Time charter equivalent (TCE): formula and worked example

Why shipping uses TCE

Under a voyage charter, the shipowner is paid freight per tonne and pays the voyage costs: fuel (bunkers), port disbursements and canal tolls. Under a time charter, the charterer pays a daily hire and covers the voyage costs. The two contracts pay in different units, so owners convert every voyage offer into a TCE in dollars per day. It is also the standard earnings figure in freight indices and in the results of listed shipping companies.

Operating costs such as crew, maintenance and hull insurance are left out of the TCE. The owner pays them under both contracts, so they do not change which offer is better. Comparing the TCE with the daily operating cost then shows the margin the ship earns per day.

Step 1: net freight

Gross freight = cargo × freight rate = 58,000 t × $20.50 = $1,189,000. Commissions come off the gross freight: an address commission to the charterer, 3.75% here, which is common in dry bulk, and the broker's commission, 1.25%. Net freight = gross freight × (1 − 3.75% − 1.25%) = $1,129,550.

Step 2: voyage days, including the ballast leg

The voyage starts when the ship leaves its previous discharge port and ends when it has discharged this cargo, so the empty ballast leg to the load port counts. Sea days = distance in nautical miles ÷ speed in knots ÷ 24: 8,050 nm at 13 knots is 25.80 days. Add the days in port for loading, discharging and waiting, 6 here, for 31.80 voyage days. Real estimates also add a weather margin to the sea days.

Step 3: voyage costs and the TCE

Bunkers are usually the largest voyage cost. At 30 tonnes of fuel a day and $580 per tonne, the sea passage burns $448,942 of fuel. With $11,400 of fuel in port and $210,000 of port and canal costs, the voyage costs are $670,342. The voyage result is $1,129,550 − $670,342 = $459,208, and

TCE = $459,208 ÷ 31.80 days = $14,440 per day

The offer on the table is a time charter at $15,000 a day for the same period. At 13 knots the time charter pays better.

Worked example: voyage estimate and TCE at two speeds

Yellow cells are the inputs, the same for both speeds except row 8. Column B is the voyage at 13 knots, column C slow-steamed at 11.5 knots. Ship, route and rates are fictional.

Worked example: voyage estimate and TCE at two speeds

	A	B	C
1	Voyage estimate	13.0 knots	11.5 knots
2	Cargo (t)	58,000	58,000
3	Freight rate ($ per t)	20.50	20.50
4	Address commission	3.75%	3.75%
5	Brokerage	1.25%	1.25%
6	Net freight ($)	1,129,550	1,129,550
7	Ballast + laden distance (nm)	8,050	8,050
8	Service speed (knots)	13.0	11.5
9	Sea days	25.80	29.17
10	Port days	6.0	6.0
11	Voyage days	31.80	35.17
12	Fuel at 13 knots (t per day)	30.0	30.0
13	Fuel at this speed, cube rule (t per day)	30.00	20.77
14	VLSFO price ($ per t)	580	580
15	Bunkers at sea ($)	448,942	351,317
16	Bunkers in port ($)	11,400	11,400
17	Port & canal costs ($)	210,000	210,000
18	Voyage costs ($)	670,342	572,717
19	Voyage result ($)	459,208	556,833
20	TCE ($ per day)	14,440	15,834
21	Time-charter offer ($ per day)	15,000	15,000
22	Better option	Time charter	Voyage charter

Illustrative freight, hire and bunker prices. Operating costs (crew, maintenance, insurance) are paid by the owner in both options and are left out of the TCE.

Slow steaming: the cube rule

Fuel burn rises steeply with speed. A common rule of thumb says daily consumption grows with the cube of speed: fuel per day = fuel at reference speed × (speed ÷ reference speed)^3. At 11.5 knots the ship burns 30 × (11.5 ÷ 13)^3 = 20.77 tonnes a day instead of 30. The voyage takes 35.17 days instead of 31.80, but the bunker bill falls to $351,317, the voyage result rises to $556,833 and the TCE to $15,834, now above the time-charter offer.

The best speed is not always the slowest. High freight rates make every extra day expensive and push the optimum up, high bunker prices push it down. Chart the TCE at a range of speeds to find the peak. Real speed-consumption curves come from the ship's performance data, and the exponent is often between 2.5 and 4 rather than exactly 3.

What a TCE estimate can get wrong

The TCE is only as good as the days and costs behind it. Port time that runs longer than planned, waiting at anchor, a weather margin left out or a bunker price that moves before the ship refuels all change the result. Demurrage, paid by the charterer when loading or discharging takes longer than the agreed laytime, can win part of the lost time back. Carbon costs, such as EU ETS allowances for voyages to and from EU ports, are a growing voyage cost, measured in the same way as emissions in the guide on scope 1, 2 and 3 emissions.

Common mistakes

• Leaving out the ballast days. The ship earns nothing on the way to the load port, but those days belong to the voyage. Dividing by laden days only overstates the TCE.
• Using gross freight. Address commission and brokerage are paid out of the freight. Deduct them before the voyage costs.
• Deducting operating costs. Crew and maintenance are not voyage costs. Deducting them gives a figure that cannot be compared with a time-charter rate.
• Assuming fuel per day is fixed. Daily consumption depends strongly on speed. Recalculate it for every speed you test.
• Comparing different periods. A 35-day voyage and a 30-day time charter cover different time. Compare TCE with the hire for a similar period and market.
• Forgetting port fuel and waiting time. Ships burn fuel in port and at anchor. Small daily figures add up over a week of waiting.