Sunday, 26 September 2010

What’s the best option?

Many of the decisions we make are choices between 2 or more alternatives. When the outcomes of the alternatives are known with certainty, deciding between them is relatively easy. However, since the environment we live in is fraught with uncertainty, things become more difficult. This uncertainty prevents us from making an accurate estimate of the outcome and makes the decision for the best alternative difficult. But uncertainty also offers new opportunities; new information helps to improve our decision and generate more value. In business many of the decisions that need to be made are of that kind. Take for example a manufacturer introducing a new product. It needs to decide on the number of products to make, not knowing how many customers will buy it. Should it first do a test run with the new product? This kind of decision making can benefit a lot from what Operations Research has to offer, it can support companies in answering the question: What’s the best option?

A much used technique in business in finding the best option is the net present value analysis (NPV). By comparing the discounted cash outflows (investments) and discounted cash inflows (revenues) it can be inferred whether the project will add value or not. The trouble with this approach is however that it is incapable to put a value on the uncertainty involved in the decision. To illustrate, assume a company that needs to decide to invest in a new technology that would cost them €650 million to develop and that total (discounted) revenues over the coming 5 years would be €500 million. The NPV of the project (-€150 million) would result in a negative advice to invest in the technology. But is that really the best option? In the above example the company doesn’t know for sure that the expected revenues will be equal €500 million, this depends on the number and price of the products that it will sell after investing the €650 million. The NPV analysis can only capture part of these uncertainties, for example by running a scenario analyses on a range of possible market prices and sales for the product. That way an upper and lower bound of the NPV can be estimated, but it doesn’t help incorporate the variance across the different scenarios into the decision. There is a better way to put a value on the uncertainty by applying a real options approach.

A real option approach uses option valuation techniques to value decisions. In the above example the option was whether or not to invest €650 million to earn €500 million, with much uncertainty about the expected revenues. Real option analysis uses the famous Black & Scholes option valuation model to value this decision, although other models are used as well. The B&S model takes a number of arguments. In a real option valuation the stock price (S) in de B&S model is equal to the estimated present value of the cash inflows (=revenues). The exercise price (X) is equal the present value of the cash outflow (=investments). Uncertainty (σ) is measured by taking the standard deviation of the growth rate of the future cash flows (in our example the volatility in revenue for the new product). The time to expire (t) is the period during which the option can be exercised. Dividends (δ) are the cost incurred to preserve the option. The risk free interest rate (r) is set to the yield of a riskless security (are there any nowadays?) with same maturity as the duration of the option.

Assuming volatility (σ) of 35% standard deviation and a 5 year risk free rate of 2.5% the option value becomes €129 Million, assuming no option preservation cost. That would mean that investing in the new technology really is an opportunity! The difference between the NPV value of the project and the value based on real options approach shows the value of the flexibility the company has because it can wait and invest when uncertainty on product price and sales are resolved, for example by applying market research or running a test with the new product. Note that using the B&S model assumes that revenue (=stock price) follows a lognormal distribution with a constant level of volatility. That may not be the case for the decision at hand. The lognormal distribution also causes the increase in option value when the duration is increased. In practice assuming lognormal returns is probably not valid. There is a way around it (Monte Carlo option valuation for example), I’ll discuss it in a later blog entry.

A real option approach not only offers a better way to value the uncertainty in a decision, it also provides a framework that helps identify and prioritise the key levers management can pull to increase the payoff of the opportunity. In essence all six parameters in de B&S model offer a lever to pull. It allows management to proactively deal with the uncertainty involved in the decision. For example the effect of the entry of competitors with a similar product after 2,5 years (it would cost €56 Million dropping the option value to €73 Million) or the expected increase in revenue from marketing strategies around the product. With real options your able to tell which option is best!