After year 3, free cash flows are expected to grow at a constant 5% a year indefinitely. The discount rate is 10%. The firm has debt of $50 million, cash of $20 million and has 10,000,000 shares outstanding. What is the price of the stock

The price of the stock = $26.69

Explanation:

Missing question at inception is as follows "A firm expects the following free cash flows: Year 1: $10 million, Year 2: $12 million, Year 3: $15 million"

Year   Cash-flows"million    D. rate at 10%     Discounted cash flows

1                 10                         0.9091                          9.0910

2                 12                         0.8264                         9.9168

3                 15                         0.7513                          11.2695

4                 315                       0. 7513                         236.6595

Total                                                                            $266.9368

The price of the stock = Total Present value of cash flows / Number of Shares outstanding

The price of the stock = $266,936,800 / 10,000,000 shares

The price of the stock = $26.69368

The price of the stock = $26.69

Thus, the price of the stock is $26.69 per share

Note:

Present value of future cash flows at year 3 = 15*(1.05/10%-5%)  = 15*(1.05/5%) = 15 * 21 = $315 million

Discount rate for each year = 1/(1+r)^1 = 1/(1+0.10)^1 = 1/1.10 = 0.90909

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