Vale plc has the following profit-after-tax history and dividend-per-share history:

Year	T - n	Profit after tax	Dividend per share
This year	T0	10,800,000	5.40
Last year	T-1	8,900,000	4.92
2 years ago	T-2	6,300,000	4.48
3 years ago	T-3	5,500,000	4.083
4 years ago	T-7	3,500,000	3.71
5 years ago	T-5	2,600,000	3.38

Two years ago the number of issued ordinary shares was increased by 30 per cent (at the beginning of the financial year t - 1). Four years ago a rights issue doubled the number of shares (at the beginning of financial year t - 3). Today there are 100 million ordinary shares in issue with a total market value of 190m. Vale is quoted on the Alternative Investment Market. Vale's directors are committed to shareholder wealth maximization. Required a. Explain the following dividend theories and models and relate them to Vale's policy: i. Dividends as a residual; ii. Signaling; iii. Clientele preferences.

b. The risk-free return on government securities is currently 6.5 per cent, the risk premium for shares above the risk-free rate of return has been 5 per cent per annum and Vale is in a risk class of shares which suggests that the average risk premium of 5 should be adjusted by a factor of 0.9. The company's profits after tax per share are expected to continue their historic growth path, and dividends will remain at the same proportion of earnings as this year. Use the dividend valuation model and state whether Vale's shares are a good buying opportunity for a stock market investor.