Holiiaa

BRUCE HONIBALL’S INVENTION

Principles of Corporate Finance

7th Edition

Richard A. Brealey and Stewart C. Myers

MEMORANDUM

To: Bruce Honiball

From: Sheila Cox

Re: Gibb River Bank Equity-Linked Deposits

Bruce, thank you for your memo. I think you may be onto a winner with the equity-linked deposits, though my calculations suggest that we can’t afford to be quite as generous as you propose.

Spotting the option. Think of it this way. Whatever happens to Australian share prices, depositors under your scheme get back their initial investment of $A100 at the end of the year. If share prices rise by y percent, they also receive a bonus of .5y  $A100. For example, if prices rise by 10 percent, the bonus is .5  .10  $A100 = $A5. If share prices fall, depositors do not receive any bonus. Thus

Share prices fall Share prices rise by y%

Repayment of deposit $A100 $A100

Bonus zero .5y  $A100

The key questions are: Is this a good deal for Gibb Bank depositors? If it is, can we afford to offer it to them? We can answer these questions by considering an alternative investment strategy that generates the same results.

Valuing the option. Suppose an investor buys a 1-year call option on the market index with an exercise price equal to its current level. Let’s call the current level of the index 100. The payoff on this call option is:

Share prices fall Share prices rise by y%

Payoff on call zero y  $A100

In other words, the bonus payment on the equity-linked deposit is exactly half the payoff on an option to buy the market index at its current level of 100.

Now it is easy to see how to value the equity-linked deposit. Value is equal to the present value of $A100 received at the end of the year plus half the present value of a call option. To value the payment of $A100, we simply discount at the current interest rate. For example, if the interest rate is 5 percent, the value of the...