CT8 - APRIL 2012 - QN 7

The remuneration package for the CEO of a quoted company in the tax year 2012/13 includes a bonus proportional to the excess of the share price over 100p at 5 April 2013 at a rate of £50,000 per penny.

The company’s Finance Director wants to hedge the cost of this bonus as at 6 April 2012. The share price at that date is S0 = 90p.
The continuously compounded interest rate is 1% p.a. and the share price volatility is 18% p.a.

(i) Explain the bonus in terms of an option on the share price.

The solution states that the answer is 5 mil call options with strike price 100p and maturity 1 year. I'm not sure I understand this. COuld someone please explain?

 

Hi Anna_04

The way i understand this is as follows:
- since the directors receive a "payoff" only if the share price exceeds £1 after 1 year, then this (the bonus) has to be a call option K=£1, (T-t)=1yr. So the payoff at expiry is max(St-£1,0)
- We are also told that the bonus increases at a rate of £50,000 per pence of shares
- If £1 of bonus equals 1 call option, then there are 50,000 call options per pence of shares
- Rationalising in terms of £s, gives us 50,000/0.01 = 5m calls

Hope this kind of makes sense. The solutions don't explain anything properly unfortunately.