Which formula represents terminal value using the growing perpetuity method?

Which formula represents terminal value using the growing perpetuity method?

• A. TVn(GP) = FCFn*(1+g)/(w-g)
• B. TVn(GP) = FCFn*(1-g)/(w+g)
• C. TVn(GP) = FCFn*(1+g)* (w-g)
• D. TVn(GP) = FCFn*(1+g)+(w-g)

Answer: (A)

This question tests the Gordon growth model for terminal value in a growing perpetuity. When cash flows are expected to grow at a constant rate forever, the value of those future cash flows starting in the next period is the next-period cash flow divided by the difference between the discount rate and the growth rate. The terminal value at time n is TVn = FCFn × (1 + g) / (w − g). Here FCFn is the free cash flow in period n, (1 + g) projects it to period n+1, and (w − g) reflects discounting the growing perpetuity at the cost of capital less the growth rate. This aligns with the standard Gordon growth formula for a perpetuity that grows at rate g. Why the others don’t fit: using (w + g) in the denominator misplaces the relationship between discounting and growth, multiplying by (w − g) instead of dividing changes the fundamental PV structure, and adding (w − g) to the cash flow breaks the perpetuity valuation form.

This question tests the Gordon growth model for terminal value in a growing perpetuity. When cash flows are expected to grow at a constant rate forever, the value of those future cash flows starting in the next period is the next-period cash flow divided by the difference between the discount rate and the growth rate.

The terminal value at time n is TVn = FCFn × (1 + g) / (w − g). Here FCFn is the free cash flow in period n, (1 + g) projects it to period n+1, and (w − g) reflects discounting the growing perpetuity at the cost of capital less the growth rate. This aligns with the standard Gordon growth formula for a perpetuity that grows at rate g.

Why the others don’t fit: using (w + g) in the denominator misplaces the relationship between discounting and growth, multiplying by (w − g) instead of dividing changes the fundamental PV structure, and adding (w − g) to the cash flow breaks the perpetuity valuation form.