The Swift Company is planning to finance an expansion. The principal executives of the company agree that an industrial company such as theirs should finance growth by issuing common stock rather than by taking on additional debt. Because they believe that the current price of Swift$$s common stock does not reflect its true worth, however, they have decided to sell convertible bonds. Each convertible bond has a face value equal to $$1,000$ and can be converted into $25$ shares of common stock. Show your calculations where necessary.

$(1).$ What would be the minimum price of the stock that would make it beneficial for bondholders to convert their bonds? Ignore the effects of taxes or other costs. Explain.

$(2).$ What would be the benefits of including a call provision with these bonds? Explain. Show your calculation where necessary.