In terminal value using a growing perpetuity, which formula represents value?

In terminal value using a growing perpetuity, which formula represents value?

• A. FCFn(1+g)/(WACC - g)
• B. FCFn/(WACC - g)
• C. FCFn*(1+g)/WACC
• D. FCFn/(WACC + g)

Answer: (A)

Terminal value in a growing perpetuity comes from valuing all future cash flows that grow at rate g forever. The value is based on the next year’s free cash flow divided by the difference between the discount rate and the growth rate: FCF_{n+1} / (WACC - g). Since FCF_{n+1} = FCF_n × (1+g), the terminal value can be written as FCF_n × (1+g) / (WACC - g). This requires WACC > g for convergence. If you omit the growth (use FCF_n / (WACC - g)), you’re not accounting for the perpetual growth, which underestimates the value. If you use FCF_{n+1} / WACC, you’re ignoring the growth in perpetuity. If you use WACC + g in the denominator, that deviates from the Gordon growth model and miscalculates the discounting.

Terminal value in a growing perpetuity comes from valuing all future cash flows that grow at rate g forever. The value is based on the next year’s free cash flow divided by the difference between the discount rate and the growth rate: FCF_{n+1} / (WACC - g). Since FCF_{n+1} = FCF_n × (1+g), the terminal value can be written as FCF_n × (1+g) / (WACC - g). This requires WACC > g for convergence.

If you omit the growth (use FCF_n / (WACC - g)), you’re not accounting for the perpetual growth, which underestimates the value. If you use FCF_{n+1} / WACC, you’re ignoring the growth in perpetuity. If you use WACC + g in the denominator, that deviates from the Gordon growth model and miscalculates the discounting.