Learning-Curve Tender Pricing and the Value of a Promised Follow-On Order
Precision Gears and Tooling has been invited to tender for 350 machined housings for a pump maker. A pilot batch of the first 50 housings, completed last month for another customer, absorbed 1,200 direct labour hours in total; the plant has historically achieved a 90% learning rate on this family of work and expects the same curve to apply. Direct labour is paid ₹520 an hour and variable overhead is recovered at ₹150 per direct labour hour. Material is ₹6,800 per housing. Fixed overhead is absorbed at ₹310 per direct labour hour on a budgeted 40,000 hours; the plant is presently at 78% of budgeted hours. The buyer has told the sales team that the order will be placed at a fixed price and that a follow-on order for 200 more housings at the same price will follow if delivery is on time. A competitor is understood to have quoted ₹18,200. The sales director wants to bid ₹17,500 to be certain of winning the order and the follow-on business.
1. Work out the minimum bid price for the 350 housings, and state clearly which of the given cost figures are relevant and why.
Read the worked answer
Step 1 - Position on the curve. The pilot batch gives a cumulative average of 1,200 ÷ 50 = 24 hours per unit for the first 50 units. Learning index b = log 0.90 ÷ log 2 = −0.1520.
Step 2 - Cumulative average at 400 units. 24 × (400 ÷ 50)^−0.152 = 24 × 8^−0.152 = 24 × 0.7290 = 17.496 hours.
Step 3 - Incremental hours. Total for 400 units = 17.496 × 400 = 6,998.4 hours; less 1,200 already worked = 5,798.4 hours for the 350 units, i.e. 16.57 hours per unit.
Step 4 - Relevant cost per unit.
- Labour: 16.57 × 520 = ₹8,616
- Variable overhead: 16.57 × 150 = ₹2,485
- Material: ₹6,800
- Total relevant cost ≈ ₹17,901 per unit, so the minimum bid is about ₹17,900.
Excluded: the 1,200 pilot hours are sunk (already charged to another customer); fixed overhead absorption of ₹310 per hour would add ₹5,137 per unit but the plant is at 78% of budgeted hours, so the cost is not incremental and including it would overprice the bid; the ₹18,200 competitor quote is market information, not a cost.
Conclusion: at ₹17,500 the firm would lose about ₹400 per unit, or ₹1,40,000 on the order.
2. Evaluate the sales director's argument that a loss on the first order is justified by the 200-unit follow-on order at the same price.
Read the worked answer
Assume a 95% learning rate applies after unit 400 (the rate typically flattens as the curve matures; this must be flagged as an assumption).
b₂ = log 0.95 ÷ log 2 = −0.0740. Cumulative average at 600 units = 17.496 × (600 ÷ 400)^−0.074 = 17.496 × 0.9704 = 16.98 hours. Total for 600 = 10,187 hours; less 6,998 for the first 400 = 3,189 hours for the 200 units, i.e. 15.94 hours per unit.
Marginal cost of the follow-on per unit = 15.94 × (520 + 150) + 6,800 = 10,680 + 6,800 = ₹17,480.
Net effect at a price of ₹17,500:
- First order: 350 × (17,500 − 17,901) = −₹1,40,350
- Follow-on: 200 × (17,500 − 17,480) = +₹4,000
- Combined: −₹1,36,350
The follow-on does not rescue the bid because learning has largely exhausted itself: the marginal cost falls only from ₹17,901 to ₹17,480, about 2%. Three further points: the follow-on is a statement of intent, not a contract, so it cannot be relied on in a fixed-price bid; winning the first order locks 5,798 labour hours into a loss-making job when capacity might be used for profitable work; and the competitor's ₹18,200 indicates the market clears above the relevant cost. Recommend bidding ₹18,200-18,600, which secures a contribution and still tests the competitor's resolve.
3. The finance manager argues that because the 1,200 pilot hours are sunk, they should be ignored entirely and the learning curve applied from the very first unit of the new order. Comment.
Read the worked answer
The finance manager is confusing two different things: cost relevance and position on the learning curve.
- As a cost, the ₹6,24,000 of pilot labour (1,200 × 520) is sunk and must not be loaded onto the tender. That part of the argument is correct.
- As a technical fact, the 1,200 hours fix where the organisation now stands on the curve. The 350 new units are units 51 to 400, not units 1 to 350. Restarting the curve from unit 1 would overstate the hours, because it would assume the workforce relearns a process it has already done.
Quantify the error: applying the curve from scratch, average for 350 units = 24 × 350^−0.152 = 24 × 0.4155 ≈ 9.97 hours, total 3,490 hours - roughly 2,300 hours fewer than the correct 5,798, understating relevant cost by about ₹15.4 lakh and leading to a bid far below cost.
The correct treatment: the past hours enter the calculation only as the anchor of the curve; the cost attached to them does not enter the bid. Two further cautions: if the pilot workforce has since been redeployed or the process changed materially, the curve position is doubtful and the bid should be stress-tested; and if the pilot batch was loss-making and management wants to recover it here, that is a pricing decision to be taken openly, not buried in a cost estimate.