Can somebody please help me with this dividend equation

DIVt - DIVt-1 = 0.5(0.6EPSt - DIVt-1)

(a) Give an economic interpretation of this equation in terms of how the firm chooses dividends
(b) Now calculate the dividend in period t, when the EPS in period t is 50p and DIVt-1 is 20p

I would be forever grateful if somebody could explain to me how to work out this problem. I am revising for an exam, but am stuck on this revision question (also cannot find a solution in any of the study material provided).

Thank you in advance

The dividend policy decision for a firm is very important and thus, the way managers go about making dividend policy decisions and whether or not they follow a precise set of guidelines or specific strategies to make these decisions will impact on the value of the firm. It can also have an impact on the future performance of the firm.

Based on his findings, Lintner (1956) developed a dividend model. The dividend model described the relationship between the previous period’s dividend, the current period’s dividend and the future targeted dividend payout in the next period. The estimated equation the model is as follows:

DIVt – DIVt-1 = adj*(DIVt+1*EPSt – DIVt-1)

DIVt is the dividend for the current period (DIVt means DIV sub t)
DIVt-1 is the dividend for the previous period
Adj is the adjustment rate
DIVt+1 is the target dividend ratio
EPSt is the earning per share for the current period.

So in our model

DIVt - DIVt-1 = 0.5(0.6EPSt - DIVt-1)

adj = 0.5
DIVt+1 = 0.6

(a)
Our model indicates that the difference of current dividend and previous dividend is equal to (the adjustment rate of 0.5) times the whole of (targeted dividend ratio of 0.6 times the current earnings per share minus the previous dividend).

(b)
When

EPS = 50p
DIVt-1 = 20p

Then

DIVt - 20 = 0.5(0.6*50 - 20)
DIVt = 0.5(0.6*50 - 20) + 20
= 25

So the dividend for the current period is 25p.