Suppose you started a new all-equity financed company that is expected to generate an ROE of 15% indefinitely. The current book value per share equals $30. The required return on the stock equals 12% and you expect to grow at a constant rate of 5% forever. What is the value of the stock of the startup company

The value of the stock at start-up = $67.5

Explanation:

According to the dividend valuation model , the current price of a stock is the present value of the expected future dividends discounted at the required rate of return  

This principle can be applied as follows:  

The value of stock today is the present value of the future return discounted at the required rate of return

The return can be computed as the ROE × Book value of share

Return = 15%× 30 =4.5

Price of stock today = D× (1+g)/r-g

D= current return, g- growth rate, r-required rate of return

DATA: D= 4.5, g= 5%, r= 12%

PV  = 4.5× (1.05)/(0.12-0.05)

= 67.5

The value of the stock at start-up = $67.5

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