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Working note 01, , Mahé Chadeffaud and Hugo Marotin

Financing need of a supply contract: a Monte Carlo study

Abstract

A supply contract consumes cash before it returns any. The supplier asks for a deposit at order and the balance at shipment, freight and customs are paid on the way, and the public buyer pays after acceptance. We simulate the cash balance of a contract from award to payment and read two quantities from it: the peak financing need and the day the balance turns positive again. The simulation sets how much financing a bid requires and which payment terms reduce it. All figures use simulated contracts with a fixed seed.

1. The cash balance of one contract

We express every flow as a share of the contract value. With a buyer advance a, a supplier deposit d, a purchase cost k, freight and customs f(t), and a buyer payment π received at t_pay, the cash balance on day t is

C(t) = a·1{t ≥ t_adv} − d·k·1{t ≥ t_ord} − (1 − d)·k·1{t ≥ t_ship} − f(t) + (1 − a)·π·1{t ≥ t_pay}

The financing need of the contract is the depth of its lowest point, N = −min C(t). The dates are random. Manufacturing time, transit time and the buyer's payment delay each follow a log-normal law, and a contract delivered in two lots repeats the shipment and payment steps. A small share of payments arrive incomplete.

CONTRACT CASH PATHSContract cash paths · 12 of 600 simulatedmedian of 600single contracts050100150-100%-50%0%days since awardcash balance (% of value)median low -76% · back above 0 day 66600 sims over 150 days · simulated, not live results
Figure 1. Twelve of 600 simulated cash paths and their median. Each step is a payment out or a payment in.

2. Distribution of the peak need

Across 600 simulated contracts the median contract needs about three quarters of its value at its lowest point. The contracts on the right of the distribution combine a high purchase cost, high freight and no buyer advance. A bid financed for the median would run short on half of the contracts, so we size the financing on the 95th percentile.

PEAK FINANCING NEEDPeak financing need · 600 simulated contractsmedian95th percentile0%30%60%90%120%00.51peak financing need (% of contract value)relative frequencyP50 76% · P95 86% of valuepeak need = lowest point of the cash balance · simulated, not live results
Figure 2. Distribution of the peak financing need. The red dashed line marks the 95th percentile used to size financing.

3. Deposits and advances

Two contract terms move the need directly: the supplier deposit at order and the advance some public buyers pay at signature. We rerun the simulation on a grid of deposits for three advance levels, 300 contracts per point.

FINANCING SENSITIVITYP95 peak need · deposit and advanceno buyer advance10% advance30% advance10%20%30%40%50%60%40%60%80%100%supplier deposit at orderP95 peak need (% of value)30% advance lowers P95 by 12 pts at a 30% deposit300 sims per point · simulated, not live results
Figure 3. 95th percentile of the peak need by supplier deposit, for three levels of buyer advance.

The deposit moves part of the purchase earlier in time, but the buyer pays only after delivery, when deposit and balance have both left. The peak need is therefore the same whatever the deposit, which only changes how long the money is tied up. The buyer advance arrives before any outflow and lowers the whole curve. Tender documentation that offers an advance therefore reduces the financing a bid requires, and the bid price can reflect it.

4. Use in a bid

For each lot we run the simulation with the payment terms published in its tender documentation. The 95th percentile of N, multiplied by the lot value, gives the financing to arrange before bidding. Its cost over the expected duration enters the bid price.

5. Limits

The laws used here are assumptions chosen to be realistic. On live data the payment delay comes from the buyer's own history (working note 02), and the purchase cost from supplier quotations for the lot.