Question

1.)The company where you work is being sold for $240,000. The company’s income statement indicates current profits of $8,000, which have yet to be paid out as dividends. Assuming the company will remain on the market in the infinite future, and the interest rate will remain constant at 4%, at what constant rate does the owner believe that the profits will grow?

Answer 1

The model in the question asked is growing perpetuity.

Price of the company is $240000, dividends for the current year are $8000 and interest rate is 4%.

The formula for calculating price of a company under growing perpetuity is as follows:

Price(P₀) = Dividend to be paid next year(D₁) /(Interest rate(r) - growth%)

i.e., P₀ = D₁ / (r-g)

Given :

P₀ = $240000

Dividend for the current year = $8000. So dividend for next year will be $8000x(1+g)

r =4%

Therefore, Growth % is calculated as follows: $240000 = [$8000(1+g)] / (4% - g%)

i.e, by simplyfying we get

1.2 - 30g = 1+g

31g = 0.2

Therefore g=0.65%

Thus the owner believes that profits will grow at a constant rate of 0.65% in infinite future.

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