Estimating Product Cost Part 1

The Problem
I frequently am required to estimate product cost in the middle of some meeting with little or no preparation. As you gain more experience with building product, you soon are able to estimate a product's cost quickly for a production rate you are experienced with. The issue gets more complicated when you are asked to estimate product cost for production rates that you have no experience with. Unfortunately, this situation occurs far more than most engineers would care to admit. The answers are important — I have been working in start-ups where the question of product cost is critical to when you will hit profitability. You need to be able to estimate product cost at various production rates.

My Approach

I really had not thought about this question much until one day I was sitting in yet another vendor' s product cost presentation. During this seemingly endless presentation, there was a table that looked something like this.

Diplexer Cost
Component Cost Versus Volume
Annual Volume Cost
10K $100.00 20K$93.00
40K $86.49 80K$80.44
160K $74.81 This table was unusual because the price breaks occurred at points related by factors of 2. A quick check with my calculator verified that the our component costs would drop by 7% for each doubling of our annual component consumption. As I thought about it, this made sense. Doing a detailed, "bottoms-up" quote requires a lot of work. You must get quotes from all the vendors who make the parts that you must buy at the quantities that you must quote. Most of the time, customers do not end up buying at the rates they want you to estimate costs for. To make things easier, my vendors must be using a simple formula to estimatetheir product costs for the different production rates that customers were requesting. As it was for me, it is hard for them to constantly ask their vendors to quote on quantities that will never be ordered. This prompted me to try the following cost model for all my components. ${C_N} = {C_R} \cdot {(1 - r)^{lo{g_2}\left( {\frac{N}{R}} \right)}}$ Where CN is the component cost at a production rate of N, CR is the reference production rate R (say 10K per year), and r is the discount rate per doubling. In real life, price breaks occur at discrete points. However, a continuous model is useful for cost estimation purposes. This model almost always worked for component consumption rates less 100K units per year. I found that the discounting rates varied from 5% to 10% per doubling of annual component consumption. I also applied the model to the overall product cost and found that my total unit product cost reduced in cost by an average of 7% for each doubling of annual production rates. I have used this model for the last 10 years with good agreement with reality. This has proven to be a useful way to estimate how product cost varies with annual production rates. To illustrate how to apply this approach, let's work through an example. Example I often tell people that when it comes to manufacturing cost, the manufacturer with the highest production rates wins the game ("he with the most volume wins"). In a recent meeting, I was told that a competitor is reporting similar margins to ours, but his average selling price is 21 % lower than ours. His annual volume is 8x our annual volume ($2^3$ or 3 doublings). I responded that based on volume alone, our competitor has a 21% cost advantage over us. After discussing the situation for a while, everyone in the room agreed that a product cost advantage of ~20% would explain what we were seeing. A Competing Model Armed with my observation, I figured someone else has seen this relationship. I found only one article on the Internet that mentioned that PC costs were seen to drop by 10% for every doubling of volume. So this characteristic has been observed in other markets. Further research showed me that there was another relationship that was also common. It used the following model. ${C_N} = {C_R}\cdot{\left( {\frac{N}{{{N_R}}}} \right)^q}$ Where q is a parameter that varies for each product. This model matches mine in performance exactly. It turns out that we can show that both models are equivalent. I prefer my approach because I can estimate the discount rate by simply estimating the number of doubling over the reference rate and multiplying by 7%. Equivalence Demonstration I will begin with the form of the equation that I use and step-by-step get to the alternate form. ${C_N} = {C_1}\cdot{\left( {1 - r} \right)^{lo{g_2}\left( {\frac{N}{R}} \right)}}$ ${log_2}\left( {{C_N}} \right) = {log_2}\left( {{C_1}} \right) + {log_2}\left( {\frac{N}{R}} \right) \cdot {log_2}\left( {1 - r} \right)$ ${log_2}\left( {{C_N}} \right) = {log_2}\left( {{C_1}} \right) + \left( {{log_2}\left( N \right) - {log_2}\left( R \right)} \right)\cdot{log_2}\left( {1 - r} \right)$ ${log_2}\left( {{C_N}} \right) = {log_2}\left( {{C_1}} \right) - {log_2}\left( R \right) \cdot {log_2}\left( {1 - r} \right) + {log_2}\left( N \right)\cdot{log_2}\left( {1 - r} \right)$ ${C_N} = {\text{ }}\frac{{{C_R}}}{{{R^{{{\log }_2}\left( {1 - r} \right)}}}}\cdot{N^{lo{g_2}\left( {1 - r} \right)}} = {C_1}\cdot{N^q}$ The derivation can be reversed to convert the alternate form to my form. Thus, the forms are equivalent. Extending the Model I mentioned that this model works for production volumes less than 100K. For higher annual production volumes, the rate of cost reduction reduces. For my products, I have seen the discount rate decrease from the 7% to 2% per doubling on production rates higher than 100K per year. The exact annual production rate and discount rate breakpoints vary by vendor. Real Component Pricing Example There is often some strategy used in the pricing of components. Here is a table product pricing table from a vendor that shows a bit of strategy being used. The vendor figured out that my total annual usage of this part was about 100K. He wanted all of our business, so he gave us a quote that was high for annual rates less than 100K but low for rates greater than 100K. Basically, he wanted to ensure that we would be tempted to make him the sole source on this part. Because of this strategy, my pricing function does not apply as well to this situation. Optical Component Cost Component Cost Versus Volume Annual Volume Cost 1K$14.40
10K $13.34 50K$12.56
100K $11.38 250K$11.08
500K $10.68 1000K$10.29

You can see the discontinuity in the cost function on the following chart.

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