Consider the following information about two firms, A and B:

The stock of firms A and B are equally risky.

Dividends are taxed at $40\%,$ capital gains at $20\%.$

Investors demand an expected after$-$tax rate of return of $10\%.$

Investors expect A to be worth $$112\mathrm{.}50$ next year and B to be worth $$102\mathrm{.}50.$ However, a $$10$ dividend is also widely forecasted for firm B so the total pre$-$tax profit is the same: $$112\mathrm{.}50.$

Show that logically Firm B must sell at a lower price today. Explain or comment on your solution as you proceed step$-$by$-$step. Finally, provide an intuitive conclusion, i$.$e$.,$ one that could be easily understood by a non$-$finance reader.