Question

**Using the free cash flow valuation model to price an
IPO -** *Personal Finance Problem*

Assume that you have an opportunity to buy the stock of CoolTech, Inc., an IPO being offered for $7.69 per share. Although you are very much interested in owning the company, you are concerned about whether it is fairly priced. To determine the value of the shares, you have decided to apply the free cash flow valuation model to the firm's financial data that you've accumulated from a variety of data sources. The key values you have compiled are summarized in the following table (find table below)

**a.** Use the free cash flow valuation model to
estimate CoolTech's common stock value per share.

**b.** Judging by your finding in part a and the
stock's offering price, should you buy the stock?

**c.** On further analysis, you find that the
growth rate in FCF beyond 2023 will be 3% rather than 2%. What
effect would this finding have on your responses in parts
**a** and **b**?

**Free Cash Flow**

**Year (t). FCF**

2020. $720,000

2021. $840,000

2022. $970,000

2023. $1,060,000

**Other Data**

Growth rate of FCF, beyond 2023 to infinity = 2%

Weighted average cost of capital = 9%

Market value of all debt = $2,760,000

Market value of preferred stock = $1,100,000

Number of shares of common stock to be issued = 1,100,000

Answer #1

**a]**

total firm value = present value of FCF

present value of FCF = present value of FCF until 2023 + present value of terminal value at 2023

terminal value = 2024 FCF / (WACC - constant growth rate)

2024 FCF = 2023 FCF * (1 + 2%)

present value = future value / (1 + WACC)^{number of
years}

Present value, or total firm value = $13,809,644

total equity value = total firm value - market value of debt - market value of preferred stock

total equity value = $13,809,644 - $2,760,000 - $1,100,000 = $9,949,644

value per share = total equity value / number of shares issued = $9,949,644 / 1,100,000 = $9.05

**b]**

Yes, you should buy the stock as the value per share is higher than the offer price per share

**c]**

If the growth rate is 3%, present value, or total firm value = $15,758,488

total equity value = $15,758,488 - $2,760,000 - $1,100,000 = $11,898,488

value per share = total equity value / number of shares issued = $11,898,488 / 1,100,000 = $10.82

There would be no change in the answer to B, as the value per share is still higher than the issue price per share.

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