In Scenario 1, all of the profit is ploughed back into the business.
In Year 1, the business makes £140,000 in profit before tax. Profit after tax is therefore = 0.7 x £140,000 = £98,000. The assets are therefore worth £1, 098,000 at the end of the first year.
In the second year, it makes 14% of £1,098,000 = £153,720. After-tax profit is therefore £107,604. The assets are therefore £1,205,604.
In the third year, it makes 14% of £1,205,604 = £168,785. After-tax profit is therefore £118,149.
Therefore, the accumulated value of the assets (and the value of the investor's wealth) is £1,323,753.
In Scenario 2, half of the profit is ploughed back into the business and half is distributed as dividend.
At the end of Year 1, the assets are worth £1,049,000, after having given half of the after-tax profit in dividend.
In Year 2, the after-tax profit is 0.7 x (14% of 1,049,000) = £102,802. Half of this is distributed in dividend, so the assets are worth £1,100,401.
In Year 3, the after-tax profit is 0.7 x (14% of 1,100,401) = £107,839. Half of this is distributed in dividend, so the assets are worth £1,154,321.
The investor has received dividend of £49,000 at the end of Year 1, £51,401 at the end of Year 2, and £53,920 at the end of Year 3. The accumulated (or rolled up) value of these at 7% interest would be 49,000(1.07)^2 + £51,401 (1.07) + £53,920 = £165,019.
Therefore the investor's wealth is £1,154,321 + £165,019 = £1,319,339.
It's just saying that the investor's wealth is greater if the profits are ploughed back rather than given in dividends since the assets are growing at 14% pa, so after tax, the growth is 0.7 x 14% = 9.8% (rather than the 7% growth obtained on dividend income).
