Opportunity cost of capital (机会成本)：Money received today can be invested immediately to earn a return. For example, $100 deposited at 5% interest becomes $105 in one year. Receiving that $100 one year later means forgoing $5 of potential earnings.

Inflation (通货膨胀)：Over time, the general price level tends to rise, eroding the purchasing power of money. $100 today can buy more goods and services than $100 will buy in the future.

Risk and uncertainty (风险与不确定性)：Future cash flows are inherently uncertain — there is always some probability that promised future payments may not materialise. A dollar in hand today carries no such risk.

Preference for current consumption (当前消费偏好)：People generally prefer to consume now rather than later. To persuade them to defer consumption, they must be compensated — this compensation is the interest rate or required rate of return.

Short-term government bills have the lowest return because they carry minimal risk. They are backed by the government (virtually no default risk), and their short maturity (typically 90 days) means they have negligible interest rate risk — their price barely fluctuates when market rates change. They represent the closest approximation to the risk-free rate.

Long-term government bonds also carry little default risk, but their longer maturity exposes them to significant interest rate risk: when market interest rates rise, bond prices fall, and this effect is amplified for longer-duration bonds. Investors therefore demand a maturity premium over short-term bills to compensate for this additional price volatility and the uncertainty of tying up capital for an extended period.

Ordinary shares bear the highest risk and therefore command the highest historical return. Shareholders face business risk (the company's operations may fail), financial risk (if the company is leveraged), and market/systematic risk (economy-wide factors affecting all equities). Unlike bondholders, shareholders are residual claimants — they are last in line in liquidation and their dividends are not guaranteed. The additional return they earn above bonds is called the equity risk premium.

WACC 的目的是衡量当前的融资成本 (forward-looking cost)：WACC is used as a discount rate for evaluating future investment projects. It must therefore reflect the company's current cost of raising capital, not what the company paid historically. Market values capture what investors are actually willing to pay for the company's debt and equity right now.

Book values 是 historical cost (历史成本)：Book value of equity reflects the original amount shareholders invested, adjusted for retained earnings and accounting policies. It does not reflect changes in business performance, market conditions, or risk perceptions since that time. A company's equity might have a book value of $10 million but a market value of $100 million — using book value would massively overweight debt in the WACC calculation.

D/V 和 E/V 必须反映真实的资本结构 (actual capital structure)：The weights in WACC (D/V and E/V) should represent the proportions in which the company would actually raise new financing. Market values better approximate these proportions because they reflect the opportunity cost to investors — what they could receive by selling their claims today.

与 CAPM 的一致性 (consistency with CAPM)：The cost of equity derived from CAPM is based on market data (share price, market returns). Using book-value weights alongside a market-derived cost of equity would create an internal inconsistency in the WACC calculation.

NPV directly measures value creation (直接衡量价值创造)：NPV tells us the absolute dollar amount by which a project increases shareholder wealth. IRR only provides a percentage return and does not indicate the scale of value created. A small project with a high IRR may create far less value than a larger project with a lower IRR. [这就是你写的 scale argument，保留即可]

Multiple IRR problem (多重 IRR 问题)：When a project has non-conventional cash flows (e.g., alternating positive and negative cash flows), the IRR equation can produce multiple solutions, making it impossible to determine which one is the "correct" rate of return. NPV does not suffer from this problem — it always produces a single, unambiguous value.

Reinvestment rate assumption (再投资率假设)：IRR implicitly assumes that interim cash flows are reinvested at the IRR itself, which is often unrealistically high. NPV assumes reinvestment at the cost of capital (the discount rate), which is a more realistic and conservative assumption.

Mutually exclusive projects (互斥项目)：When comparing two mutually exclusive projects, the one with the higher IRR is not necessarily the better choice. NPV correctly identifies the project that maximises shareholder wealth by accounting for both scale and the timing of cash flows.

价格跌穿认购价的风险 — Rights become "underwater"：A 17.5% discount means the subscription price is set close to the current market price ($2.78 × (1−0.175) ≈ $2.29). If the share price declines by more than 17.5% during the offer period — due to market-wide movements or negative reactions to the dilution — the subscription price will exceed the market price, making the rights worthless. Shareholders would simply buy shares cheaper on the open market.

认购率低 — Low take-up rate：With a narrower margin of safety, shareholders are less motivated to exercise their rights. The financial benefit of exercising (the "value of the right") is smaller with a shallow discount, so shareholders — particularly those facing liquidity constraints — may choose to let their rights lapse rather than investing additional capital for a marginal gain.

承销成本增加 — Higher underwriting costs：The underwriter bears the risk of purchasing any shares not taken up by existing shareholders. A shallower discount increases the probability that the issue will be undersubscribed, which raises the underwriter's risk exposure. Consequently, the underwriter will demand a higher fee, increasing the total cost of the capital raise for ABBA.

融资目标可能失败 — Risk of failing to raise target capital：If significant numbers of shareholders do not exercise or sell their rights, and the underwriter is exposed to large volumes, the rights issue may fail to raise the full $360,000 needed for ABBA's new investments. This could force the company to seek alternative, potentially more expensive financing, or delay its investment plans.

市场信号负面 — Negative signalling：A shallow discount may signal to the market that management is either overconfident about the share price stability or unwilling to offer shareholders an attractive deal. This can create negative market sentiment, potentially putting further downward pressure on the share price during the offer period — exacerbating risk ①.