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Published on April 17, 2008

Author: AscotEdu

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E-Finance:  E-Finance Professors: Jonathan Berk Brett Trueman Miguel Cantillo Richard Lyons Web: http://www.haas.izio.convene.com My Details:  My Details Jonathan Berk phone: 510-642-3367 email: berk@haas.berkeley.edu www: haas.berkeley.edu/~berk Office: F634 Email:  Email This is the preferred way to contact me Please make sure you are on the email class distribution lists I regard any announcement I make by email as equivalent to my making that announcement in class. What is the course about?:  What is the course about? There are two kinds of e-finance courses Guest lecture/War story/Case Study type Lecture Type This course will be the latter kind How will it be administered?:  How will it be administered? Each of us will deliver two weeks on our area of expertise At the end of each two week module, you will be assigned a group assignment. Your grade will be an equal weighting of the four assignments. Group Dynamics:  Group Dynamics Groups may be no bigger than 4 students. You will be assigned into groups by the GSI You will have a new group for each assignment Web based help in this Module:  Web based help in this Module My lecture notes will be available on my web page (which can either be accessed directly or through the class web page). All examples worked in the lectures will be available on my web page as Mathematica worksheets or PDF files. Introduction:  Introduction I will talk about a systematic way to think about how to value growth Most of my colleagues (except for Miguel) are here and so can speak for themselves… Valuing Growth:  Valuing Growth Theoretical model Traditional Methods Introduction to Options Real Options The Option to Invest Derive a real options based model Traditional Methods:  Traditional Methods Rather informal Basically discounted cashflow models --- Gordon Growth Estimate a expected cashflow and a growth rate (sometimes more than one) and compute value Method is clearly only a rough estimate That is how it is used. What is a Financial Option?:  What is a Financial Option? Call An option to buy an underlying security (for example, a stock) for a fixed price (that is, the strike or exercise price) on or before a certain date (expiration date). Put An option to sell the underlying security (for example, a stock) for a fixed price (that is the strike or exercise price) on or before a certain date (expiration date). Call Option:  Call Option Mr Optimist holds a 3 month call option on Sun Microsystems. It is a european option with a strike of $100. Stock option contracts are written on 100 shares. What would the holder of the contract do (and so what is the value of the contract and his profit) in 3 months if Sun Microsystems goes to $110 $90 Value of the position at expiration:  Value of the position at expiration What is the price of the call? Stock Price Put Option:  Put Option Ms Pessimist holds a 3 month put option on Sun Microsystems. It is a european option with a strike of $100. What would the holder of the contract do (and so what is the value of the contract and her profit) in 3 months if Sun Microsystems goes to $110 $90 Value of the position at expiration:  Value of the position at expiration Stock Price Option Terms:  Option Terms Exercising the Option Enforcing the contract, i.e., buy or selling the underlying asset using the option Striking, Strike, or Exercise Price The fixed price specified in the option contract for which the holder can buy or sell the underlying asset. Expiration Date The last date on which the contract is still valid. After this date the contract no longer exists. European vrs. American Options:  European vrs. American Options European A European option can only be exercised on the exercise date. American An American option can be exercised on any date up to the exercise date. Important Question:  Important Question Can an option ever be free? An option not an obligation Option Quotations:  Option Quotations Let’s check out some options prices Concept question: Is this the same thing as the Stock price? Strike price? Options on GM Where do these prices come from?:  Where do these prices come from? There are two answers: Supply and demand the CBOE determines the price You can also calculate the price using a formulae, if you know the stock price Black-Scholes Option Pricing Formula:  Black-Scholes Option Pricing Formula Where t is the time to expiration (NOT today) and Real world example:  Real world example Calculate the price of an February 50 Microsoft call. Microsoft Today’s Yield Curve Options on Microsoft What is a Real Option?:  What is a Real Option? A real option is an option where the underlying asset is a real asset For example: Have you ever wondered why you come across empty lots in the middle of an otherwise built up area? With the price of gold so low, why have only about 20% of mines been closed down? NPV rule:  NPV rule The NPV rule that says invest whenever the NPV>0 assumes the investment is a one time choice that cannot be delayed. How realistic is this assumption? Simple Example:  Simple Example Assume you have the opportunity to invest in a riskless project that will generate $100 forever. It will cost you $750 today to make the investment. Assume interest rates will either be 10% or 20% tomorrow and will stay that way forever. Assume both states are equally likely under the risk neutral measure. Assume the current short rate is 12% What is the discount rate for the project:  What is the discount rate for the project Since the project is riskless it is the riskless rate on a bond that pays $1 forever --- the consol rate What is the consol rate? What is the NPV of the investment opportunity?:  If you invest today it is: If you wait and see what happens it is: You obviously will not invest if rates go to 20% What is the NPV of the investment opportunity? What do you do?:  What do you do? Even though this is a positive NPV investment opportunity, you pass it up Why? Because, by giving it up you give up the option of investing tomorrow. This option is worth more than the NPV of investing today Another way to think about this is that by waiting you leave open the option of capturing an even larger NPV if the cost of capital drops. What would this investment opportunity sell for? Another Example:  Another Example It is just after the Oakland fire. You are a builder and you have just bought a plot of land in the fire zone. The land cost $50,000. The price at which you can sell a house on the land is $100/sqft. The optimal size of a house to build at this point is a 2500 sq. ft. If you wait and see what other builders do, you think there is a 50% probability that other builders will begin to build larger houses, so that in 5 years the optimal house size will be 5000 sq. ft. Both building costs and interest rates will be constant at $75/sq.ft. and 10%. What should you do? What would you do if interest rates were 20%. What is the general lesson?:  What is the general lesson? The value of the real option essentially derives from the fact that your downside is limited at zero, but the upside has no limit. This real option is imbedded in all investment decisions that can be delayed and can be a source of an enormous amount of the value of the investment opportunity To value growth, which essentially is just a collection of investment opportunities, we have to value these kinds of real options OK, lets get back to valuing growth:  OK, lets get back to valuing growth Why does a company with no cashflows have a positive value? A naïve view might be --- it is much more likely to fail than succeed A sophisticated view recognizes that if you fail all you can lose is your investment. The benefits of success are unlimited (e.g. Microsoft, IBM, etc) How important is the real option? Check out Amazon.com! Amazon The Value of Growth:  The Value of Growth The growth opportunities of a firm can be thought about at the value of all future positive NPV investments Each of these investments represent a real option because nobody forces you to invest in a negative NPV project What’s wrong with just assuming a growth rate?:  What’s wrong with just assuming a growth rate? Valuing a firm by projecting out an expected growth rate ignores the fact that it might not be optimal to grow at that rate, that is, the option component of growth. This is like trying to value an option using the expected return on the stock. A Thought Experiment:  A Thought Experiment Ceteris paribus, what would you expect to happen to the growth rate of a firm when interest rates rise (fall)? What about the riskiness of the firm? What about the risk?:  What about the risk? Amazon might be worth a tremendous amount, but I think it is fair to say there is a great deal of uncertainty about this value Does this translate into a huge risk premium? A naïve view might be --- large uncertainty yes, but it is idiosyncratic. Things like who will dominate the internet book market. So, just buy all the internet book companies and diversify away the risk. To answer these kinds of questions you need a model. What should such a model contain?:  What should such a model contain? Technical uncertainty that is idiosyncratic Market uncertainty that is related to the overall economy and so has systematic components Uncertainty about whether you will be able to capture the market, even if you successfully develop the product Uncertainty about your overall ability to conduct the R&D. Technical Uncertainty:  Technical Uncertainty N stages that need to developed before the product can be brought online Let n(t) the be the number of completed states at time t It is uncertain whether a stage will be completed in the next period. If the stage is attempted it is completed with probability . If it is not attempted then the project stays in its current stage for sure What about the cost?:  What about the cost? If the firm decides to try to go to the next stage, it incurs a cost d(t) is the periodic net cashflow if the project were completed today Note that the costs have both fixed and variable components Does this make intuitive sense? If the firm does not try to go to the next stage, it incurs no cost. We will call this mothballing the project How does the firm decide?:  How does the firm decide? It chooses the path that maximizes value If this was a one shot thing, it would proceed if the NPV is positive Of course, if it is a one shot thing then the value of not proceeding is zero. Since the firm can mothball the project, the mothballed project will have value, so even if the NPV of investing is positive, the firm will not invest if the value of mothballing is greater. To formalize this decision we need to figure out these values Value of the completed project:  Value of the completed project Upon completion the project generates the net cashflow d(t) every period until a competitor produces a superior product that takes the market away. To value these cashflows we need to model two things Risk of obsolescence Discount rate Risk of obsolescence:  Risk of obsolescence We will assume that this risk is idiosyncratic and independent of everything else It this realistic? Every period there is a (1-py) probability that the project will be terminated We will keep track of whether the cashflow is alive in the following way: Value of the completed project:  Value of the completed project where What is the value before N stages are completed?:  What is the value before N stages are completed? Assume no fixed costs and no learning (a=0) In this case the value of the project is homogeneous in d. What is the intuition? So the optimal policy in this case is as follows: Decide at t=0 whether to invest invest iff h(0)>0 If you do decide to invest, develop until you complete all stages What is the intuition here? Lets begin to generalize ….:  Lets begin to generalize …. What if you do not know p? well you have some guess, which you update in a Bayesian way. Value with no fixed costs:  Value with no fixed costs In the paper we show that the form of the solutions is similar. How does the intuition change? An important result is that the risk premium of the R&D is the same as the risk premium of the completed project. Why is this? What happens when there are fixed costs (a>0):  What happens when there are fixed costs (a>0) The existence of fixed costs has a number of important consequences Optimal investment policy is different The project is mothballed/abandoned in response to changes in d The risk premium of the R&D exceeds that of the completed project Optimal Investment Policy with fixed costs:  Optimal Investment Policy with fixed costs At each stage there is a threshold number of failures that you will tolerate. If the number of failures is above this threshold, then you abandon the project. It turns out that this threshold is the same one as the one with no fixed costs. Why? If it is below the threshold, then there is a d*(n,m) such that the R&D is undertaken iff d > d*(n,m) Only this decision is a function of systematic risk and so only this decision commands an extra risk premium Value when p is known (Value with no option):  Value when p is known (Value with no option) Risk Premium when p is known:  Risk Premium when p is known Value when p is unknown and n=m:  Value when p is unknown and n=m Number of failures that trigger abandonment (m*):  Number of failures that trigger abandonment (m*) Risk Premium with no stages complete:  Risk Premium with no stages complete Risk Premium with 5 stages complete:  Risk Premium with 5 stages complete Risk Premium with 16 stages complete:  Risk Premium with 16 stages complete Realized Return (n=m=0):  Realized Return (n=m=0) Realized Return (d(t)=9):  Realized Return (d(t)=9) Next Lecture:  Next Lecture Applications Harvard Case --- Arundel Partners Pricing Internet Stocks Preparation Read the case and be prepared to discuss it in class I will cold call.

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