| 不可預測事件（如猝死）後股價即時反應 | Consistent with efficiency（唔代表無效率） |
D7. 點解 EPS 喺回購後上升？
回購減少股數，但總淨利不變。因此：
但 P/E 不變，因為股價唔變（回購唔改變每股價值），EPS 上升係因為股數減少。現金股利則令股價下跌 DPS，EPS 不變，P/E 亦不變（P 同 E 同比例下降）。
歷年試題詳解 · Practice Answers Official English answers from Review Notes + 中文摘要
以下係 Review Notes 入面練習題嘅官方英文解答（考場可直接引用呢啲英文），並附中文摘要。先自己試，再對答案。
Q1 · Lecture 1 — Golden Mining / L-Mobile（2025-26 Midterm）
a. There is a separation of ownership and control in modern corporations. Agency problems occur when there is a conflict of interest between shareholders and managers — i.e. when managerial goals are different from shareholder goals.
b. Yes, Golden Mining appears to have significant agency problems. No, the CEO's reasons are incorrect: his reasoning focused on maximising company size (empire-building) rather than shareholder value. Maximising profit is not the correct goal of financial management, because profits are not cash flows and can be manipulated. Overpaying for the acquisition hurts shareholder value.
c. No, L-Mobile shows no significant agency problems. Yes, the CEO's decision aligns with long-term shareholder value. Long-term strategic thinking often aligns with shareholder wealth maximisation; to maximise shareholder value, CEOs need to consider different factors including risks; the investment may increase future cash flows and benefit long-term firm value.
d. Two additional measures not mentioned: (i) the managerial labour market (managers worry about their reputation); (ii) the market for corporate control (the threat of takeover).
🇨🇳 中文：a. 所有權同控制權分離。b. 有 agency problem，CEO 追求規模而唔係股東價值，利潤≠現金流可被操縱。c. 無重大 problem，長遠投資符合股東財富。d. 管理層勞動力市場、收購威脅。
Q2 · Lecture 1&2 — TopMart Acquisition（2024-25 Midterm）
a. No, the acquisition does not guarantee an increase in shareholder wealth. (i) There are risks that the potential synergies will not materialise or deliver the expected value. (ii) If TopMart overpaid for the target, the acquisition could result in a negative NPV, reducing shareholder wealth. Expansion in size does not by itself increase shareholder value.
b. By linking executive compensation to stock-price performance, the interests of managers and shareholders are aligned. Executives are incentivised to make decisions that enhance shareholder value and to avoid decisions that harm the company's long-term value, since such decisions directly affect their personal interest.
c. The scenario reflects the strong form of market efficiency. The sharp decline in the stock price before the announcement suggests that some investors acted on leaked (inside) information, consistent with the strong form, in which all public and private information is reflected in the price.
d. If the market overreacts, the stock price will fall excessively on the announcement day and then gradually recover to its fair value. The fund manager could capitalise on the overreaction by purchasing the shares at the undervalued price after the announcement, earning an abnormal return as the price recovers.
🇨🇳 中文：a. 唔保證，協同效應有風險，買貴咗會負 NPV。b. 薪酬掛鉤對齊利益。c. strong form，公告前已跌＝內部消息。d. 過度反應後可低買賺 abnormal return。
Q3 · Lecture 3 — AquaGen Rights Issue（2024-25 Midterm）
a. An IPO is the first time a company offers its shares to the public on a stock exchange. An SEO is an equity issue by a company that is already listed to raise additional capital.
b. New market value = 400,000 × $120 + 80,000 × $100 = $56,000,000.
c. N = 400,000 / 80,000 = 5 rights per new share.
d. Ex-rights price = ($120×5 + $100)/6 = $56,000,000 / 480,000 = $116.67.
e. Value of a right = $120 − $116.67 = $3.33 (equivalently ($116.67 − $100)/5).
🇨🇳 中文：b. $56M；c. 5 份權；d. $116.67；e. $3.33。
Q4 · Lecture 4 — Techtronic Bond（2024-25 Final）
a. (Non-callable) C = $80. If rates rise to 9%: P₁ = 80 + 80/0.09 = $968.89. If rates fall to 6%: P₁ = 80 + 80/0.06 = $1,413.33.
b. (Callable, called if rates fall) Setting P₀ = $1,000:
c. Three methods: (i) Firm commitment — the underwriter buys all shares and bears the risk; (ii) Best efforts — the underwriter sells as many as possible for a commission, bears no risk, and may withdraw; (iii) Dutch auction — shares are sold at the lowest clearing price from accepted bids.
🇨🇳 中文：a. $1,164.61；b. C≈$77.63 (7.76%)；c. 三種發行方式。
Q5 · Lecture 5 — HK&China Gas Dividend（2023-24 Final）
a. If the dividend is declared: Pex = $100 − $4.41 = $95.59. If not declared: the price remains $100.
b. Current value of the firm = $4.41×18,660M + $1,500B/1.10 = $1,445.92B.
c. Special dividend DPS = $15B/18,660M = $0.803. Price after = $95.59 − $0.803 = $94.787; wealth per share = $94.787 + $0.803 = $95.59. Under repurchase: shares repurchased = $15B/$95.59 = 156.92M; price unchanged at $95.59; wealth per share the same. Shareholder wealth per share is the same under both alternatives.
d. Special dividend: EPS unchanged at $6.63; P/E = $94.787/$6.63 = 14.30. Repurchase: new shares = 18,660M − 156.92M = 18,503.08M; net income = $6.63×18,660M = $123,715.8M; EPS = $6.686; P/E = $95.59/$6.686 = 14.30. EPS rises under repurchase; the P/E ratio is the same in both cases.
🇨🇳 中文：a. $95.59；b. $1,445.92B；c. 每股財富相同；d. EPS 回購後升，P/E 相同。
Q6 · Lecture 2 — CAR Diagram（Oil exploration）
The diagram does not support the efficient markets hypothesis. The CAR should remain relatively flat following the announcement. The diagram reveals that the CAR rose in the first month, only to drift down to lower levels in later months. Such movement violates the semi-strong form of the EMH, because an investor could earn abnormal profits while the stock price gradually decreases.
🇨🇳 中文：唔支持 EMH。CAR 應平穩；持續回落違反 semi-strong，可賺 abnormal profit。
Q7 · Lecture 2 — Founder's Death
No, I do not agree. The stock price would have adjusted before the death only if investors had perfect forecasting ability. The 12.5% increase indicates the market reacted immediately to new, unpredictable information — which is precisely consistent with efficiency. The fact that the price rose indicates the market considered the founder a liability to the firm.
🇨🇳 中文：唔同意。即時反應不可預測資訊正體現效率；股價上升反映創辦人係公司嘅負資產。
Q8 · Lecture 2 — Newtech Chip-Testing Device
Although illegal, the lead engineer can profit by purchasing the stock before the news release, as this involves acting on inside information. If the market is efficient up to the semi-strong form, no systematic profit can be made by trading on publicly available information; the price should immediately and fully adjust upon announcement, so no abnormal return can be expected from purchasing after the WSJ article.
🇨🇳 中文：工程師用內部資訊可獲利（非法）；公告後買入唔能賺 abnormal return（semi-strong 有效）。
Q9 · Lecture 3 — Yuexiu Rights Issue（2023-24 Midterm）
a. New market value = 3,096M×$11.10 + 929M×$9 = $42,726.6M.
b. PX = $42,726.6M/(3,096M+929M) = $10.62.
c. Value of a right = $11.10 − $10.62 = $0.48.
d. Stock prices fall after a rights announcement because of: (i) dilution from the lower subscription price; (ii) managers may time the issue using informational advantage, signalling overvaluation; (iii) a possible intent to reduce the debt-equity ratio (financial distress); (iv) a funding need due to unanticipated earnings shortfalls.
e. The investor can (i) subscribe at the subscription price (if the stock is fairly priced and may rise); (ii) sell the rights (if the stock is overpriced and will fall); (iii) do nothing and let the rights expire (if the price has fallen below the subscription price).
🇨🇳 中文：a. $42,726.6M；b. $10.62；c. $0.48；d. 稀釋、擇時、降負債、盈利不足；e. 認購／賣 rights／失效。
Q10 · Lecture 4 — Cathay Pacific Voting
a. With straight voting, more than 50% of the vote is required to appoint a director. Virgin Atlantic holds only 9.99%, so it cannot appoint any director.
b. With cumulative voting: X = 1/(10+1)×6,437,200,203 + 1 = 585,200,019 shares. Since Virgin Atlantic holds 643,076,181 shares (> the requirement), it can appoint at least one director.
c. Unlikely to succeed. Virgin Atlantic holds only 9.99%, while Swire (45%) and Air China (29.99%) together hold more than 50% and can veto any change. Swire benefits from straight voting and has no incentive to agree to the change.
🇨🇳 中文：a. straight 需>50%，Virgin 9.99% 無法任命；b. cumulative 需 585M 股，可任命≥1 名；c. 唔會成功，大股東可否決。
Q11 · Lecture 4 — Logan Callable Bond（2023-24 Midterm）
a. (Non-callable) C = $75. Rates rise to 9% (30%): P₁ = 75+75/0.09 = $908.33. Rates fall to 6% (70%): P₁ = 75+75/0.06 = $1,325.00.
b. (Callable, called if rates fall) Setting P₀ = $1,000:
c. The price in part (a) is higher than par of $1,000. This is because the probability of rates falling (70%) exceeds that of them rising (30%); as bond prices move inversely with interest rates, the expected price increase pushes the market value above par. The coupon rate (7.5%) currently equals the market rate.
🇨🇳 中文：a. $1,116.28；b. C≈$74.50 (7.45%)；c. 高於面值，因利率跌概率高。
Q12 · Lecture 4 — Wuxi Apptec Voting Cost（2023-24 Midterm）
a. Straight voting: shares needed = 387,076,150/2 + 1 = 193,538,076; total cost = ×$50.10 = $9,696M.
b. Cumulative voting: percentage needed = 1/(7+1) = 12.5%; shares = 387,076,150×0.125 + 1 = 48,384,520; total cost = ×$50.10 = $2,424M.
🇨🇳 中文：a. straight 需 193.5M 股，$9,696M；b. cumulative 需 48.4M 股，$2,424M。
Q13 · Lecture 5 — Tencent New Issue（2023-24 Final）
a. V₀ = $96,000 + $1,810,000/1.11 = $1,726,630.63.
b. Current price = $1,726,630.63/24,000 = $71.94; DPS = $96,000/24,000 = $4.00; ex-dividend price = $71.94 − $4.00 = $67.94.
c.i. Total dividend needed = $5.20×24,000 = $124,800; new funds required = $124,800 − $96,000 = $28,800. New shareholders' year-1 claim = $28,800×1.11 = $31,968; old shareholders' year-1 claim = $1,810,000 − $31,968 = $1,778,032. V₀ = $124,800 + $1,778,032/1.11 = $1,726,630.63 (unchanged, per MM).
c.ii. Issue price = $1,778,032/1.11/24,000 = $66.74; shares sold = $28,800/$66.74 = 431.51 shares.
🇨🇳 中文：a. $1,726,630.63；b. $67.94；c.i. V₀ 不變（MM）；c.ii. 發行價 $66.74，431.51 股。
Q14 · Lecture 5 — Luckin Coffee（2023-24 Midterm）
The Luckin Coffee case is a prime example of the agency problem. The executives (agents) were expected to act in the best interest of the shareholders (principals), but instead acted in their own self-interest, engaging in accounting fraud to inflate the company's sales by 88%. When the fraud was discovered, the stock price plummeted from $47.22 to $1.38 and the company was delisted, causing significant losses to shareholders. To prevent such issues, the company could (a) implement stricter internal controls and auditing processes, (b) establish a clear code of conduct and ethical guidelines, (c) introduce an independent board of directors, and (d) strengthen external regulation.
🇨🇳 中文：典型 agency problem，管理層會計欺詐損害股東；預防措施包括內部控制、行為守則、獨立董事會、外部監管。