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Merry Christmas
A digital platform under a listed company, Garage Entertainment, has obtained dual ISO 27001 (Information Security Management) and ISO 27701 (Privacy Information Management) certifications. 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 on the company's stock is traded in the market. The relevant data are as follows:
The current stock price is NT$150
The exercise price is NT$145
The warrant 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
A European warrant may not be exercised early; it can only be exercised at maturity
The scenario assumptions for the fundraising results are as follows:
If the fundraising amount passes NT$3 billion, the stock price immediately rises by 12% on the announcement date and rises by another 6% within one month.
If the fundraising amount does not pass this threshold, the stock price rises by only 3% and then enters a consolidation phase.
The investor Xiaohua, a minor whose legal representative operates via online filing, purchases 20,000 warrant units. A warrant transaction tax of 0.1% is levied on both purchases and sales; transaction fees are disregarded. After the stock price has fully reflected the second-stage increase, Xiaohua directly sells the warrants without actually exercising them.
The following standard normal distribution values are given 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 sequence:
1. The underlying stock price after the announcement
2. The underlying stock price one month later
3. The intrinsic value of the warrant at the time of sale
4. Whether the warrant still has time value at that 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, as the expiration date approaches, the warrant's leverage and time value experience decay.
IV. Under the successful fundraising scenario, calculate:
1. The total proceeds 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 represents an asymmetric payoff and high risk, high return.