Different types of costs are:
If we take storage costs into account, to avoid an arbitrage opportunity, the futures price must equal the spot price compounded over the life of the futures contract at the risk-free rate, plus the future value of the storage costs over the life of the contract.
When a trader buys an asset and sells a futures contract to create a risk-free position, the futures price must be higher by enough to cover the storage costs.
Different types of benefits are:
As a cost incurred from holding the asset increases the futures price, a benefit (monetary or non-monetary) generated from holding the asset should result in a lower futures price. They are just different sides of the same token.
This model is called the cost-of-carry model. It is the most general form of the futures pricing formula we shall encounter.
According to the cost-of-carry model: F0 = S0[1 + (repo rate)](contract life / 360) + (Storage Cost) - (Income from Asset)
31 = 30 [ 1 + (repo rate)](180/360) + 0 => repo rate = 6.77%.
F0(T) = 450 (1.0435) 9/12 + 11.5 (1.0435) 9/12 = $476.5
Note that the present value of the storage costs is given so you need to compound it to get the future value in nine months.
The price of the futures contract should be F0(T) = 45 (1.0435) 9/12 + 1.15 = $47.61. The value of a long futures contract equals the difference between the two prices: $47.61 - $46 = $1.61.
High end price assumes that oil is bought at the high price and the higher borrowing rate is used. FHI = S0 [ 1 + RF (t/360)] + Storage Cost + Income = 30.83 [1 + (0.09)](180/360) + 0 = $32.19.
Low and futures price uses the lower price of oil and the low rates at which funds may be lent out. FLOW = 30.25 [1 + (0.08)](180/360) + 0 = $31.44.