Exclusive use rule determines if government sale is tax-free

We are a truck dealership. The State Department of Public Works (DPW) wishes to buy two trucks that are taxable under IRC Section 4051. The DPW proposes to use these trucks for one year after which time we agree to accept the trucks as trade-ins and the DPW agrees to buy two new trucks for the retail price, less the agreed upon value of the trade-ins. The DPW told us that no excise tax should be imposed because sales to the DPW are tax-free. Is that correct? If the sales are taxable, how would the value of the of the trade-in affect the amount of the tax due when, in a year, the DPW purchases the two new trucks?