Dividends and share repurchase analysis

can anyone help me understand the logic behind this example in CFAI curriculum ?

Consider a US corporation with a corporate income tax rate of 40 percent. The corporation needs to report as taxable income only 30 percent of dividends received from other corporations—that is, it takes a 70 percent deduction on that type of dividend income in calculating taxes owed. Assume that both capital gains and reported dividends (dividends net of any deductible amount) are taxed at 40 percent. What is $1 of dividends worth in terms of capital gains for such a corporate investor?

the solution is as follows:

Because 70 percent of the dividend is excluded from taxation, the effective tax rate on dividends, TD, is 0.4(1 – 0.7) = 0.12. Thus, a $1 dividend is worth (1 – 0.12)/(1 – 0.4) = $1.47 of capital gains for the corporate investor described.

The effective tax rate for dividends is 0.3*0.4= 12% versus the whole 40% for capital taxes gains. So earning $1 of dividends means a return of $0.88, the same return for capital gains taxed at 40% means that you need after-tax capital gains of $0.88, which translates to 0.88/0.6= $1.47, or 1.47(1-t)=0.88.

Hope this helps.

yeah , thanks a lot for the help