Translation contract: indexation, volume and discount
The communications unit manages a translation framework contract. In 2023 the total cost was €600,000. Of this, 70% was external translation and 30% internal review, treated as fixed. For 2024 the unit forecasts a 15% increase in external volume and a 2.4% rise in the external price index; a renegotiated framework discount of 5% will apply to all external charges. Internal review cost is expected to stay unchanged. For 2025, planners assume external volume grows a further 4%, the external price index rises 1.8%, and internal review costs increase by 2%. The discount remains. A colleague claims that the 2024 increase is driven mainly by the price index and that removing the discount would add less than €25,000 to the 2024 total. You must test both claims and produce the two annual totals.
1. Calculate the total contract cost for 2024 and for 2025, showing the external and internal components separately.
Read the worked answer
2023 external spend = 70% × €600,000 = €420,000; internal review = €180,000.
2024 external: apply volume and index multiplicatively: €420,000 × 1.15 × 1.024 = €494,592. The 5% discount applies to this indexed charge: €494,592 × 0.05 = €24,729.60, so net external = €469,862.40. Add internal €180,000 → 2024 total = €649,862.40.
2025 external: €469,862.40 × 1.04 × 1.018 = €497,452.72 (rounded). Internal = €180,000 × 1.02 = €183,600. 2025 total = €681,052.72.
The order of multiplication does not matter, but the discount must be applied after indexation and volume, because it is a percentage of the final external charge.
2. Test the colleague's two claims: (a) the 2024 increase is driven mainly by the price index; (b) removing the discount would add less than €25,000 to the 2024 total.
Read the worked answer
The 2024 increase is €649,862.40 − €600,000 = €49,862.40, or 8.31%.
Decompose the external change from the 2023 base of €420,000:
- volume effect: €420,000 × 0.15 = €63,000
- price effect: €420,000 × 0.024 = €10,080
- interaction: €63,000 × 0.024 = €1,512
- discount: −€24,729.60 Sum = €49,862.40, which reconciles.
Claim (a) is false: volume contributes €63,000, far more than the price effect of €10,080. Claim (b) is technically true: removing the discount adds €24,729.60, which is €270.40 below €25,000. However, the margin is very thin; a slightly different volume or index assumption would reverse it, so the claim should not be treated as robust.