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Auction No. 66 – Advanced Wireless Services (AWS- 1) Attachment C
Smoothing Formula Equations
Ai = (C * Bi) + (( 1- C) * Ai- 1)
Ii+ 1 = smaller of (( 1 + Ai) * N) and M
X i+ 1 = Ii+ 1 * Yi
where,
Ai = activity index for the current round (round i)
C = activity weight factor
Bi = number of bidders submitting bids on the licenses in the current round (round i)
Ai- 1 = activity index from previous round (round i- 1), A0 is 0
Ii+ 1 = percentage increment for the next round (round i+ 1)
N = minimum percentage increment or percentage increment floor
M = maximum percentage increment or percentage increment ceiling
X i+ 1 = dollar amount associated with the percentage increment
Yi = provisionally winning bid amount from the current round
Examples
License 1 C= 0.5, N = 0.1, M = 0.2
Round 1 (2 bidders submitting bids, provisionally winning bid = $1, 000,000)
1. Calculation of percentage increment for round 2 using the smoothing formula: A1 = (0.5 * 2) + (0.5 * 0) = 1
I2 = The smaller of (( 1 + 1) * 0.1) = 0.2 or 0.2 (the maximum percentage increment)
2. Calculation of dollar amount associated with the percentage increment for round 2 (using I2 from above):
X2 = 0.2 * $1, 000,000 = $200,000
3. Minimum acceptable bid amount for round 2 = $1,200,000
Round 2 (3 bidders submitting bids, provisionally winning bid = $2, 000,000) 1. Calculation of percentage increment for round 3 using the smoothing formula:
A2 = (0.5 * 3) + (0.5 * 1) = 2 I3 = The smaller of (( 1 + 2) * 0.1) = 0.3 or 0.2 (the maximum percentage increment)
2. Calculation of dollar amount associated with the percentage increment for round 3 (using I3 from above):
X3 = 0.2 * $2, 000,000 = $400,000
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3. Minimum acceptable bid amount for round 3 = $2,400,000
Round 3 (1 bidder submitting bids, provisionally winning bid = $2,400,000)
1. Calculation of percentage increment for round 4 using the smoothing formula: A3 = (0.5 * 1) + (0.5 * 2) = 1.5
I4 = The smaller of (( 1 + 1.5) * 0.1) = 0.25 or 0.2 (the maximum percentage increment)
2. Calculation of dollar amount associated with the percentage increment for round 4 (using I4 from above):
X4 = 0.2 * $2,400,000 = $480,000
3. Minimum acceptable bid amount for round 4 = $2,880,000
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