Barun Kumar De (SmartPlay Technologies)
Abstract:
Option is a financial instruments which gives right to buy or sell of an asset at a pre-determined price at the end of a specified time period (European option) or anytime within a specified time period (American option). To get this right a trader needs to pay a certain amount which is called option price. We can use this option pricing model to decide on different business strategies in IP business. In this process we map the different parameters used in option pricing model are mapped into different investment parameters. Then we apply option pricing model to determine whether one should delay the investment, abandon a project, expand/ contract a project.
Introduction to option:
An option gives buyer right, but not obligation, to buy (call option) or to sell (put option) a financial asset (say share of a company) at an agreed price (strike price) during a certain period of time or on a specific date (exercise date). In European option the right for buy and sell can be executed only on the specific date where as in American option the right can be executed anytime before the exercise date. For this buyer pays a certain amount to the seller which is called price of the option.
On the exercise date, if the share price is more than the exercise price, buyer of call option will exercise the option and will make profit. But if the share price is below the exercise price, then the buyer will not exercise the option. Considering the price which buyer has paid to the seller to purchase the option below is the payoff
Exercise price = K
Share price at the date of exercise = S_{T}
Payoff of the buyer of call option = S_{T } - K, when S_{T }> K
(Without adjusting the price of option) = 0, when S_{T }≤ K
Payoff of the buyer of put option = 0, when ST > K
(Without adjusting the price of option) = K . ST, when ST ≤ K
The pricing of option is determined by Black . Scholes model,
Price for call option c = S_{0}N(d_{1}) - K^{e-rT}N(d_{2}) where
d_{1 }= [ln (S_{0}/K) + (r + σ^{2}/2)T+ / σÂ√T
d_{2 }= d_{1 }- σÂ√T = = [ln (S_{0}/K) + (r - σ^{2}/2)T] / σÂ√T
where
S_{0}= Todayâ€™s stock price
r = continuously compounded risk free rate
σ = stock price volatility
T = option maturity period
K = exercise period
N(x) = cumulative probability distribution for a standardized normal distribution
Price of put option = K^{e-rT}N(-d_{2})- S_{0}N(d_{1})
Application of Real Option:
Option to Abandon an IP: Now let us assume that a company wants to invest in a hard IP (say a PHY). The investment has following stages
- Design of the hard IP, layout, physical verification and GDSII generation â€“ assume USD 450K
- Manufacturing of test chip using shuttle â€“ assume USD 150K
- Characterization of the test chip for electrical and protocol conformance â€“ USD 250K
Also other assumptions are
- Development of the IP will take one year
- The value of expected revenue today is USD 800K with a standard deviation 80%
- Cost of capital for the company is 10%
Now, if we use traditional NPV analysis them
Expected NPV of the project = -450 + 800 â€“ 400 x e^{-0.1}= USD (-12K). As the expected NPV is negative the firm decided not to invest
But the investment on test chip manufacturing and testing of test chip can be treated as option where
K = USD 400K, S_{0}= USD 800K, r = 10%, σ = 80%
So price of the option will be = USD 475K
[d_{1}= (0.693 + 0.42) / 0.8 = 1.39, d_{2 }= (0.693 - 0.22) / 0.8 = 0.59, N(d_{1}) = 0.92, N(d_{2}) = 0.72]
So the expected NPV of the project is = -450 + 475 = USD 25K. As the expected NPV is positive, the firm can decide to invest.
The reason for that the firm has an option of abandon the project and not go for test chip and test chip characterization after one year if the expected revenue decreases.
The probability of abandon = 1 â€“ N(d_{2}) = 1 â€“ 0.72 = 0.28 = 28%
Option to Delay an IP Development: The Black-Schole model of option pricing can be modified for a stock giving dividend at a constant rate of q as follows
For call option = S_{0}e^{-qT}N(d_{1}) â€“ Ke^{-rT}N(d_{2}) with modifies value of d_{1} and d_{2} as follows
d_{1} = [ln (S0/K) + (r - q + σ^{2}/2)T] / σ√T
d_{2} = d1 - σ√T = = [ln (S0/K) + (r â€“ q - σ^{2}/2)T] / σ√T
For put option = Ke^{-rT}N(-d_{2}) - S_{0}e^{-qT}N(-d_{1})
Let us assume that an IP company can buy a patent for an exclusive architecture of an IP at USD 1M and the company expects acquisition of this patent will give them USD 250K additional profit every year for the IP lifetime (say 5 years). But the profit expectation has a standard deviation of 80%. Also the cost of capital for the company is 10%.
So if we apply NPV model then the
Expected NPV = -1000 + 250 (e^{-0.1} + e^{-0.2} + e^{-0.3} + e^{-0.4} + e^{-0.5}) = -1000 + 935 = -65K. As the project has negative NPV the company should not buy the patent
But the company has an option of not investing immediately and to postpone the investment anytime in the 5 years. If the additional profit increases then the company may decide to invest. If we map this in option pricing then K = 1000K, S_{0} = 935K, T = 5, r = 0.1, σ = 0.8, q = 1/5 = 0.2
So d1= 0.577, d2 = -1.21. So the option price = 935 x e-0.2x5 x N (0.577) â€“ 1000 x e-0.1x5 x N (-1.21) = USD 178.79K. Hence it is worthy to buy the patent
Determining Premium needed for Buyout in IP Royalty Deal
In lot of scenarios, IP deal involves royalty payment. Now the revenue from royalty is dependent on the numbers of SoC gets sold in the SoC lifetime. Hence there is uncertainty involved in the royalty amount from both seller and buyer side. To limit their payout buyer of an IP wants buy out option in many of those deals. The buyout option allows buyer to pay a certain amount of money to the seller and stop all future royalty payment. Buyer will go for buyout option when he will see that potential cash outflow from royalty is more than the buyout price. Now seller should charge some money for this buyout option. We can determine the money the seller should charge to buyer using option pricing model.
Let us assume the buyer expect USD 30K revenue each year from royalty for the next 5 years (typically SoC lifetime) with a standard deviation of 50%. The buyout price is USD 125K. The cost of capital for the IP Company is 10%. Hence the buyout option can be viewed as a put option where
S0 = PV of the future royalty payment = 30 (e^{-0.1}+ e^{-0.2}+ e^{-0.3}+ e^{-0.4}+ e^{-0.5}) = USD 112.3K
K = Buyout price = USD 125K, T = 5, σ = 0.5, r = 0.1, q = 1/5 = 0.2
So d_{1 }= 0.016, d_{2}= -1.1
So the price of option = 125 x e-0.1 x 5 x N (1.1) â€“ 112.3 x e-0.2 x 5 x N (-0.016) = USD 45.2K
Hence the IP seller should charge USD 45.2K for the buyout option
Now in real life the future payment from the IP royalty cannot be constant. At the initial stage when the SoC will get introduced in the market the revenue from royalty payment is low. With time as more and more SoC gets sold in the market the revenue from royalty payment increases. Let us assume the growth of the royalty payment is 2% every year. In that scenario
S0 = PV of the future royalty payment = 30 (e^{-0.1+0.02}+ e^{-0.2+0.04}+ e^{-0.3+0.06}+ e^{-0.4+0.008}+ e^{-0.5+0.1}) = USD 118.75K
K = Buyout price = USD 125K, T = 5, Ã³ = 0.5, r = 0.1, q = 0.2 + 0.02 = 0.22
So d_{1}= -0.023, d_{2}= -1.14
So the price of option = 125 x e-0.1x5 x N (1.14) â€“ 118.75 x e-0.22x5 x N (0.023) = USD 45.94K
Author Biography
Barun Kumar De is currently working as Senior Business Development Manager in SmartPlay Technologies. SmartPlay is second largest VLSI design Services Company in India. Barun is involved in IP business and turnkey SoC design services business in SmartPlay. Before that Barun has worked in companies like Wipro, SoftJin, Open-Silicon, Texas Instruments and Atrenta. He has done is B.E. in electronics and telecommunication from Jadavpur University and MBA from IIM Calcutta