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Principles of Corporate Finance Chapter 23 Real Options Ninth Edition Slides by Matthew Will McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 23-2 Topics Covered The Value of Follow-On Investment Opportunities The Timing Option The Abandonment Option Flexible Production Aircraft Purchase Options A Conceptual Problem 23-3 Corporate Options 4 types of “Real Options” 1 - The opportunity to expand and make follow-up investments. 2 - The opportunity to “wait” and invest later. 3 - The opportunity to shrink or abandon a project. 4 - The opportunity to vary the mix of the firm’s output or production methods. Value “Real Option” = NPV with option - NPV w/o option 23-4 Microcomputer Forecasts Example – Mark I Microcomputer ($ millions) 1982 After-tax operating cash flow (1) Capital investment (2) Increase in working capital (3) Net cash flow (1)-(2)-(3) 450 0 -450 NPV at 20% = - $46.45, or about -$46 million 1983 100 0 50 60 Year 1984 159 0 100 59 1985 295 0 100 195 1986 185 0 -125 310 1987 0 0 -125 125 23-5 Microcomputer Forecasts Example – Mark II Microcomputer Option 900 PV (exercise price) 3 676 1.1 OC N (d1 ) P N (d 2 ) PV ( EX ) d1 log[ P / PV ( EX )] / t t / 2 log[. 691 / .606] .606 / 2 .3072 d 2 d1 t .3072 .606 .9134 N ( d1 ) .3793 N ( d 2 ) .1805 Call Value [.3793 467} [.1805 676] $55.12million 23-6 Microcomputer Forecasts Example – Mark II Microcomputer ($ millions) Forecasted cash flows from 1982 1982 After-tax operating cash flow Increase in working capital Net cash flow Present Value @ 20% Investment, PV @ 10% Forecasted NPV in 1985 ………. 467 676 Year 1985 807 900 -93 NPV(1982) =PV(inflows) -PV(investment) = 467 – 676 = - $209 million 1986 220 100 120 1987 318 200 118 1988 590 200 390 1989 370 -250 620 1990 0 -250 250 23-7 Microcomputer Forecasts Example – Mark II Microcomputer (1985) Distribution of possible Present Values Probability Present value in 1985 Expected value Required investment ($807) ($900) 23-8 Option to Wait Intrinsic Value Option Price Stock Price 23-9 Option to Wait Intrinsic Value + Time Premium = Option Value Time Premium = Vale of being able to wait Option Price Stock Price 23-10 Option to Wait More time = More value Option Price Stock Price 23-11 Timing Option Example Possible cash flows and end-of-period values for the malted herring project are shown. The project costs $180 million, either now or later. The figures in parentheses show payoffs from the option to wait and to invest later if the project is positive-NPV at year 1. Waiting means loss of the first year’s cash flows. The problem is to figure out the current value of the option. 23-12 Timing Option Example High demand generates $25 million and a value of $250 million at the end of the year. Low demand generates $16 million and no value. High Demand Low Demand (25 250) 1 200 .375 Total return (16 160) 1 200 .12 Total return Risk neutral return = 5% 23-13 Timing Option Example The next step requires the calculation of the probability of there being a high demand for the malted herring project. Expected return (Prob of high demand) .375 (1 Prob of high demand) (-.12) Expected return .05 Prob of high demand .343 The option value is now determined as follows. (.343 70) (.657 0) Option Value 1.05 $22.9 million 23-14 Option to Wait Example – Development option Cash flow Office Bldg Office Bldg 240 NPV>0 Wait 100 NPV<0 100 Hotel NPV>0 240 Cash flow from hotel 23-15 Option to Abandon Example - Abandon Mrs. Mulla gives you a non-retractable offer to buy your company for $150 mil at anytime within the next year. Given the following decision tree of possible outcomes, what is the value of the offer (i.e. the put option) and what is the most Mrs. Mulla could charge for the option? Use a discount rate of 10% 23-16 Option to Abandon Example - Abandon Mrs. Mulla gives you a non-retractable offer to buy your company for $150 mil at anytime within the next year. Given the following decision tree of possible outcomes, what is the value of the offer (i.e. the put option) and what is the most Mrs. Mulla could charge for the option? Year 0 Year 1 Year 2 120 (.6) 100 (.6) 90 (.4) NPV = 145 70 (.6) 50 (.4) 40 (.4) 23-17 Option to Abandon Example - Abandon Mrs. Mulla gives you a non-retractable offer to buy your company for $150 mil at anytime within the next year. Given the following decision tree of possible outcomes, what is the value of the offer (i.e. the put option) and what is the most Mrs. Mulla could charge for the option? Year 0 Year 1 Year 2 120 (.6) 100 (.6) 90 (.4) NPV = 162 Option Value = 162 - 145 = 150 (.4) $17 mil 23-18 Option to Abandon Example – Ms. East - Revenues 3.73 3.05 2.50 2.50 2.05 1.68 23-19 Option to Abandon Example – Ms. East – Cash Flows 3.03 2.35 1.80 1.80 1.35 .98 23-20 Option to Abandon Example – Ms. East – Value 2.5 PV $2.29million 1.09 3.05 p 2.05(1 p ) Expected return .06 2.29 Prob of up change .382 Prob of down change .618 APV -1.108 3.803 $2.695milli on 23-21 Tanker Example Value of Tanker Value in operation Cost of reactivating Mothballing costs Value if mothballed Tanker Rates 23-22 Aircraft Purchase Option The option to purchase an aircraft provides the holder both the ability to obtain a lower price as well as receive the aircraft sooner. Both have value to the aircraft buyer, thus the option has value. 23-23 Aircraft Purchase Option Value of aircraft purchase option—the extra value of the option versus waiting and possibly negotiating a purchase later. The purchase option is worth most when NPV of purchase now is about zero and the forecasted wait for delivery is long. 23-24 Real Option Barriers Practical reasons exist why real options are not always feasible to use. 1. 2. 3. Valuation of real options can be complex and sometimes it is impossible to arrive at the “perfect” answer. Real options do not always have a clear structure their path and cash flows. Competitors also have real options, which an alter the value of your options by altering the underlying assumptions and environment that serves as the basis of your valuation. Given these limitations, real options are not always the best approach when valuing projects. 23-25 Web Resources Click to access web sites Internet connection required www.puc-rio.br/ www.decisioneering.com