Value of a growing cash flow discounted at 10%

Question

A company produces $100 of cash flow this year, and that cash flow is expected to grow by $5\%$ per year indefinitely. Comparable investments return $10\%$ a year. What is a fair price for the company?

Short answer

$2000. A growing perpetuity is worth cash flow divided by (discount rate minus growth rate): $100/(0.10-0.05)=2000$ , valid since growth is below the discount rate.

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Lessons behind this question

Market Model and Risk-Neutral Valuation
Expectation, Mean, and Variance
Conditional Expectation and Variance Revisited

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