Option Valuation

Submitted By sridevi007
Words 960
Pages 4
Option Valuation

Chapter 21

Intrinsic and Time Value intrinsic value of in-the-money options = the payoff that could be obtained from the immediate exercise of the option for a call option: stock price – exercise price for a put option: exercise price – stock price

the intrinsic value for out-the-money or at-themoney options is equal to 0 time value of an option = difference between actual call price and intrinsic value as time approaches expiration date, time value goes to zero
21-2

Determinants of Option Values
Call + – + + + – Put – + + + – +

Stock price Exercise price Volatility of stock price Time to expiration Interest rate Dividend rate of stock

21-3

Binomial Option Pricing consider a stock that currently sells at S0 the price an either increase by a factor u or fall by a factor d (probabilities are irrelevant) consider a call with exercise price X such that dS0 < X < uS0 hence, the evolution of the price and of the call option value is uS0 Cu = (uS0 – X) C S0 dS0 Cd = 0
21-4

Binomial Option Pricing (cont.) now, consider the payoff from writing one call option and buying H shares of the stock, where Cu − Cd uS0 − X H= = uS0 − dS0 uS 0 − dS0 the value of this investment at expiration is Up Down Payoff of stock HuS0 HdS0 Payoff of calls –(uS0 – X) 0 Total payoff HdS0 HdS0
21-5

Binomial Option Pricing (cont.) hence, we obtained a risk-free investment with end value HdS0 arbitrage argument: the current value of this investment should be equal to its present discounted value using the risk-free rate H is called the hedge ratio (the ratio of the range of call option payoffs and the range of the stock price) the argument is based on perfect hedging, or replication (the payoff of the investment replicates a risk-free bond)
21-6

Binomial Option Pricing – Algorithm
1. given the end of period stock prices, uS0 and dS0,...

Similar Documents

Free Essay

Real Options Valuation

...E R 2 | s p RiN g 2 0 0 8 Journal of APPLIED CORPORATE FINANCE A MO RG A N S TA N L E Y P U B L I C AT I O N In This Issue: Valuation and Corporate portfolio Management Corporate portfolio Management Roundtable Presented by Ernst & Young 8 Panelists: Robert Bruner, University of Virginia; Robert Pozen, MFS Investment Management; Anne Madden, Honeywell International; Aileen Stockburger, Johnson & Johnson; Forbes Alexander, Jabil Circuit; Steve Munger and Don Chew, Morgan Stanley. Moderated by Jeff Greene, Ernst & Young Liquidity, the Value of the Firm, and Corporate Finance 32 Yakov Amihud, New York University, and Haim Mendelson, Stanford University Real Asset Valuation: A Back-to-Basics Approach 46 David Laughton, University of Alberta; Raul Guerrero, Asymmetric Strategy LLC; and Donald Lessard, MIT Sloan School of Management Expected Inflation and the Constant-Growth Valuation Model 66 Michael Bradley, Duke University, and Gregg Jarrell, University of Rochester Single vs. Multiple Discount Rates: How to Limit “Influence Costs” in the Capital Allocation process 79 The Era of Cross-Border M&A: How Current Market Dynamics are Changing the M&A Landscape 84 Transfer pricing for Corporate Treasury in the Multinational Enterprise 97 The Equity Market Risk premium and Valuation of Overseas investments John Martin, Baylor University, and Sheridan Titman, University of Texas at Austin Marc Zenner, Matt......

Words: 9906 - Pages: 40

Black Scholes Valuation of Microsoft Employee Stock Options April 2000

...Microsoft Stock Options, we started by examining the value by using the Black-Scholes Valuation method. We were given that the time period would be T=6 years, and that both the strike price (K) and the Stock Price (S0) were equal to 66.625. When examining the case provided, it gave the data for both volatility and the risk-free rate in 2000. The volatility for this case in 2000 was 0.33 and the risk-free rate was 6.20%. Next, we calculated d1 and d2 in order to evaluate the price of the call option. D1 and d2 were both calculated at 0.63427 and -0.17406, respectively. This was determined by using the formulas to find d1 and d2 using the Black-Scholes method of valuation. Lastly, using the Black-Scholes method, the price of the call following all of these conditions was determined to by \$29.31. So, the value of 70 million options is simply 70 million multiplied by the price of the call, \$29.31. This was found to be \$2,052,045,496.29. This data can be seen in Table 1 in the appendix. Next, I examined the value of the 70 million options when T followed the distribution of: 10% at 4 years, 20% at 5 years, 40% at 6 years, 20% at 7 years, and 10% at 8 years. Following this distribution set, and calculating the summation of all 70 million options at each different time, T, gave a smaller valuation when compared to the value of all 70 million options at one time, T=6 (\$2,040,710,000.00 vs all at T=6, \$2,052,045,496.29). The following distribution of the call options at......

Words: 1595 - Pages: 7

Mw Petroleum

...Valuation is the estimation of an asset’s value, whether real or financial, based on variables perceived to be related to future investment returns, on comparison with similar assets, or, when relevant, on estimates of immediate liquidation proceeds (Pinto, Henry, Robinson, Stowe; 2010). Correct valuation of real assets can present challenges to financial analysts. Different models can be used to arrive at the closest estimate of value and yet certain issues will always arise. This case attempts to tackle two approaches in real asset valuation: Discounted Cash Flow (DCF) analysis and the issues surrounding such, as well as the Black-Scholes Model for Real Options. Questions to be addressed in the study are: 1. Evaluate Amoco’s and Apache’s corporate objectives and strategies. Is it reasonable to expect that the MW properties are more valuable to Apache than to Amoco? What sources of value most plausibly account for the difference between buyer and seller? 2. Structure and execute a DCF valuation of all the MW reserves. How much are the reserves worth? Is your estimate more likely to be biased high or low? What are the sources of bias? 3. How would you structure an analysis of MW as a portfolio of assets in place and options? Specifically, which parts of the business should be regarded as assets in place and which as options? What kinds of options are present? Should this approach yield a higher or lower value that the DCF approach? 4. Execute the analysis you structured in...

Words: 996 - Pages: 4

Financial Analysis

...2 Graduate Thesis By Teia R. Merring Copenhagen Business School Strategic and financial analysis and valuation of B&O 0 1 Executive Summary................................................................................2 Introduction............................................................................................6 1.1Motivation.................................................................................................................. 6 1.2Problem Specification................................................................................................ 8 1.3Problem Identification................................................................................................ 8 1.4Problem Handling .................................................................................................... 10 1.5Structure and Methodology...................................................................................... 12 1.5.1Introduction and Presentation........................................................................... 12 1.5.2Strategic Analysis............................................................................................. 12 1.5.3Financial Statement Analysis ........................................................................... 13 1.5.4Prognoses and Budgets..................................................................................... 14 1.5.5Valuation.......................................

Words: 60014 - Pages: 241

Asgxb

...on the corresponding valuation date of every Individual; Hindu Undivided Family and Company at the rate of 1% of the amount by which the net wealth exceeds Rs.15 Lakhs. Education Cess of 3% is not leviable on the amount of Wealth Tax. Applicability of wealth tax:  1.  Individual: The following persons treated as ‘individual’ u/s 3 of the wealth tax. a) Legal hires of an Individual. b) Holder of an impartible estate. c) Hindu deities (it means formal a god/goddess ) d) Trustees of a trust who are liable u/s 21A. e) Trade unions  2.  HUF  3.  Company  4.  AOP chargeable u/s 21AA : Situation Shares of members of an AOP are determinate or known. Shares of members of an AOP are indeterminate or unknown. Wealth Tax assessment Interest of members in the assets of the AOP shall be valued as per Rule 16 and 17 of Schedule III. Wealth tax is levied on the AOP. It is liable to tax at the rate leviable upon and recoverable from an individual who is any Indian citizen and resident. Valuation Date: Sec.2 (q): It refers to the 31st March immediately preceeding the assessment year. This provision does not apply to – a. Company registered U/s 25 of the companies Act, 1956 b. Co­operative society and c. Any social club d. Any political party e. Any mutual fund U/s 10(23D) CHARGEABILITY Individual HUF / Companies Nationality Residential Status Location of assets as on the valuation date Residential Status Location of assets as on the valuation......

Words: 12386 - Pages: 50

Free Essay

Fsdfsd

...a multiples analysis, calculating and defending an estimate of Crocs value. Soln: Comparable companies analysis – Done to determine appropriate valuation multiple for Crocs, Inc. • • Selected peer group based on industry, business and financial characteristics Included explosive growth stocks such as Lulelemon & Under Armour having similar prospects for growth and ROIC as Crocs, Inc. and some mature, stabilized businesses with stable industry growth rates – Nike, Deckers & Timberland. This mix will help us provide valuation from an aggressive sales growth and maturing sales context. Some characteristics used in selection include – o Primary or at least significant portion of business revenue comes from footwear & apparel – analogous to Crocs primary business o Has product appeal to large group of customers o Has distinct product attributes (innovative/creative) and differentiation from competition o Has wide range of distribution channels o CAGR Sales growth, COGS to Sales & Significantly less debt exposure on their balance sheets o Have characteristics of high octane growth and show signs of maturity and stabilizing long-term growth similar to well established footwear brands. • Valuation Multiples The objective was to compare operating metrics and valuation multiples in a peer group to that of Crocs, Inc. for equity valuation. The market multiple model is based on the idea that on average, a company, over time would have roughly the same value as its peers.......

Words: 2072 - Pages: 9

Words: 317 - Pages: 2

Hanson

...ultimately reduced their business risk. In analyzing the financial risk, the continuous acquisitions have definitely increased the operational risk for the company. Since the case didn’t provide us with the financial statements for Monmouth, we can assume that in order to complete the acquisition they have to issue stocks as they exhausted (or will pretty soon exhaust) their debt capacity. 2. Based on the DCF valuation and using a WACC of 8.25% (the beta assumed to be 1, the average beta of comparable firms and the coupon rate to be 7.96%, the rate for BB rated companies) and a growth rate of 5.5%. The fair price is \$40.4 per share for Robertson, lower than the \$50 offered by Simmons to sell their stocks but higher than the current market price of \$30. As for the peer multiples, and due to the lack of information for the comparable companies we only managed to calculate the EBIAT multiple, the earnings multiple and the book value multiple using the three comparable companies, Actuant Corp, Snap On Inc., and Stanley Works. The result of the multiple valuation showed a fair price of \$40.1 per share based on the EBIAT multiple and a value of \$29.61 per share based on the earnings multiple. Both prices are below the fair price calculated by the DCF. Only the book value multiple exceeded the DCF fair value with a value of \$65.25. The first two multiples failed to capture the future potential and growth of the corporation, where the DCF managed to include it as a factor in......

Words: 681 - Pages: 3

Fair Value

...According to 820-10-35-54-c, it was reasonable to determine that market is not active. Because the adjustments were based on management’s assumption, FFC didn’t used level 1 inputs in the income approach valuation technique (present value technique). In addition, significant adjustment inputs includes credit adjustment (level 3 inputs) and liquidity risk adjustment (level 3 inputs), and implied rate of return (level 2 inputs) under ASC 820-10-35-48/52. According to ASC 820-10-35-37A, when the inputs are categorized within different levels of the hierarchy, the entire instrument should be in the same level of hierarchy as the lowest level inputs that is significant to the entire measurement. So, CDO should be categorized within level 3 of the fair value hierarchy. Instrument 2 There was no significant decrease in the volume and activity for the MBS, because no significant factors occurred. Therefore, the market should be still active, even the market became increasingly volatile with some declined activity in the Q4 2012. In my opinion, FFC should still use market approach valuation because (1) quoted prices were highest priority inputs in accordance with ASC 820-10-35-37 (2) the theoretical income-approach pricing model needed significant assumption. In the market approach valuation, quoted prices for the similar observed transactions was level 2 inputs. Then, FFC should classify the MBS into level 2 of the fair value hierarchy. Instrument 3 According to...

Words: 775 - Pages: 4

Ias 36 Criticism and Amendments

...• IMPAIRMENT OF ASSETS: A GUIDE TO APPLYING IAS 36 IN PRACTICE. • PUBLISHED IN MARCH 2014. Explanation of the basis of key assumptions and the valuation approach used to determine the recoverable amount (IAS 36.132(encouraged), 134(d)(i)-(v), (e)(i)-(v), 135(d)) • Key assumptions usually left out. • If discussed they were not sufficient. • Key assumptions include gross margin, government bond rates, exchange rate for the period, raw material price, inflation, market share, etc. • Comparative information is required Where goodwill or indefinite life intangibles have been allocated to a CGU (or group of CGUs), but no impairment has been recognized, reasonably possible changes in assumptions if such changes would cause the unit’s carrying amount to exceed its recoverable amount (IAS 36.134(f), IAS 36.135(e)) • Sensitivity Analysis is not provided. • If provided, it is not consistent. • If book value increases, investors would expect a clear sensitivity analysis. • sensitivity analysis should incorporate all key assumptions (beyond discount rate and growth rate) . Description of the entity’s CGU when it recognises or reverses an impairment loss for the CGU during the period (IAS 36.130(d)(i)) • Disclosures did not provide description. • If they did, they lacked substance. • Users did not have an idea of the impact of the impairment on the financial activities. Explanation of the events and circumstances that contributed to the impairment loss or reversal (IAS......

Words: 403 - Pages: 2

Free Essay

Accounting Case

...After reading the case, we need to figure out three questions, which are a. FFC’s determination of whether the respective markets for the instruments were active or inactive and whether there was a significant decease in the volume and level of activity for the instruments. b. The valuation technique used by FFC c. The classification in the fair value hierarchy for each input into the fair value measurement and how these classifications affects classification in the fair value hierarchy of the entire instrument. We will answer these questions by each instrument separately: First, Collateralized Debt Obligation (CDO) Before September30th, 2010, FFC was in an active market, and it determined the fair value of the CDO by using a market-based valuation technique that relies on inputs such as quotes prices for similar CDO securities and requires only insignificant adjustments. After that, there was a significant decrease in the volume and level of activities and the CDO’s market was not active. Besides, significant adjustments are required to determine fair value as of the measurement date given the lack of recent and relevant transactions. The valuation techniques FFC used for CDO is income approach, because this way could maximize the use of relevant observable input and minimize the use of unobservable inputs. There are two factors FFC mainly considered in the fair value measurement. Frist, FFC considered the implied rate of return on September 30, 2010,......

Words: 470 - Pages: 2

Fin/Gm571 Week 2 Text Problems

...rate of return for Bill: n = 4 r = ? PV = -\$195,000 PMT = 0 FV = \$168,000 r = ? PV = r = -3.66% A11. (Calculating the PV and FV of an annuity) Assume an ordinary annuity of \$500 at the end of each of the next three years. a. What is the present value discounted at 10%? b. What is the future value at the end of year 3 if cash flows can be invested at 10%? a. to get present value: n = 3 r = ? PV = ? r = 10% PMT = \$500.00 FV = 0 PV = PV = \$1,243.43 b. to get future value: n = 3 r = ? PV = 0 r = 10% PMT = \$500.00 FV = ? FV= FV = \$1,655 Chapter 5 A1. (Bond valuation) A \$1,000 face value bond has a remaining maturity of 10 years and a required return of 9%. The bond’s coupon rate is 7.4%. What is the fair value of this bond? Calculating PV factor i= required return = 9% = 0.09 n= 10 years Coupon Rate to get value Annuity Cash Flow of \$1000 to get present value Cash flow= \$1000 * 7.4/100 = \$74 Cash flow=...

Words: 524 - Pages: 3

Csv Forcasting and Risks

...INTRODUCTION To value the business we need to forecast some or all of the following depending upon which model of valuation we intend to use: dividends, future free cash flows, earnings per share, EVA which itself requires NOPAT and the Balance Sheet. Note that even if we are interested in cash flows we will usually forecast these using the indirect method rather than the direct method because the basic building blocks of profitability, growth, investment and financing are more readily framed in terms of accrual based accounting and moreover corporate tax is profit based – ultimately we are interested in the prospects for profitability. We should use at least two methods of valuation to value a company and in any one method look to undertake some sensitivity analysis or scenario analysis. The forecasting should be comprehensive and be conditional upon the corporate and business strategy, the accounting analysis and the financial analysis. Importantly, the forecasts should impound the evidence on key financial variables such as sales growth, EPS over time and ROE over time.EVIDENCE ON SALES GROWTH AND EARNINGS We begin with some evidence which is useful in the context of a forecast. But do remember this is what occurs on average. If the forecast is largely at variance from the evidence then this will need explaining within the context of the business strategy or the accounting. In addition if strategy or accounting changes we need to assess the consequences for the forecast...

Words: 302 - Pages: 2

Acca

...f92007 2008 2009 2010 2011 2012 2013 Pilot Dec Jun Dec Jun Dec Jun Dec June Dec Jun Dec Jun Funding of working capital 3 3 4 2 2 3 Overtrading 2 Cash management 3 1 2 Receivables management 3 4 3 2 1 3 2 2 3 Inventory management (EOQ) 4 3 3 4 2 NPV with inflation and/or tax 4 2 4 3 2 3 1 1 1 1 1 Return on capital employed 4 2 1 Payback period 2 Lease or buy 1 Capital rationing 1 1 Replacement 1 3 1 Internal rate of return 4 2 4 2 1 Risk and uncertainty 2 1 1 1 Sources of finance 2 4 4 2 3 3 3 4 Rights issue 3 2 1 4 3 4 Dividend policy 3 4 3 Theories of gearing 1 1 2 Weighted average cost of capital 1 1 3 1 2 2 4 2 3 4 3 2 Capital asset pricing model 1 3 2 4 1 4 2 Share / business valuation 1 2 1 1 2 4 3 4 4 4 Market efficiency 1 2 2 Forecasting exchange rates 2 4 3 Foreign exchange risk management 2 4 4 3 3 4 3 3 Interest rate risk 2 3 Financial ratios 1 3 2 4 2 4 Please do read the following notes carefully: 1 The purpose of this table is to help you find which questions to practice for specific topics. Do not use this table to try and predict what will be in the next exam - the examiner does deliberately repeat topics! The numbers in the columns are the question number in the exam. Many questions cover more than one area of the syllabus - that is why the same question number sometimes appears more than once, 2 For latest course notes, free audio & video lectures, support and forums please visit...

Words: 314 - Pages: 2