Gregg graduated several years ago with his MBA. He founded Alpha Industries upon graduation and has worked hard to build the business. In the year that just ended, Alpha’s free cash flow was negative $10 million due to a significant capital expenditure. Alpha expects to realize free cash flow of negative $5 million in one year, $0 (zero) in two years, and positive $5 million in three years. After three years, free cash flow is expected to grow at a constant rate forever.
Gregg just received an offer for his company from a private equity firm. He is tempted to take the offer but he wants to understand how the offer price was determined. In particular, he is trying to estimate the long-term constant growth rate in free cash flow. Assume that the required return is 16%. If Gregg was just offered $50 million for his business, determine the constant growth rate in free cash flow after three years that would justify this offer price.
To determine the constant growth rate in free cash flow that would justify the offer price of $50 million, we need to use the discounted free cash flow method. This method calculates the present value of future cash flows, taking into account the required return rate.
First, let's calculate the present value of the expected future cash flows after three years (Year 4 onwards). We will use the formula:
PV = CF / (r - g)
Where PV is the present value, CF is the cash flow, r is the required return rate, and g is the constant growth rate.
In Year 4, the expected free cash flow is $5 million, so:
PV4 = $5 million / (0.16 - g)
In Year 5, the expected free cash flow is also $5 million, so:
PV5 = $5 million / (0.16 - g)^2
In Year 6 and onwards, the free cash flow is expected to grow at a constant rate forever. Let's assume this constant growth rate is denoted as g_infinity. The present value of these cash flows can be calculated as:
PV6_onwards = [FCF6 / (r - g_infinity)] / (1 + r)^3
Next, we sum up the present values of all the future cash flows:
PV_total = PV4 + PV5 + PV6_onwards
Now, we can solve for the constant growth rate g that justifies the offer price of $50 million:
$50 million = -($10 million) + (-$5 million) / (1 + 0.16) + PV_total
Substituting the values we have:
$50 million = -($10 million) + (-$5 million) / 1.16 + (PV4 + PV5 + PV6_onwards)
Simplifying the equation:
$50 million + $10 million - (-$5 million) / 1.16 = PV4 + PV5 + PV6_onwards
Now, substitute the PV values:
$60 million / 1.16 = $5 million / (0.16 - g) + $5 million / (0.16 - g)^2 + [FCF6 / (0.16 - g_infinity)] / (1 + 0.16)^3
Simplifying and rearranging the equation to isolate g_infinity:
[FCF6 / (0.16 - g_infinity)] / (1 + 0.16)^3 = $60 million / 1.16 - $5 million / (0.16 - g) - $5 million / (0.16 - g)^2
Now, we can solve for g_infinity using numerical methods or trial and error. Since the equation involves a complex expression, it's recommended to use numerical tools such as Excel or financial calculators to find the value of g_infinity that satisfies the equation.
Keep in mind that this estimation is based on the assumptions provided and the accuracy of the estimation depends on the accuracy of the assumptions. Additionally, other factors such as the business's risk profile and industry conditions should also be considered when evaluating an offer price.