VALUATION: NET PRESENT VALUE COMPARED TO OPTION PRICING METHODS: VALUATION: NET PRESENT VALUE COMPARED TO OPTION PRICING METHODS VALUING FLEXIBILITY An extension of time value of money


Slide2: To this point we have used the net present value - - NPV (or sometimes called the discounted cash flow - - DCF) approach and applied it to project valuation and valuation of the firm In the past 15 years, theoretical and computational advances have allowed finance practitioners to adopt FINANCIAL OPTION PRICING TECHNIQUES to the valuation of investment decisions These techniques are sometimes termed REAL OPTIONS Option pricing methods may be superior to the traditional DCF/NPV approaches for project evaluation because they explicitly capture the value of flexibility


Slide3: To review: the NPV approach for valuing a project assumes the project has an expected life, say t years, and that the free cash flows (fcf) are to be discounted at a risk-adjusted rate which is the cost of capital We subtract the initial investment outlay from the resulting present value of the cash flows The result is a NPV that must be positive to accept the project as a feasible investment project However, this standard approach fails to account for the flexibility that management may have in investing If the project goes badly, its life may be less than t years because of a decision to scale back or to abandon the project If the project is successful, it may be expanded or extended


Slide4: Finally, the investment may not be made immediately! The project can be deferred to another year The real options framework which we are about to outline takes these types of managerial flexibility into account ---- while the traditional NPV analysis assumes them away ---- THE OPTION ---- An option gives its owner the right (but not the obligation) to buy or sell an asset at a predetermined price --- called the strike or exercise price--- for a predetermined period of time --- called the life of the option --- The right to take action is flexibility The necessity of taking action is inflexibility


Slide5: CALL options give the right to buy PUT options give the right to sell Options can be found on both the assets and the liabilities sides of the balance sheet On the asset side of the balance sheet we find mostly options of flexibility --- a firm that has the options to shut down, defer their start, expand, contract, or abandon is more flexible and therefore usually more valuable than a firm without these options Asset options are important for value but also because they provide explicit criteria for deciding when operations should be opened, closed, or abandoned


Slide6: Options on the liabilities side of the balance sheet are relatively easy to recognize ---- convertible debt and preferred stock give the holder the right to exchange them for stock at a predetermined conversion ratio --- therefore they contain call options Warrants allow their owner to buy shares at a fixed price --- again a call option Executive stock options are warrants held by management The standard approach --- NPV --- requires that we subtract the market value of these liabilities from the enterprise value to estimate the value of equity Liability options affect the WACC


Slide7: --- RELATIONSHIP BETWEEN REAL OPTIONS AND NPV ANALYSIS--- Let’s do a simple example: You are deciding to invest $2,000 in a new project The cash flow per product from the project is $200, but can change to either $300 or $100 at the end of the year and change with equal probability After the change, the cash flow stays at the new changed level thereafter --- way too simplified, but ok for our demo here Expected future cash flow is then $200, which is ½ probability of $300 and ½ probability of $100, or written as E(cash flow) = ½($300) + ½($100) = $200 [just the mean], where E = expected value operator


Slide8: Assume the cost of capital is 10 % --- convenient Assume that one unit of product can be sold immediately, and one per year thereafter The NPV of the project is given by:


Slide9: The NPV rule is the maximum, determined today, of the expected value = 200 ---- implicitly assuming the project is undertaken today, or not at all What about deferring until we have some more information?


Slide10: Using the option, one can defer, then decide to invest given more information If the cash flow is only $100 then you will not exercise the option to invest But, if the cash flow is $300 per unit, you will exercise the option to invest The NPV is $200 to invest immediately But the NPV should you defer is higher at $590.91 Therefore, given the flexibility, you will defer The value of this call option (with an exercise price of $2,000, a one year life, and a variance determined by the cash flow spread of $200 per unit (300 – 100), and an underlying risky asset that has a value without flexibility of $200) = 590.91 – 200 = $390.91


Slide11: The NPV is the maximum, decided today, of the expected discounted cash flows or zero The option value is the expected value of the maximums, decided when information arrives, of the discounted cash flows in each future state of nature, or zero:


Slide12: These two methods use information quite differently NPV forces a decision based on today’s expectation of future information Option valuation allows the flexibility of making decisions in the future contingent on the arrival of information Option pricing methods capture the value of flexibility while NPV does not The value of a project using option pricing will always be greater than the value of the project using NPV --- except for the case where the project is not chosen because NPV< 0 This difference may be small if NPV is very high and flexibility is unlikely to be used


Slide13: The biggest differences occur when NPV is close to zero, that is, when the decision about whether to undertake the project is a close call Option value is dependent on time of expiration, uncertainty or volatility about the present value, cash flows lost to competitors who have fully committed, investment cost, risk free interest rate and expected present value of cash flows from investment Longer time to expiration allows us to learn more about uncertainty and increases option value With flexibility in place, an increase in uncertainty increases option value Loss of cash flow to competitors will clearly decrease option value


Slide14: An increase in the risk-free interest rate, such as the Treasury Bond rate, will increase option value since it will increase the time value of money advantage in deferring the investment cost A higher investment cost will reduce NPV (without flexibility) and therefore reduce option value An increase in the present value of the project will increase the NPV (without flexibility) and therefore increase the option value


Slide15: We can classify some options: Abandonment Option – sell or abandon a project --- this option works like an American PUT on the stock market – the American PUT can be exercised at any time --- like the right to abandon a gold mine Option to defer – the option to defer an investment to develop a property is formally equivalent to an American CALL option on the stock market Option to expand --- the option to expand the scale of a project is formally equivalent to an American CALL Option to extend or shorten – one can extend the life of an asset by paying a fixed amount of money which is the exercise price --- conversely, it is possible to shorten --- the option to extend is a CALL and the option to shorten is a PUT