Real Options for Engineering Systems

Real Options for Engineering Systems Session 1: What s wrong with the Net Present Value criterion? Stefan Scholtes Judge Institute of Management, CU Slide 1 Main issues of the module! Project valuation: Making an economic case for a technology project! Design optimisation: adding design features to technology projects to make them economically more attractive! Making an economic case for a project: Convince the board that the company can do nothing better with the investment capital than investing it in the project " Compare project payoffs with alternative investment opportunities within the company and in the market place " Take existing portfolio of projects and long-term strategic considerations into account (alignment of project with existing strengths and strategic positioning of the company) Stefan Scholtes Judge Institute of Management, CU Slide 2 Page 1

CFO s point of view! Finance department: A project consists of an initial investment followed by a stream of future cash flows! Invest in the project if there is no better alternative investment opportunity! Two major problems: " Cash flows of the project depend on external uncertainties " Cash flows depend on our (and our competitors ) management decisions during the life time of the project! How can we compare streams of uncertain payoffs which depend on future decisions (which in turn depend on uncertain events)?! Let s first look at how projects are evaluated in practice Stefan Scholtes Judge Institute of Management, CU Slide 3 A quick look into the manager s project valuation toolbox! Break-even analysis! Accounting rates of return! Net present value! Real options Stefan Scholtes Judge Institute of Management, CU Slide 4 Page 2

Break-even analysis! Input: " Initial investment " Projected cash flows over a number of periods! Break-even point: " Number of periods necessary for the sum of discounted cash flows to exceed the initial investment! Making a case for the project: " Compare break-even point with company benchmark Stefan Scholtes Judge Institute of Management, CU Slide 5 Accounting rates of return! Input: " Projected book value of investment over the life time of the project " Projected profits of the project over its lifetime! Accounting rate of return: average profit / average book value! Making a case for the project: " Compare the ratio with company benchmark Stefan Scholtes Judge Institute of Management, CU Slide 6 Page 3

Net present value! Most popular valuation criterion! Inputs: " Initial investment " Projected cash flows over the life time of the project " Discount rate! NPV = Present value of cash flows minus initial investment! Making a case for the project: " NPV>0! Let s have a closer look at NPV Stefan Scholtes Judge Institute of Management, CU Slide 7 NPV: underlying alternative investment opportunities! The NPV criterion is equivalent to comparing the project with a single alternative investment opportunity: " deposit y into a bank account that pays r% interest per period and withdraw the cash flows when they occur! If the life time of the project is T periods with cash flows x=(x 1,,x T ) and interest is compounded continuously then y = t = 1 rt xt! y is called the present value (PV) of the cash flow stream! Net present value NPV = PV initial investment! Economic case: Invest in the project if NPV>0 T e Stefan Scholtes Judge Institute of Management, CU Slide 8 Page 4

First problem with NPV: Simplistic and in-flexible investment alternative! Notice that we are not comparing the project with a more flexible account which would allow us to withdraw at nonscheduled times or withdraw non-scheduled amounts if opportunities arise! Lesson 1: Using NPV assumes a single and inflexible investment alternative " In an attempt to make up for this, companies typically assume a higher discount rate than the normal fixed interest in a bank account but this only means that a realistic investment alternative is replace by a virtual one! Inflexibility of the alternative is in line with the tacit (but unrealistic) NPV assumption that the cash flows are fixed, i.e., not influenced by management decisions or uncertain exogenous events Stefan Scholtes Judge Institute of Management, CU Slide 9 Second problem with NPV: The forecast is always wrong! Let s have a look at a spreadsheet example (open NPV.xls worksheet Project Plan)! Cash flow calculated on the basis of forecasted demand " Demand in period t is uncertain and depends on endogenous (price) and exogenous (economy, fashion, competitors) variables " Unknown demands in periods 1,,t-1 may help us to predict demand in period t more accurately (statistical dependence)! Lesson 2: NPV is a function of uncertain quantities and therefore itself uncertain Stefan Scholtes Judge Institute of Management, CU Slide 10 Page 5

Let s formalize this! Mathematically: NPV depends on uncertain quantities X 1,,X n (random variables): NPV=NPV(X 1,,X n )! A function of a random variable is itself a random variable " A single number (even the mean) is very limited information about a random variable " Can make a better economic case from knowledge of the NPV distribution! If we can t get the distribution then we want at least some of its characteristics: " expected NPV " variance of NPV " 95% confidence interval for NPV Stefan Scholtes Judge Institute of Management, CU Slide 11 Distributions and Value at risk NPV cumulative distribution function 100.0% 90.0% 80.0% 70.0% 60.0% 50.0% 40.0% 30.0% 20.0% 10.0% 0.0% - 1,500,000-1,000,000-500,000 0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 10% VAR is roughly 500,000 5% VAR is roughly 800,000 Stefan Scholtes Judge Institute of Management, CU Slide 12 Page 6

The flaw of the averages! In practice, decisions are often made on the basis of expected NPV alone! Naïve approach: Let s work with expected demands " Let s assume marketing department has given us price 1000 and expected demands! Is the NPV then the expected NPV? " Let s look at our example spreadsheet! Lesson 3: The flaw of the averages : Plugging expected values into uncertain cells in a spreadsheet does not give expected values of the formula cells! Mathematically: E( f ( X)) f ( E( X)) Stefan Scholtes Judge Institute of Management, CU Slide 13 Uncertainty: the naïve approach! If cash flow is uncertain, then replace it by its expectation and discount as before to obtain expected NPV! Which gamble would you prefer? 50% 1000 20 20 50% - 900 50% 50% 101-1! Expected cash flow in period 1 is 50 Stefan Scholtes Judge Institute of Management, CU Slide 14 Page 7

A little less naïve! Can t compare apples with bananas! Different risk levels need to be reflected in the valuation! Risk-adjusted discount rate: Discount rate = risk-free rate + risk premium! What s the appropriate risk premium? " Discount rate should be the expected return on an asset with comparable risk (same risk class )! Theory: Capital Asset Pricing Model (CAPM)! Practice: " Find projects with comparable risks and use the average return on these projects as discount rate " Specify a company-internal discount rate Stefan Scholtes Judge Institute of Management, CU Slide 15 Constant risk premium! Taking a constant risk premium assumes that the risk in passing from year n to year n+1 is the same for all n! Conical uncertainty: where-ever a sample path of scenarios leads me, the uncertainty ahead of me remains the same " Analogy to repeated gamble Stefan Scholtes Judge Institute of Management, CU Slide 16 Page 8

Conical uncertainty Expectation Measure of variation / risk Time Stefan Scholtes Judge Institute of Management, CU Slide 17 Conical uncertainty Sample path Expectation Time Precise repetition of Uncertainty pattern Stefan Scholtes Judge Institute of Management, CU Slide 18 Page 9

Example: Brownian motion! Continuous form: dx = α dt + σ dz! Discrete form: x( t) x( t 1) =α + σz where Z is a standard normal variable (mean 0, variance 1)! Brownian motion assumption: increments x(t)-x(t-1) and x(s)-x(s-1) are independent for t s! Expectation and variance of increments are linear functions of time: t x( t) x(0) = E( x( t) x(0)) = V ( x( t) x(0)) = x( s) x( s 1) E( x( s) x( s 1)) = αt V ( x( s) x( s 1)) = σ Stefan Scholtes Judge Institute of Management, CU Slide 19 s= 1 t s= 1 t s= 1 2 t Non-conical uncertainty! Examples: " Future demand for a new product (versus future demand for an established product) " Research uncertainty of an R&D project " Regulatory uncertainty in the pharmaceutical industry! Characteristics of non-conic uncertainty: " Uncertainty that is largely resolved after a few periods " Variance of unknown quantities do not tend to infinity over time (e.g. mean reversion property vs. Brownian motion)! Constant risk-premium concept does not capture non-conic uncertainties! How about adjusting risk-premium over time?! Risk of the project depends not only on time but also on the path of the resolved uncertainties " Example: high demand vs low demand scenario materializes after one year future risk (after year 1) depends on the scenario Stefan Scholtes Judge Institute of Management, CU Slide 20 Page 10

A closer look at discount rates! Discount rate: inverse interest rate! Interest rate: opportunity cost of capital (per and period) " Return over one period of the best investment alternative " Not clear what best means a priori in the presence of uncertainty " Assumes that we can sell the asset on the market after one period! Conceptually better: " For each cash flow period define a sensible investment strategy that results in a sellable asset at the time of the period cash flow " Use the return of this investment strategy as the discount rate for this particular period cash flow Stefan Scholtes Judge Institute of Management, CU Slide 21 Random discount rates! Value of an alternative investment strategy depends on unfolding of future uncertainties " Even the value of a fixed interest rate account changes when the base rate changes! Therefore: Opportunity cost of capital is a random process (random and time-dependent)! Practice: Replace the random process by its long-run average! Caution! NPV depends nonlinearly on the discount rate # flaw of the averages Stefan Scholtes Judge Institute of Management, CU Slide 22 Page 11

The flaw of the averages and discount rates! Taking as discount rate an average rate is conceptually wrong because NPV depends nonlinearly on the discount rate (flaw of the averages) " Way out: simulate, using historic period returns instead of averages! Jensen s inequality: the NPV calculation on the basis of average rate of return is lower than the expected NPV based on historic returns! See Flaw of the averages for discount rates.xls Stefan Scholtes Judge Institute of Management, CU Slide 23 Third problem with NPV: No managerial activity! NPV assumes that the cash flows of the project are fixed! Even if cash flows are random and simulation is used to evaluate expected NPV, there is no managerial flexibility in the model! Typically, management acts depending on the unfolding of uncertainties! Typical actions " Increase marketing efforts " Abandon project " Grow project! Let s look at an example (see NPV.xls, worksheet expansion option) Stefan Scholtes Judge Institute of Management, CU Slide 24 Page 12

Summary! Company should invest in a project if there are no better investment alternatives! NPV-criterion has severe drawbacks: " Discount approach assumes comparison of project with only one, and a rather in-flexible, alternative investment (this overvalues the project) " Risk-premium approach does not properly account for project risk (whether this is in favour of the project or not depends on the level of the risk-premium) " NPV criterion is based on FIXED cash flow projections and does not take managerial flexibility into account (this undervalues the project) Stefan Scholtes Judge Institute of Management, CU Slide 25 Back to the basics! Invest in a project if that s the best you can do with your money! Starting point: Company is engaged in a portfolio of projects! A project portfolio generates a random stream of cash flows! Want a combination of projects so that the stream of cash flows is desirable ( optimal )! Cash flows depend on " Exogenous uncertainties " Decisions of project managers in reaction to unfolding uncertainties and external decisions (e.g. regulation) " Exogenous decision and reactions to internal decisions (e.g. by competitors, government, etc.) " Decisions of portfolio managers (e.g. reballancing, abandonment of individual projects) Stefan Scholtes Judge Institute of Management, CU Slide 26 Page 13

Investing in a new project To make an economic case for a new project we need to argue that adding the new project to the existing project portfolio (and therefore abandoning or down-sizing other projects) increases the desirability of the stream of future cash flows Stefan Scholtes Judge Institute of Management, CU Slide 27 The courtroom! Innocence hypothesis: The project does not add value to the portfolio! Jury: The decision maker! Prosecutor: I want the project in the portfolio " Need to construct a case that the project adds value to the company s portfolio " In particular: need to argue how the portfolio re-balancing should be done (i.e. where the money should come from)! Defence lawyer: I don t want the project in the portfolio " Need to reply to the prosecutors case by constructing alternative investments and arguing that these are more beneficial to the company than investing in the project! Question: Why don t we use as innocence hypothesis that the project adds value to the portfolio? Stefan Scholtes Judge Institute of Management, CU Slide 28 Page 14

Using a computer! Prosecutor: Build a stochastic (scenario-based) computer model of the project, including decision points and decision rules (plans of action for all possible scenarios)! Defence lawyer: Build a stochastic model of a sensible alternative investment strategy (using projects or assets from within the company or in the market place), including possible decision points and decision rules! Jury: Decide whether there is a case for the project on the basis of the (random) difference between the cash flow streams of the project and the alternative investment strategy " Can use simulation to estimate the distribution of the difference between the cash flow streams of the two investments for given decision rules " Jury will also take strategic issues into account Stefan Scholtes Judge Institute of Management, CU Slide 29 Simulation Results 250000 Settings 200000 150000 100000 50000 95% Mean 5% 0 periods 1+2 periods 3+4 periods 5+6-50000 -100000-150000 Difference between project cash flow and alternative investment cash flow Stefan Scholtes Judge Institute of Management, CU Slide 30 Page 15

What s the problem with this approach?! Meaning of optimal decision rule is not clear " What is optimal for cash flow in period 1 may be bad for cash flow in other periods " What is optimal in one scenario may be bad in another! Approach allows us to compare investments with regard to risk but not with regard to flexibility " Alternative investment is often more flexible e.g. investments in stock portfolio! Most importantly: Model is complex " But: there may be no simple solution to a complex problem " If we could only do something that was similar to the above but simpler! Research: Suggest rules of thumb to practitioners which are conceptually sound but have some simple intuitive interpretation " Academics adds to practitioners confidence that they are doing the right thing by following their intuition Stefan Scholtes Judge Institute of Management, CU Slide 31 Conclusion! NPV criterion has serious pitfalls! The courtroom is a sensible model for project appraisal! Complexity of cases for or against a project is a serious hurdle to acceptance in practice " But then again: there may not be a simple solution to this complex problem! More questions than answers Stefan Scholtes Judge Institute of Management, CU Slide 32 Page 16