Timberly Construction makes a lump$-$sum purchase of several assets on January $1$ at a total cash price of $$800,000.$ The estimated market values of the purchased assets are building, $$486,200$; land, $$289,850$; land improvements, $$65,450$; and four vehicles, $$93,500.$

Required:

$1-$a$.$ Allocate the lump$-$sum purchase price to the separate assets purchased.

$1-$b$.$ Prepare the journal entry to record the purchase.

$2.$ Compute the first$-$year depreciation expense on the building using the straight$-$line method, assuming a $15-$year life and a $$30,000$ salvage value.

$3.$ Compute the first$-$year depreciation expense on the land improvements assuming a five$-$year life and double$-$declining$-$balance depreciation.