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Real Options and Capital Budgeting Real Options • Traditional capital budgeting analysis: • estimates cashflows each period • discounts to get NPV • firm decides to invest/not invest BIG PROBLEM: Traditional analysis assumes that a firm’s only choice is accept/reject the project. THIS IS NOT TRUE!! In a real business situation, firms face many choices with respect to how to operate a project, both before it starts and after it is underway. Eg. Flexibility: • use a production technology that is adaptable • can produce more than one product • if market for one product goes down, can switch production to the other • the option to change production if the firm wants to (the flexibility) is valuable • makes the project worth more • traditional NPV analysis assumes cashflows fixed, will not change with future business conditions – ignores the value of this option Eg. Abandonment • firm invests in project • after a time the firm may be able to shut down production if things are not going well • option to abandon • traditional analysis assumes that the firm either takes the project and runs it for its life, or rejects it • But…the ability to start a project and shut it down (perhaps temporarily) if conditions warrant is valuable Eg. Option to Delay • traditional analysis assumes firm accepts project now or never invests • But…what if firm has choice to delay making decision? • Wait and see how things develop and then decide to invest or not • The choice to delay if the firm wants is valuable • Other examples of valuable options (choices) a firm may have include: • option to expand/shrink production • option to move into new market • R&D gives the option to develop new products if they become viable • development options on natural resources • et cetera Real Options • Any time a firm has the ability to make choices, there is a value added to the project in question • traditional NPV analysis ignores this value • the study of real options attempts to put a dollar value on the ability to make choices How are real options valued? Three major ways: 1) Use methods developed for pricing financial options • Black-Scholes Model • Discussed in “What’s It Worth?” article • May be problems 2) Decision trees • look at this method here 3) Stochastic optimization problems • like (2) but using far more complicated (and realistic) models for the probability of different events occurring Option to Delay • simple example from “Irreversibility, Uncertainty and Investment”, Robert Pindyck [Journal of Economic Literature, 1991] • for $800 a firm can build widget factory • makes 1 widget per year • factory is built instantly • investment is irreversible • if factory built, first widget produced immediately • no costs of manufacturing • no taxes • appropriate discount rate is 10% Option to Delay • the price of widgets is currently $100 • next year the price will be either $150 (50% probability) or $50 (50% probability) • whatever price holds next year will hold forever after year 0 year 1 year 2 Price = $150 Price = $150 Price = $100 Price = $50 Price = $50 Traditional NPV Analysis Expected year 1 price = E[price] = 0.5($150) + 0.5($50) = $100 E[price] NPV 800 100 t 1 (1 r ) t 100 800 100 t 1 (1.1) t 100 800 100 0.1 $300 Standard analysis says NPV > 0, so start project. Option to Delay • BUT… firm has another option. Delay the choice of whether to invest or not. • Wait until next year to decide. • Can see what price turns out to be before making decision. • If you delay, you lose on the year 0 sales ($100). • The bad part of delaying – lost sales. • But, you get to see what price will be before making irreversible investment. • The good part of delaying, reduced uncertainty. CASE 1: If delay and price turns out to be $50: 800 50 NPV 11 . t 1 (11) t . 800 50 . 11 01 . 227.27 • NPV < 0 , so firm will not invest. • From today’s perspective, NPV = 0 if price turns out to be $50. CASE 2: If delay and price turns out to be $150: 800 150 NPV 11 . t 1 (11) t . 800 150 . 11 01. 772.73 Firm will invest if the price goes to $150. • the essence of the option to delay is that it allows the firm to avoid the “bad” outcome • delay deciding until you see what the state of the world is: • you lose some sales on delay • if the market turns out to be bad, you do not invest and do not take the loss • does the avoided loss make the foregone sales worthwhile? Price = $150 NPV = 772.73 NPV = ?? Price = $50 NPV = 0 NPV in year 0 of delaying project = (0.5)(772.73) + (0.5)(0) = $386.36 • the NPV of delaying ($386.36) is more than the NPV of starting immediately ($300) • therefore, firm should delay start of project • the flexibility of being able to wait another year to decide whether to invest or not is worth an additional $86.36 • Does this mean that firms should always delay projects? • No, if probability of high price in this example was 90% it would be best to start immediately Option to Abandon • ability to abandon a project if things are not going well is valuable • allows firm to avoid bad outcomes • value of the option to abandon can be calculated in similar way to option to delay • see example handout Capital Rationing Capital Rationing • Usual assumption is that firm should accept all NPV>0- projects • What if firm has a number of NPV>0 projects, but doe not have resources to take on all of them? • This is situation of capital rationing • Limited amount of capital to invest • Must decide how to best invest the limited resources Sources of Rationing Two types of capital rationing: 1. Soft rationing: capital constraint imposed internally by the firm • Head office may assign a budget to each division • If soft rationing is leading to a division foregoing many NPV>0 projects, then the budget should be changed 2. Hard rationing: capital constraint imposed on firm by the capital markets • Firm has limited internal cash, cannot borrow and cannot (or will not) issue new equity • In a perfect world, there would never be externally imposed capital constraints • In perfect world, firm could simply announce it had a good project to invest in, show investors the risk and return projections, and then investors would be willing to invest equity in/lend to the project • However, the world is not perfect. • There are several reasons that firms may be unable or unwilling to bring in external financing for a good projects: 1. Firm and investors may disagree on value of project • Management may lack creditability • Especially true for smaller, newer firms, or firms with poor records 2. Flotation Costs • It costs money to issue new shares/bonds • The additional cost may make raising money to finance a project not worthwhile • Flotation costs are higher for smaller issues, so small firms are affected the most (also higher for equity issues compared to debt). 3. Underpriced shares • Firms shares may be trading below their true value • Management knows that the shares are undervalued (management has better info about firm than market = asymmetric information) • Selling shares to raise funds to finance a project means that shareholders get a good project, but are selling part of the firm at a discount • In some cases the project will not be worthwhile and firm will skip project • Biggest effect on firms with high degree of asymmetric information (complicated firms, new firms, firms with few analysts following them) • Note: firms can benefit from having cash on hand available. • Can fund NPV>0 projects that without accessing markets • Do not have to skip a good projects because of reasons above • Assuming a firm is subject to capital rationing, how should it solve for the optimal investment strategy, given the constraint? Example: • Firm has $10 million available for investment, 3 potential projects Cashflows (millions) Project Year 0 Year 1 Year 2 NPV @ 10% A -10 30 5 21.4 B -5 5 20 16.1 C -5 5 15 11.9 • Simply choosing highest NPV means choose A • Uses up total budget • NPV = 21.4 • However you could take B and C instead – Uses up entire budget – Total NPV = 28 – B and C is the better choice • Best combination of projects is fairly obvious in this case, but may not be in more complicated situations Solving for Optimal Decision in Capital Rationing Problems • Common way to approach capital rationing problem is to use the profitability index PV of project ' s FCFF PI initial investment • PI shows which projects give “most value for your money” • PI = value of project per dollar invested • Choose project with highest PI, and keep choosing projects until your budget runs out • From previous example: Project PI A 3.1 B 4.2 C 3.4 • Solution by PI: choose B and C Problems with Profitability Index • If projects chosen via PI do not exhaust the budget, you may not get the optimal solution Example • Required return = 10%, budget constraint = $100 Cashflows Year 0 Year 1 P.I. NPV -5 8 1.454 2.27 -5 7 1.272 1.36 -100 120 1.091 9.09 Problems with Profitability Index • PI says take first two projects for total NPV = 2.27 + 1.36 = 3.63 • This leaves $90 of budget unspent • Better to take third project by itself, for total NPV = 9.09 • Reason: PI has difficulty in comparing projects of different sizes • Note: As long as your answer using PI uses up entire budget the NPV should be the maximum possible Problems with Profitability Index • PI also runs into problems if there is more than one constraint faced by firm • Projects are mutually exclusive (if you take one you cannot take the other) • Projects are dependant (you can only take on one project, if you have already taken another) • Budget constraints in more than one period • Etc. • The usual approach to capital rationing situations is to solve for the optimal investment using optimization software on a computer • Maximize an objective function subject to certain constraints • Can use “Solver” on Excel Investments of Unequal Lives Investments of Unequal Lives • When comparing mutually exclusive alternatives, NPV does not always give correct choice as to the best alternative if they are of different lengths • e.g. comparing Machine A to Machine B where B costs more but lasts longer • NPV does not take into account the different lifespans of the projects Investments of Unequal Lives Example – Machine A costs $10,000 and increase profits by $5000/year. It lasts 6 years. – Machine B costs $5,500 and increases profits by $5000/year. It lasts 3 years – Discount rate = 10% 6 5000 NPVA 10000 t $11,776.31 t 1 (1.1) 3 5000 NPVB 5500 t $6,934.26 t 1 (1.1) • A has highest NPV • A is best choice if this is a “one time deal” • If you will only buy a machine once and never replace it • More commonly, machines have to be replaced as they wear out • If replacement of machines as they wear out is relevant, there are two methods to correctly compare the alternatives 1. Project Replication 2. Equivalent Annuities Project Replication • Find a common multiple of the two life lengths • Use this as total project length for both alternatives, where each alternative is repeated the appropriate number of times • Calculate NPV over this common time frame and compare Equivalent Annuities • Equate the NPV of each alternative to an annuity • The length of the annuity equals the life of the project • Solve for annuity payment that would give the same NPV • The annuity payment represents the value per year created by the project • Since projects are now on a common time frame (per year), can simply compare Optimal Replacement Time • It may sometimes pay to replace a machine before the end of its “natural” life • May happen if: • Better machine becomes available • Salvage value is decreasing as machine ages • Machine becomes more expensive to operate or less efficient overtime • Optimal time to replace a machine is just a special case of comparing projects of unequal lives Example: • A machine you always need for your production process • Lasts a maximum of three years before replacement needed • It becomes less efficient over time • When replaced, you will replace with an identical (but new) machine • How often should you replace? • Discount rate=10% (example continued) Year 0 1 2 3 Cashflow -60000 40000 35000 25000 Salvage value 30000 15000 0 if sold this year • To solve, compare 3 projects of unequal lives: replace in year 1 vs. replace in year 2 vs. replace in year 3