# Bruce Honniball

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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 fallShare prices rise by y%

Repayment of deposit\$A100\$A100

Bonuszero.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 fallShare prices rise by y%

Payoff on callzeroy (( \$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 promised payment is 100/1.05 = \$95.24. Valuing the call option could be harder. Fortunately, Black and Scholes have devised a formula that does the trick.[1] We need the following inputs:

Current level of index100

Exercise price of call option100
Interest rate5.0%
Time to maturity1 year
Volatility of index25%

The only number that I had to estimate is the volatility of the Australian equity index. I simply calculated the standard deviation of market returns over the past 20 years, which was about 25 percent. You can put in your own figure if you feel that market volatility is likely to change. Using my inputs, the Black-Scholes formula says the call option is worth \$A12.28.[2] Remember that the value of an equity-linked deposit is equal to the present value of the promise of \$A100 plus half the value of a call option. Therefore the value of the deposit is 95.24 + .5 ( 12.28 = \$A101.38. If this estimate is right, we would be taking in \$A100 from depositors and offering them in exchange an investment worth \$A101.38. In other words, each \$A100 of deposits would have a net present value for us of + 100 - 101.38 = - \$A1.38. It appears that the upside on the equity linked deposits is just a bit too generous. However, suppose we cut the bonus to \$A3 for each 10 percent rise in the index. Then the value of the deposit falls to 95.24 + .3 ( 12.28 = \$A98.92. This gives NPV of + 100 – 98.92 = + \$A1.08, which should cover administrative costs and provide a modest profit.

How could we reduce risk? That depends on how we invest the depositors’ money. Australian government debt could provide a safe 5 percent return, but would not protect us if share prices take off and oblige us to pay out large bonuses to depositors. Suppose instead that we invest \$95.24 at 5 percent. We would then be sure that we could pay back the initial deposit (95.24 ( 1.05 =...