L9 - Binomial OPM and Option to Delay

L9 - Binomial OPM and Option to Delay - FINS3641 SAV Week...

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Unformatted text preview: FINS3641 SAV Week 10: Binomial OPM and Valuation Implication of the Option to Delay FINS3641 SECURITY ANALYSIS AND VALUATION PART 4 CONTINGENCY CLAIM VALUATION MODELS Week 10 Binomial Option Pricing Model Valuation Implication of the Option to Delay Topics: The binomial option pricing model explained Application of option pricing models to the valuation of patents and undeveloped reserves in natural resources Learning Outcomes: Learn how best to value patents and undeveloped reserves of natural resources Reading: Damodaran Chapters 5, 28 1 FINS3641 SAV Week 10: Binomial OPM and Valuation Implication of the Option to Delay The Binomial Option Pricing Model Step 1: Set the number of evaluation periods between inception (when the real option is 1st available on the table) and option maturity (last chance to exercise the real option before it becomes obsolete) If you increase the number of discrete periods, the paths taken by the underlying asset will become more continuous and contain less jumps Step 2: Determine the “Value” of the underlying asset price paths: there are 2 periods and 6 nodes (A to F) in the following display t = 0 t = 1 t = 2 D SUU=100 B SU=70 A S = 50 E SUD=50 C SD=35 F SDD=25 2 FINS3641 SAV Week 10: Binomial OPM and Valuation Implication of the Option to Delay The Binomial Option Pricing Model (cont’d) Step 3: Look up the risk free rate (one may form a perfectly hedged portfolio to remove option risk, hence can’t use any rate higher than the risk free rate to discount the future cash flows of the real option): suppose rf = 11% per period Step 4: Compute the value of the corresponding call option at each node starting from the very last period and work backwards to the current point in time Suppose we are pricing a call option with an exercise price of $40 and 2 periods left to maturity Stock Call option D D SUU=100 B SU=70 CUU=60 B CU=33.96 E SUD=50 E CUD=10 When t = 2, i) Node D (SUU = 100, X = 40): CUU = max (0, 100‐40) = $60 ii) Node E (SUD = 50, X = 40): CUD = max (0, 50‐40) = $10 When t = 1, i) Node B: CU Δ units of shares – Borrowing. One period later at t = 2, if stock price takes on SUU, the synthetic call or the replicated portfolio is worth Δ × SUU – B(1+rf) = 100 Δ ‐ 1.11 B CUU = 60 SUD, the synthetic call or the replicated portfolio is worth Δ × SUD – B(1+rf) = 50 Δ ‐ 1.11 B CUD = 10 Solving Δ = 1 and B = 36.04. Hence CU = 1 × 70 – 36.04 = $33.96 3 FINS3641 SAV Week 10: Binomial OPM and Valuation Implication of the Option to Delay The Binomial Option Pricing Model (cont’d) Stock Call option C SD=35 E SUD=50 F 25 C CD=4.99 E CUD=10 F CDD=0 When t = 2, i) Node E (SUD = 50, X = 40): CUD = max (0, 50‐40) = $10 ii) Node F (SDD = 25, X = 40): CUU = max (0, 25‐40) = $0 When t = 1, i) Node C: CD Δ units of shares – Borrowing. One period later at t = 2, if stock price takes on SUD, the replicated portfolio is worth Δ × SUD – B(1+rf) = 50 Δ ‐ 1.11 B CUD = 10 SDD, the replicated portfolio is worth Δ × SDD – B(1+rf) = 25 Δ ‐ 1.11 B CDD = 0 Solving Δ = 0.4 and B = 9.01. Hence CD = 0.4 × 35 – 9.01 = $4.99 4 FINS3641 SAV Week 10: Binomial OPM and Valuation Implication of the Option to Delay The Binomial Option Pricing Model (cont’d) Stock Call option A S=50 B SU=70 C SD=35 A C=19.78 B CU=33.96 C CD=4.99 When t = 0, i) Node A: C Δ units of shares – Borrowing. One period later at t = 1, if stock price takes on SU, the replicated portfolio is worth Δ × SU – B(1+rf) = 70 Δ ‐ 1.1 B CU = 33.96 SD, the replicated portfolio is worth Δ × SD – B(1+rf) = 35 Δ ‐ 1.1 B CD = 4.99 Solving Δ = 0.8278 and B = 21.61. Hence C = 0.8278 × 50 – 21.61 = $19.78 You may ask why we study the binomial model and then turn to the next few pages to realise that we are using the BS model instead! Since the BS model is for European options with no early exercise feature, we know its value is lower than the value computed by other models that allow for early exercise, allowing analysts to arrive at the lower bound and a conservative estimate of the value of the option and/or the firm. 5 FINS3641 SAV Week 10: Binomial OPM and Valuation Implication of the Option to Delay Uncovering Options Embedded in Projects / Investments / Acquisitions i) Option to delay taking up an investment: A firm has an exclusive right to develop and market a patented product such as pharmaceuticals for a specified period of time ‐ Biota was incorporation in 1985 to commence R&D on a flu vaccine. It wasn’t until 1989 that Zanamivir, the world's first neuraminidase inhibitor, was discovered. (R&D expenses the premium paid to acquire the exclusive right to develop the patented drug called “Relenza”) Biota signed the licence and development agreement with the Glaxo Group for Zanamivir in 1990, commenced clinical trial in 1993 and received FDA approval in 1999 for use of Relenza in treating influenza. (Monies spent on the agreement, various stages of clinical trial, and getting regulatory approval exercise price paid to commence the development of Relenza) The flu vaccine “Relenza” was launched and sold around the world later in the same year as the drug received FDA approval (Royalties obtained from the sale of Relenza cash flows from the project; In this example, Biota opted not to delay the production and sale of the patented drug Relenza) mine undeveloped resources due to its possession of a tenement for a specified period of time – think Fortescue on the purchase of its first tenement in 2003 and followed through by the geological reports ( the premium paid to acquire the exclusive right to mine the proven deposits) before putting the infrastructure (housing, roads, rails and ports) and plants & equipments in place to facilitate the commencement of mining in 2005 ( pay the exercise price to exercise the right to mine the land) 6 FINS3641 SAV Week 10: Binomial OPM and Valuation Implication of the Option to Delay Uncovering Options Embedded in Projects / Investments / Acquisitions (cont’d) ii) Option to expand a seed investment: A firm may invest in a project/acquisition that may lead to further investment to expand the scale of the existing project/acquisition and/or embark on other opportunities. Think BHP’s acquisition WMC in 2005 and the subsequent documentation in 2006 of the expansion option provided by the Olympic Dam iii) Option to abandon an investment if the cash flows do not measure up (will provide local examples in the next lecture) Why do we have to identify, study and value these real options separately? What fails the traditional NPV analysis? Traditional capital budgeting / NPV analysis fails to consider fully the value of the above options: i) It just answers the question of whether the project is a “good” one if taken today, i.e., accept if the project’s NPV > 0 or IRR > hurdle rate, and decline if the project’s NPV < 0 or IRR < hurdle rate ii) It does not answer the question of whether the project is a “good” one if taken at a later date. NPV analysis “ignores” the fact that a project may have an embedded option to delay, expand or abandon. Hence it doesn’t incorporate the time value of the embedded option into the analysis a “bad” project by the standard of the NPV analysis today may in fact be a “good” one had the time value of the embedded option been incorporated into the analysis. (NB: We emphasize on “ignore” to inform readers that the traditional NPV analysis is silent, i.e., does not say the rights to this project are worthless) 7 FINS3641 SAV Week 10: Binomial OPM and Valuation Implication of the Option to Delay Interpreting / Presenting the Option to Delay as a Call Option Options that are currently out of the money with –ve NPV today do not mean these options are worthless due to the time value (option to delay) of these options. X = Upfront investment cost upon the decision to exercise the real option i. ii. iii. iv. v. vi. vii. Exclusive Right: to develop and market a patented product; to mine the underground resources for the next n years Premium: the cost incurred to acquire the exclusive right, e.g. expenses spent on R&D for Biota’s flu vaccine; money paid by Fortescue for the tenement and geological surveys BEFORE the GO AHEAD. Current Value of the Underlying asset: PV(expected cash flows) of the developed product, e.g. royalties expected from the sales of pharmaceuticals; net profit expected from sales of proven resources Exercise Price: Upfront investment costs to develop the product/resource, e.g., costs associated with clinical trials, license agreement and regulatory approvals for pharmaceuticals; costs to put infrastructure and P&E in place for mining Time to Maturity (n): the time the firm can hold off competition for pharmaceuticals; the time left for the exclusive mining right Cost of Delay: the loss of cash flows from project delay. e.g., charge a div. yield of 1/n to ensure that firms don’t sit on patents until the very last day of its life. Once a patent is viable, not exercising creates a cost. Volatility (the most difficult to estimate): Variance in cash flows from similar products in the past Variance in present values from capital budgeting simulations Average variance of values of firms in the same industry 8 FINS3641 SAV Week 10: Binomial OPM and Valuation Implication of the Option to Delay Valuing a Product Patent: Avonex Biogen, a bio‐technology firm, has a patent on Avonex, a drug approved by FDA to treat multiple sclerosis, for the next 17 years, and it plans to produce and sell the drug by itself. The key inputs on the drug are as follows: S = PV of Cash Flows expected from Introducing the Drug Now (from capital budgeting) X = Initial Cost of Developing the Drug for Commercial Use today (from capital budgeting) t = Patent Life r = Riskless Rate (17‐year T.Bond rate) 2 = Variance in PV of Expected CFs (average variance in firm value for listed bio‐tech firms) y = Expected Cost of Delay = 1/17 = $ 3.422 billion = $ 2.875 billion = 17 years = 6.7% = 0.224 = 5.89% d1 = 1.1362 d2 = ‐0.8512 N(d1) = 0.8720 N(d2) = 0.2076 Call Value= 3,422 × e(‐0.0589)(17) × (0.8720) ‐ 2,875 × exp(‐0.067)(17) × (0.2076)= $ 907 million which is made up of: NPV = option intrinsic value = immediate exercise value = max (0, 3422m – 2875m) = $547 m The time value of the option = C – intrinsic value = 907 – 547 = 360 m In summary the current value of the drug as: i) a patent with the embedded option to delay commercialization on the basis of Option Valuation = $907 m ii) a commercial product on the basis of traditional capital budgeting or NPV analysis (which ignores the time value of the option to delay commercialization) = $547 m iii) The difference in the current value of the drug obtained by the two valuation approaches is due to the time value of the option to delay = $360 m 9 FINS3641 SAV Week 10: Binomial OPM and Valuation Implication of the Option to Delay Patent Life and the Last Moment to Exercise In this graph, the BS model is used to compute the value of the drug as a patent annually for the remaining 17 years of patent life using a different dividend yield (y) and the reduced time left for the exclusive right (t) while holding other inputs constant, i.e., Figure 28.4: Patent value versus Net Present value 1000 900 800 Exercise the option here: Convert patent to commercial produc 700 600 Today, y = 1/ 17 and t = 17 1 yr later, y = 1/ 16 and t = 16 2 yr later, y = 1/ 15 and t = 15 … 16 yr later, y = 1 and t = 1 500 400 300 200 100 0 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Number of years left on patent Value of patent as option Net present value of patent The BS values are then compared to the NPV of the drug as a commercial product to determine the optimal timing to exercise the option. Should Biogen develop the drug now or wait? Since the drug is currently worth more as a patent ($907m) than as a commercial product ($547m), Biogen may wait. Other things being equal, the drug will worth more as a commercial product than as a patent in about 9 years’ time. Hence, they is no further reason to delay the commercialization of Avonex by that time. In practice, competition for the development of a MS drug may cut short the delay and the life of the exclusive right, and force Biogen to fast track the development and stay ahead of its competitors. 10 FINS3641 SAV Week 10: Binomial OPM and Valuation Implication of the Option to Delay Valuing a Firm with Patents: There are two approaches to value of a firm with i) ii) iii) a mixture of patented products already in commercial production, exclusive rights to a number of patents yet to be commercially developed, and ongoing R&D that may potentially lead to a pipeline of future patents Approach No. 1: Value based on conventional DCF valuation where the growth rate in future cash flows and estimated period of growth takes into consideration the 2nd and 3rd components Best for established firms that have significant assets in place, dozens of patents that have been approved and/or in the pipeline Approach No. 2: Value of commercial products (using DCF valuation) + Value of existing patents (using option pricing) + (Value of New patents that will be obtained in the future – Cost of obtaining these patents) Best for small firms with little assets in place and just one or two patents that have been approved For the 1st component on commercial products using DCF valuation discount the cash flows expected over their commercial lives by the cost of capital be conservative about the growth rate applied to the CFs to avoid double counting the 2nd & 3rd components For the 2nd component on existing patents, apply the option pricing model to value each patent separately information is harder to get and typically proprietary known only to the managers of the firm For the 3rd component, will have a zero value if the firm earns its cost of capital from R&D require data on the firm’s past successes and failure to determine the ratio of the value of patents to the amount spent on R&D, hence harder to estimate for young firms 11 FINS3641 SAV Week 10: Binomial OPM and Valuation Implication of the Option to Delay Applying the 2nd Approach to Biogen 1st Component ‐ Value of Biogen’s Existing Products: Biogen had two commercial products, a drug to treat Hepatitis B and Intron. At the time of this valuation, the drugs were licensed to other pharmaceutical firms. The license fees were expected to generate $ 50 million in after‐tax cash flows each year for the next 12 years. Since these cash flows were guaranteed contractually, the pre‐tax cost of debt of 7% of the licensing firms was used (i.e., the payment is ranked ahead of the shareholders of the licensing firms and we only need to consider the default risk of the licensing firms): Present Value of License Fees = $ 50 million (1 – (1.07)‐12)/.07 = $ 397.13 million 2nd Component ‐ Value of Biogen’s Existing Patent = $ 907 m (page 9) 12 FINS3641 SAV Week 10: Binomial OPM and Valuation Implication of the Option to Delay 3rd Component ‐ Value of Biogen’s R&D: Biogen continued to fund research into new products, spending about $ 100 million on R&D in the most recent year. R&D expenses were expected to grow 20% a year for the next 10 years, and 5% thereafter. It was assumed that every dollar invested in research would create $ 1.25 in value in patents (refer to the textbook for estimation of this figure using return and cost of capital) for the next 10 years, and break even after that (i.e., every $ 1 invested in R&D would generate $ 1 in patent value). Given the significant amount of risk for this component, the cost of capital was estimated to be 15% on the basis of the average cost of equity of young listed biotech firms with no revenue from commercial products. Yr Value of R&D Cost Excess Value Present Value Patents (at 15%) 1 $ 150.00 $ 120.00 $ 30.00 $ 26.09 2 $ 180.00 $ 144.00 $ 36.00 $ 27.22 3 $ 216.00 $ 172.80 $ 43.20 $ 28.40 4 $ 259.20 $ 207.36 $ 51.84 $ 29.64 5 $ 311.04 $ 248.83 $ 62.21 $ 30.93 6 $ 373.25 $ 298.60 $ 74.65 $ 32.27 7 $ 447.90 $ 358.32 $ 89.58 $ 33.68 8 $ 537.48 $ 429.98 $ 107.50 $ 35.14 9 $ 644.97 $ 515.98 $ 128.99 $ 36.67 10 $ 773.97 $ 619.17 $ 154.79 $ 38.26 $ 318.30 13 FINS3641 SAV Week 10: Binomial OPM and Valuation Implication of the Option to Delay Combined Value of Biogen: The value of Biogen as a firm is the sum of all three components – $ 397.13 million, the present value of cash flows from existing products, + $ 907 million, the value of existing patents in Avonex (as an option) and + $ 318.30 million, the value of future patents created by future R&D: = $1622.43 million Since Biogen had no debt outstanding, value per share = firm value ÷ the number of shares outstanding (35.5 million) = $ 1,622.43 million / 35.5 = $ 45.70 Valuation Issues: i) If a firm has a significant number of equity options outstanding to management, subtract the option value from the firm value before dividing the difference by the number of shares outstanding. ii) This approach is best for firms that have little established assets in place and derive the bulk of their value from one or two patents like Biota iii) This approach is not appropriate for firms like Merck and Pfizer (US) and CSL (Aust) which have a portfolio of commercial products and patents, why? The need to estimate future CFs and is already hard enough for one patent These firms do not derive their value from the options attached to their patents but from their much more conventional capacity to generate cash flows. 14 FINS3641 SAV Week 10: Binomial OPM and Valuation Implication of the Option to Delay Estimating Inputs for Options to Mine Undeveloped Natural Resource: Input Estimation Process 1. S: Value of Estimated Reserves of the Natural Resource Expert (Geologist) estimates of the quantity of reserves × (current unit price – current unit variable cost) where variable cost includes the cost of production, State and Federal taxes and duties/royalties Costs associated with making the site operational - transport facilities and infrastructure, plants and equipments 2. X – Estimated Cost of Developing the Reserve 3. t - Time to Expiration 4. – Volatility in value of underlying asset 5. y - Net Production Revenue, Dividend Yield or Cost of Delay 6. Development Lag Relinquishment Period for sites that are leased for a fixed period, t = the life of the lease. Otherwise, Time to exhaust inventory – divide the estimated quantity of reserves by the capacity output rate Based on both the variability of the price of the resources and variability of available reserves (While some portion of reserves may have already proven, the rest may be likely. Hence we may see a range of potential reserves) Annual cash flow generated every year as a percentage of the market value of the reserves. The time lag between the decision to extract the natural resource and the actual extraction. Discount S, the value of estimated reserves, by the expected loss of cash flows during the development period. 15 FINS3641 SAV Week 10: Binomial OPM and Valuation Implication of the Option to Delay Valuing an Oil Reserve Consider an offshore oil property with the following information and estimates: Estimated oil reserve of 50 million barrels of oil the marginal value per barrel of oil is $12 per barrel currently (Price per barrel ‐ marginal cost per barrel) the development lag is two years the present value of the development cost is $12 per barrel (or $600 mil ÷ 50 mil barrels) t the firm has the rights to exploit this reserve for the next twenty years y once developed, the net production revenue each year will be 5% of the value of the reserves. rf the riskless rate is 8% the variance in oil prices is 0.03. The above translates into the following inputs for option valuation: S discount the value of the estimated reserves by the length of the development lag at the dividend yield = (50 m barrels × $12 margin per barrel) / (1.05)2 = $ 544.22 million X = Present Value of development cost = $12 * 50 m = $600 million Using the BS model: d1 = 1.0359 N(d1) = 0.8498 d2 = 0.2613 N(d2) = 0.6030 (‐0.05)(20) (‐0.08)(20) Call Value = 544 .22 exp (0.8498) ‐ 600 (exp (0.6030) = $ 97.08 million ($0 intrinsic value + $ 97.08 mil time value) Summary: On the basis of traditional capital budgeting analysis, the property is a poor investment and will take value from the firm if accepted since NPV or $544.22 m – $600 m < 0. On the basis of option valuation, although the property is currently out of the money since S < X or 544.22 m < 600 m, it is a valuable property because of the option time value, i.e., the potential to create value if oil prices go up. Pay no more than 97.08 million for the oil property. 16 FINS3641 SAV Week 10: Binomial OPM and Valuation Implication of the Option to Delay Extending the option pricing approach to value firms with undeveloped reserves Below are the arguments to apply and how best to apply option pricing models to value natural resource firms We may consider the undeveloped assets owned by a natural resource company as options and hence apply option pricing model to value the firm, i.e., the firm is a portfolio of options to mine and develop natural resources. For stock options, you know an index option is cheaper than the sum of individual stock options written on the constituent stocks. Due to diversification, the index has lower a variance than the sum of individual stock variances and hence a lower premium. For real options on natural resources and for firms with hundreds of sites producing the same natural resource, it will be easier if we group all the assets as a portfolio of assets value the firm as a (single) option written on a portfolio of assets rather than valuing each asset as a separate option and adding all the separate options to arrive at the value of the firm. Why is this portfolio approach acceptable and why won’t it underestimate the aggregate value of the various sites? The assets are perfectly correlated with regard to the price of the underlying resource. Hence there won’t be any diversification benefit, i.e., value of the option written on a portfolio of asset = the sum all the options written on individual assets. Similarly, for natural resource firms with multiple resources, separate the assets that mine different resources into different groups value each group of assets as an option written on a portfolio of assets producing a common resource sum up the value of options written on different groups of assets to arrive at the value of the firm. 17 FINS3641 SAV Week 10: Binomial OPM and Valuation Implication of the Option to Delay Estimating Inputs for Firms with (Multiple) Undeveloped Reserves: Input to model Value of underlying asset Exercise Price Time to expiration on option Riskless rate Variance in value of asset Dividend yield / cost of delay Corresponding input for valuing firm The sum of estimated values of reserves from various sites owned by the firm, discounted back at the dividend yield for the development lag. Estimated cumulated cost of developing all the reserves today Weighted average relinquishment period across all reserves owned by firm or estimate of when reserves will be exhausted, given current production rates. Riskless rate corresponding to the life of the option Variance in the price of the natural resource Estimated annual net production revenue as a percentage of the value of the reserve. 18 FINS3641 SAV Week 10: Binomial OPM and Valuation Implication of the Option to Delay Valuing Gulf Oil’s Undeveloped Reserves Consider the following information that was made public in early 1984 when Gulf Oil was a takeover target It had estimated (undeveloped) reserves of 3038 million barrels of oil price of oil was $22.38 per barrel; production cost, taxes & royalties were estimated at $7 per barrel. y Gulf was expected to have net production revenues each year of approximately 5% of the value of the developed reserves. The development lag is approximately two years The average cost of developing these reserves was estimated to be $10 a barrel in present value dollars t The average relinquishment life of the reserves is 12 years. rf The bond rate at the time of the analysis was 9.00%. the variance in oil prices is 0.03. The above translates into the following inputs for option valuation: S = Value of estimated reserves discounted back for period of development lag at dividend yield = 3038 * ($ 22.38 ‐ $7) / 1.052 = $42,380.44 X = Estimated development cost of reserves = 3038 * $10 = $30,380 million Using the Black‐Scholes model, 1 = 1.6548 N(d1) = 0.9510 d2 = 1.0548 N(d2) = 0.8542 d (‐0.05)(12) (0.9510) ‐30,380 (exp(‐0.09)(12) (0.8542)= $ 13,306 million Call Value= 42,380.44 exp Summary: DCF analysis would have valued the undeveloped reserves of Gulf oil at $12 billion ($42,308 m – $30380 m) Once again, the higher option value is due to the option time value at ~$1.3 billion (13,306 m ‐12,000 m) 19 FINS3641 SAV Week 10: Binomial OPM and Valuation Implication of the Option to Delay Valuing Gulf Oil Besides the undeveloped reserves, Gulf Oil had free cash flows to the firm from its oil and gas production of $915 million from already developed reserves these cash flows are likely to continue for ten years (the remaining lifetime of developed reserves) The share price was $70. It had 165.30 million shares outstanding, and total debt of $9.9 billion The firm’s WACC was 12.5%. Given the additional assets and information, we may estimate the value of Gulf Oil as follows: Value of undeveloped reserves (from the previous page)# = $ 13,306 million ‐10 = 5,066 million Value of production in place* = $ 915(1 ‐ 1.125 )/.125 Total value of firm = $ 18,372 million Less Outstanding Debt = $ 9,900 million Value of Equity = $ 8,472 million Value per share = $ 8,472/165.3 = $51.25 * There is no option attached to the developed reserves which are valued by traditional DCF models. # Valuing undeveloped reserves as an option implies that a change in volatility in oil prices without any change to its (mean) level of prices will have an impact on the value of oil companies, and more so for those with more undeveloped reserves. 20 ...
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