A US consulting firm sent an invoice of 200,000 to a UK client firm. The spot rate of pound when the invoice was sent was $1.30. The invoice should only be paid by the UK firm six months from now. Forecasted spot rates six months from now are given as below:

forecasted rate	probability
$1.25	0.30
$1.27	0.50
$1.30	0.20

The six-month forward rate is $1.25.

Required: If the invoice is to be paid six months from now, illustrate by showing your calculations, whether the US firm will be better off by using forward contract to hedge their forex transaction risk in this scenario.