Precision Auto Components: Two Years of Productivity Numbers That Disagree
Precision Auto Components makes one machined bracket. In Year 1 it sold 20,000 pieces at Rs 500; in Year 2 it sold 24,000 at Rs 520. Inputs (Rs lakh): labour 75.0 in Year 1 (50,000 hours at Rs 150 an hour) and 89.1 in Year 2 (54,000 hours at Rs 165); material 30.0 and 40.0; energy and capital-related costs 10.0 and 12.0. Two things changed in Year 2 besides volume. The company started buying out a sub-assembly it used to machine in house; the bought-out item accounts for Rs 6 lakh of the material increase and released roughly 4,000 labour hours. It also launched a premium variant selling at Rs 520 that consumes about 8% more material per piece, and 4,000 of the Year 2 pieces are this variant. The MD's incentive is value added per rupee of input measured at selling price; the union's incentive is pieces per labour hour. Both rose. The CFO is not convinced the plant is genuinely more productive.
1. Compute labour productivity and multi-factor productivity for both years, in value terms and at constant price. Which results does the CFO's doubt rest on?
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Labour productivity (pieces per labour hour): Year 1 = 20,000 ÷ 50,000 = 0.400. Year 2 = 24,000 ÷ 54,000 = 0.444, an improvement of 11.1%. Hours rose 8% while output rose 20%, so this gain is real, not arithmetic.
Multi-factor productivity at actual selling price: Year 1 input = 75.0 + 30.0 + 10.0 = Rs 115.0 lakh; productivity = 100.0 ÷ 115.0 = 0.870. Year 2 input = 89.1 + 40.0 + 12.0 = Rs 141.1 lakh; productivity = 124.8 ÷ 141.1 = 0.885. That is up 1.7%.
At constant price (Year 1 price of Rs 500): Year 2 output = 24,000 × 500 = Rs 120.0 lakh; productivity = 120.0 ÷ 141.1 = 0.850, which is 2.2% below Year 1. The entire apparent gain, and more, comes from the Rs 20 price rise, worth Rs 4.8 lakh on 24,000 pieces against a genuine productivity gain of only about Rs 2.2 lakh.
The CFO is right for three testable reasons. (1) Price: value-based measures at current prices convert pricing power into 'productivity' whenever output prices rise faster than input prices. (2) Outsourcing: the 4,000 released hours flatter labour productivity; on the original in-house hours of about 58,000, pieces per hour would be 0.414, a gain of only 3.4%. (3) Mix and material: material cost per piece rose from Rs 150 to Rs 166.7, an 11% worsening, because of the premium variant, and that is invisible in a revenue-to-cost ratio. Physical partial measures show a real labour gain; total factor productivity at constant price shows a decline.
2. The MD proposes to pay management bonuses on value added per rupee of input at selling price, and the union on pieces per labour hour. Critique both schemes and state the measure you would put in their place.
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Both schemes reward something the plant can manipulate without becoming more efficient.
Value added per rupee of input at selling price pays for price increases and for buying in work. A manager who raises the price 4% or outsources a sub-assembly improves the bonus without touching method, layout, quality or scrap. It also mixes price and volume effects, so nobody can tell which lever moved.
Pieces per labour hour ignores the material and capital consumed and ignores quality. It is satisfiable by running the line faster with more rework - the scrap and rework figures need to be attached to it, otherwise the union is paid to make defective brackets quickly.
A workable replacement combines four elements. First, output measured at constant prices using an internal price index or the prior year's prices, so price changes cannot be scored as productivity. Second, total input cost including bought-out content, so insourcing and outsourcing decisions are neutral rather than rewarded. Third, at least one physical partial measure per department for the operator level, because shop-floor people influence hours per piece, not rupees of value added. Fourth, a quality and delivery gate: scrap, first-pass yield and on-time delivery must not deteriorate, or the gain is clawed back.
For the MD's scorecard, use constant-price multi-factor productivity with a rolling three-year baseline, and report labour, material and energy partials beside it. That design survives the two events in this case: the premium variant would no longer look like a productivity gain, and the buy-out would not be scored as an improvement.