XYZ corporation is expecting free cash flow of $100 million next year, and it will grow by 3% per year indefinitely afterward. XYZ’s discount rate is 12%. XYZ has $300 million worth of long term bonds outstanding, and 10 million shares of stock outstanding. What is a fair value for a share of XYZ? Do not include the $ sign and answer to the nearest $0.01.
Question
XYZ corporation is expecting free cash flow of 300 million worth of long term bonds outstanding, and 10 million shares of stock outstanding. What is a fair value for a share of XYZ? Do not include the 0.01.
Solution
To calculate the fair value of a share of XYZ, we first need to calculate the value of the firm using the Gordon Growth Model, which is used to determine the intrinsic value of a stock if its dividends, dividends growth rate, and discount rate are all known.
The formula for the Gordon Growth Model is:
V = FCF / (r - g)
where: V = value of the firm FCF = free cash flow r = discount rate g = growth rate
Substituting the given values into the formula:
V = 1,111.11 million
Next, we need to calculate the value of the equity. This is done by subtracting the value of the long-term bonds from the value of the firm:
Equity Value = V - Debt = 300 million = $811.11 million
Finally, to find the fair value per share, we divide the equity value by the number of shares outstanding:
Fair Value per Share = Equity Value / Number of Shares = 81.11
So, the fair value for a share of XYZ is $81.11.
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