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Merry Christmas
A digital platform under a listed company, Garage Entertainment, has passed dual certification for ISO 27001 (Information Security Management) and ISO 27701 (Privacy Information Management). In 2025, the company partnered with Taiwan Power Company to hold a charity screening of the film Avatar, raising funds for children in a war zone. The market views this as an ESG event and believes the activity may improve the company’s future cash flow and valuation.
A European call warrant based on the company’s stock is traded in the market. The relevant information is as follows:
The current stock price is NT$150
The strike price is NT$145
The warrant’s market price (premium) is NT$4.2
The conversion ratio is 10
The remaining term is 4 months
The annualized risk-free interest rate is 1.2%
The annualized volatility is 28%
No dividends are paid
European warrants cannot be exercised early; they may only be exercised at expiration
The scenario assumptions for the fundraising results are as follows:
If the fundraising amount passes NT$3 billion, the underlying stock price immediately rises 12% on the announcement date and rises another 6% within one month.
If the fundraising amount does not pass this threshold, the stock price rises only 3% and then enters consolidation.
The investor Xiaohua (a minor, with transactions conducted online by a legal representative) purchases 20,000 warrant units. A 0.1% warrant transaction tax is levied on both purchases and sales; commissions are not considered. After the stock price fully reflects the second-stage increase, Xiaohua directly sells the warrants without actually exercising them.
The following standard normal distribution values are known in the Black–Scholes model:
N(d1) = 0.62
N(d2) = 0.55
The questions are as follows:
I. Use the Black–Scholes model to calculate the theoretical price (fair value) of the call warrant at the time of purchase, and determine whether the warrant is underpriced or overpriced in the market. Explain whether event-driven volatility could justify this premium.
II. Assuming that the fundraising amount passes the threshold, calculate in order:
1. The underlying stock price after the announcement
2. The underlying stock price one month later
3. The warrant’s intrinsic value when sold
4. Whether the warrant still has time value at this point, and explain why
III. Calculate the following for the warrant at the time of purchase:
1. The effective leverage
2. The underlying stock price at the break-even point
Explain why the warrant’s leverage and time value decay as the expiration date approaches.
IV. Under the successful fundraising scenario, calculate:
1. The total amount received from selling the warrants
2. The net profit after deducting purchase and sale transaction taxes
3. The return on investment (ROI)
Determine whether this investment constitutes an asymmetric payoff and a high-risk, high-return investment.
V. Compare call warrants and futures with respect to the following three points. Each point must be limited to 40 words and must include at least one of the following English words: pass, margin, exposure, downside.
1. Maximum possible loss
2. Method of funding required (premium vs. margin)
3. Whether they are suitable for investors with limited funds or minors