In the country of Ambiguostan, the government is providing salt-mine concessions to USalt & Co, but due to recent elections, will be revoking these concessions in 9 years. Since the salt business will be booming for years to come, USalt & Co is a highly traded stock and will continue its operations until the concessions expire. In that year, it will pay dividends of $13 million out of their profits and then shut down. Currently there are 450,000 shares of USalt & Co stock in the market. Ambigoustan\'s interest rate is 10% (you can assume it will not change). What would be the present value of a share of USalt & Co stock (rounded to the nearest dollar)?
12.25
13000000/450000 = 28.89
28.89/(1.1)^9 = 12.25 = PV
To calculate the present value of a share of USalt & Co stock, we need to determine the present value of the dividends that will be received over the next 9 years, as well as the present value of the price received when the company shuts down.
To find the present value of the dividends, we can use the formula for the present value of a growing perpetuity:
PV = (D / (r - g))
Where:
PV = Present Value
D = Dividend
r = Interest Rate
g = Growth Rate
In this case, the dividend is $13 million, and the growth rate is 0% since it remains constant. The interest rate is 10%.
PV_dividends = (13,000,000 / (0.10 - 0)) = 130,000,000
Now, we need to calculate the present value of the final price received when the company shuts down. Since this amount is received only in the last year, we don't need to discount it.
PV_shutdown = $13,000,000
To find the present value of a share of USalt & Co stock, we divide the present value of the dividends and the present value of the shutdown price by the total number of shares:
Present Value per share = (PV_dividends + PV_shutdown) / Number of Shares
Present Value per share = (130,000,000 + 13,000,000) / 450,000
Present Value per share = 300
Therefore, the present value of a share of USalt & Co stock would be $300 (rounded to the nearest dollar).