Numerical example

DCF Valuation Problem: TechGrowth Inc.

Problem:

TechGrowth Inc. is projected to generate the following free cash flows to the firm (FCFF) over the next five years:

• Year 1: $10 million
• Year 2: $12 million
• Year 3: $14 million
• Year 4: $16 million
• Year 5: $18 million

Beyond Year 5, TechGrowth is expected to maintain a constant growth rate of 3% per year indefinitely. The company's weighted average cost of capital (WACC) is 10%.

1. Calculate the present value of the free cash flows during the explicit forecast period (Years 1-5).
2. Calculate the terminal value of the company at the end of Year 5.
3. Calculate the enterprise value of TechGrowth Inc.
4. If TechGrowth has debt of $50 million, calculate the equity value.

Solution:

1. Present Value of Explicit Forecast Period Cash Flows:

   Discount each year's FCFF back to the present using the WACC of 10%.

   • Year 1: $10 million / (1.10)^1 = $9.09 million
   • Year 2: $12 million / (1.10)^2 = $9.92 million
   • Year 3: $14 million / (1.10)^3 = $10.52 million
   • Year 4: $16 million / (1.10)^4 = $10.93 million
   • Year 5: $18 million / (1.10)^5 = $11.18 million

   Total Present Value of Explicit Forecast Period Cash Flows =
   $9.09 million + $9.92 million + $10.52 million + $10.93 million + $11.18 million = **$51.64 million**
   

2. Terminal Value Calculation:

   Use the Gordon Growth Model to calculate the terminal value at the end of Year 5. First, calculate the FCFF for Year 6:

   • FCFF Year 6 = FCFF Year 5 * (1 + Growth Rate) = $18 million * (1 + 0.03) = $18.54 million

   Calculate the terminal value:

   • Terminal Value = FCFF Year 6 / (WACC - Growth Rate) = $18.54 million / (0.10 - 0.03) = $18.54 million / 0.07 = $264.86 million

   Discount the terminal value back to the present:

   • Present Value of Terminal Value = $264.86 million / (1.10)^5 = $164.23 million

3. Enterprise Value Calculation:

   The enterprise value is the sum of the present value of the explicit forecast period cash flows and the present value of the terminal value:

   • Enterprise Value = $51.64 million + $164.23 million = $215.87 million

4. Equity Value Calculation:

   Subtract the value of debt from the enterprise value:

   • Equity Value = Enterprise Value - Debt = $215.87 million - $50 million = $165.87 million

Summary:

• Present Value of Explicit Forecast Period Cash Flows: $51.64 million
• Terminal Value at the End of Year 5: $264.86 million
• Present Value of Terminal Value: $164.23 million
• Enterprise Value of TechGrowth Inc.: $215.87 million
• Equity Value of TechGrowth Inc.: $165.87 million