What is the formula for Terminal Value using a perpetuity growth model (TVn(GP))?

What is the formula for Terminal Value using a perpetuity growth model (TVn(GP))?

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

Answer: (C)

In a perpetuity growth model, terminal value represents the value of a forever-going stream of cash flows that grow at rate g and are discounted at the firm’s cost of capital. The standard Gordon growth form is TV_n = FCF_{n+1} / (WACC - g). If you’re given the final forecasted year’s cash flow, FCF_n, you convert to next year’s cash flow by multiplying by (1+g), giving TV_n = FCF_n*(1+g) / (WACC - g). This requires WACC to be greater than g. For example, if FCF_n = 100, g = 3%, and WACC = 10%, TV_n = 100*1.03 / (0.10 - 0.03) ≈ 1,471.43. The other forms misplace growth or use the wrong denominator. Using a plus in the denominator (WACC + g) or using no growth in the denominator (WACC) or using (1 - g) in the numerator does not reflect the Gordon growth logic of perpetual cash flows growing at g and being discounted by WACC minus g.

In a perpetuity growth model, terminal value represents the value of a forever-going stream of cash flows that grow at rate g and are discounted at the firm’s cost of capital. The standard Gordon growth form is TV_n = FCF_{n+1} / (WACC - g). If you’re given the final forecasted year’s cash flow, FCF_n, you convert to next year’s cash flow by multiplying by (1+g), giving TV_n = FCF_n*(1+g) / (WACC - g). This requires WACC to be greater than g.

For example, if FCF_n = 100, g = 3%, and WACC = 10%, TV_n = 100*1.03 / (0.10 - 0.03) ≈ 1,471.43.

The other forms misplace growth or use the wrong denominator. Using a plus in the denominator (WACC + g) or using no growth in the denominator (WACC) or using (1 - g) in the numerator does not reflect the Gordon growth logic of perpetual cash flows growing at g and being discounted by WACC minus g.