# Basic investment growth math help.

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Is there anything wrong with doing approximate math on a growth stock like this:

Earnings are 4000.

Grows at 10% for 10 years.

Earnings in year 10 will be 11640.

11640 / current shares = 25.

25 x multiple of 15 = 375.

If we knew those were the numbers, what is the stock worth today? 375? Or is this where we add in a discount rate?

Thanks.

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Is there anything wrong with doing approximate math on a growth stock like this:

Earnings are 4000.

Grows at 10% for 10 years.

Earnings in year 10 will be 11640.

11640 / current shares = 25.

25 x multiple of 15 = 375.

If we knew those were the numbers, what is the stock worth today? 375? Or is this where we add in a discount rate?

Thanks.

I get different figures

4000(1.1)^10 = 10375 in year 10 earnings or about \$22.28 per share in earnings

Placing an arbitary multiple of 15x on this figure yields a price per share near \$335 in year 10.

Since this is the expected future value in year 10 then you would need to discount this back at a suitable rate to determine the price today. Depending on the rate you choose, the value will be different. The rate will be determined by your assessment of other investment opportunities and the risk involved in this one.

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Most of the market moves are psychological. Who is to say 20x or 30x is the right multiple. The average market multiple is 15x historically. My rule of thumb is that if you can buying an above average non-cyclical stock (faster growth, sticker moat, higher ROIC) for 15x or less, its a good bargain.

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Is there anything wrong with doing approximate math on a growth stock like this:

Earnings are 4000.

Grows at 10% for 10 years.

Earnings in year 10 will be 11640.

11640 / current shares = 25.

25 x multiple of 15 = 375.

If we knew those were the numbers, what is the stock worth today? 375? Or is this where we add in a discount rate?

Thanks.

The most important thing is that you understand why you are calculating what. I highly recommend Joel Greenblatts "The Little Book that Beats the Market" in this regard. He provides a clear and easy to understand explanation for the math behind evaluating companies. That's his thought process:

[*]Assuming no growth, what are next year's earnings of \$ 4,000 worth today?

If you assume that you can earn 6% risk free on your money in other investments, they are worth \$ 3,760 today (= \$ 4,000 - 6% or \$ 4,000 x 0.94).

6% is your discount rate – you don't actually earn 6% today but 6-7% is the historical average for the 10y US government bond yield (the closest you can get to risk free money).

[*]According to this logic, what are \$ 4,000 earned 2 years from now worth today?

\$ 3,534.40 (=\$ 4,000 × 0.94 × 0.94).

Ten years from now? \$ 2,154.46 (= \$ 4,000 × 0.94^10).

[*]Now assuming 10% growth, what are next years earnings worth today?

\$ 4,160 (= \$ 4,000 + (10% - 6%) or \$ 4,000 + 4% or \$ 4,000 × 1.04).

[*]In your example, earnings in year 10 are worth today: \$ 5,920.97 (= \$ 4,000 × 1.04^10).

Divided by current shares (current share count 465.6?): \$ 12.72 per share (= (\$ 4,000 × 1.04^10) / 465.6).

Slapping a 15 multiple on it, the intrinsic value of one share is \$ 190.75.

[*]Don't forget: If the company doesn't need to reinvest all the earnings to finance its growth, you earn money between now and year 10. The money is going to be paid out as dividends, they buy back shares or it's simply piling up within the company. Assuming the company doesn't do stupid things with this money you can add it to your valuation (discounted to today's value) .

That said, this is the theory – you shouldn't predict 10% yearly growth lightly, but that's a whole other story.

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