Butterworth plc is a UK listed business. For many years it has paid an annual dividend on its ordinary shares that was 8 per cent higher than that of the previous year. The market expects that this pattern will continue. The dividend paid just under a year ago was £0.43 per share. The current cum-dividend share price is £6.78.

An opportunity has arisen for the business to undertake a project that will require an immediate outflow of cash equal to the amount of the planned dividend. The cash that was to be used for the dividend is the only source of cash for the project. The project will have just one cash payoff, which will occur in three years’ time. The directors intend that, if the project is undertaken, the proceeds of the payoff will all be paid to shareholders by increasing the dividend expected in three years’ time.

If the project is undertaken, the amount of the payoff, and the directors’ intention to use it all to augment the normal dividend due in three years’ time, will be publicly announced.

(a) What amount will the dividend per share, in three years’ time, need to be such that shareholders will be indifferent between receiving this year’s dividend and the cash being used for the project? Assume that the Gordon dividend growth model and the assertion of Modigliani and Miller on dividends are both valid. (Ignore taxation in this calculation.)

(b) Explain the Gordon dividend growth model and the assertion of Modigliani and Miller on dividends.

(c) Explain why, in practice, the shareholders may not be indifferent to the company missing this year’s dividend and undertaking the project, even if the increased dividend expected in three years’ time equals the amount calculated in (a).