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ct2: question 16.19

S

shefali

Member
can anyone plz explain question 16.19...its way too complicated. Cant get the logic behind the dividend rolled up @ 7% given in the solution...plzzz help:confused: :mad:
 
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).
 
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thanx....

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).
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thanx a lot ma'am for the solution, it surely helped a lot but plz explain that how does the figure for profit before tax (140000) arises...?
 
Oops - that was the very first stage! Sorry for not making that clear. We are told that the company earns a 14% return on its assets (of £1m).
 
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