In April, Apple’s iTunes shifted from its one size fit all 99 cents pricing strategy to a three tier pricing strategy ($0.69, $0.99, and $1.29) per song. This makes perfect sense to me, as I have previously written, some songs are worth more than others.

I have been waiting to hear how this change has affected profits. Apple has been mum on the results so far. Glenn Peoples, a reporter for Billboard, did a great analysis on the effects on sales right after the new pricing strategy was implemented. At that time, the prices of 40 out of Apple’s Top 100 songs (which represent roughly $4.6 million of Apple’s approximately $23.5 million of monthly U.S. sales) had been increased to $1.29 while the others remained at 99 cents. Glenn found that the average song priced at $1.29 had lost sales and dropped from the #42 rank to #45. This makes sense, a boost in price leads to lower sales (in this case, sales decreased by 300 per day, or 6.12%). The good news is that the increase in price (30 cents more on the volume sold) more than compensated for this loss of volume. In fact, revenue increased for this average song by $1,083 per day. Pretty impressive, don’t you think?

I decided to do a back-of-the-envelope calculation to extend Glenn’s analysis on the Top 100. By applying the above discussed factor (for all songs that increased their price to $1.29: volume decreased by 6.12%, but revenues on the remaining 93.88% of songs that do sell increase by 30 cents per song), I estimate that the joint profits of iTunes and music labels increased by 26.9% (due to increased per unit profits as well as a reduction in variable costs from selling fewer digital singles) and that artists earn an additional 24.6% in royalties That’s a great windfall. While this is a solid start, there’s far more that can be done to set better prices such as:

1. A demand curve needs to be constructed for each song (which is eminently doable with software). Much like yield management does for each airline flight, demand for each song has to be monitored to set prices. Any demand change (from increased air play, touring, and so on) provides an opportunity to increase profits.

2. Prices need to fully fluctuate. Are consumers going to be confused if instead of $0.69, $0.99, and $1.29 prices, they are now between $0.69 - $1.29 (allowing, say, a $0.77 price to be charged)? I doubt it.

Remember, my profit calculations are only for 4.6 million out of Apple’s 23.5 million sales. Prices in this sample only increased. There’s a great opportunity to discount the price of slower selling songs to generate sales that otherwise would not have occurred.

As iTunes is experiencing, small changes in prices can lead to big profits the very next day.

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Optional to Read: Ballpark Analysis and Assumptions.

I don’t normally do quantitative analysis in blogs, but feel it important to show how I estimated the 26.9% increase in profits. As I do for my expert witness work in litigation, absent actual data, I use the best available data and conservative assumptions for my analysis.

I assume that the breakdown for a typical 99 cent song is: iTunes variable costs, 10 cents; iTunes fixed costs, 9 cents; iTunes operating profit, 10 cents; In terms of music labels, there’s no data on the breakdown so I simply do a rough 1/3 breakdown. Record label variable costs, 24 cents; Record label overhead/marketing, 23 cents; Record label operating profit, 23 cents (this is generous and actually works against me, given that Warner Music’s 2008 operating margin is 4.5%).

Thus, jointly iTunes and music labels earn 33 cents in operating profit per song sold.

40 songs of top 100 songs (40%) increased to $1.29.

Assume that 40% of top 100 songs are priced at $1.29 (40% * 4.6 million = 1.84 million songs).

Applying the same factor as in Billboard’s analysis: due to price hike, sales volume of $1.29 songs decrease by 6.12% (1.84 mn * 93.8% = 1.76 mn).

Since a price increase to $1.29 represents an additional $0.30 of pure profit, profits increase by 1.76mn * $0.30 = $528,000 per month.

However, compared to pre-$1.29 market, 6.12% (80,000) fewer songs sold. Profit from these lost sales must be deducted from new profit estimates. 80,000 * 33 cents = $26,400.

Additionally, the overhead allocation to the 80,000 fewer songs of 32 cents (9 to Apple, 23 to labels) must now be covered: 80,000 * 32 = $25,600.

Artists of $1.29 songs also benefit. Assuming a 15% royalty rate, royalties at 99 cents were $273,240 (1.84 mn * 14.85 cents). At $1.29, royalties increase to $340,560 (1.76 mn * 19.35 cents). Thus, royalties to artists rise by $67,320

Joint total new monthly profits for iTunes 100 = $408,700 [528K – 26.4 K(volume decrease) – 25.6K (fixed overhead) – 67.3K (additionally royalties)].

Before iTunes went to $1.29, profits from its Top 100 = 4.6 million * 33 cents = $1.52 million.

Percent change in profits: $408,700/$1,520,000 = 26.9%.

Please feel free to contact me with any questions on my analysis.