Suppose you have estimated the free cash flows to equity holders over the next five years as follows:

Year 1: $33.2 million
Year 2: $35.8 million
Year 3: $42.3 million
Year 4: $36.9 million
Year 5: $40.5 million

You expect FCFE to remain constant at $38.6 million after year 5. If the company’s cost of equity is 13%, the WACC is 12%, the YTM is 10%, and the tax rate is 34%, then what is the value of the firm’s equity (in millions)?

Question

Suppose you have estimated the free cash flows to equity holders over the next five years as follows:

Year 1: $33.2 million
Year 2: $35.8 million
Year 3: $42.3 million
Year 4: $36.9 million
Year 5: $40.5 million

You expect FCFE to remain constant at $38.6 million after year 5. If the company’s cost of equity is 13%, the WACC is 12%, the YTM is 10%, and the tax rate is 34%, then what is the value of the firm’s equity (in millions)?

BlackTom AI · Accepted Answer

We start by restating the problem and the options to keep the context clear.
Question: Suppose you have estimated the free cash flows to equity holders over the next five years as follows: Year 1: 33.2, Year 2: 35.8, Year 3: 42.3, Year 4: 36.9, Year 5: 40.5 (in millions). After year 5, FCFE remains a constant 38.6 million. If the cost of equity is 13%, the WACC is 12%, the YTM is 10%, and the tax rate is 34%, what is the value of the firm’s equity (in millions)?
Answer options: $181.20m, $209.38m, $317.24m, $274.54m

Option-by-option analysis:
Option 1: $181.20 million. This would require a relatively aggressive discounting that undervalues the later cash flows. If you discount the first five FCFE values at a lower rate than the growth-adjusted perpetuity value, you might land near this figure, but that would typically involve using a discount rate around or below 10% for the near-term cash flows or a much smaller terminal value than the actual perpetuity value implied by a stable 38.6 million forever. The math as shown in other options tends to yield a higher total, suggesting this is too low given the cash flows and the perpetuity assumption.
Option 2: $209.38 million. This amount would arise from discounting the early FCFE years with a moderate rate and obtaining a smaller terminal value, or from using an alternate combination of discount rate and perpetuity. If the perpetuity value were mis-specified or discounted at a much higher rate, you could shrink the total, but the numbers here typically require a terminal value that’s not much larger than the present value of the near-term cash flows. This option underplays the impact of the perpetual FCFE of 38.6 million.
Option 3: $317.24 million. This figure can be obtained if one uses the WACC (12%) to discount all FCFE cash flows, including the terminal value derived from the perpetual FCFE, rather than using the cost of equity. Specifically, the present value of the five-year FCFE stream at 12% together with the present value of the perpetuity starting in year 6 (38.6 / 0.12, discounted back five years) sums to approximately 317 million. The result aligns with the calculations where the discount rate applied to all cash flows is the WACC, yielding a larger terminal value and higher total equity value.
Option 4: $274.54 million. This would come from a scenario that discounts the near-term FCFE at 12% but uses a different terminal value, or perhaps applies a different treatment to the perpetuity (e.g., growth in perpetuity or misalignment between discount rate and cash flow horizon). In standard FCFE valuation, if the terminal value is computed as a perpetuity of 38.6 million, using a discount rate lower than the one used for near-term cash flows tends to push the total toward the higher end; this option sits between the near-term PVs and a plausible terminal value but falls short of the higher total produced by using 12% for all cash flows in the calculation.

A key conceptual point: there are two common ways to price equity when you have FCFE and a perpetuity assumption. One uses the cost of equity (13%) as the discount rate for all FCFE cash flows, including the terminal value. The other, which yields the 317.24 figure, uses the WACC (12%) as the discount rate for both the early FCFE years and the terminal perpetuity value. The problem statement provides both rates intentionally; choosing which rate to apply changes the result. Here, applying the 12% rate across the board gives a value very close to $317 million, matching the third option.

Summary of the reasoning pattern: compute the present value of FCFE for years 1–5 using the chosen discount rate, then compute the terminal value at year 5 using the perpetuity formula (FCFE in perpetuity divided by the discount rate), and discount that terminal value back to present value. The total sum is the equity value. The numbers align with applying the 12% rate (WACC) for the discounting, which yields about 317.24 million.

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