The city may purchase, by agreement or by condemnation, all property that may be necessary for carrying out any particular drainage plan, or the making of any drainage improvement, and the same shall be paid for out of any available funds and the cost of the purchase shall be added to the cost of the improvement and charged against the property in the territory specially benefited thereby. The city may sell and convey any part of any such property unappropriated for such improvement at such terms and for such consideration as it may see fit, and the proceeds thereof shall become a part of the special fund out of which the cost of the improvement may be defrayed. Only the cost of property actually appropriated for such improvement shall be included in any assessment made under the provisions hereof. (Code 1941, Art. 128-2)