Any person living upon a private road may be credited on account of his highway taxes in any year an amount equal to the value of the work which the town superintendent may deem necessary to be done in such year upon such road. The town superintendent shall issue to him a statement containing the name of the person, the location of the road, the amount of work so deemed necessary to be done, and the value thereof. Such statement shall be presented to the town board at its annual meeting for the audit of town accounts, and if approved by such board, and such work shall have been done, an order shall be issued directing the supervisor to pay the sum specified in such statement to the person therein named, or his assignee, out of moneys in the hands of the supervisor available for highway purposes. The amount so paid in any year shall not exceed the amount payable by the person named in such statement on account of moneys levied in such town for the repair and improvement of highways as provided in this chapter. This section shall not apply to private roads or rights of way over lands of the owner thereof used by him for his own convenience.