Question

Suppose Compco Systems pays no dividends but spent 54.84 bilion on share repurchases iast year. If Compco's equity cost of capital is 12.7%, and if the amount spent en repurchases is expected to grow by 8.2% per yoar, estimate Compco's market capitalization. it Compco has 6.2 billon shares outstanding, to what stock price does this correspond? Compco's market capitalization will bes bilion. (Round to two decimal places.)

Answer 1

Compco's market capitalization is estimated using the growing perpetuity formula, resulting in an estimated value of $1,218.67 billion. Given 6.2 billion shares outstanding, the stock price would be $196.56 per share.

Step-by-step explanation:

To estimate Compco's market capitalization, we can treat the share repurchases as a sort of perpetuity that grows at a constant rate. Since Compco Systems spends $54.84 billion on share repurchases and this amount is expected to grow at a rate of 8.2% each year, while the equity cost of capital is 12.7%, we can use the formula for the value of a growing perpetuity to estimate the market capitalization:

Market Capitalization = Repurchase / (Cost of Capital - Growth Rate)

Market Capitalization = $54.84 billion / (0.127 - 0.082)

Market Capitalization = $54.84 billion / 0.045 = $1,218.67 billion (rounded to two decimal places).

With 6.2 billion shares outstanding, to find the stock price, we divide the market capitalization by the number of shares:

Stock Price = Market Capitalization / Shares Outstanding

Stock Price = $1,218.67 billion / 6.2 billion shares = $196.56 per share (rounded to two decimal places).