# The Option to Delay!

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1 The Option to Delay! When a firm has exclusive rights to a project or product for a specific period, it can delay taking this project or product until a later date. A traditional investment analysis just answers the question of whether the project is a good one if taken today. Thus, the fact that a project does not pass muster today (because its NPV is negative, or its IRR is less than its hurdle rate) does not mean that the rights to this project are not valuable. 26

2 Valuing the Option to Delay a Project! PV of Cash Flows from Project Initial Investment in Project Project has negative NPV in this section Project's NPV turns positive in this section Present Value of Expected Cash Flows on Product 27

3 Example 1: Valuing product patents as options! A product patent provides the firm with the right to develop the product and market it. It will do so only if the present value of the expected cash flows from the product sales exceed the cost of development. If this does not occur, the firm can shelve the patent and not incur any further costs. If I is the present value of the costs of developing the product, and V is the present value of the expected cashflows from development, the payoffs from owning a product patent can be written as: Payoff from owning a product patent = V - I if V> I = 0 if V I 28

4 Payoff on Product Option! Net Payoff to introduction Cost of product introduction Present Value of cashflows on product 29

5 Obtaining Inputs for Patent Valuation! Input Estimation Process 1. Value of the Underlying Asset Present Value of Cash Inflows from taking project now This will be noisy, but that adds value. 2. Variance in value of underlying asset Variance in cash flows of similar assets or firms Variance in present value from capital budgeting simulation. 3. Exercise Price on Option Option is exercised when investment is made. Cost of making investment on the project ; assumed to be constant in present value dollars. 4. Expiration of the Option Life of the patent 5. Dividend Yield Cost of delay Each year of delay translates into one less year of value-creating cashflows Annual cost of delay = 1 n 30

6 Valuing a Product Patent: Avonex! Biogen, a bio-technology firm, has a patent on Avonex, a drug 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: PV of Cash Flows from Introducing the Drug Now = S = \$ billion PV of Cost of Developing Drug for Commercial Use = K = \$ billion Patent Life = t = 17 years Riskless Rate = r = 6.7% (17-year T.Bond rate) Variance in Expected Present Values =σ 2 = (Industry average firm variance for bio-tech firms) Expected Cost of Delay = y = 1/17 = 5.89% d1 = d2 = N(d1) = N(d2) = Call Value= 3,422 exp ( )(17) (0.8720) - 2,875 (exp (-0.067)(17) (0.2076)= \$ 907 million 31

7 The Optimal Time to Exercise! Patent value versus Net Present value Exercise the option here: Convert patent to commercial product 600 Value Number of years left on patent Value of patent as option Net present value of patent 32

8 Valuing a firm with patents! The value of a firm with a substantial number of patents can be derived using the option pricing model. Value of Firm = Value of commercial products (using DCF value + Value of existing patents (using option pricing) + (Value of New patents that will be obtained in the future Cost of obtaining these patents) The last input measures the efficiency of the firm in converting its R&D into commercial products. If we assume that a firm earns its cost of capital from research, this term will become zero. If we use this approach, we should be careful not to double count and allow for a high growth rate in cash flows (in the DCF valuation). 33

9 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 that it had licensed to other pharmaceutical firms. The license fees on these products were expected to generate \$ 50 million in after-tax cash flows each year for the next 12 years. To value these cash flows, which were guaranteed contractually, the pretax cost of debt of the guarantors was used: Present Value of License Fees = \$ 50 million (1 (1.07) -12 )/.07 = \$ million 34

10 Value of Biogen s Future R&D! Biogen continued to fund research into new products, spending about \$ 100 million on R&D in the most recent year. These 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 (valued using the option pricing model described above) for the next 10 years, and break even after that (i.e., generate \$ 1 in patent value for every \$ 1 invested in R&D). There was a significant amount of risk associated with this component and the cost of capital was estimated to be 15%. 35

11 Value of Future R&D! Yr Value of R&D Cost Excess Value Present Value Patents (at 15%) 1 \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$ \$

12 Value of Biogen! The value of Biogen as a firm is the sum of all three components the present value of cash flows from existing products, the value of Avonex (as an option) and the value created by new research: Value = Existing products + Existing Patents + Value: Future R&D = \$ million + \$ 907 million + \$ million = \$ million Since Biogen had no debt outstanding, this value was divided by the number of shares outstanding (35.50 million) to arrive at a value per share: Value per share = \$ 1, million / 35.5 = \$

13 The Real Options Test: Patents and Technology! The Option Test: Underlying Asset: Product that would be generated by the patent Contingency: If PV of CFs from development > Cost of development: PV - Cost If PV of CFs from development < Cost of development: 0 The Exclusivity Test: Patents restrict competitors from developing similar products Patents do not restrict competitors from developing other products to treat the same disease. The Pricing Test Underlying Asset: Patents are not traded. Not only do you therefore have to estimate the present values and volatilities yourself, you cannot construct replicating positions or do arbitrage. Option: Patents are bought and sold, though not as frequently as oil reserves or mines. Cost of Exercising the Option: This is the cost of converting the patent for commercial production. Here, experience does help and drug firms can make fairly precise estimates of the cost. Conclusion: You can estimate the value of the real option but the quality of your estimate will be a direct function of the quality of your capital budgeting. It works best if you are valuing a publicly traded firm that generates most of its value from one or a few patents - you can use the market value of the firm and the variance in that value then in your option pricing model. 38

14 Example 2: Valuing Natural Resource Options! In a natural resource investment, the underlying asset is the resource and the value of the asset is based upon two variables - the quantity of the resource that is available in the investment and the price of the resource. In most such investments, there is a cost associated with developing the resource, and the difference between the value of the asset extracted and the cost of the development is the profit to the owner of the resource. Defining the cost of development as X, and the estimated value of the resource as V, the potential payoffs on a natural resource option can be written as follows: Payoff on natural resource investment = V - X if V > X = 0 if V X 39

15 Payoff Diagram on Natural Resource Firms! Net Payoff on Extraction Cost of Developing Reserve Value of estimated reserve of natural resource 40

16 Estimating Inputs for Natural Resource Options! Input Estimation Process 1. Value of Available Reserves of the Resource Expert estimates (Geologists for oil..); The present value of the after-tax cash flows from the resource are then estimated. 2. Cost of Developing Reserve (Strike Price) Past costs and the specifics of the investment 3. Time to Expiration Relinqushment Period: if asset has to be relinquished at a point in time. Time to exhaust inventory - based upon inventory and capacity output. 4. Variance in value of underlying asset based upon variability of the price of the resources and variability of available reserves. 5. Net Production Revenue (Dividend Yield) Net production revenue every year as percent of market value. 6. Development Lag Calculate present value of reserve based upon the lag. 41

17 Valuing an Oil Reserve! Consider an offshore oil property with an estimated oil reserve of 50 million barrels of oil, where the present value of the development cost is \$12 per barrel and the development lag is two years. The firm has the rights to exploit this reserve for the next twenty years and the marginal value per barrel of oil is \$12 per barrel currently (Price per barrel - marginal cost per barrel). Once developed, the net production revenue each year will be 5% of the value of the reserves. The riskless rate is 8% and the variance in ln(oil prices) is

18 Inputs to Option Pricing Model! Current Value of the asset = S = Value of the developed reserve discounted back the length of the development lag at the dividend yield = \$12 * 50 /(1.05) 2 = \$ (If development is started today, the oil will not be available for sale until two years from now. The estimated opportunity cost of this delay is the lost production revenue over the delay period. Hence, the discounting of the reserve back at the dividend yield) Exercise Price = Present Value of development cost = \$12 * 50 = \$600 million Time to expiration on the option = 20 years Variance in the value of the underlying asset = 0.03 Riskless rate =8% Dividend Yield = Net production revenue / Value of reserve = 5% 43

19 Valuing the Option! Based upon these inputs, the Black-Scholes model provides the following value for the call: d1 = N(d1) = d2 = N(d2) = Call Value= exp (-0.05)(20) (0.8498) -600 (exp (-0.08)(20) (0.6030)= \$ million This oil reserve, though not viable at current prices, still is a valuable property because of its potential to create value if oil prices go up. 44

20 Extending the option pricing approach to value natural resource firms! Since the assets owned by a natural resource firm can be viewed primarily as options, the firm itself can be valued using option pricing models. The preferred approach would be to consider each option separately, value it and cumulate the values of the options to get the firm value. Since this information is likely to be difficult to obtain for large natural resource firms, such as oil companies, which own hundreds of such assets, a variant is to value the entire firm as one option. A purist would probably disagree, arguing that valuing an option on a portfolio of assets (as in this approach) will provide a lower value than valuing a portfolio of options (which is what the natural resource firm really own). Nevertheless, the value obtained from the model still provides an interesting perspective on the determinants of the value of natural resource firms. 45

21 Valuing Gulf Oil! Gulf Oil was the target of a takeover in early 1984 at \$70 per share (It had million shares outstanding, and total debt of \$9.9 billion). It had estimated reserves of 3038 million barrels of oil and the average cost of developing these reserves was estimated to be \$10 a barrel in present value dollars (The development lag is approximately two years). The average relinquishment life of the reserves is 12 years. The price of oil was \$22.38 per barrel, and the production cost, taxes and royalties were estimated at \$7 per barrel. The bond rate at the time of the analysis was 9.00%. Gulf was expected to have net production revenues each year of approximately 5% of the value of the developed reserves. The variance in oil prices is

22 Valuing Undeveloped Reserves! Inputs for valuing undeveloped reserves Value of underlying asset = Value of estimated reserves discounted back for period of development lag= 3038 * (\$ \$7) / = \$42, Exercise price = Estimated development cost of reserves = 3038 * \$10 = \$30,380 million Time to expiration = Average length of relinquishment option = 12 years Variance in value of asset = Variance in oil prices = 0.03 Riskless interest rate = 9% Dividend yield = Net production revenue/ Value of developed reserves = 5% Based upon these inputs, the Black-Scholes model provides the following value for the call: d1 = N(d1) = d2 = N(d2) = Call Value= 42, exp (-0.05)(12) (0.9510) -30,380 (exp (-0.09)(12) (0.8542) = \$ 13,306 million 47

23 Valuing Gulf Oil! In addition, Gulf Oil had free cashflows to the firm from its oil and gas production of \$915 million from already developed reserves and these cashflows are likely to continue for ten years (the remaining lifetime of developed reserves). The present value of these developed reserves, discounted at the weighted average cost of capital of 12.5%, yields: Value of already developed reserves = 915 ( )/.125 = \$ Adding the value of the developed and undeveloped reserves Value of undeveloped reserves = \$ 13,306 million Value of production in place = \$ 5,066 million 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 = \$

24 Putting Natural Resource Options to the Test! The Option Test: Underlying Asset: Oil or gold in reserve Contingency: If value > Cost of development: Value - Dev Cost If value < Cost of development: 0 The Exclusivity Test: Natural resource reserves are limited (at least for the short term) It takes time and resources to develop new reserves The Option Pricing Test Underlying Asset: While the reserve or mine may not be traded, the commodity is. If we assume that we know the quantity with a fair degree of certainty, you can trade the underlying asset Option: Oil companies buy and sell reserves from each other regularly. Cost of Exercising the Option: This is the cost of developing a reserve. Given the experience that commodity companies have with this, they can estimate this cost with a fair degree of precision. Real option pricing models work well with natural resource options. 49

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