Economic Models to Value Spectrum Rohit Prasad Associate Professor, MDI Gurgaon International Workshop on Spectrum Management National Institute of Communication Finance April 29, 2013

Agenda Tragedy of the Commons Pricing Practices Difference between market and administered prices Economic Models Reflections on the 2013 auction

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Tragedy of the Commons

What is being valued? The right to exclusively transmit signals for a specified Service Technology Frequency range Geographical area With rules on power levels etc.

Why is it being valued? Why are exclusive rights given? Why are these rights valuable?

Tragedy of the commons If operators are given free access to a scarce resource there will be congestion/overuse and reduction of social welfare – Toll is recommended In the absence of spectrum sensing technology, even without scarcity, there could be congestion (unlike roads) Hence exclusive rights

Why rights valuable? Those given rights earn supernormal profits, and these supernormal profits represent the value of the rights

Example Consider a common pasture of a village where the five people can potentially graze their cattle. Each head of cattle costs Rs. 100 which can be raised at 13% interest. Thus Rs. 13 is the marginal cost of putting another cattle to pasture. As the number increases the value reduces due to the lower availability of pasture per cattle.

No. of cattle Price per cattle at the end of 1 year Average Revenue per cattle Total revenue from grazing Marginal revenue Excess over interest due to bank Exercise 1: How many cattle will graze? Exercise 2: How many cattle should graze?

Solutions Toll – Exercise 3: What should be the toll Privatization – Exercise 4: What is the value of the pasture? No. of cattle Price per cattle at the end of 1 year Average Revenue per cattle Total revenue from grazing Marginal revenue Excess over interest due to bank

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Mechanisms to discover value

Market mechanism – Operators gather data and build models, based on which they place bids in an auction Bureaucratic mechanism – Bureaucrats gather data and build models, based on which they decide on an administered price – May use a discount – Administered price may be different from value

Pricing Practice Captive users use radio frequencies for their communication network not in the business of providing telecom service Commercial users in the business of providing telecom services using radio frequencies Most spectrum in control of government agencies – captive users

Pricing Practice Auctions – License (2G spectrum) in 1995 – Migrated to revenue share in 1999 – License (2G spectrum) in 2001, – 3G, BWA spectrum in to 2012: 2G ‘spectrum price’ benchmarked to value discovered in 2001 auction – administered price progressively diverges from market value

Pricing Practice AuctionAdministered Price Commercial spectrum 1995, 2001, 2010, , Captive spectrumNASince 1980s

Sample Calculation for Captive Spectrum A. Royalty charges for single carrier radio spectrum (Usually below 1 GHz). – Annual Royalty per Carrier (in Rs.) = MxW, where, M is distance factor and W is bandwidth factor – Values of M are: Distance Category Max. Distance (Km) Royalty(in Rs.) I<= II<= III>5 <= IV>25 <= V>60 <= VI>120 <= VII>

Limitations Band neutral Demand neutral Geography neutral Technology neutral

Administered Price for frequencies in 800 MHz band On formula basis: Annual spectrum usage charges = Royalty charges + License Fee Royalty charges for 1 spot frequency of 25 KHz bandwidth per annum is : Rs 4800 (a) To start operation, minimum 5 pairs of frequencies are required, hence royalty charges for 5 pairs of frequencies : 4800x2x5 = 48,000 Rs This 5 pair of frequencies will support a maximum of 450 subscribers/ users. Hence, we have to calculate license fee for 450 hand held or mobile radio sets. License fee for 1 set per annum is : Rs 100 (b) License fee for 450 sets per annum is : 100x450 = 45, 000 Rs Hence, annual spectrum usage charges per annum per 5 pairs of frequencies of 25 KHz bandwidth each : (a) + (b) : 48,000+45,000 = 93,000 Rs

That is annual spectrum usage charges per annum per 125 KHz bandwidth or MHz bandwidth is : 93,000 Rs. Annual spectrum usage charges per annum per 1 MHz bandwidth is : 93,000/0.125 = 7,44,000 Rs This amount is same throughout India. Other alternative use for this band may be for mobile telephony purposes. Through Auction : During November 2012, Government of India put 800 MHz spectrum for auction in 22 service areas. For provision of services, entire India has been divided in to 22 service areas. 5 MHz block of 800 MHz band spectrum was put for auction with the following reserved price in different service areas.

First Time Auction reserve price for 2G spectrum (800 MHz band) Service Area 1st Reserved Price(Rs. Crore ) Per annum price Per annum per 1 MHz price Delhi Mumbai Maharashtra Gujarat Andhra Pradesh Karnataka Tamil Nadu Kolkata Kerala Punjab Haryana Uttar Pradesh (E)

First Time Auction reserve price for 2G spectrum (800 MHz band) Service Area 1st Reserved Price(Rs. Crore ) Per annum price Per annum per 1 MHz price Uttar Pradesh (W) Rajasthan Madhya Pradesh West Bengal Himachal Pradesh Bihar Orissa Assam North East Jammu & Kashmir

There is a wide difference in value of spectrum in different service areas of India – Minimum is Rs 4 lakhs and maximum is 4.5 Rs crores Findings: – As per formula based charges, spectrum charges per annum per MHz are Rs 7,44,000 and they are constant throughout the India If we see the existing usage of this particular band, it is mostly used in Metro service areas only. In metros like Delhi and Mumbai, formula based spectrum charges are very low compared to auction determined or auction reserve price. In type C service areas viz, North East, Assam, Himachal Pradesh, J&K etc, there are no usages and formula based spectrum charges are high compared to auction determined or auction reserve price.

Administered Price for UAS License

Subscriber Linked Criteria Additional spectrum beyond startup amount allocated on the basis on subscriber milestones and attracts additional usage charges

Sample Subscriber Linked Criteria

Difference between market and administered price

Market PriceAdministered Price Based on biddingBased on administrative decision Based on market informationBased on administrative information Does not take social impact into account ( externalities) Takes social impact into account ( externalities) Susceptible to market collusionSusceptible to misuse of discretionary power Administrative pricing in India has tended to be focused on capabilities rather than demand unchanging over long periods (static) rather than responsive to changing conditions ( dynamic) driven by engineers rather than economists Non-transparent

EXTERNALITIES AND MARKET INEFFICIENCY An externality refers to the uncompensated impact of one person’s actions on the well- being of a bystander. Externalities cause markets to be inefficient, and thus fail to maximize total surplus. Two types of externalities 1.Negative : Adverse Impact on the bystander. 2.Positive: Beneficial Impact on the bystander.

Externalities: Examples Negative Externalities: – Automobile exhaust – Cigarette smoking – Carbon emissions of telecom towers Positive Externalities: – Research into new technologies – Diffusion of mobile telephony and data services Provision of basic services Productivity increase

EXTERNALITIES AND MARKET INEFFICIENCY Negative externalities lead markets to produce a larger quantity than is socially desirable at lower price – Tax needed Positive externalities lead markets to produce a smaller quantity than is socially desirable at higher price – Subsidy needed

Economic Models of Valuation

“Nothing is more useful than water; but it will purchase scarce anything. A diamond on the contrary, has scarce any value in use, but a great quantity of other goods may …be had in exchange of it.” Adam Smith

Economic Models of Valuation Focuses on demand as well as supply Values something in terms of the additional surplus earned by its possession ( opportunity cost) Explicitly factors externalities

Economic Models Cash Flow Production Function Benchmarking with closest market value

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Cash Flow Method Imagine you get access to a park Using some playground equipment I am able to earn Rs. 100 of revenue My costs are Rs. 40 What is my profit? If I had put the investment I made in the park in the next best alternative I would have made Rs. 35 What is my ‘supernormal profit’? Exercise 5: What is the value of the park to me?

Cash Flow Method 25/(1+r) + 25/(1+r)^2 + … Problem: the earning in the alternative investment cannot be determined without knowing the value of the park So we are going to have to solve an equation! Assume park was being given for a year Let the rate of interest be 10% Denote value by v Earning in alternative investment = v.10% Then v = (60 – v. 10%)/(1+ 10%) Profit

Suppose park being given in perpetuity V = (60 – v. 10%)/(1+ 10%) + (60 – v. 10%)/(1+ 10%) 2 + (60 – v. 10%)/(1+ 10%) 3 + … Using formula on sum of geometric series, V = (60 – v. 10%)/ 10% V = 60/(2. 10%)

Application to Spectrum Start with ‘representative firm’ with subscribers in proportion to its spectrum holding, 6.2 MHz Cash Flow in a Year = Revenue – (License Fee +Spectrum Charge + Network Cost + Administration, Marketing, & Operational Cost) Revenue = subscribers. ARPU Network cost assessed by taking average number of BTSs held by operator with 6.2 MHz of spectrum Admin, marketing and operations 28% of revenue Assume return on investment in alternative use is 20%

Extracting Value of 1800 MHz Let the percentage of 900 MHz spectrum be 60% Then 60%. Value of 900 MHz + 40%. Value of 1800 MHz = value of blended spectrum Let ‘k’ represent the additional productivity of 900 MHz spectrum – This is different in different markets 60%. K. Value of 1800 MHz + 40%. Value of 1800 MHz = value of blended spectrum Solve equation for value of 1800 MHz

Service Area Price of contracted spectrum Metro % of 900 MHz spectrum Price of 1800 Mhz spectrum Delhi Mumbai Kolkata Category A 0.00 Maharashtra Gujarat Andhra Pradesh Karnataka Tamil Nadu Category B 0.00 Kerala Punjab Haryana Uttar Pradesh (West) Uttar Pradesh (East) Rajasthan Madhya Pradesh West Bengal, Andaman & Nicobar Category C Himachal Pradesh Bihar Orissa Assam North East Jammu & Kashmir Table 7: Price of contracted spectrum 1800 MHz Rs. Crore per MHz 2010 (20 year license)

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Production Function Method Production function gives the total number of subscribers that can be serviced, for any given combination of spectrum and BTSs – Derived by statistical estimation using data on subscribers, spectrum and BTSs of operators in relevant circles over relevant years Allows estimation of the number of BTSs saved by possessing an additional unit of spectrum Cost of BTSs saved represents value of spectrum

Method of estimation We estimate a Cobb Douglas production function Very general specification that encompasses diminishing returns, economies of scale Used widely in the literature

Data We use a panel data collected over 7 years across all the 23 circles for different GSM operators providing services in their respective circles Estimate statistically significant values of A, β, γ Ln A = β = 1.23 γ = 0.66 Limitation: Data not available at sub-circle level

Feb 12, NUS49 Model for Allocative Efficiency First Order Condition Price Ratio Quantity RatioProductivity Ratio

Benchmarking with Auction Values Many methods – Sector -specific – General Sector-specific – Value in Percentage increase in revenue per MHz/Percentage increase in BTSs – Adaptive expectations Such methods are relevant at proximate times

Limitations of Economic Models Sensitive to assumptions Difficult to factor externalities

Auctions Need to guard against collusion ( reserve price) Possibility of winner’s curse

Failure of 1800 MHz auction Divergence between value of 1800 MHz and 2100 MHz – 1800 MHz % in value – More valuable in cat B and cat C circles That is why benchmarking reserve price to 2100 MHz resulted in poor bidding in Metros but OK results in cat B and cat C

Concluding Thoughts Economists and engineers both invaluable for valuation Academics and practitioners need to provide inputs Auctions cannot be discarded without understanding reasons for failure New technological possibilities Can NICF lead the way?

Thank you