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Averaging Methodology
We propose the following methodology:
| Step 1 | Calculate the renewal price for each licence, using formula 2 above |
| Step 2 | Calculate the population-weighted average per-capita renewal price |
| Step 3 | Calculate the weighted-average renewal prices by multiplying the weighted average per-capita renewal price by the relevant renewal population coverage |
Ideally, population coverages would be determined as at the time of renewal. In reality this is not possible as re-licensing is to take place in advance, and the Ministry is confined to using census data (i.e. 5-yearly snapshots of actual populations).
Expected populations for Step 2 of the methodology could be calculated by projecting the 2001 census data forward. The Ministry has stated that it would apply the same population growth rate to all licences within a particular Averaging Group. Therefore, if 2010 populations are to be calculated by rolling forward 2001 populations, with the same rate of population growth applied to each licence, such a step would be redundant. The escalation of the populations would be netted out in the averaging calculation (Step 3). Nevertheless, using the most up to date census data is important, to ensure that the most recent actual data is used. We therefore recommend using 2001 census population data for calculations undertaken before 2006 census data is available.
Worked example
The following table sets out a worked example. Assume the following inputs:
| Varible | Input | ||||
| z | 2.00% | ||||
| r | 11.00% | ||||
| Pn | 0.75% | ||||
| Pr | 1.50% | ||||
| Renewal date | 2010 | ||||
| Original licence data | |||||
| Start date | End date | Duration | V1 | 2001 pop'n | |
| Licence 1 | 1990 | 2010 | 20 | $1,000 | 10,000 |
| Licence 2 | 1995 | 2010 | 15 | $8,000 | 12,500 |
| Licence 3 | 1998 | 2010 | 12 | $7,000 | 5,000 |
| Licence 4 | 2003 | 2010 | 7 | $15,000 | 20,000 |
Step 1: Calculate individual licence renewal prices
| V1 | V1 if 20 year duration | 2010 renewal price | |
| Licence 1 | $1,000 | $1,000 | $2,191 |
| Licence 2 | $8,000 | $9,342 | $16,825 |
| Licence 3 | $7,000 | $9,399 | $15,048 |
| Licence 4 | $15,000 | $29,831 | $39,256 |
| Total | $73,320 |
Step 2: Calculate Population-weighted per capita average renewal price (using 2001 populations). Use of the 2001 populations assumes that the same population growth rate is applied to each licence.
| 2010 renewal price | 2001 pop'n | Weighted average $ / cap | |
| Licence 1 | $2,191 | 10,000 | 1.54 |
| Licence 2 | $16,825 | 12,500 | 1.54 |
| Licence 3 | $15,048 | 5,000 | 1.54 |
| Licence 4 | $39,256 | 20,000 | 1.54 |
Step 3: Recalculate averaged renewal prices (multiply weighted average per capita price by 2001 populations)
| 2010 renewal price | 2001 pop'n | Weighted average $ / cap | Average renewal prices | |
| Licence 1 | $2,191 | 10,000 | 1.54 | $15,436 |
| Licence 2 | $16,825 | 12,500 | 1.54 | $19,294 |
| Licence 3 | $15,048 | 5,000 | 1.54 | $7,718 |
| Licence 4 | $39,256 | 20,000 | 1.54 | $30,871 |
| $73,320 | $73,320 |
This methodology will produce the same total revenue from renewal of the licences as if they were not averaged.
Grandfathered Licences
A number of licences were grandfathered into the current regulatory framework, paying a price set by legislation at the time of grandfathering.
The methodology above can be used to calculate an averaged per capita price for auctioned or tendered licences within an Averaging Group, which can then be applied to the grandfathered licences to determine their renewal prices. This approach has the potential drawbacks of averaging as a whole,3 particularly in terms of creating a licence value for one licensee based on what all the other licensees in the region were paying.
3 Covec's October 2003 paper noted amongst other things the potential for reduced welfare, arbitrary imposition of distortions on original market signals, distortions in the secondary market for spectrum and setting of precedents for future auctions.
